Mathematics College

## Answers

**Answer 1**

The **range** of this set of **data** is 30 ≤ y ≤ 80.

What is a range?

In Mathematics, a **range** is the set of all real numbers that connects with the elements of a domain.

Additionally, the vertical extent of any **graph** of a function represents all **range** values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the **graph** shown above, we can reasonably and logically deduce the following domain and **range**:

Domain = 0 ≤ x ≤ 24 or [0, 24].

Range = 30 ≤ y ≤ 80 or [30, 80].

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## Related Questions

The championship record for a baseball team in a certain year was 52 games won and 14 games lost. What is the win percentage?

### Answers

The win **percentage** is 79%

How to find the percentage?

Suppose the value of which a thing is expressed in **percentage** is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first **divide **the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

[tex]\dfrac{a}{100} \times b[/tex]

Given;

Number of games won=52

Number of games lost=14

Now, total games played= 14+52=66

Percentage of games won;

=(games won/total games)x100

= 52x100/66

=78.78

Therefore, the win **percent** will be 79%

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The graph of the linear function passes through the points (4, 24) and (6, 30).

What is the equation of the function?

y =x +?

### Answers

The **equation **of the **graph **that passes through the points (4, 24) and (6, 30) is y = 3x + 12

What is the equation of line of the graph?

The **slope**-**intercept form **is expresses as;

y = mx + b

Where m is slope and b is y-intercept.

The **point**-**slope form **is expressed as;

y - y₁ = m( x - x₁ )

Given that the the graph passes through the points (4, 24) and (6, 30).

First, determine the **slope**.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( 30 - 24 )/( 6 - 4 )

Slope m = ( 6 )/( 2 )

Slope m = 3

Next, plug the slope m = 3 and point 1 ( 4,24) into the **point-slope form **and simplify.

y - y₁ = m( x - x₁ )

y - 24 = 3( x - 4 )

y - 24 = 3x - 12

y = 3x - 12 + 24

y = 3x + 12

Therefore, the **equation **of **line **is y = 3x + 12,

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Determine whether the set S spans R2. If the set does not span R2, then give a geometric description of the subspace that it does span.

S = {(-1, 2), (2, -1), (1, 1)}

A. S spans R2.

B. S does not span R2. S spans a line in R2.

C. S does not span R2. S spans a point in R2.

### Answers

A set S spans R^2 if any element of R^2 can be written as linear **combination** of elements of S the set S **spans** R2.

(a) Given that S={ (1,-1),(2,1) }

Let (x,y) be the **any element** in R^2.

(x,y) = C1(1,-1)+C2(2,1)

(x,y) = (c1+2c2,-c1+c2)

x = c1+2c2

y = -c1+c2

x+y = 3c2

c2= {x+y}/{3}

c1 = c2-y

= {x+y}/{3}-y

={x-2y}/{3}

So for any element (x,y) in R^{2} we have the **constants** c_1,c_2 so that (x,y) can be written as,

(x,y)= {(x-2y)}/{3}(1,-1) + {(x+y)}/{3}(2,1)

So S= { (1,-1),(2,1) } spans R^2.

(b) Given that S = { (1,1) }

Let (x,y) be the any element in R^2.

(x,y)=c_1(1,1)

(x,y)=(c_1,c_1)

x=c_1,y=c_1

If** x,y are distinct** then do not get a value of c_1 so that (x,y) = c_1(1,1).

So set S= { (1,1) } does not span R^2.

(c) Given that S= { (0,2),(1,4) }

Let (x,y) be the any element in R^2.

(x,y)=c_1(0,2)+c_2(1,4)

(x,y)=(c_2,2c_1+4c_2)

x=c_2

y=2c_1+4c_2

c_1={y-4c_2} / {2}

={y-4x} / {2}

So (x,y)= {(y-4x)}/{2}(0,2)+x(1,4)

So any element of R^2 can be written as written as linear combination of elements of **Set S.**

Hence set S={ (0,2),(1,4) } spans R^2.

