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3 years ago

11

HURRY!!!This table represents a proportional relationship. Use the table to identify the constant of proportionality between the

ratio of the number of laps to the number of swimmers. A 2-column table with 4 rows. Column 1 is labeled Number of Swimmers with entries 20, 18, 14, 9. Column 2 is labeled Number of Laps with entries 240, 216, 168, 108.

2 answers:

Shtirlitz [24]3 years ago

5 0

Answer:

its 12

Step-by-step explanation:

noname [10]3 years ago

5 0

Answer:the answer is 12

Step-by-step explanation:

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Pam has 90 m of fencing to enclose an area in a petting zoo with two dividers to separate three types of young animals. The thre

andrew-mc [135]

Answer:

The area function is

$A=\frac{135}{2}x-\frac{9}{2}x^2$ .

The domain and range of A is $(0,15m)$ and $(0, 253.125 m^2]$ .

Step-by-step explanation:

The given length of fencing is $90 m$ .

Let the length and width of each pen be $x$ and $y$ respectively as shown in the figure.

As there are 3 pens, so, the total area,

$A= 3 xy \;\cdots (i)$

From the figure the total length of fencing is $6x+4y$ .

Here, for a significant area for the animals, $x>0$ as well as $y>0$ as $x$ and $y$ are the sides of ben.

From the given value:

$6x+4y=90\;\cdots (ii)$

$\Rightarrow y=\frac {45}{2}-\frac{3x}{2}$

Now, from equation (i)

$A=3x\left(\frac {45}{2}-\frac{3x}{2}\right)$

$\Rightarrow A=\frac{135}{2}x-\frac{9}{2}x^2\;\cdots (iii)$

This is the required area function in the terms of variable $x$ .

For the domain of area function, from equation (ii)

$x=15-\frac{2y}{3}$

$\Rightarrow x$ [as y>0]

So, the domain of area function is $(0,15m)$ .

For the range of area function:

As $x \rightarrow 0$ or $y\rightarrow 0$ , then $A\rightarrow 0$ [from equation (i)]

$\Rightarrow A>0$

Now, differentiate the area function with respect to $x$ .

$\frac {dA}{dx}=\frac{135}{2}-9x$

Equate $\frac {dA}{dx}$ to zero to get the extremum point.

$\frac {dA}{dx}=0$

$\Rightarrow \frac{135}{2}-9x=0$

$\Rightarrow x=\frac{15}{2}$

Check this point by double differentiation

$\frac {d^2A}{dx^2}=-9$

As, $\frac {d^2A}{dx^2}$ , so, point $x=\frac{15}{2}$ is corresponding to maxima.

Put this value back to equation (iii) to get the maximum value of area function. We have

$A=\frac{135}{2}\times \frac {15}{2}-\frac{9}{2}\times \left(\frac {15}{2}\right)^2$

$\Rightarrow A=253.125 m^2$

Hence, the range of area function is $(0, 253.125 m^2]$ .

4 0

4 years ago

Solve for x. 3(x−7)=6(x−10) Enter your answer in the box. x =

Oksi-84 [34.3K]

Answer:

X = 13

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

4 0

3 years ago

Determine whether the statement is true or false, and explain why.

Sedbober [7]

Answer:

True

Step-by-step explanation:

The integral

$\int\limits^1_0 {xe^{10x}} \, dx$

in the integral we have a product of a monomial: $x$

and an exponential function: $e^{10x}$

In general case, when we have a combination of these two things you can use the integration by parts, where $x$ will be $u$ and $e^{10x}$ will be $dv$ .

The statement is true

3 0

3 years ago

50 apples cost $25.how much would 75 apples cost

inessss [21]

Answer:

150

Step-by-step explanation: one apple cost $0.50, so 75/ $0.50= 150

6 0

3 years ago

What is the slope and y-intercept of y=16,500 - 1,500x?

MaRussiya [10]

Y=mx+b
m=slope
b=yint

y=16500-1500x
y=-1500x+16500

slope is -1500
yintercept is 16500

7 0

4 years ago