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Tanzania [10]
3 years ago
10

RES Find (fºg)(1) Ax) = x2 - 1 g(x)= v a 0 c. 4. b. d. 18 Help pls

Mathematics
2 answers:
Crank3 years ago
8 0
Yea The answer is A 0
slava [35]3 years ago
3 0

Answer:

A

Step-by-step explanation:

So we have the two functions:

f(x)=x^2-1\\g(x)=\sqrt x

And we want to find:

(f\circ g)(1)

This is the same as:

f(g(1))

So, to find the answer, find g(1) first:

g(x)=\sqrt x\\g(1)=\sqrt1\\g(1)=1

Now, substitute this value for g(1):

f(g(1))\\=f(1)

And plug this into f(x):

f(x)=x^2-1\\f(1)=(1)^2-1\\f(1)=1-1=0

Therefore:

f(1)=f(g(1))=(f\circ g)(1)=0

Our answer is A

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HELPPPP 100 points if you help!!!!
nignag [31]

Answer:

Part A)

Chorus:

c(t)=15(1.12)^t

Band:

b(t)=2t+30

Part B)

After 9 years:

The chorus will have about 41 people.

And the band will have 48 people.

Part C)

About approximately 11 years.

Step-by-step explanation:

We are given that there are 15 people in the chorus. Each year, number of people in the chorus increases by 12%. So, the chorus increases exponentially.

There are 30 people in the band. Each year, 2 new people join the band. So, the band increases linearly.

Part A)

Since after each year, the number of people in the chorus increases by 12%, the new population will be 112% or 1.12 of the previous population.

So, using the standard form for exponential growth:

c(t)=a(r)^t

Where <em>a</em> is the initial population and <em>r</em> is the rate of change.

We will substitute 15 for <em>a </em>and 1.12 for <em>r</em>. Hence:

c(t)=15(1.12)^t

This represents the number of people in the chorus after <em>t</em> years.

We are given that 2 new people join the band each year. So, it increases linearly.

Since there are already 30 people in the band, our initial point or y-intercept is 30.

And since 2 new people join every year, our slope is 2. Then by the slope-intercept form:

b(t)=mt+b

And by substitution:

b(t)=2t+30

This represents the number of people in the band after <em>t</em> years.

Part B)

We want to find the number of people in the chorus and the band after 9 years.

Using the chorus function, we see that:

c(9)=15(1.12)^9\approx41.59\approx41

There will be approximately 41 people in the chorus after 9 years.

And using the band function, we see that:

b(9)=2(9)+30=48

There will be 48 people in the band after 9 years.

Part C)

We want to determine after approximately how many years will the number of people in the chorus and band be equivalent. Hence, we will set the two functions equal to each other and solve for <em>t</em>. So:

15(1.12)^t=2t+30

Unfortunately, it is impossible to solve for <em>t</em> using normal analytic methods. Hence, we can graph them. Recall that graphically, our equation is the same as saying at what point will our two functions intersect.

Referring to the graph below, we can see that the point of intersection is at approximately (10.95, 51.91).

Hence, after approximately 11 years, both the chorus and the band will have approximately 52 people.

5 0
2 years ago
The image below shows two parallel lines cut by a transversal. What is the value of A
rewona [7]

<u>Answer</u>

59°


<u>Explanation</u>

There are 2 parallel line and one transverse.

Angles in a straight line add up to 180°

∴ 180 - (2a + 3) = 180 - 2a -3

                        = 177 - 2a

The angle (177 - 2a) corresponds to angle a in the diagram. The two corresponding angles are equal.

∴ 177 - 2a = a

  177 = a + 2a

3a  = 177

a = 177/3

  = 59°

3 0
3 years ago
I need help with this page
arlik [135]

Answer:

check image below

Step-by-step explanation:

6 0
1 year ago
Is y=8200(1.19)x a growth or decay and what is the percentage
Bad White [126]

Answer:

Growth 119

Step-by-step explanation:

It is positive and the percentage is 1.19 with the decimal moved 2 places to to the right.

6 0
2 years ago
Read 2 more answers
A. They will spend $53.97 on 3 pizzas. What is the price of each pizza? Show all your work.
STALIN [3.7K]

how much money did they start off with?

5 0
2 years ago
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