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a study was conducted to help determine which of the top two political parties the general population would prefer to vote for in the up-coming election. in determining whom to include in the sample, two stages were involved. at the first stage, a random sample of 50 individuals was selected from each of the 20 regions in the country and then pooled into a combined sample of 1,000. at the second stage, these 1,000 individuals were divided into 5 income-level groups, and a random sample of 50 from each group was selected. Select all of the statements regarding the sampling design in the above scenario that are true:

The study does not involve a voluntary response.

The first stage creates a stratified random sample.

The whole study creates a multistage random sample.

The second stage involves simple random sampling only.

### Answers

The true statements are the study does not involve a voluntary response, the first stage creates a stratified random sample and the whole study creates a multistage **random sample.**

In the given question,thestudy done ideally creates a **multistage random sample**. There are two parts to the sampling process for the study in the given question. Initially, a combined sample of thousand of individualswas assembled by combining a randomly selected sample of fifty individuals, that were from each of the 20 regions of each nation. The next step was to choose a random sample of fifty individuals from every one of the five income groups represented among those **1,000 individuals.**

Additionally, because the study doesn't entirely rely on a **discretionary**answer, individualswere picked by a random sample approach rather than explicitly or through self-selection. A stratified random sample is also created during the initialstep. This shows that a random sample was drawn from each **subgroup** after the dataset was separated into groups.

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The scatter plot below shows the population of a village (P) over time (t). Describe the relationship between the population of the village and time.

A. The population is decreasing over time.

B. The population is increasing over time.

C. The population remains roughly the same.

D. None of these

### Answers

The correct option regarding the **relationship **between the population of the village and time is given as follows:

**A. **The population is decreasing over time.

How to describe the relationship?

The **variables **of the scatter plot are given as follows:

Input variable: time t.Output variable: Population p.

From the **points **on the scatter plot, we have that when the value of t increases, the value of P decreases.

This means that the scatter plot shows a decreasing relationship, and thus the correct option is given by **option A.**

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Eric works at the deil on the weekends to earn extra money he makes 10 per hour making sandwiches and 14 per hour delivering orders eric puts half of his total earning in a savings account for college he wants to know how much he saves each week help i need answers fast

### Answers

**Answer:**

you do it step by step so it can be expressed

Reciprocity and Reciprocal Theorems: Prove these two theorems (which are written in Lecture Notes 2). Hint: write the condition of F(x, y, z) 0 into explicit forms x-x(y,x) or z-z(x,y), you can then calculate their differentials, manipulate the terms, to get those theorems.

### Answers

The** partials** ∂y/∂x = 1 and ∂z/∂x = -1, so we get the **Reciprocal Theorem**.

Reciprocity Theorem: Let F(x, y, z) be a** continuous function** of x, y, and z, then we have

∂F/∂x = (∂F/∂y)x - (∂F/∂z)y

This is proven by writing the **condition** of F(x, y, z) = 0 into explicit forms x-x(y,z) or z-z(x,y). Then from the chain rule, we have

∂F/∂x = (∂F/∂y)(∂y/∂x) + (∂F/∂z)(∂z/∂x)

And since x = x(y,z) and z = z(x,y), the partials ∂y/∂x = -1 and ∂z/∂x = 1, so we get the** Reciprocity Theorem.**

Reciprocal Theorem: Let F(x, y, z) be a continuous function of x, y, and z, then we have

(∂F/∂y)x + (∂F/∂z)y = F(x, y, z)

This is proven by writing the condition of F(x, y, z) = 0 into explicit forms x-x(y,x) or z-z(x,y). Then from the chain rule, we have

∂F/∂x = (∂F/∂y)(∂y/∂x) + (∂F/∂z)(∂z/∂x)

And since x = x(y,x) and z = z(x,y), the partials ∂y/∂x = 1 and ∂z/∂x = -1, so we get the **Reciprocal Theorem**.

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Can some help me solve this geometry question?

