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lapo4ka [179]
2 years ago
5

The average value of the function y = x² – 1 on [0, 12] is

Mathematics
1 answer:
shusha [124]2 years ago
3 0

Answer:

47.

Step-by-step explanation:

1) the rule:

f_{avr}=\frac{1}{b-a} \int\limits^b_a {f(x)} \, dx ,

where a;b are 0 and 12, f(x)=x²-1.

2) according to the rule above:

f_{avr}=\frac{1}{12-0} \int\limits^{12}_0 {(x^2-1)} \, dx=\frac{1}{12}(\frac{x^3}{3}-x)|^{12}_0=48-1=47.

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Aliun [14]

Answer:

x=3

Step-by-step explanation:

Since both triangles are similiar, this means they can have different sized sides, but they are just scaled versions of each other. This also means that no matter what sides they have, their angles are going to be the exact same

Knowing this, it helps to draw them out side by side so you can match them up easier. Both of them have a 90 degree angle, and more specifically they are 45-45-90 triangles (45-45-90 is a special right triangle). You can point this out since they give us a 90 degree angle and two angles that are congruent in the same triangle. In order for that to work, they HAVE to be 45-45-90

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we can use the equation 15x = 45, since 45 is what the side angle should equal.

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2 years ago
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3 years ago
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<h2><u>Answer</u><u> </u><u>:</u></h2>

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3 years ago
The number of pages that Kline can read varies directly with the time he spends reading if he reads 13 pages in 25 minutes how m
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3 years ago
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solniwko [45]

Answer:

(- 1, 8 ) and (5, 2 )

Step-by-step explanation:

Given the 2 equations

y = - x + 7 → (1)

y = 0.5(x - 3)² → (2)

Substitute y = 0.5(x - 3)² into (1)

0.5(x - 3 )² = - x + 7 ← expand and simplify left side

0.5(x² - 6x + 9) = - x + 7 ( multiply both sides by 2 )

x² - 6x + 9 = - 2x + 14 ( subtract - 2x + 14 from both sides )

x² - 4x - 5 = 0 ← in standard form

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Equate each factor to zero and solve for x

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3 years ago
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