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Allushta [10]
3 years ago
13

The volume of a rectangular prism is given by the expression 10x^3+46x^2-21x-27. The area of the base of the prism is given by t

he expression 2X^2+28x-9. Which of the following Expressions represents the height of the prism? (V=Bh) a)28x-3 b)3x-5 c)5x+3 d)42x+3
Mathematics
2 answers:
grigory [225]3 years ago
7 0

Answer: The answer is C.)

Step-by-step explanation:

(5x+3)x(2x^2+8x-9)=10x^3+46x^2-21x-27.

Everything checks out.

(Plus I got it right on the assignment ;)

andrezito [222]3 years ago
5 0
H = V/B

h =  \frac{10x^3+46x^2-21x-27}{2x^2+8x-9} = 5x + 3 \\  \\ c)5x+3



The base of the prism is given by the expression 2X^2+8x-9
then c)5x+3
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Answer:

<em>35.11 ft</em>

<em></em>

Step-by-step explanation:

This given situation can be thought of as triangle \triangle PQR where PQ is the length of pole.

PR is the length of rope.

and QR is the distance of bottom of pole to the point of fastening of rope to the ground.

And \angle Q \neq 90^\circ

Given that:

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To find:

Side QR = ?

Solution:

We can apply Sine Rule here to find the unknown side.

Sine Rule:

\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}

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\dfrac{PR}{sinQ}=\dfrac{PQ}{sinR}\\\Rightarrow sin Q =\dfrac{PR}{PQ}\times sinR\\\Rightarrow sin Q =\dfrac{51}{44}\times sin58^\circ\\\Rightarrow \angle Q =79.41^\circ

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\angle P +\angle Q +\angle R =180^\circ\\\Rightarrow \angle P +58^\circ+79.41^\circ=180^\circ\\\Rightarrow \angle P = 42.59^\circ

Let us use the Sine rule again:

\dfrac{QR}{sinP}=\dfrac{PQ}{sinR}\\\Rightarrow QR =\dfrac{sinP}{sinR}\times PQ\\\Rightarrow QR =\dfrac{sin42.59}{sin58}\times 44\\\Rightarrow QR = 35.11\ ft

So, the answer is <em>35.11 ft</em>.

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