### Answers

The** length of NQ **for this problem is given as follows:

NQ = 5.

How to obtain the length NQ?

In this problem, we have two** similar triangles, **meaning that their side lengths are proportional.

The **lengths **for this problem are given as follows:

NO = 8.NQ = x.QR = x - 1.QP = 5.

The **similar triangles** are given as follows:

PQR and PNO.

The **equivalent **side lengths are given as follows:

5 and 5 + x.x - 1 and 8.

Hence the **proportional relationship **is given as follows:

5/(5 + x) = (x - 1)/8

Applying** cross multiplication,** we have that:

(x + 5)(x - 1) = 40

x² + 4x - 5 = 40

x² + 4x - 45 = 0.

Hence:

(x + 9)(x - 5) = 0.

The **positive **solution is:

x - 5 = 0

x = 5.

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two-finger morra is a game in which two players each hold up one or two fingers. the payoff, in dollars, is the total number of fingers shown. r receives the payoff if the total is even, and c receives the payoff if the total is odd. write the payoff matrix.

### Answers

Payoff **matrix**: R (row player) receives payoff if **total number** of fingers shown is even, C (column player) receives payoff if total number of fingers shown is odd.

**Two-finger **morra is a game in which two players take turns holding up either one or two fingers. The payoff for the game is the total number of fingers shown, with the player whose **total **is even (R) receiving the payoff, and the player whose total is odd (C) receiving the payoff. This game can be represented in a payoff matrix, which is a table that shows the payoffs for each player in each possible situation. For two-finger morra, the payoff matrix would have two rows and two **columns**, representing the two players, R and C. The top row would show the payoffs for R when the total **number **of fingers is even, and the bottom row would show the payoffs for R when the total number of fingers is odd. Similarly, the left column would show the payoffs for C when the total number of fingers is even and the right column would show the payoffs for C when the total number of fingers is odd.

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The measure of an interior angle of a regular polygon is 162º. Find the number of sides in the polygon.

_______sides

### Answers

**Answer:**

20 sides

**Step-by-step explanation:**

The number of sides of a regular polygon, if each of its interior angles is 162° is 20.

HELPPPPP PLEASEEEE URGENT

### Answers

The table 1 **represent **the **function **From the given figure.

**What is function ?**

The function in mathematical terms is the **mapping **of each member of a set (named as a domain) to another set of members (named as a codomain). This term has a different meaning from the same word that is used every day, such as "the tool works well." The concept of **function **is one of the basic concepts of mathematics and any quantitative science. The terms "function", "mapping", "map", "transformation" and "operator" are usually used synonymously.

In function, there are several important terms, including:

The **domain **is the area of origin of the function f denoted by Df.

**Codomain **is the area where the f function area is denoted by Kf.

The range is the result **area **which is a subset of the codomain. The function range f is denoted by Rf.

PROPERTIES OF FUNCTIONS

1. INJECTIVE FUNCTION

Called **one-on-one** function. Suppose the function f represents A to B, then the function f is called a one-on-one function (injective), if each two different elements in A will be mapped to two different elements in B. Furthermore, it can be said briefly that f: A → B is injective function if a ≠ b results in f (a) ≠ f (b) or equivalent if** f (a) = f (b)** then the effect is a = b.

2. SURJECTIVE FUNCTION

Function f: A → B is called a function to or objective function if and only if for any b in the B domain can be at least one an in domain A so **f (a) = b **applies. In other words, a codomain of the objective function is the same as its range.

3. BIJECTIVE FUNCTION

A mapping off:** A → B **is such that f is both an injective and objective function at once, so it is said "f is a function of wisdom" or "A and B are in one-to-one correspondence".

Therefore, The table 1 **represent **the function From the given figure.

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If f(x)= 2*, find and simplify (i) f(x²)ƒ(1)

### Answers

The value of given **function** is (i)** f(x²) = 2*x²** and (ii)** f(1) = 2*1 = 2.**

What does the mathematical term "function" mean?

