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3 years ago

May someone assist me?

Mathematics

1 answer:

raketka [301]3 years ago

3 0

Answer:

<h2>15 is the answer.</h2>

Step-by-step explanation:

The side lengths are equal - supposedly

30 25

? ?

25 + ? = 45

-25 - 25

? = 20

45 - 30 = 15

The question mark should be equal to 15.

Hope this helps,

Kavitha

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A, b, c, and d please

DIA [1.3K]

<h2>Answers / Step-by-step explanation:</h2><h3>a. What is the length of one side of the square.</h3>

Looking at the image, the radius (r) of the circle appears to cover half of the length of a side of the square. Hence, the side of the square has a length of 2r.

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<h3>b. The formula A= πr² is used to find the area of a circle. The formula A=4r² can be used to find the area of the square. Write the ratio of the area of the circle to the area of the square in the simplest form.</h3>

$Ratio=\frac{\pi r^{2} }{4r^2} =\frac{\pi}{4}$ .

Notice that the value "r²" disappears from the expression because is being multiplied and divided by it at the same time.

$Ratio=\frac{4\pi }{16} =0.7854.$

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c. Complete the table.

To complete each cell of the table, simply take the equation of the asked parameter and substitute the value of r by the number indicated in the title of the column. For example, column 3 should be filled out like this:

Area of Circle (units²): π(3)²or 9π.

Length of 1 Side of the Square: 2r= 2(3)= 6.

Area of Square (units²)= 4r²= 4(3)²= 36.

Ratio: $\frac{\pi}{4}$ .

Do the same for all the other columns.

The answers to the table are presented on the attached image.

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d. What can you conclude about the relationship between the area of the circle and the square?

They will always have the same value, π/4, regardless of the size of the square and circle. As long as the circle borders meet the square's at the middle of each side of the square, the relationship will be the same.

4 0

1 year ago

Find all of the equilibrium solutions. Enter your answer as a list of ordered pairs (R,W), where R is the number of rabbits and

zloy xaker [14]

Answer:

$(0,0)$ $(4000,0)$ and $(500,79)$

Step-by-step explanation:

Given

See attachment for complete question

Required

Determine the equilibrium solutions

We have:

$\frac{dR}{dt} = 0.09R(1 - 0.00025R) - 0.001RW$

$\frac{dW}{dt} = -0.02W + 0.00004RW$

To solve this, we first equate $\frac{dR}{dt}$ and $\frac{dW}{dt}$ to 0.

So, we have:

$0.09R(1 - 0.00025R) - 0.001RW = 0$

$-0.02W + 0.00004RW = 0$

Factor out R in $0.09R(1 - 0.00025R) - 0.001RW = 0$

$R(0.09(1 - 0.00025R) - 0.001W) = 0$

Split

$R = 0$ or $0.09(1 - 0.00025R) - 0.001W = 0$

$R = 0$ or $0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

Factor out W in $-0.02W + 0.00004RW = 0$

$W(-0.02 + 0.00004R) = 0$

Split

$W = 0$ or $-0.02 + 0.00004R = 0$

Solve for R

$-0.02 + 0.00004R = 0$

$0.00004R = 0.02$

Make R the subject

$R = \frac{0.02}{0.00004}$

$R = 500$

When $R = 500$ , we have:

$0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

$0.09 -2.25 * 10^{-5} * 500 - 0.001W = 0$

$0.09 -0.01125 - 0.001W = 0$

$0.07875 - 0.001W = 0$

Collect like terms

$- 0.001W = -0.07875$

Solve for W

$W = \frac{-0.07875}{ - 0.001}$

$W = 78.75$

$W \approx 79$

$(R,W) \to (500,79)$

When $W = 0$ , we have:

$0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

$0.09 - 2.25 * 10^{-5}R - 0.001*0 = 0$

$0.09 - 2.25 * 10^{-5}R = 0$

Collect like terms

$- 2.25 * 10^{-5}R = -0.09$

Solve for R

$R = \frac{-0.09}{- 2.25 * 10^{-5}}$

$R = 4000$

So, we have:

$(R,W) \to (4000,0)$

When $R =0$ , we have:

$-0.02W + 0.00004RW = 0$

$-0.02W + 0.00004W*0 = 0$

$-0.02W + 0 = 0$

$-0.02W = 0$

$W=0$

So, we have:

$(R,W) \to (0,0)$

Hence, the points of equilibrium are:

$(0,0)$ $(4000,0)$ and $(500,79)$

4 0

2 years ago

Complete the table of values for y=2x squared + x

Lapatulllka [165]

Answer:

y=2x^2 + 2x - 3 x -2 -1 0 1 2

Step By Step Explanation:

The values can be find by plugging the x values in the equation which gives us the y value ,

x -2 -1 0 1 2

y 1 -3 -3 1 9

(b) Plot the points on the graph and join by a smooth curve.

(d) solve 2x^2 + 2x - 3 = 1

Subtract 1 from both the sides ,

2x^2 + 2x - 2 = 0

Factoring out the 2 from the equation ,

2(x^2 + x - 1) = 0

x^2 + x - 1 = 0

Apply the quadratic formula

x=(-1-sqrt(5))/2 and x = (-1+sqrt(5))/5

5 0

3 years ago

Find the end behavior of f(x)= x^2+6x+6

AlladinOne [14]

Answer:

falls to the left and rises to the right

Step-by-step explanation:

6 0

3 years ago

2/5 as a decimal and percent

lukranit [14]

Decimal: .4
Percent: 40%

7 0

2 years ago