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3 years ago

I need help with this problem??

Mathematics

1 answer:

aalyn [17]3 years ago

4 0

No I think it’s a 90 degree rotation because the notations above PQR indicates only 1 rotation...

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I'm not exactly sure how to solve this or what the answer is.

arlik [135]

Answer:

9x^2-49

Step-by-step explanation:

FOIL

8 0

3 years ago

What is 1/2 of 14? this is an algebraic expression!!

Vikentia [17]

1/2 of 14 is 7. multiply 14/1 to 1/2.

3 0

2 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

2 years ago

Help! i need the answer to this question plsss NO LINKS AND NO DOING IT JUST FOR THE POINTS Will give brainliest to the first se

Alex_Xolod [135]

2745

Step-by-step explanation:

solve it like simultaneously

180x+120y greater than 5145

180x+120y greater than 2400

eliminate x

y will now be greater than 2745

5 0

2 years ago

A rectangular prism has a volume of 1,500

goblinko [34]

Answer:

1500 = 748h

Step-by-step explanation:

Data:

l=34, w=32

Volume=1500

Write an equation of volume of a rectangular prism:

Volume= L x W x H

Substitute Values:

1500=34 x22 x h

Simplify:

1500=748h

7 0

3 years ago