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2 years ago

7

Cheyenne works 15 hours a week at the movie theater. She earns $8 an hour. Which statement about her weekly income is true?

1 answer:

Anni [7]2 years ago

6 0

Answer:C- Her net income is less than $120.

Step-by-step explanation:

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A rancher wants to fence in an area of 1500000 square feet in a rectangular field and then divide it in half with a fence down t

VLD [36.1K]

Answer:

6000 ft

Step-by-step explanation:

Let length of rectangular field=x

Breadth of rectangular field=y

Area of rectangular field= $1500000$ square ft

Area of rectangular field= $l\times b$

Area of rectangular field= $x\time y$

$1500000=xy$

$y=\frac{1500000}{x}$

Fencing used ,P(x)= $x+x+y+y+y=2x+3y$

Substitute the value of y

P(x)= $2x+3(\frac{1500000}{x})$

$P(x)=2x+\frac{4500000}{x}$

Differentiate w.r.t x

$P'(x)=2-\frac{4500000}{x^2}$

Using formula: $\frac{dx^n}{dx}=nx^{n-1}$

$P'(x)=0$

$2-\frac{4500000}{x^2}=0$

$\frac{4500000}{x^2}=2$

$x^2=\frac{4500000}{2}=2250000$

$x=\sqrt{2250000}=1500$

It is always positive because length is always positive.

Again differentiate w.r.t x

$P''(x)=\frac{9000000}{x^3}$

Substitute x=1500

$P''(1500)=\frac{9000000}{(1500)^3}>0$

Hence, fencing is minimum at x=1 500

Substitute x=1 500

$y=\frac{1500000}{1500}=1000$

Length of rectangular field=1500 ft

Breadth of rectangular field=1000 ft

Substitute the values

Shortest length of fence used= $2(1500)+3(1000)=6000 ft$

Hence, the shortest length of fence that the rancher can used=6000 ft

3 0

3 years ago

Suppose you solved a second-order equation by rewriting it as a system and found two scalar solutions: y = e^5x and z = e^2x. Th

xenn [34]

Answer:

The solutions are linearly independent because the Wronskian is not equal to 0 for all x.

The value of the Wronskian is $\bold{W=-3e^{7x}}$

Step-by-step explanation:

We can calculate the Wronskian using the fundamental solutions that we are provided and their corresponding the derivatives, since the Wroskian is defined as the following determinant.

$W = \left|\begin{array}{cc}y&z\\y'&z'\end{array}\right|$

Thus replacing the functions of the exercise we get:

$W = \left|\begin{array}{cc}e^{5x}&e^{2x}\\5e^{5x}&2e^{2x}\end{array}\right|$

Working with the determinant we get

$W = 2e^{7x}-5e^{7x}\\W=-3e^{7x}$

Thus we have found that the Wronskian is not 0, so the solutions are linearly independent.

3 0

3 years ago

A person who is 5 feet tall is standing 126 feet from the base of a tree, and the tree casts a 140 foot shadow. The person's s

Eva8 [605]

Hope this helps but if you got any other questions feel free to ask :) cause I suckeeeeddd at Geometry but I had to pass lolllll

8 0

3 years ago

Solve for the equation 4a-8=28

hoa [83]

4a-8=28
add 8 to both sides to start to isolate the variable (a)
-8+8 cancels each other out
28+8=36
4a=36
to completely isolate the variable divide both sides by 4
4a÷4=a
36÷4=9
a=9

6 0

3 years ago

Jordan buys 2 baseball jersey and gloves that cost $44. She gives the clerk two fifty dollar bills to pay the exact amount. How

butalik [34]

Answer: 2 ÷ 44 ≈ x x

x is 22

Step-by-step explanation:

4 0

3 years ago