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3 years ago

For the graphed exponential equation, calculate the average rate of change from x = −2 to x = 1.

Mathematics

2 answers:

marishachu [46]3 years ago

8 0

At x = -2, y = -4
At x = 1, y = 3
You have two pairs (1,3)(-2,-4).
You have to figure out the rate of change
(y2-y1)/(x2-x1)
(-4-3)/(-2-1)
Which the answer is b 7/3 hope this helps.

blagie [28]3 years ago

3 0

At x = -2, y = -4
At x = 1, y = 3
This gives you two ordered pairs (1,3) and (-2,-4).
Use the slope formula to find slope(rate of change)
(Y2-y1)/(x2-X1)
(-4-3)/(-2-1)
M = -7/-3 = 7/3

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Find the length of the arc and express your answer as a fraction times pie

Elina [12.6K]

Solution:

Given a circle of center, A with radius, r (AB) = 6 units

Where, the area, A, of the shaded sector, ABC, is 9π

To find the length of the arc, firstly we will find the measure of the angle subtended by the sector.

To find the area, A, of a sector, the formula is

$\begin{gathered} A=\frac{\theta}{360\degree}\times\pi r^2 \\ Where\text{ r}=AB=6\text{ units} \\ A=9\pi\text{ square units} \end{gathered}$

Substitute the values of the variables into the formula above to find the angle, θ, subtended by the sector.

$\begin{gathered} 9\pi=\frac{\theta}{360\degree}\times\pi\times6^2 \\ Crossmultiply \\ 9\pi\times360=36\pi\times\theta \\ 3240\pi=36\pi\theta \\ Divide\text{ both sides by 36}\pi \\ \frac{3240\pi}{36\pi}=\frac{36\pi\theta}{36\pi} \\ 90\degree=\theta \\ \theta=90\degree \end{gathered}$

To find the length of the arc, s, the formula is

$\begin{gathered} s=\frac{\theta}{360\degree}\times2\pi r \\ Where \\ \theta=90\degree \\ r=6\text{ units} \end{gathered}$

Substitute the variables into the formula to find the length of an arc, s above

$\begin{gathered} s=\frac{\theta}{360}\times2\pi r \\ s=\frac{90\degree}{360\degree}\times2\times\pi\times6 \\ s=\frac{12\pi}{4}=3\pi\text{ units} \\ s=3\pi\text{ units} \end{gathered}$

Hence, the length of the arc, s, is 3π units.

4 0

1 year ago

∠CAT and ∠TAD is a linear pair. If m∠CAT = 14 and m∠TAD = x+10, find x. (show work please)

marissa [1.9K]

Answer:

156

Step-by-step explanation:

Since, ∠CAT and ∠TAD is a linear pair.

Therefore,

∠CAT + ∠TAD = 180°

14° + (x + 10)° = 180°

(x + 24)° = 180°

x + 24 = 180

x = 180 - 24

x = 156

3 0

3 years ago