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3 years ago

Simplify this expression. 3x2(7x2 − 9)

Mathematics

1 answer:

kirill115 [55]3 years ago

4 0

<span>3x2(7x2 − 9)
Multiply 3x^2 by 7x^2 and -9(Use distributive property)
Final Answer: D.) 21x^4 - 27x^2</span>

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Let theta be an angle in quadrant II such that cos theta = -2/3

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Answer:

So we have $\csc(\theta)=\frac{3 \sqrt{5}}{5} \text{ and } \tan(\theta)=\frac{-\sqrt{5}}{2}$ .

Step-by-step explanation:

Ok so we are in quadrant 2, that means sine is positive while cosine is negative.

We are given $\cos(\theta)=\frac{-2}{3}(\frac{\text{adjacent}}{\text{hypotenuse}})$ .

So to find the opposite we will just use the Pythagorean Theorem.

$a^2+b^2=c^2$

$(2)^2+b^2=(3)^2$

$4+b^2=9$

$b^2=5$

$b=\sqrt{5}$ This is the opposite side.

Now to find $\csc(\theta)$ and $\tan(\theta)$ .

$\csc(\theta)=\frac{\text{hypotenuse}}{\text{opposite}}=\frac{3}{\sqrt{5}}$ .

Some teachers do not like the radical on bottom so we will rationalize the denominator by multiplying the numerator and denominator by sqrt(5).

So $\csc(\theta)=\frac{3}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}=\frac{3 \sqrt{5}}{5}$ .

And now $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}=\frac{\sqrt{5}}{-2}=\frac{-\sqrt{5}}{2}$ .

So we have $\csc(\theta)=\frac{3 \sqrt{5}}{5} \text{ and } \tan(\theta)=\frac{-\sqrt{5}}{2}$ .

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Answer:

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Charles begins finding the volume of a trapezoidal prism using the formula A = One-half(b1 + b2)h to find the prism's base area.

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Answer:

The expression that can be used to represent the volume of the trapezoidal prism is $(2x^3+6x^2)$

Step-by-step explanation:

step 1

Find the area of the trapezoidal base

The area of a trapezoid is given by the formula

$A=\frac{1}{2}(b_1+b_2)h$

we have

$b_1=(x+2)\ units\\b_2=(x+4)\\h=x$

substitute

$A=\frac{1}{2}(x+2+x+4)x$

$A=\frac{1}{2}(2x+6)x$

$A=(x+3)x\\A=(x^2+3x)\ units^2$

step 2

Find the volume of the trapezoidal prism

we know that

The volume of the prim is given by

$V=Bh$

where

B is the area of the base

H is the height of the prism

we have

$B=(x^2+3x)\ units^2$

$H=2x\ units$

substitute

$V=(x^2+3x)2x\\V=(2x^3+6x^2)\ units^3$

therefore

The expression that can be used to represent the volume of the trapezoidal prism is

$(2x^3+6x^2)$

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