Solve the given equation for h B=V/h Solve the given equation for V B=V/h

This talented group of dogs has 25 yards of ribbon. They want to cut the ribbon to make bows and awards. If each piece of ribbon needs to be 3/4 of a yard, how many bows will they be able to make?

The total number of yards =25 yards

Each piece of ribbon = 3/4 of a yard

Hence, the number of bows they can make is:

3/4 × 25 yards

= 18.75 bows.

8 0

3 years ago

Verify the following identity. <img src="https://tex.z-dn.net/?f=-%5Cfrac%7Bcos%283x%29%2Bcos%285x%29%7D%7Bsin%283x%29-

kogti [31]

Recall the angle sum identities:

cos(a + b) = cos(a) cos(b) - sin(a) sin(b)

cos(a - b) = cos(a) cos(b) + sin(a) sin(b)

sin(a + b) = sin(a) cos(b) + sin(b) cos(a)

sin(a - b) = sin(a) cos(b) - sin(b) cos(a)

Notice that adding the first two together, and subtract the last from the third, we get two more identities:

cos(a + b) + cos(a - b) = 2 cos(a) cos(b)

sin(a + b) + sin(a - b) = 2 sin(b) cos(a)

Let a = 4x and b = x. Then

cos(5x) + cos(3x) = 2 cos(4x) cos(x)

sin(5x) - sin(3x) = 2 sin(x) cos(4x)

Now,

$-\dfrac{\cos(3x)+\cos(5x)}{\sin(3x)-\sin(5x)}=\dfrac{\cos(5x)+\cos(3x)}{\sin(5x)-\sin(3x)}=\dfrac{2\cos(4x)\cos x}{2\sin x\cos(4x)}=\dfrac{\cos x}{\sin x}=\cot x$

as required.

4 0

4 years ago

Many smartphones, especially those of the LTE-enabled persuasion, have earned a bad rap for exceptionally bad battery life. Batt

BartSMP [9]

Answer:

Null hypothesis: the variance in hours of usage for talking is not greater than the the variance in hours of usage for internet.

$H_o$ : $\sigma _1 ^2 \leq \sigma _2^2$

Alternative hypothesis: the variance in hours of usage for talking is greater than the the variance in hours of usage for internet.

$H_a : \sigma_1^2 > \sigma_2^2$

$\mathbf{s_ 1 =16.11}$

$\mathbf{s_2 = 7.98}$

Step-by-step explanation:

Let $x_1$ and $x_2$ be the two variables that represents the battery life in hours for talking usage and battery life in hours for internet usage respectively.