A function is a link or expression that contains one or more variables. There is a **collection** of **inputs** and **outputs**.

A function is a relationship between a number of inputs and outputs. Simply described, a function is an **association** between inputs in which each input is coupled to exactly one output. There is a range, codomain, and domain for every function. A **function** is typically referred to as f(x), where x is the input.

Applications of **functions** include population, distance traveled, and discovering profit. When using functions, one enters a number into the formula or locates the independent variable on a table or graph before computing the **dependent** **variable** that results.

(i) f(x²) =** 2*x²**

(ii) f(1) = **2*1 = 2**

So, f(x²) =** 2*x²** and f**(1) = 2**

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Santiago has planned a basketball game for the weekend.

The chance of snow on Saturday is 35%, with a 70% chance on

Sunday. If these probabilities are independent, what is the

chance that it will snow on both days?

### Answers

The **probability **that it will snow on **both days, **given the chances of snow on Saturday and Sunday, is 24.5%.

How to find the probability ?

The chance of it **snowing **on** both days** is calculated by multiplying the probability of it snowing on Saturday by the **probability **of it snowing on Sunday. If the probabilities are independent, we can assume that one event occurring doesn't affect the other event, therefore the probability of both events happening is just the product of the individual event probabilities.

So, the chance of it snowing on both days is:

P(Saturday and Sunday) = P(Saturday) x P(Sunday)

P(Saturday and Sunday) = 0.35 x 0.70

P(Saturday and Sunday) = 24.5 %

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2.1.3 Quiz: What Is a Function?

Question 2 of 10

If f(x) = 2x² +5√(x-2), complete the following statement:

f(6) =_______

### Answers

A statement, rule, or legislation that establishes the link between the independent variable and the **dependent variable** (the dependent variable). f ( 6 ) = 82 .

What is the definition of a function?

Domain of [tex]$2 x^2+5 \sqrt{x-2}:\left[\begin{array}{cc}\text { Solution: } & x \geq 2 \\ \text { Interval Notation: } & {[2, \infty)}\end{array}\right]$[/tex]

Range of [tex]$2 x^2+5 \sqrt{x-2}:\left[\begin{array}{cc}\text { Solution: } & f(x) \geq 8 \\ \text { Interval Notation: } & {[8, \infty)}\end{array}\right]$[/tex]

**Interception **zones on the axis [tex]$2 x^2+5 \sqrt{x-2}$[/tex] : None .

Asymptotes of [tex]$2 x^2+5 \sqrt{x-2}$[/tex] : None .

Points of Extremity [tex]$2 x^2+5 \sqrt{x-2}$[/tex] : Minimum (2,8) .

[tex]f(x) = 2x^{2} +5\sqrt{(x-2} \\f (6) = 2 *(6^{2} ) + \sqrt{6 - 2} \\ = 82[/tex]

the type of conduct or activity appropriate to a person, thing, or institution; the reason why something is made or existing; role. any formal event or occasion that is held in public or among friends. a component that affects or is influenced by other components: Availability and demand determine price.

As a set of inputs with one output for each, a function is defined as a relationship between them. A **function**, expressed simply, is an association between inputs where each input is connected to one and only one output. Each function has a range or codomain. f(x), where x is the input, is a common way to refer to a function.

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Find all possible 2×2

matrices A that for any 2×2 matrix B, AB = BA.

Hint: AB = BA must hold for all B. Try matrices B that have lots of zero entries.

### Answers

**Answer:**

**Step-by-step explanation:**

Consider the following four matrices:

(1000),(0010),(0100),(0001).

See what happens when you solve the equation AB=BA

for each of those four (let B

be each one of those four). To facilitate it, write A=(acbd)

You will get a set of equations for the entries of a

which are easily solved. This trick is quite general.

Three vertices of a parallelogram are shown in the figure below.

Give the coordinates of the fourth vertex.

