Answer:
A = 240 in²
Step-by-step explanation:
8 triangles with base of 96/8 = 12 and height 5
A = 8(½(12)(5)) = 240 in²
Expand the integrand:
![(2x - 3) (4x^2 + 1) = 8x^3 - 12x^2 + 2x - 3](https://tex.z-dn.net/?f=%282x%20-%203%29%20%284x%5E2%20%2B%201%29%20%3D%208x%5E3%20-%2012x%5E2%20%2B%202x%20-%203)
Then integrate using the power rule:
![\displaystyle \int (8x^3-12x^2+2x-3) \, dx = 2x^4 - 4x^3 + x^2 - 3x + C](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%288x%5E3-12x%5E2%2B2x-3%29%20%5C%2C%20dx%20%3D%202x%5E4%20-%204x%5E3%20%2B%20x%5E2%20-%203x%20%2B%20C)
By the fundamental theorem of calculus, the definite integral has a value of
![\displaystyle \int_0^2 (2x-3)(4x^2+1) \, dx = \left(2x^4 - 4x^3 + x^2 - 3x\right)\bigg|_{x=2} - \left(2x^4 - 4x^3 + x^2 - 3x\right)\bigg|_{x=0}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_0%5E2%20%282x-3%29%284x%5E2%2B1%29%20%5C%2C%20dx%20%3D%20%5Cleft%282x%5E4%20-%204x%5E3%20%2B%20x%5E2%20-%203x%5Cright%29%5Cbigg%7C_%7Bx%3D2%7D%20-%20%5Cleft%282x%5E4%20-%204x%5E3%20%2B%20x%5E2%20-%203x%5Cright%29%5Cbigg%7C_%7Bx%3D0%7D)
![\displaystyle \int_0^2 (2x-3)(4x^2+1) \, dx = 32 - 32 + 4 - 6 = \boxed{-2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_0%5E2%20%282x-3%29%284x%5E2%2B1%29%20%5C%2C%20dx%20%3D%2032%20-%2032%20%2B%204%20-%206%20%3D%20%5Cboxed%7B-2%7D)
It would be 3^x=14 and you just have to find out what number raised to 3 equals 14
The sum of the given decimal numbers is -7.68
<h3>Sum of decimal numbers</h3>
Decimal numbers are numbers that contains decimal points. Given the expression below;
4.62 + (−12.3).
Convert to fraction to have:
4.62 + (−12.3) = 462/100 - 123/10
Find the LCM
4.62 + (−12.3) = 462-1230/100
4.62 + (−12.3) = -768/100
4.62 + (−12.3) =-7.68
Hence the sum of the given decimal numbers is -7.68
Learn more on sum of numbers here; brainly.com/question/25734188
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Answer:
-16
Step-by-step explanation:
-k² -(3k-5n)+4n k=-1 , n= -2
= -(-1)² - ( 3(-1) -5(-2) )+4(-2)
= -1-(-3+10)-8
= -1-(7)-8
= -1-7-8
= -16