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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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Is pi 3.14 or 22/7 whis of this is pi?
Tomtit [17]

Answer:

Both

Step-by-step explanation:

22/7 is the fraction version of pi

4 0
3 years ago
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Find the zeros of the function. Enter the solutions from least to greatest . h(x) = (- 4x - 3)(x - 3) lesser x = greater
icang [17]

9514 1404 393

Answer:

  -3/4, 3

Step-by-step explanation:

The zeros are the values of x that make h(x)=0. Those are the values of x that make the factors of h(x) be zero.

  -4x -3 = 0   ⇒   x = -3/4

  x -3 = 0   ⇒   x = 3

The zeros of the function are -3/4 and 3.

3 0
3 years ago
Pls help me with this :)<br><br><br> .
san4es73 [151]

Answer:

35 is the answer thank u 35 is a real answer

3 0
3 years ago
What value of x will make the given triangles congruent?
Molodets [167]
Because you're trying to make them congruent, equal the two expressions to each other. 

So, for #10 you would equal them so it would look like this. 
2x+2=5x-19

Then you would just go ahead and simplify

2x+2=5x-19
-2x     -2x
---------------
2= 3x -19
+19    +19
---------------
21=3x
---  ----
3     3

x=7

This means that x should be 7. You can check this just by plugging it in

2x+2
2(7)+2 = 16

5x-19
5(7)-19= 16

Same with #11.

x+8=3x-14
-x     -x
--------------
8=2x-14
+14   +14
--------------
22=2x
---  ----
2     2

x=11

Check. 

x+8
11+8= 19

3x-14
3(11) - 14 = 19
6 0
3 years ago
28.4.2 Test (CST): Transformations, Congruence, and Similarities, Part 2
frez [133]

Answer:

R'(2,4)

Step-by-step explanation:

When doing translations you subtract or add within the coordinates like a normal problem.

If it helps you, write it as seperate equations like:

1-1 and 5-1

Hope that helps ✓

8 0
2 years ago
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