(-4,9)

(-6,-5)

(1.-7)

### Answers

**Answer:**

(3, 7)

**Step-by-step explanation:**

Given that **points (-4,9), (-6,-5), and (1.-7)** are three **vertices of a parallelogram** with **segments connecting** them in order, you want the point that is the **fourth vertex**.

Parallelogram

The diagonals of a parallelogram bisect each other, which means they have the same midpoint:

((-4, 9) +(1, -7))/2 = ((-6, -5) +(x, y))/2

Multiplying by 2 and subtracting the point on the right side, we have ...

(-4, 9) +(1, -7) -(-6, -5) = (x, y)

(-4 +1 +6, 9 -7 +5) = (x, y) = (3, 7)

**The fourth vertex is (3, 7)**.

__

*Additional comment*

In general three points can define three possible parallelograms. Here, the segments connecting the points are presumed to be the sides of the parallelogram, so reducing the number of possibilities to just one.

The fact that the diagonal midpoints are the same is useful for solving a variety of problems involving parallelograms.

How do you factor this problem by grouping?

4x∧3-3x∧2-28x+21

### Answers

**Answer:**

(x^2 - 7)(4x - 3)

**Step-by-step explanation:**

first, we split the expression by grouping the first two terms in parentheses and the last two terms in parentheses. this gives us:

[tex](4x^{3}-3x^{2})(-28x+21)[/tex]

next, we factor out the GCF of each group. this gives us:

[tex]x^{2}(4x-3)-7(4x-3)[/tex]

finally, all you have to do is take each factored-out term and put them together into a group/expression. the leftover expression from both groups is the same value, so you get:

[tex](x^{2}-7)(4x-3)[/tex]

hope this helped, good luck!

PLS HELPP

Which line is parallel to the liney=4x+5?

A)y=-4x+2

B) y=4x+3

C)4x+5

D)y=-1/4x+9

### Answers

**Answer:**

c

**Step-by-step explanation:**

it is 4×+5 which is easy as u tines it by fixing the sum into parts and its eisier

the solid with a semicicular base of radius 5 whose cross sections perpendicular to the base and parallel to the diameter are squares

### Answers

The **volume** of the solid with the given **semi-circular base** with radius 5 units is equal to **333.33 cubic units**.

As given in the question,

**Radius** of the semicircular base = 5 units

Equation of the circle is given by :

x² + y² = r²

⇒ x² + y² = 5²

⇒ x² + y² = 25

⇒ x = √25 - y²

Cross section is perpendicular to the base and it is parallel to the diameter are squares:

Diameter is double of the radius

s = 2x

= 2√25 - y²

**Volume** of the given solid is equal to :

V = [tex]\int\limits^5_0 {s^{2} } \, dy[/tex]

= [tex]\int\limits^5_0 {( 2\sqrt{25 - y^{2} }) ^{2} } \, dy[/tex]

= [tex]\int\limits^5_0 {( 4({25 - y^{2} }) } \, dy[/tex]

= 100y - 4y³/3 (for limit 0 to 5)

= ( 500 - 500/3 ) - 0

= 500 ( 1 - 1/3 )

= 500( 2/3 )

= 1,000/3

= 333.33 cubic units.

Therefore, the **volume** of the given solid with the given measures is equal to 333.33.

The above question is incomplete, the complete question is :

Use the general slicing method to find the volume of the following solid.

The solid with a semicircular base of radius 5 whose cross sections perpendicular to the base and parallel to the diameter are squares. Place the semicircle on the xy-plane so that its diameter is on the x-axis and it is centered on the y-axis. Set up the integral that gives the volume of the solid. Use increasing limits of integration.

