a baby weights 7 pounds at birth. the table shows the birth weight after each month of life, up to six months

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

3 years ago

Read 2 more answers

Nathaniel works as a baker and makes several batches of muffins every morning. each batch requires 1 1/7 cups of sugar. for a la

kramer

The amount of sugar he will use is 5.22 cups of sugar, and the number of boxes needed to pack the muffins is 13.71 boxes.

<h3>How do we solve a word problem?</h3>

This word problem question can be solved as follows:

Amount of sugar he will use = 1 1/7 * 4 4/7 = 1.142857142857143 * 4.0.571428571428571 = 5.22 cups of sugar

Number of boxes needed to pack the muffins for the meeting = 4 4/7 * 3 = 4.0.571428571428571 * 3 = 13.71 boxes

Learn more about how to solve word problems here: brainly.com/question/13732946.

#SPJ1

8 0

2 years ago

A Ferris wheel has a diameter of 42 feet. It rotates 3 times per minite. Approximately how far will a passenger travel during a

UkoKoshka [18]

Hello!

First of all we will need to find the circumference, as it is the distance around the wheel. We will use 3.14 for pi.

42(3.14)=131.88

Now we multiply by three to see how far they go in a minute.

131.88(3)=395.64

Now we multiply by 5 to see five minutes.

395.64(5)=1974.2

A passenger will travel approximately 1978.2 feet in 5 minutes.

I hope this helps!

5 0

3 years ago

Read 2 more answers

Microsort is a genetics company that advertises a product that supposedly increases the chance of a female birth for couples pla

Brut [27]

The correct answer is C

8 0

3 years ago

HELP ME WITH THIS! 1/3 a = 7/9

andreyandreev [35.5K]

Answer:

a = 2 $\frac{1}{3}$