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2 years ago

5

Finding the value of powers powers of 8

1 answer:

HACTEHA [7]2 years ago

8 0

4 and 2 8 and 1 ok mark brainlest and I’ll do more answers

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For what values of θ is sinθ < cosθ when 0 ≤ θ < π ?

zysi [14]

<h3>Answer: $0 \le \theta < \frac{\pi}{4}$ </h3>

=========================================================

How to get this answer:

Use the unit circle to note that $\sin\theta = \cos\theta = \frac{\sqrt{2}}{2}$ when $\theta = \frac{\pi}{4}$ (aka 45 degrees)

Beyond this point, cosine is smaller than sine. This means that anything from 0 to pi/4 will have sine be smaller than cosine. It might help to graph y = sin(x) and y = cos(x) on the interval from x = 0 to x = pi.

The two curves y = sin(x) and y = cos(x) intersect at the point $\left(\frac{\pi}{4}, \frac{\sqrt{2}}{2}\right)$

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Here's a more detailed picture of whats going on.

$\sin \theta < \cos \theta\\\\\sin \theta < \sqrt{1-\sin^2\theta}\\\\\sin^2 \theta < 1-\sin^2\theta \\\\2\sin^2 \theta < 1\\\\\sin^2 \theta < \frac{1}{2}\\\\\sin \theta < \sqrt{\frac{1}{2}}\\\\\sin \theta < \frac{1}{\sqrt{2}}\\\\\sin \theta < \frac{\sqrt{2}}{2}\\\\\theta < \arcsin\left(\frac{\sqrt{2}}{2}\right)\\\\\theta < \frac{\pi}{4}\\\\$

Intersect the intervals $0 \le \theta < \pi$ and $\theta < \frac{\pi}{4}$ and you'll end up with the final answer $0 \le \theta < \frac{\pi}{4}$

4 0

2 years ago

A parallelogram-shaped tile has an area if 48 in.2. The base of the tile measures 12in. What is the measure of bits height

malfutka [58]

Answer:

height = 4 in

Step-by-step explanation:

The area (A) of a parallelogram is calculated using the formula

A = base × height ← substitute values

48 = 12 × height ( divide both sides by 12 )

4 = height

4 0

3 years ago

14+5x= 3(-x+3)-11<br> Find x

Lelu [443]

Answer:

x=-2

Step-by-step explanation:

$14+5x=3\left(-x+3\right)-11$

$3\left(-x+3\right)-11$ ← ( Expand)

$14+5x=-3x-2$

$14+5x-14=-3x-2-14$ ← ( Subtract 14 from both sides)

$5x=-3x-16$

$5x+3x=-3x-16+3x$

$8x=-16$

$\cfrac{8x}{8}=\cfrac{-16}{8}$ ← ( Divide both sides by 8)

$x=-2$

~

7 0

2 years ago

Mr. Ramos invests $500 at a simple interest rate of 6%. How much interest will he earn in one year?

kiruha [24]

Answer:$30

Step-by-step explanation: $500 x .06 = $30

4 0

3 years ago

Solve the simultaneous equations <br> 3x + 4y = 5<br> 2x - 3y = 9

lisabon 2012 [21]

We label each equation

3x + 4y = 5 (1)

2x – 3y = 9 (2)

We now want to get rid of one of the variables (x or y). Lets get rid of x:

We need (1) and (2) to have the same number of x's so we multiple (1) by 2 and (2) by 3 so they both have 6 x's

6x + 8y = 10 (1)*2

6x - 9y = 27 (2)*3

Now to get rid of the x's we take one of the equations from the other. It is easier to do (2)*3 -(1)*2

6x - 9y = 27 (2)*3

6x + 8y = 10 (1)*2

-17y = 17

If we devide this equation by -17 we get

y = -1

We can plug this value of y into (1) to get

3x -4 = 5

add 4 to both sides of the equation

3x = 9

Divide by 3

x = 3

Now to check put x and y into (2)

6 - (-3) = 9

As this is true, we have the solution

x = 3, y = -1

8 0

3 years ago