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the distribution system for the herman company consists of three plants, two warehouses, and four customers. plant capacities and shipping costs per unit (in $) from each plant to each warehouse are as follows: customer demand and shipping costs per unit (in $) from each warehouse to each customer are as follows: choose the correct network representation of this problem. (i) (ii) (iii) (iv) formulate a linear programming model of the problem. for subtractive or negative numbers use a minus sign even if there is a sign before the blank. let xij represents relation between plants to warehouses or relation between warehouses to customers. min fill in the blank 2 x14 fill in the blank 3 x15 fill in the blank 4 x24 fill in the blank 5 x25 fill in the blank 6 x34 fill in the blank 7 x35 fill in the blank 8 x46 fill in the blank 9 x47 fill in the blank 10 x48 fill in the blank 11 x49 fill in the blank 12 x56 fill in the blank 13 x57 fill in the blank 14 x58 fill in the blank 15 x59 s.t. 1) fill in the blank 16 x14 fill in the blank 17 x15 < fill in the blank 18 2) fill in the blank 19 x24 fill in the blank 20 x25 < fill in the blank 21 3) fill in the blank 22 x34 fill in the blank 23 x35 < fill in the blank 24 4) fill in the blank 25 x46 fill in the blank 26 x47 fill in the blank 27 x48 fill in the blank 28 x49 fill in the blank 29 x14 fill in the blank 30 x24 fill in the blank 31 x34

### Answers

All** variables** must be greater than or** equal to **0, indicating that no shipping is allowed if the cost is negative.

The network representation of the Herman Company distribution system is as follows:

Plants (P1, P2, P3) -> Warehouses (W1, W2) -> Customers (C1, C2, C3, C4).

**A linear programming model** of the problem can be formulated as:

Minimize Z = 2x14 + 3x15 + 4x24 + 5x25 + 6x34 + 7x35 + 8x46 + 9x47 + 10x48 + 11x49 + 12x56 + 13x57 + 14x58 + 15x59

Subject to:

x14 + x15 ≤ 2

x24 + x25 ≤ 3

x34 + x35 ≤ 4

x46 + x47 + x48 + x49 ≤ 5

x14 + x24 + x34 ≤ 6

x15 + x25 + x35 ≤ 7

x46 + x56 + x66 ≤ 8

x47 + x57 + x67 ≤ 9

x48 + x58 + x68 ≤ 10

x49 + x59 + x69 ≤ 11

All** variables** ≥ 0

The objective of this problem is to minimize the total shipping cost from plants to warehouses and **warehouses** to customers. The constraints represent the limited capacities of each plant, warehouse and customer and the **maximum** number of units that can be shipped from each plant to each warehouse or each warehouse to each customer. All variables must be greater than or** equal to **0, indicating that no shipping is allowed if the cost is negative.

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18. Subtract:

8.50

- 4.75

19. Multiply:

X

0.625

5

20. Divide: 0.04)26.4

### Answers

**Answer:**

**18.**

**3.25**

**19.**

**3.125**

**20.**

**-26.36**

**Step-by-step explanation:**

A cylindrical pottery vase has a diameter of 4.3 inches and a height of 11 inches. What is the surface area of the vase? Use the formula SA= B+ Ph, since the vase has a bottom but no top. Use 3.14 for TT and round to the nearest tenth of a square inch.

### Answers

**Answer: To find the surface area of the cylindrical vase, we can use the formula:**

**SA = B + Ph**

**Where B is the area of the base (the circular top of the vase), P is the perimeter of the circular top of the vase, and h is the height of the vase.**

**We know that the diameter of the vase is 4.3 inches and the height of the vase is 11 inches. To find the radius of the base, we can divide the diameter by 2:**

**r = 4.3 inches / 2 = 2.15 inches**

**The area of the base is given by πr², so:**

**B = πr² = π * 2.15² = 14.65 square inches**

**To find the perimeter of the circular top we can use 2πr:**

**P = 2πr = 2 * 3.14 * 2.15 = 13.64 inches**

**Now we can substitute these values into the formula:**

**SA = B + Ph = 14.65 + 13.64 * 11 = 260.04 square inches**

**Rounded to the nearest tenth, the surface area of the vase is 260.0 square inches.**

**Step-by-step explanation:**

Solve the initial value problem 2yy' + 3 = y^2 + 3x with y(0) = 9. 1. To solve this, we should use the substitution u = _____ With this substitution, y = _____

y' = _____

Enter derivatives using prime notation (e.g., you would enter y' for dy/dx). 2. After the substitution from the previous part, we obtain the following linear differential equation in x, u, u'. 3. The solution to the original initial value problem is described by the following equation in x, y.

