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3 years ago

Write the product as a sum: 14cos(39x)sin(19x)

Mathematics

1 answer:

charle [14.2K]3 years ago

4 0

Recall that

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

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

Adding these together gives

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

To get 14 cos(39x) sin(19x) on the right side, multiply both sides by 7 and replace a = 19x and b = 39x :

7 (sin(19x + 39x) + sin(19x - 39x)) = 14 cos(39x) sin(19x)

7 (sin(58x) + sin(-20x)) = 14 cos(39x) sin(19x)

7 (sin(58x) - sin(20x)) = 14 cos(39x) sin(19x)

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What’s the answer to this question if your right I’ll keep giving you points

andreyandreev [35.5K]

$\huge\text{$m\angle O=\boxed{11^{\circ}}$}$

Since we know that all angles in a triangle add up to $180^{\circ}$ , we can solve for $x$ and substitute it back into $(x-5)^{\circ}$ to find $m\angle O$ .

$\begin{aligned}m\angle N+m\angle O+m\angle P&=180\\(5x-8)+(x-5)+(6x+1)&=180\end{aligned}$

Remove the parentheses and combine like terms.

$\begin{aligned}5x-8+x-5+6x+1&=180\\(5x+x+6x)+(-8-5+1)&=180\\12x-12&=180\end{aligned}$

Add $12$ to both sides of the equation.

$\begin{aligned}12x-12&=180\\12x&=192\end{aligned}$

Divide both sides of the equation by $12$ .

$\begin{aligned}x=16\end{aligned}$

Now that we have the value of $x$ , we can substitute it back into $(x-5)^{\circ}$ to find $m\angle O$ .

$\begin{aligned}m\angle O&=(x-5)\\&=16-5\\&=\boxed{11}\end{aligned}$

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3 years ago

8. The can shown below has a diameter of 5 inches and a height of 6.5 inches. The can's label covers the entire lateral surface

USPshnik [31]

Answer:

H. 102.05

Step-by-step explanation:

The circumference is 5pi = 15.7

15.7 * 6.5 = 102.05

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3 years ago

Jordan is a manager of a car dealership. He has two professional car washers, Matthew and Arianna, to clean the entire lot of ca

Maslowich

If we say there are 100 cars in a lot (It's an arbitrary number. You can use any number you want), Matthew can wash 100 cars in 14 hours or 7.14 cars an hour. Arianna can wash 100 cars in 11 hours or 9.09 cars an hour. Together, in an hour they can wash 7.14 + 9.09 or 16.23 cars. So to wash 100 cars it would take them 100/16.23 = 6.16 or about 6 hours.
You can do this with variables as well.
Matthew has a rate of x/14 while Arianna has a rate of x/11. Together their rate is x/14 + x/11= x/y
Divide both sides by x, you would get 1/14 + 1/11 = 1/y
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4 years ago

Which sequence of transformations will result in an image that maps onto itself?

Trava [24]

The sequence that will result in an image maps into itself is:
D ) reflect over the y-axis and then reflect again over the y-axis.

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3 years ago

What is the sum of 1/2 and 1/3

Elena-2011 [213]

Answer:

i am wrong dont do what i am doing

Step-by-step explanation: