1 cm equals 10 mm how many millimeters does 2.5 cm equal label your answer

Given the following exponential function, identify whether the change

kodGreya [7K]

It shows a change in growth, and has a percentage rate that is positive, I .

7 0

3 years ago

let sin(θ) =3/5 and tan(y) =12/5 both angels comes from 2 different right trianglesa)find the third side of the two tringles b)

statuscvo [17]

In a right triangle, we haev some trigonometric relationships between the sides and angles. Given an angle, the ratio between the opposite side to the angle by the hypotenuse is the sine of this angle, therefore, the following statement

$\sin (\theta)=\frac{3}{5}$

Describes the following triangle

To find the missing length x, we could use the Pythagorean Theorem. The sum of the squares of the legs is equal to the square of the hypotenuse. From this, we have the following equation

$x^2+3^2=5^2$

Solving for x, we have

$\begin{gathered} x^2+3^2=5^2 \\ x^2+9=25 \\ x^2=25-9 \\ x^2=16 \\ x=\sqrt[]{16} \\ x=4 \end{gathered}$

The missing length of the first triangle is equal to 4.

For the other triangle, instead of a sine we have a tangent relation. Given an angle in a right triangle, its tanget is equal to the ratio between the opposite side and adjacent side.The following expression

$\tan (y)=\frac{12}{5}$

Describes the following triangle

Using the Pythagorean Theorem again, we have

$5^2+12^2=h^2$

Solving for h, we have

$\begin{gathered} 5^2+12^2=h^2 \\ 25+144=h^2 \\ 169=h^2 \\ h=\sqrt[]{169} \\ h=13 \end{gathered}$

The missing side measure is equal to 13.

Now that we have all sides of both triangles, we can construct any trigonometric relation for those angles.

The sine is the ratio between the opposite side and the hypotenuse, and the cosine is the ratio between the adjacent side and the hypotenuse, therefore, we have the following relations for our angles

$\begin{gathered} \sin (\theta)=\frac{3}{5} \\ \cos (\theta)=\frac{4}{5} \\ \sin (y)=\frac{12}{13} \\ \cos (y)=\frac{5}{13} \end{gathered}$

To calculate the sine and cosine of the sum

$\begin{gathered} \sin (\theta+y) \\ \cos (\theta+y) \end{gathered}$

We can use the following identities

$\begin{gathered} \sin (A+B)=\sin A\cos B+\cos A\sin B \\ \cos (A+B)=\cos A\cos B-\sin A\sin B \end{gathered}$

Using those identities in our problem, we're going to have

$\begin{gathered} \sin (\theta+y)=\sin \theta\cos y+\cos \theta\sin y=\frac{3}{5}\cdot\frac{5}{13}+\frac{4}{5}\cdot\frac{12}{13}=\frac{63}{65} \\ \cos (\theta+y)=\cos \theta\cos y-\sin \theta\sin y=\frac{4}{5}\cdot\frac{5}{13}-\frac{3}{5}\cdot\frac{12}{13}=-\frac{16}{65} \end{gathered}$

4 0

1 year ago

15. A restaurant has one type of milk that has 2% fat and another that has 7% fat. how many quarts of each type does the restaur

krek1111 [17]

<span>B. 16 quarts of the 2% milk and 24 quarts of the 7% milk First, let's create an equation to solve. x = quarts of 2% milk (40-x) = quarts of 7% milk So we have the equation x*2 + (40-x)*7 = 40*5 Now to solve for x x*2 + (40-x)*7 = 40*5 x*2 + 7*40 - 7*x = 40*5 x*2 - 7*x = 40*5 - 7*40 -5*x = - 2*40 x = 2*8 x = 16 So we need 16 quarts of 2% milk and 40-16 = 24 quarts of 7%, which matches option "B".</span>

5 0

2 years ago

Mr.Thompson is on a diet. He currently weighs 250 pounds. He loses 3 pounds per month. Write an equation that models Mr.thompson

jekas [21]

250-3m

m represents months

Not an equation but an expression since I don’t know the number of months he was on the diet.

6 0

3 years ago

Read 2 more answers

Which bacteria sample (A or B) had a smaller initial population? What was that value?

zubka84 [21]