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3 years ago

Trig questions:

Mathematics

1 answer:

navik [9.2K]3 years ago

8 0

Question 1
Because the period is 2π, and the amplitude is 1obtain
f(x) = sin(x)
Because the horizontal shift is π, obtain
f(x) = sin(x - π)
Because the vertical shift is -4, obtain
f(x) = sin(x - π) - 4

Answer: 1. f(x) = sin(x - π) - 4

Question 2
The radius is 36/2 = 18 in.
1 revolution (360°) is the circumference, which is
2π(18) = 36π in
When the revolution is 62°, the distance traveled is
(62/360)*(36π) = (31/5)π in

Answer: 3. (31π)/5

Question 3.
Consider f(x) = 3cos(2x-π) - 1
f(0) = 3cos(-π) - 1 = -4
f(π/2) = 3cos(0) - 1 = 2
Rate of change = (2+4)/(π/2) = 12/π

From the graph, the rate of change of g(x) is
3/(π/2) = 6/π

Consider h(x) = sin(x) - 4
h(0) = 0 - 4 = -4
h(π/2) = 1 - 4 = -3
Rate of change = (-3+4)/(π/2) = 2/π
Therefore h(x) has the smallest rate of change

Answer: h(x)

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In an auditorium, a charity show is conducted in order to raise at least $3,750. The auditorium can accommodate up to 180 specta

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Answer:

See explanation

Step-by-step explanation:

Let $x,\ x\ge 0$ be the number of students and $y,\ y\ge 0$ be the number of adults on the show.

1. Tickets cost $15 for students, so x student tickets cost $15x.

Tickets cost $25 for adults, so y adult tickets cost $25y.

Total cost of all tickets is $(15x + 25y).

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$15x+25y\ge 3,750$

2. The auditorium can accommodate up to 180 spectators, hence

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3. We get the system of inequalities:

$\left\{\begin{array}{l}x\ge 0\\y\ge 0\\x+y\le 180\\15x+25y\ge 3,750\end{array}\right.$

Plot all solutions sets to each inequality and the common region is the solution set to the system of inequalities. This region is not empty, so the charity will reach its goal. For example, if they sell 50 students tickets and 125 adult tickets, they will raise $\$(15\cdot 50+25\cdot 125)=\$3,875$

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3 years ago

If f(x) = 7x+6 and g(x)=8x-4 find f(g(-2))

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Answer:

$f(g(-2))=-134$

Step-by-step explanation:

So we have the two functions:

$f(x)=7x+6\text{ and } g(x)=8x-4$

And we want to find f(g(-2)).

First, let's find g(-2):

$g(-2)=8(-2)-4$

Multiply:

$g(-2)=-16-4$

Subtract:

$g(-2)=-20$

Now, substitute:

$f(g(-2))=f(-20)$

Now, find the value of f(-20):

$f(-20)=7(-20)+6$

Multiply:

$f(-20)=-140+6$

Add:

$f(-20)=-134$

So:

$f(g(-2))=-134$

And we're done!

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Answer:

He must survey 123 adults.

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