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babymother [125]

2 years ago

13

A rectangle is bounded by the x-axis and the semicircle y = √(36 – x^2). Write the area A of the rectangle as a function of x, a

nd determine the domain of the area function.

1 answer:

Dafna11 [192]2 years ago

8 0

A(x)=2x·√36-x²
this is the answer.

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The function f(x)=125(0.9)x models the population of a species of fly in millions after x years.

deff fn [24]

Answer: (B) 3 times as fast

<u>Step-by-step explanation:</u>

rate of change is the "slope" between the given interval.

f(x) = 125(.9)ˣ

f(1) = 125(.9)¹

= 112.5

f(5) = 125(.9)⁵

= 73.8

$\dfrac{f(5) - f(1)}{5 - 1} = \dfrac{73.8-112.5}{5-1} = -\dfrac{38.7}{4} = -9.675$

********************

f(11) = 125(.9)¹¹

= 39.2

f(15) = 125(.9)¹⁵

= 25.7

$\dfrac{f(15) - f(11)}{15 - 11} = \dfrac{39.2-25.7}{15-11} = -\dfrac{13.5}{4} = -3.375$

********************

The rate of change from years 1 to 5 is approximately 3 times the rate of change from years 11 to 15.

7 0

3 years ago

According to data from a medical association, the rate of change in the number of hospital outpatient visits, in millions, in

GaryK [48]

Answer:

a) $f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+264,034,000$

b) f(t=2015) = 264,034,317.7

Step-by-step explanation:

The rate of change in the number of hospital outpatient visits, in millions, is given by:

$f'(t)=0.001155t(t-1980)^{0.5}$

a) To find the function f(t) you integrate f(t):

$\int \frac{df(t)}{dt}dt=f(t)=\int [0.001155t(t-1980)^{0.5}]dt$

To solve the integral you use:

$\int udv=uv-\int vdu\\\\u=t\\\\du=dt\\\\dv=(t-1980)^{1/2}dt\\\\v=\frac{2}{3}(t-1980)^{3/2}$

Next, you replace in the integral:

$\int t(t-1980)^{1/2}=t(\frac{2}{3}(t-1980)^{3/2})- \frac{2}{3}\int(t-1980)^{3/2}dt\\\\= \frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}+C$

Then, the function f(t) is:

$f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+C'$

The value of C' is deduced by the information of the exercise. For t=0 there were 264,034,000 outpatient visits.

Hence C' = 264,034,000

The function is:

$f(t)=0.001155[\frac{2}{3}t(t-1980)^{3/2}-\frac{4}{15}(t-1980)^{5/2}]+264,034,000$

b) For t = 2015 you have:

$f(t=2015)=0.001155[\frac{2}{3}(2015)(2015-1980)^{1/2}-\frac{4}{15}(2015-1980)^{5/2}]+264,034,000\\\\f(t=2015)=264,034,317.7$

3 0

3 years ago

5. The coordinates of the points A and B are (0, 6)

ella [17]

I need to answer two questions to ask again sorry

8 0

3 years ago

Someone please help me, I need the type of statement and reason.

RideAnS [48]

The type of statement is a congruent

5 0

3 years ago

What is the area? <br> (20 points)

Korolek [52]

Answer:

246 ft^2

Step-by-step explanation:

First, break it into smaller rectangles:

3*6=12

6*9=54

15*12=180

Add the areas together

12+54+180=246

The area of the figure is 246 ft^2

3 0

2 years ago