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2 years ago

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Rectangular prism P has length of 6.5 inches, a width of 4 inches, and a height of 8 inches. The volume of rectangular prism Q i

s 2 times the volume of rectangular prism P. What is the volume of rectangular prism Q?

1 answer:

Yuliya22 [10]2 years ago

3 0

Answer:

416

Step-by-step explanation:

6.5 x 4 x 8 = 208

208(2)=416

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B) Let g(x) =x/2sqrt(36-x^2)+18sin^-1(x/6)<br><br> Find g'(x) =

jolli1 [7]

I suppose you mean

$g(x) = \dfrac x{2\sqrt{36-x^2}} + 18\sin^{-1}\left(\dfrac x6\right)$

Differentiate one term at a time.

Rewrite the first term as

$\dfrac x{2\sqrt{36-x^2}} = \dfrac12 x(36-x^2)^{-1/2}$

Then the product rule says

$\left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 x' (36-x^2)^{-1/2} + \dfrac12 x \left((36-x^2)^{-1/2}\right)'$

Then with the power and chain rules,

$\left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-1/2} + \dfrac12\left(-\dfrac12\right) x (36-x^2)^{-3/2}(36-x^2)' \\\\ \left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-1/2} - \dfrac14 x (36-x^2)^{-3/2} (-2x) \\\\ \left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-1/2} + \dfrac12 x^2 (36-x^2)^{-3/2}$

Simplify this a bit by factoring out $\frac12 (36-x^2)^{-3/2}$ :

$\left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-3/2} \left((36-x^2) + x^2\right) = 18 (36-x^2)^{-3/2}$

For the second term, recall that

$\left(\sin^{-1}(x)\right)' = \dfrac1{\sqrt{1-x^2}}$

Then by the chain rule,

$\left(18\sin^{-1}\left(\dfrac x6\right)\right)' = 18 \left(\sin^{-1}\left(\dfrac x6\right)\right)' \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{18\left(\frac x6\right)'}{\sqrt{1 - \left(\frac x6\right)^2}} \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{18\left(\frac16\right)}{\sqrt{1 - \frac{x^2}{36}}} \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{3}{\frac16\sqrt{36 - x^2}} \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{18}{\sqrt{36 - x^2}} = 18 (36-x^2)^{-1/2}$

So we have

$g'(x) = 18 (36-x^2)^{-3/2} + 18 (36-x^2)^{-1/2}$

and we can simplify this by factoring out $18(36-x^2)^{-3/2}$ to end up with

$g'(x) = 18(36-x^2)^{-3/2} \left(1 + (36-x^2)\right) = \boxed{18 (36 - x^2)^{-3/2} (37-x^2)}$

5 0

2 years ago

20 POINTS! Please help, best answer will recessive brainliest answer points as well as 5 stars and a thank you. :)

valentina_108 [34]

Answer:

(3) Diagonals are perpendicular

Step-by-step explanation:

5 0

2 years ago

A total of 259 tickets were sold to a benefit concert for a total of $5,312. Two types of tickets were sold: adult tickets were

jeyben [28]

Answer:

113

Step-by-step explanation:

Let the number of adult tickets sold =a

Let the number of student tickets sold =s

A total of 259 tickets were sold, therefore:

a+s=259

Adult tickets were sold for $24 each and student tickets were sold for $16 each.

Total Revenue = $5,312

Therefore:

24a+16s=5,312

We solve the two derived equations simultaneously.

From the first equation

a=259-s

Substitute a=259-s into 24a+16s=5,312

24(259-s)+16s=5,312

6216-24s+16s=5,312

-8s=5,312-6216

-8s=-904

Divide both sides by -8

s=113

Therefore, 113 student tickets were sold.

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3 years ago

GrogVix [38]

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3 years ago

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