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2 years ago

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

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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Complete the table.<br><br> table<br> Distances:

Sever21 [200]

Answer:79

Step-by-step explanation:78: I love the noise

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3 years ago

Read 2 more answers

Find the value of b rounded to the nearest tenth

vekshin1

Answer:

You can use the Law of Sines for this problem, but what makes it tough at first glance is that they put a step in before you can use it directly. That first step is to get m∠C. When solving a triangle, always get the third angle if you know the other two so that you can use the Law of Sines (or Law of Cosines) more directly.

The sum of the angles of any triangles is 180°. We know the measures of the two other angles. So we subtract them from 180° to find that third angle.

180° - 76° - 66° = 38°

Now we can use the proportion from the picture. Angle B measures 76°, side b is our unknown, Angle C measures 38°, and side c measures 3 units.

sin 76° sin 38°

----------- = -----------

b 3

Cross multiply to find b (the side). We carry out five places in these calculations to get more accuracy.

3 * sin 76° = b * sin 38°

b = 3 * sin 76° 3 * 0.56611 1.69832

--------------- = --------------- = ---------------- = 5.73044

sin 38° 0.29636 0.29636

To the nearest tenth, b - 5.7 units.

Step-by-step explanation:

google hope this helps

6 0

2 years ago

Triangles Unit Test part 1 A length of rope is stretched between the top edge of a building and a stake in the ground. The head

musickatia [10]

Answer:

The building is 32 feet tall.

Step-by-step explanation:

Consider the figure drawn below representing the given scenario.

AB represents the height of building, BC is the distance between the stake and building, C represents the stake at ground level, and DE represents the height of the tree growing halfway between building and stake.

Since the tree is growing halfway between B and C, therefore, the point E divides the line segment BC into 2 equal parts.

Therefore, $BE = EC$ or E is the midpoint of BC.

Also, from the figure, it is clear that both tree and building are vertical to the ground. So, DE || AB.

Now, from converse of mid-segment theorem, if a line passes through the midpoint of one side of a triangle and also parallel to the third side, then the line also passes through the midpoint of the second side and half the length of the third side (parallel side)

So,

$DE=\frac{1}{2}\times AB\\\\16=\frac{AB}{2}\\\\AB=16\times 2=32\ ft$

Therefore, the building is 32 feet tall.

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3 years ago

I have 1 hundreds, 4 ones, 2 tens, and 1 tenths. What number am I?

DaniilM [7]

Since it reads 1 hundreds, that means 100. 4 ones mean 4 * 1, which is 4. 2 tens means 2 * 10, which is 20. Add those together and you get 124. Where it reads "1 tenth", that means 0.1
Therefore, the number is 124.1

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3 years ago

during a 500-meter race, a runner ran the first 400 meters in 1 minute and 25 seconds.she finished the race i 2 minutes and 15 s

mart [117]

She ran the last 100 meters in 2:15 -1:25 = 0:50, so her average speed was

... (100 m)/(50 s) = 2.0 m/s

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3 years ago