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3 years ago

The point (16, 12) lies on the terminal side of an angle. find cos, tan, and sin

1 answer:

8 0

The terminal side means that it's 16 to the right and 12 up. Which means that the triangle made from this has the sides of 16 and 12 and the hypotenuse is 20 units long. Theta, in this case, would have 16 as it's adjacent and 12 as it's opposite.
Therefore, using the Pythagorean identities:
<span> $sin(\theta) = \frac{12}{20} = \boxed{\frac{3}{5}} \\\ cos(\theta) = \frac{16}{20} = \boxed{\frac{4}{5}} \\\ tan(\theta) = \frac{12}{16} = \boxed{\frac{3}{4}}$ </span>

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The circumference of the circle-shaped rug is 69.08 inches.

adelina 88 [10]

We can find the diameter by dividing the circumference by 3.14
d = 22

Thus, our radius is 11.
r = 11

Now, let's use the area formula ( $3.14 \cdot r^2$ ) to solve for the area.
a = $3.14 \cdot (11^2) = \boxed{379.94}$

8 0

3 years ago

At 82°F, a certain insect chirps at a rate of 61 times per minute, and at 91°F, they chirp 124 times per minute. Write an equati

Ganezh [65]

Answer:

$y=7x-513$

Step-by-step explanation:

Let

x----> the temperature in degrees Fahrenheit

y ---->insect chirping rate in times per minute

we have the ordered pairs

(82,61) and (91,124)

step 1

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{124-61}{91-82}$

$m=\frac{63}{9}=7$

step 2

Find the equation of the line

we know that

The equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope

b is the y-intercept

we have

$m=7$ ---> the units are chirps per minute/degree F

take the point (82,61)

substitute and solve for b

$61=7(82)+b$

$61=574+b$

$b=-513$

substitute

$y=7x-513$

4 0

3 years ago

Draw a line through each point using the given slope. What do you notice about the two lines?

morpeh [17]

I think the answer is that they are parallel

5 0

3 years ago

If $8259 principal is invested in a savings account that pays 5.25% interest compounded continuously how much money will be in t

VMariaS [17]

Answer:

A(10) = $13,961.50

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 5.25/100

r = 0.0525 rate per year,

Then solve the equation for A

The formula is given as:

A = Pe^rt

P = 8259

r = 0.0525

t = 10 years.

Hence,

A = 8,259.00 × e^(0.0525×10)

A = $13,961.50

Therefore, the money that will be in the account after 10 years is $13,961.50

5 0

3 years ago

For each of the terms below, give a brief definition.

irinina [24]

Answer:

term

a word or phrase used to describe a thing

Coefficient

a number for constant quantity

constant

occurring continuously over a period of time

Algebraic expression

In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations.

5 0

3 years ago