### Answers

The given** initial value problem** y(0)=8,** solution** is [tex]y=\sqrt{64e^x-3x}[/tex]

Any equation with at least one ordinary or partial derivative of an unknown function is referred to as a differential equation. Assuming that a function's rate of change with regard to x is inversely proportional to y, we may write it down as dy/dx = k/y. An equation involving the **derivative **(derivatives) of the dependent variable with respect to the independent variable is referred to as a differential equation in** calculus (**variables). The differential equation assists us in presenting a relationship between the changing quantity with respect to the change in another variable. The derivative represents nothing more than a rate of change. If y is a dependent variable, f is an unknown function, and x is an independent variable, then y=f(x) is a function.

The given **differential equation **is,

[tex]2yy'+3=y^2+3x\\\\2y\frac{dy}{dx}=y^2+3x-3\\\\(3-y^2-3x)dx+2ydy=0\\\\compare, Mdx+Ndy=0\\\\M=3-y^2-3x\\\\N=2y[/tex]

The given **equation** is not** exact** but if we **multiplied** by [tex]e^{-x}[/tex]

[tex]The D.E.\\(3-y^2-3x)e^{-x}dx+2ye^{-x}dy=0\\\\then M_y=-2ye^{-x}=N_x\\The G.S,=y^2e^{-x}+3xe^{-x}=c\\\\y(0)=8\\c=64\\hence,\\y=\sqrt{64e^x-3x}[/tex]

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Gianna is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Gianna will earn $50 every time one of her songs is played in a commercial and she will earn $100 every time one of her songs is played in a movie. Gianna's songs were played on twice as many commercials as movies and her total earnings on the royalties from all commercials and movies was $800. Graphically solve a system of equations in order to determine the number of commercials, x,x, and the number of movies, y,y, on which Gianna's songs were played.

### Answers

A **graph** of each function is shown in the image attached below.

The number of commercials (x) is equal to 8 commercials while the number of **movies** (y) is equal to 4 **movies**.

How to write and solve the system of equations graphically?

In order to graphically solve the system of **equations**, we would write two (2) equations that models the situation by assigning variables to the number of commercials and number of movies respectively, and then translate the word problem into algebraic equation as follows:

Let the variable x represent the number of **commercials**.Let the variable y represent the number of movies.

Since Gianna would earn $50 every time one of her songs is played in a **commercial** and $100 every time one of her songs is played in a movie, an **equation** which models it is given by;

50x + 100y = 800

Additionally, Gianna's songs were played on twice as many commercials as movies;

x = 2y

Next, we would use an online graphing calculator to plot the above system of **equations** with a point of intersection at (8, 4) as shown in the image attached below.

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Find the midpoint between (-1, -5) and (-5, 9) by using the Midpoint Formula.

### Answers

**Answer: Midpoints (-3/2)**

**Step-by-step explanation:**

Midpoint formula is (x1+x2)/2 , (y1+y2)/2

Plugin x values and solve

(-1 +-5)/2 = -3

Plugin y values and solve

(-5+9)/2 = 2

The midpoint is -3/2

I hope this helped you :D

The base radius and height of a circular cone are measured as 10cm

and 25cm respectively, with a possible error in measurement of as much as 0.1cm in

each. Using linear approximation, estimate the magnitude of maximum error in the

calculated volume of the cone.

### Answers

The maximum **error** in the **volume** of the **cone** is approximately 20π cubic centimeters.

How to determine the magnitude of maximum error in the volume of the cone

In this problem we must estimate the maximum **error** in the **volume** of the **cone**, based on uncertainties in **radius** and **height** of a circular cone. The volume formula for a circular cone is:

V = (π / 3) · R² · h

Where:

R - Base radius, in centimeters. h - Height, in centimeters.V - Volume, in cubic centimeters.

