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2 years ago

Verify the identity. sin(3pi - x) = sinx

1 answer:

7 0

we use the angle- sum and difference trigonometric identity to simplify the expression sin(3pi - x). This is equal to sin 3 pi cos x - cos 3 pi sin x. In this case, sin 3 pi is equal to zero while cos 3 pi is equal to -1. Hence the answer simplified is equal to sin x .

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Factor please.<br> m^2 - 64n^2

rewona [7]

Answer:

(n - 8n)(m+8n)

Step-by-step explanation:

x² - y² = (x - y)(x + y)

In this situation, the "x" = m and the "y" = 8n

So,

m² - 64n² = (n - 8n)(m+8n)

5 0

2 years ago

Read 2 more answers

1. How can a table be used to find the rate of change and the initial value? Describe the process.

rodikova [14]

Answer:

1. Pattern. 2. I don't know that one

Step-by-step explanation:

For finding the rate with a table all you do is look how far the numbers are jumping each time. Example: x: 1, 3, 5, 7, 9 y: 2, 4 ,6 ,8 , 10

Both the x and y follow a pattern, though its not the same, its still a pattern

(The Constant rate of change for x is 2 as it goes up 2 every time and the constant rate of change for y is also 2 as it goes up by 2 every time

4 0

2 years ago

At a speed of 22 revolutions per minute, how long will it take a wheel of radius 10,

Bogdan [553]

Well, if the radius is 10, then the circumference is $\frac{2*10*22}7=\frac{440}7$
What's the unit? Either way, 22 rev. per minute means each minute you go by $22*\frac{440}7=\frac{9680}7$ units per second. Now you got the linear speed, just find out the time by dividing the distance by the speed!
So, what's the unit for the radius?

5 0

3 years ago

Solve the compound inequality.

aivan3 [116]

Option D:

$x$

Solution:

Given compound inequality:

$6-x>15 \text { or } 2 x-9 \geq 3$

Let us first solve $6-x>15$ .

Subtract 6 from both sides.

$6-x-6>15-6$

$-x>9$

To reverse the inequality multiply by -1 on both sides.

$(-x)(-1)$

$x$

Now solve the next inequality $2 x-9 \geq 3$ .

Add 9 on both sides.

$2 x-9+9 \geq 3+9$

$2 x \geq 12$

Divide by 2 on both sides.

$$\frac{2 x}{2} \geq \frac{12}{2}$

$x \geq 6$

Combine the inequality.

$x$

Option D is the correct answer.

5 0

2 years ago

Find the center that eliminates the linear terms in the translation of 4x^2 - y^2 + 24x + 4y + 28 = 0.(-3, 2)(-3,- 2)(4, 0)

baherus [9]

Step 1

Given;

$4x^2-y^2+24x+4y+28=0$

Required; To find the center that eliminates the linear terms

Step 2

$\begin{gathered} 4x^2-y^2+24x+4y=-28 \\ 4x^2+24x-y^2+4y=-28 \\ Complete\text{ the square }; \\ 4x^2+24x \\ \text{use the form ax}^2+bx\text{ +c} \\ \text{where} \\ a=4 \\ b=24 \\ c=0 \end{gathered}$ $\begin{gathered} consider\text{ the vertex }form\text{ of a }parabola \\ a(x+d)^2+e \\ d=\frac{b}{2a} \\ d=\frac{24}{2\times4} \\ d=\frac{24}{8} \\ d=3 \end{gathered}$ $\begin{gathered} Find\text{ the value of e using }e=c-\frac{b^2}{4a} \\ e=0-\frac{24^2}{4\times4} \\ e=0-\frac{576}{16}=-36 \end{gathered}$

Step 3

Substitute a,d,e into the vertex form

$\begin{gathered} a(x+d)^2+e \\ 4(x+_{}3)^2-36 \end{gathered}$ $\begin{gathered} 4(x+3)^2-36-y^2+4y=-28 \\ 4(x+3)^2-y^2+4y=\text{ -28+36} \\ \\ \end{gathered}$

Step 4

Completing the square for -y²+4y

$\begin{gathered} \text{use the form ax}^2+bx\text{ +c} \\ \text{where} \\ a=-1 \\ b=4 \\ c=0 \end{gathered}$ $\begin{gathered} consider\text{ the vertex }form\text{ of a }parabola \\ a(x+d)^2+e \\ d=\frac{b}{2a} \\ d=\text{ }\frac{4}{2\times-1} \\ d=\frac{4}{-2} \\ d=-2 \end{gathered}$ $\begin{gathered} Find\text{ the value of e using }e=c-\frac{b^2}{4a} \\ e=0-\frac{4^2}{4\times(-1)} \\ \\ e=0-\frac{16}{-4} \\ e=4 \end{gathered}$

Step 5

Substitute a,d,e into the vertex form

$\begin{gathered} a(y+d)^2+e \\ =-1(y+(-2))^2+4 \\ =-(y-2)^2+4 \end{gathered}$

Step 6

$\begin{gathered} 4(x+3)^2-y^2+4y=\text{ -28+36} \\ 4(x+3)^2-(y-2)^2+4=-28+36 \\ 4(x+3)^2-(y-2)^2=-28+36-4 \\ 4(x+3)^2-(y-2)^2=4 \\ \frac{4(x+3)^2}{4}-\frac{(y-2)^2}{4}=\frac{4}{4} \\ (x+3)^2-\frac{(y-2)^2}{2^2}=1 \end{gathered}$

Step 7

$\begin{gathered} \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1 \\ \text{This is the }form\text{ of a hyperbola.} \\ \text{From here } \\ a=1 \\ b=2 \\ k=2 \\ h=-3 \end{gathered}$

Hence the answer is (-3,2)

4 0

10 months ago