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coldgirl [10]
2 years ago
9

What is the amplitude of y = 4sin3x?

Mathematics
1 answer:
MakcuM [25]2 years ago
5 0
The amplitude is 4 I believe
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During which time period does Landon's elevation change the fastest? Explain how you know?
bogdanovich [222]
<h3>1. How many inches per minute does London's elevation change between 4 minutes and 8 minutes. </h3>

The question actually asks for the slope of the line that stands for the points (4,3) \ and \ (8,6) why? because the questions tells us that London's elevation changes between 4 minutes and 8 minutes here. Hence, to find the slope of this line we have to use the following formula:

m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ But: \\ \\ P(x_{1},y_{1})=P(4,3) \\ P(x_{2},y_{2})=P(8,6)

m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ But: \\ \\ P(x_{1},y_{1})=P(4,3) \\ P(x_{2},y_{2})=P(8,6) \\ \\ So: \\ \\ m=\frac{6-3}{8-4}=0.75in/min

<em>So London's elevation changes 0.75 inches per minute</em>

<em></em>

<h3>2. During which time period does London's elevation change the fastest?</h3>

The greater the absolute value of the slope of the line the faster London's elevation changes. Since this is a Piecewise function, we must analyze each period.

  • FIRST:

→ Between 0 minutes and 4 minutes the function is constant, so there is no any change here.

→ Between 10 minutes and 14 minutes the function is constant, so there is no any change here.

→ Between 18 minutes and 22 minutes the function is constant, so there is no any change here.

So the solution is not in these parts of the function.

  • SECOND:

→ Between 4 minutes and 10 minutes the function has a positive slope, so there is change here.

In the previous item we calculated the slope between 4 and 8 minutes that is the same slope between 4 and 8 minutes and equals 0.75.

→ Between 14 minutes and 18 minutes the function has a positive slope, so there is change here.

Let's take two points here, say, (16,5) \ and \ (18,3)

m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ But: \\ \\ P(x_{1},y_{1})=P(16,5) \\ P(x_{2},y_{2})=P(18,3) \\ \\ So: \\ \\ m=\frac{3-5}{18-16}=-1 in/min

As you can see, the absolute value here is 1 that is greater than 0.75.

<em>In conclusion, London's elevation changes the fastest between 14 and 18 minutes</em>

7 0
3 years ago
A rectangular garden has a perimeter of 172 feet. The length of the garden is 24 feet more than the width. What are the dimensio
Lilit [14]
Given width is 24 less than length.
W=L-24
Perimeter = 2(W+L)=2(L-24+L)=4L-48 
But we're also given perimeter = 172'
Therefore 4L-48=172
solve for L
4L=172+48=220
L=55'
W=55-24 =  31'
Check: Perimeter = 2(W+L)=2(31+55)=2*86=172'  good!

Answer: The dimensions of the garden are 31' * 55'
6 0
3 years ago
Where does a hole occur in the graph of y = x(x+2) / x(x-3)
Morgarella [4.7K]

Answer:

A

Step-by-step explanation:

Given

y = \frac{x(x+2)}{x(x-3)} ← cancel x on numerator/ denominator

 = \frac{x+2}{x-3}

Cancelling the factor x, leaves a hole in the graph at x = 0

7 0
3 years ago
In ΔPQR, r = 4.9 cm, ∠R=21° and ∠P=104°. Find the length of p, to the nearest 10th of a centimeter.
Galina-37 [17]

Answer:7 +7=14/8Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Please go answer my recent questions ASAP.
Fiesta28 [93]

Answer:

OK, Im going to help you!!!!!!!!!!!

~Trinity aka Queensupreme

4 0
3 years ago
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