And the maximum error formula (ΔV), in cubic centimeters, is found by **total differentials**:

ΔV = (dV / dR) · ΔR + (dV / dh) · Δh

Where:

(dV / dR) - First derivative of function volume respect radius, in square centimeters.(dV / dh) - First derivative of function volume respect height, in square centimeters.ΔR - Maximum uncertainty for radius, in centimeters. Δh - Maximum uncertainty for height, in centimeters.

All **first derivatives** are shown below:

dV / dR = (2π / 3) · R · h

dV / dh = (π / 3) · R²

If we know that R = 10 cm, h = 25 cm, ΔR = 0.1 cm and Δh = 0.1 cm, then the maximum error in **volume** of **circular cylinder** is:

dV / dR = (2π / 3) · (10 cm) · (25 cm)

dV / dR = 500π / 3 cm²

dV / dh = (π / 3) · (10 cm)²

dV / dh = 100π / 3 cm²

ΔV = (500π / 3 cm²) · (0.1 cm) + (100π / 3 cm²) · (0.1 cm)

ΔV = 20π cm³

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Using the same situation you described in #3, now interpret what the part-to-part ratio 2:1 means in the situation. Use complete sentences in your answer.

#3 situation

A classroom has 50 people.

The ratio of girls to boys is 2:3, so in other words, we need to find out how many boys and girls there are, and there are 2 girls for every three boys, So, how many boys and girls are there?

The answer would be :

2x+3x=50

5x=50

x=

x=10

2x= 2×10=20

3x =3*10=30

20 girls and 30 boys.

### Answers

There are 30 **boys** and 20 **girls **in the classroom.

How to determine the number of boys and girls?

Let the variable p represent the number of **people**. Next, we would translate the given word problem into an algebraic equation by using a **ratio** as follows;

Number of girls + Number of boys = Total number of **people**

2p + 3p = 50

5p = 50

Dividing both sides of the equation by 5, we have the following:

p = 50/5

p = 10 **people**.

For the number of girls, we have:

2g = 2(10)

2g = 20 girls.

For the number of boys, we have:

3g = 3(10)

3g = 30 boys.

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In the expression n +23, 23 is a

### Answers

**Hey there!**

**Answer:**

**In the expression, 23 is the constant.**

**Hope this helps!**

Which method(s) of distributing supplies is best suited for specific items and quantities?

### Answers

**Direct delivery** is coordinating with a specific location such as a shelter, feeding site or hospital for the delivery of specific items and **quantities**

What is distributing supplies?

**Distributing** can be defined as the means of spread the product throughout the** market place** such that a large number of people can buy it.

There are five types of** Distribution **such as:

Direct distribution. This first system comprises directly performing merchandise distribution activities.Indirect distribution. A third-party-involved indirect distribution system is the second type.Intensive distribution.Exclusive distribution.Selective.

Distributing channels are important to** businesses** as they allow for the smooth delivery of goods.

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graph an equation of the form y=kx+1 which includes point m. m(2,-7)

### Answers

The **linear equation** y = - 4 · x + 1 includes **point** (x, y) = (2, - 7).

How to graph a linear function on Cartesian plane

In this problem we need to plot a **linear equation** on **Cartesian plane**, linear equations are first polynomials of the form:

y = m · x + b

Where:

x - Independent variabley - Dependent variablem - Slopeb - Intercept

If we know that b = 1 and (x, y) = (2, - 7), then the equation of the line is:

- 7 = 2 · k + 1

- 8 = 2 · k

k = - 4

y = - 4 · x + 1

Now we proceed to graph the line. First, find two **points** of the line:

x = 0

y = - 4 · 0 + 1

y = 1

x = 1

y = - 4 · 1 + 1

y = - 3

Second, plot the points on Cartesian plane.

Third, construct the line that passes through the two points.

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