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koban [17]
2 years ago
14

Find the range of the function F(x) = the integral from 0 to x of the square root of 4-t^2 dt

Mathematics
1 answer:
ioda2 years ago
8 0

Note that √(4 - t²) is defined only as long as 4 - t² ≥ 0, or -2 ≤ t ≤ 2. Then the real integral exists only if -2 ≤ x ≤ 2. (Otherwise we deal with complex numbers.)

If x = 2, then the integral corresponds to the area of a quarter-circle with radius 2. This means that the integral has a maximum value of 1/4 • π • 2² = π.

On the opposite end, if x = -2, then the integral has the same value, but the integral from 0 to -2 is equal to the negative integral from -2 to 0. So the minimum value is -π.

For all x in between, we observe that the integrand is continuous over the rest of its domain, so F(x) is continuous.

Then the range of F(x) is the interval [-π, π].

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Andre is preparing for the school play. He needs to paint a cardboard box to look like a dresser. The box is a rectangular prism
ozzi

Answer:

Step-by-step explanation:

75 is right

7 0
2 years ago
If marie wants to decorate a gift box with ribbon. She measures three pieces that she has with a ruler.They are 32. Centimeters,
Misha Larkins [42]

Answer: No, she does not have enough.

Step-by-step explanation:

1. You have the following information given in the problem above:

- The measures of the three pieces are: 32 centimeters, 41.19 centimeters and 57.8 centimeters long.

- She need 200 centimeters of ribbon for the box.

2. Therefore, you must add the measures given in the problem to know if Marie has enough ribbon to decorate the gift box. Then:

32cm+41.19cm+57.8cm=130.99cm

3. As you can see:

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Therefore, she does not have enough ribbon.

5 0
3 years ago
Mike drove 100 miles in a rental car and was charged $58.00. Jane rented the same car after Mike had rented it and was charged $
timama [110]

Answer:

y= 48 + 0.1x

x= miles driven

Step-by-step explanation:

<u>We need to calculate the fixed and variable cost (per mile) of renting a car. To do that, we will use the high-low method:</u>

Variable cost per unit= (Highest activity cost - Lowest activity cost)/ (Highest activity units - Lowest activity units)

Variable cost per unit= (65 - 58) / (170 - 100)

Variable cost per unit= $0.1 per mile

Fixed costs= Highest activity cost - (Variable cost per unit * HAU)

Fixed costs= 65 - (0.1*170)

Fixed costs= $48

Fixed costs= LAC - (Variable cost per unit* LAU)

Fixed costs= 58 - (0.1*100)

Fixed costs= $48

y= 48 + 0.1x

x= miles driven

7 0
3 years ago
What is the value of x in the equation -2/3 x +9= 4/3x -3?
HACTEHA [7]

-2/3x+9=4/3x-3 original problem add 2/3x to both sides

9=6/3x-3 simplify 6/3 to 2 and add 3 to both sides

12=2x  divide both sides by 2

x=6

hope that helps



5 0
3 years ago
The sale is for $30 this is 75 % of the original price find the original price
Sauron [17]
1. $52.80

2. 80

3. 46 people

4. 15 minutes

5. 2%

6. 147.03

I think these answers are correct but I am not 100% sure
6 0
3 years ago
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