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cestrela7 [59]
3 years ago
10

Solve the inequality: ||x-4|-2|<3

Mathematics
1 answer:
yulyashka [42]3 years ago
3 0
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Explain how you can use base 10 blocks to find 2.16÷3
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You can use 10 blocks by having 1 ten and 6 ones and then divide it into groups of 3 when you do that you are kind of subtracting when you take away 3 away each time. After that you multiply it, so you think of whatever times 3 is 16 which is 15 r1. Then your answer should be 30.
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Is it true that the order when dividing 3 real numbers does not affect the answer
Jobisdone [24]


No, it is not true

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4 divided by 2 divided by 1 equals 2, while 2 divided by 1 divided by 4 equals 0.5

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3 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
ioda

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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