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3 years ago

6

Identity each part of speech noun or verb

1 answer:

Elodia [21]3 years ago

5 0

Immigration-Noun
Stereotypes-Noun
Refugee-Noun
Emigration-Noun
Deportation -Noun
Assimilation-Noun
Naturalization-Noun
Ellis island-Noun
Statue of Liberty Noun

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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

Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it.

andrew-mc [135]

Answer:

f(x):

$x = - 4$

g(x)

$x = 1$

Step-by-step explanation:

When a function is of the form:

$f(x) = a {(x - h)}^{2} + k$

The equation of the axis of symmetry is

$x = h$

The given function is

$f(x) = 3 {(x + 4)}^{2} + 1$

We can see that h=-4

Hence the equation of axis of symmetry is

$x = - 4$

From the graph, the axis of symmetry of h(x) is the vertical line that divides the parabola into two congruent halves.

This line is

$x = 1$

4 0

2 years ago

The frog jumped 7/8 of a foot on the first jump and 2/3 of a foot on the second

Marina86 [1]

He jumped 1.542 feet
7/8 + 2/3

5 0

2 years ago

Expand this expression: 0.3(9x + 2)<br> Plz help

Vikentia [17]

Step-by-step explanation:

0.3(9x + 2) [Then we multiply to expand]

= 2.7x + 0.6 (Ans)

4 0

2 years ago

Find the area in the right tail more extreme than z= 3.01 in a standard normal distribution

Feliz [49]

<span>The area in the right tail more extreme than z= 3.01 in a standard normal distribution is given by

P(z > 3.01) = 1 - P(z < 3.01) = 1 - 0.99869 = 0.00131
</span>

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3 years ago