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Genrish500 [490]

2 years ago

7

What are the domain and range of f(x) = 2(3^x)?

1 answer:

solong [7]2 years ago

4 0

Answer:

Step-by-step explanation:

no x-intercept/zero

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Last year, Emma's scout troop sold 504 boxes of cookies. This year, her troop set a goal to sell more boxes than last year.

Leto [7]

What is the question asking

7 0

3 years ago

Save me the headache

maxonik [38]

$(9\sin2x+9\cos2x)^2=81$

Taking the square root of both sides gives two possible cases,

$9\sin2x+9\cos2x=9\implies\sin2x+\cos2x=1$

or

$9\sin2x+9\cos2x=-9\implies\sin2x+\cos2x=-1$

Recall that

$\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta$

If $\alpha=2x$ and $\beta=\dfrac\pi4$ , we have

$\sin\left(2x+\dfrac\pi4\right)=\dfrac{\sin2x+\cos2x}{\sqrt2}$

so in the equations above, we can write

$\sin2x+\cos2x=\sqrt2\sin\left(2x+\dfrac\pi4\right)=\pm1$

Then in the first case,

$\sqrt2\sin\left(2x+\dfrac\pi4\right)=1\implies\sin\left(2x+\dfrac\pi4\right)=\dfrac1{\sqrt2}$

$\implies2x+\dfrac\pi4=\dfrac\pi4+2n\pi\text{ or }\dfrac{3\pi}4+2n\pi$

(where $n$ is any integer)

$\implies2x=2n\pi\text{ or }\dfrac\pi2+2n\pi$

$\implies x=n\pi\text{ or }\dfrac\pi4+n\pi$

and in the second,

$\sqrt2\sin\left(2x+\dfrac\pi4\right)=-1\implies\sin\left(2x+\dfrac\pi4\right)=-\dfrac1{\sqrt2}$

$\implies2x+\dfrac\pi4=-\dfrac\pi4+2n\pi\text{ or }-\dfrac{3\pi}4+2n\pi$

$\implies2x=-\dfrac\pi2+2n\pi\text{ or }-\pi+2n\pi$

$\implies x=-\dfrac\pi4+n\pi\text{ or }-\dfrac\pi2+n\pi$

Then the solutions that fall in the interval $[0,2\pi)$ are

$x=0,\dfrac\pi4,\dfrac\pi2,\dfrac{3\pi}4,\pi,\dfrac{5\pi}4,\dfrac{3\pi}2,\dfrac{7\pi}4$

5 0

2 years ago

Read 2 more answers

Rewrite, differentiate and simplify:<br> 3/(2x)^3

Llana [10]

$\frac{dy}{dx}$ = - $\frac{9}{8x^{4} }$

let y = $\frac{3}{(2x)^{3} }$ = $\frac{3}{8}$ $x^{-3}$

differentiate using the power rule

$\frac{d}{dx}$ ( $ax^{n}$ ) = na $x^{n-1}$

$\frac{dy}{dx}$ = - $\frac{9}{8}$ $x^{-4}$ = - $\frac{9}{8x^{4} }$

8 0

2 years ago

For all the following, which ones represent y as a function of x, and how do you know?

earnstyle [38]

Only 25 and 28 are functions.

A function must have only one y value per x value. For 26, the y value of 0 and multiple others have two different y values. For 27, all x values less than 0 have multiple y values.

4 0

3 years ago

A friend wants to buy a pool and has two places she wants to purchase the pool with the largest volume which pool should she buy

slamgirl [31]

Answer:

20'×15 in 54 inches

Step-by-step explanation:

The Best as a pool should be rectangular in shape and 54inches deep for safety of life's

7 0

2 years ago