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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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Valentin [98]

Answer:

15 to 21

Step-by-step explanation:

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4 0
3 years ago
Use factoring to find the zeros.<br> x2 - 9x – 36 = 0
3241004551 [841]

Answer: x=12, x=-3

Step-by-step explanation: For this factored problem, you see that -36 is negative, as well at -9. This shows you that you need to find two numbers that multiply to get -36, and add up to get -9. Two numbers that both satisfy these requirements are -12 and 3. They multiply to get -36, and add to get -9.

Once you have found your values, you plug them into (x+/- __)(x+/- __), which is (x-12)(x+3).

But since the problem asks you to find the zeroes, you set each factor equal to zero, like this:

x-12=0 and x+3=0

Then solve and you have you answer!

4 0
3 years ago
Asa has 4 colored pencils. His friend purchases three times as many. If Asa’s friend buys two more 4-packs, which expression sho
daser333 [38]

24

Three times as many as four - 3(4) / 4*3/ 4+4+4

4 x 3 = 12

Then for 2 more 4 packs, it'd be 8 since it's either 2*4 or 4+4 (both equal eight)

And then you'd add them both together, 12+8=20

But since it's asking for both Asa and his friend's total amount, you'd add four more to it since 20 is just his friend's amount.

5 0
3 years ago
A resturant orders 50 pounds of hamburger every week.they sell six pounds of hamburger every day.how much hamburger is left at t
murzikaleks [220]

Answer:

8 pounds

Step-by-step explanation:

6 pounds of hamburger x 7 days a week = 42 pounds of hamburger used

50 - 42 = 8 pounds of unused hamburger at the end of the week

6 0
3 years ago
What is the multiplier for the table below? (Write multiplier as x.x)​
chubhunter [2.5K]
The average rate of change is m = 5.934

Hope this is what you were looking for.
8 0
3 years ago
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