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3 years ago

7

you return several shirts to a store the receipt shows that the amount placed back on your credit card is -30.60 each shirt is -

6.12 how many shirts did you return

1 answer:

vredina [299]3 years ago

4 0

-30.60 divided by -6.12 = 5

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James decides to walk from school to the park to play ball. The park is only 0.5 mile from the school. He leaves school at 3:15

miskamm [114]

Answer: C

Step-by-step explanation: We see that it took James 10 minutes to go 0.5 miles, so to get how many miles an hour James is traveling, we need to get the miles to 1. To do this, multiply by 2, and this will give you that it took James 20 minutes to go 1 mile. This is option C.

7 0

3 years ago

A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require

Aleksandr-060686 [28]

Answer:

$r\approx 1.084\ feet$

$h\approx 1.084\ feet$

$\displaystyle A=11.07\ ft^2$

Step-by-step explanation:

<u>Optimizing With Derivatives </u>

The procedure to optimize a function (find its maximum or minimum) consists in :

Produce a function which depends on only one variable
Compute the first derivative and set it equal to 0
Find the values for the variable, called critical points
Compute the second derivative
Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum

We know a cylinder has a volume of 4 $ft^3$ . The volume of a cylinder is given by

$\displaystyle V=\pi r^2h$

Equating it to 4

$\displaystyle \pi r^2h=4$

Let's solve for h

$\displaystyle h=\frac{4}{\pi r^2}$

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

$\displaystyle A=\pi r^2+2\pi rh$

Replacing the formula of h

$\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )$

Simplifying

$\displaystyle A=\pi r^2+\frac{8}{r}$

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

$\displaystyle A'=2\pi r-\frac{8}{r^2}=0$

Rearranging

$\displaystyle 2\pi r=\frac{8}{r^2}$

Solving for r

$\displaystyle r^3=\frac{4}{\pi }$

$\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet$

Computing h

$\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet$

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

$\displaystyle A''=2\pi+\frac{16}{r^3}$

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.

The minimum area is

$\displaystyle A=\pi(1.084)^2+\frac{8}{1.084}$

$\boxed{ A=11.07\ ft^2}$

8 0

3 years ago

Is 690,269 divisible by 9? Yes or No?

jonny [76]

Answer:

False.

Step-by-step explanation:

It is false because when dividing an odd number by an odd number, it usually isn't divisible. In this case, 690,26<u>9</u>. Is an odd number, because the last number, 9, is odd, which makes the whole thing odd. So, odd divided by odd never turns out well. (By the way the answer is 76,696.5555556).

8 0

2 years ago

Which expression is equivalent to (-3y - x) - (5y - 8x)?

Vinil7 [7]

Answer:

b

Step-by-step explanation:

plz mark brainliest

4 0

3 years ago

The area of cross section of a prism is 45cm² and its height is,10cm. Find its volume

mrs_skeptik [129]

Answer:

The Volume of triangular prism

V = 450 cm³

Step-by-step explanation:

<u><em>Explanation</em></u>:-

Given The area of cross section of a prism A = 45cm²

and height (h) = 10 cm

The Volume of triangular prism

V = ( Base area X Height )

= 45 X 10

= 450 cm³

The Volume of triangular prism

V = 450 cm³

6 0

3 years ago