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zimovet [89]
3 years ago
8

Use the graph to calculate the following

Mathematics
1 answer:
sweet-ann [11.9K]3 years ago
4 0

Answer:

f(x)= { 1  if      x≤-2

         x2      if -2<x≤0

        ln(x)     if x>0

Step-by-step explanation:

The first part of the graph (from left to right) is a constant funcion. Since there isn't any pendant, the y value is constant at y=1. This remains this way until x≤-2 (because the value at x=-2 is filled in on the line and blanked out on the curve above)

The second part of the graph, between x>-2 & x=0, is a cuadratic formula.

Finally, the last part of the graph corresponds to the formula ln(x), which is only valid for x>0.    

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Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph.
mamaluj [8]

Answer:

Option c. Reflection across the x-axis and vertical stretch by a factor of 7

Step-by-step explanation:

If the graph of the function y = cf(x) represents the transformations made to the graph of y = f(x) then, by definition:

If 0 then the graph is compressed vertically by a factor a.

If |c| > 1 then the graph is stretched vertically by a factor a.

If c then the graph is reflected on the x axis.

In this problem we have the function y = -7secx and our paretn function is y = secx

therefore it is true that

c = -7\\\\|-7|> 1\\\\-7.

Therefore the graph of y = secx is stretched vertically by a factor of 7 and is reflected on the x-axis

Finally the answer is Option c

6 0
3 years ago
Gravel is being dumped from a conveyor belt at a rate of 15 ft3/min, and its coarseness is such that it forms a pile in the shap
gayaneshka [121]

Answer:

0.13 ft/min

Step-by-step explanation:

We are given that

\frac{dV}{dt}=15ft^3/min

We have to find the increasing rate of change of height of pile  when the pile is 12 ft high.

Let d be the diameter of pile

Height of pile=h

d=h

Radius of pile,r=\frac{d}{2}=\frac{h}{2}

Volume of pile=\frac{1}{3}\pi r^2 h=\frac{1}{12}\pi h^3

\frac{dV}{dt}=\frac{1}{4}\pi h^2\frac{dh}{dt}

h=12 ft

Substitute the values

15=\frac{1}{4}\pi(12)^2\frac{dh}{dt}

\frac{dh}{dt}=\frac{15\times 4}{\pi(12)^2}

\frac{dh}{dt}=0.13ft/min

7 0
3 years ago
Mr. Hayden's Bible class collected $11
ki77a [65]

This is the only way I can think of this mathematically. This took a good 20 minutes for me. You need to guess and check. Like try 17 quarters, 50 nickels, and 37 dimes etc. until you get 11.00. My numbers are mathematically correct but we both know you cant have 18.909 quarters so. lol

Answer:

Quarters: 18.909

Nickels: 49.818

Dimes: 37.818

Somewhere around those numbers.

Step-by-step explanation:

$11.00 total in coins

Nickel = $0.05

Dime = $0.10

Quarter = $0.25

(n*0.05) + (d*0.10) + (q*0.25)

Solve the equation for q.

q=\frac{1}{2} d

(n*0.05) + (d*0.10) +( \frac{1}{2} d *0.25)

Simplify the expression.

9d + 2n = 440

d - n = -12

Multiply both sides of the equation by -9.

-9d + 9n = 108

9d + 2n = 440

Sum the equations vertically to eliminate at least one variable.

11n = 548

n=\frac{548}{11}

Substitute the given value of n into the equation d - n = -12

d-\frac{548}{11} =-12

d=\frac{416}{11}

Substitute the given value of n into the equation q=\frac{1}{2} d

q=\frac{1}{2} *\frac{416}{11}

q=\frac{208}{11}

Finally

d=\frac{416}{11}        d = 37.818

n=\frac{548}{11}        n = 49.818

q=\frac{208}{11}        q = 18.909

6 0
2 years ago
27/723 long division
Brrunno [24]

Answer:

0.03734439834

Step-by-step explanation:

8 0
3 years ago
The sum of two numbers is 72. One number is 8
Tpy6a [65]

Answer:

32 and 40

Step-by-step explanation:

Let's call the smaller number x. If the smaller number is x, the equation for this problem is 2x + 8 = 72

Equation:

2x + 8 = 72

2x = 64

x = 32

So now we know the smaller number is 32, so now add 8 and we get 40.

Therefore the 2 numbers are 32 and 40

7 0
3 years ago
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