Answer:
1.c
2.b
3. c
4.d
Step-by-step explanation:
leave an brainlest!
Answer:
The corresponding definite integral may be written as
![\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x](https://tex.z-dn.net/?f=%5Cint_a%5Eb%20%5Cmathrm%7B%284x%20%2B%2011%29%7D%5C%2C%5Cmathrm%7Bd%7Dx)
The answer of the above definite integral is
![\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x = 98](https://tex.z-dn.net/?f=%5Cint_a%5Eb%20%5Cmathrm%7B%284x%20%2B%2011%29%7D%5C%2C%5Cmathrm%7Bd%7Dx%20%3D%2098)
Step-by-step explanation:
The given limit interval is
![\lim_{||\Delta|| \to 0} \sum\limits_{i=1}^n (4c_i + 11) \Delta x_i](https://tex.z-dn.net/?f=%5Clim_%7B%7C%7C%5CDelta%7C%7C%20%5Cto%200%7D%20%20%5Csum%5Climits_%7Bi%3D1%7D%5En%20%284c_i%20%2B%2011%29%20%5CDelta%20x_i)
![[a, b] = [-8, 6]](https://tex.z-dn.net/?f=%5Ba%2C%20b%5D%20%3D%20%20%5B-8%2C%206%5D)
The corresponding definite integral may be written as
![\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x](https://tex.z-dn.net/?f=%5Cint_a%5Eb%20%5Cmathrm%7B%284x%20%2B%2011%29%7D%5C%2C%5Cmathrm%7Bd%7Dx)
![\int_{-8}^6 \mathrm{(4x + 11)}\,\mathrm{d}x](https://tex.z-dn.net/?f=%5Cint_%7B-8%7D%5E6%20%5Cmathrm%7B%284x%20%2B%2011%29%7D%5C%2C%5Cmathrm%7Bd%7Dx)
Bonus:
The definite integral may be solved as
![\int_{-8}^6 \mathrm{(4x + 11)}\,\mathrm{d}x \\\\\frac{4x^2}{2} + 11x \left \|{b=6} \atop {a=-8}} \right. \\\\2x^2 + 11x \left \|{b=6} \atop {a=-8}} \right. \\\\ 2(6^2 -(-8)^2 ) + 11(6 - (-8) \\\\2(36 - 64 ) + 11(6 + 8) \\\\2(-28 ) + 11(14) \\\\-56 +154 \\\\98](https://tex.z-dn.net/?f=%5Cint_%7B-8%7D%5E6%20%5Cmathrm%7B%284x%20%2B%2011%29%7D%5C%2C%5Cmathrm%7Bd%7Dx%20%5C%5C%5C%5C%5Cfrac%7B4x%5E2%7D%7B2%7D%20%2B%2011x%20%5Cleft%20%5C%7C%7Bb%3D6%7D%20%5Catop%20%7Ba%3D-8%7D%7D%20%5Cright.%20%5C%5C%5C%5C2x%5E2%20%2B%2011x%20%5Cleft%20%5C%7C%7Bb%3D6%7D%20%5Catop%20%7Ba%3D-8%7D%7D%20%5Cright.%20%5C%5C%5C%5C%202%286%5E2%20-%28-8%29%5E2%20%29%20%2B%2011%286%20-%20%28-8%29%20%5C%5C%5C%5C2%2836%20-%2064%20%29%20%2B%2011%286%20%2B%208%29%20%5C%5C%5C%5C2%28-28%20%29%20%2B%2011%2814%29%20%5C%5C%5C%5C-56%20%2B154%20%5C%5C%5C%5C98)
Therefore, the answer to the integral is
![\int_a^b \mathrm{(4x + 11)}\,\mathrm{d}x = 98](https://tex.z-dn.net/?f=%5Cint_a%5Eb%20%5Cmathrm%7B%284x%20%2B%2011%29%7D%5C%2C%5Cmathrm%7Bd%7Dx%20%20%3D%2098)
Answer:
angle 1= 104 angle 2= 76
Step-by-step explanation:
angle 1 equals x+66 and angle 2 equals 2x so you set up an equation where they are the sum of 180 degrees because the angles are supplementry angles.
x+66+2x=180 set the sum of the angles to 180
3x+66=180 combind like terms
3x=144 subract 66 from both sides
x=38 divide 3 from both sides
Now you put x back into the measurments
angle 1= (x+66) angle 2= 2x
(38+66) 2×38
angle 1= 104 angle 2= 76
Or after you know angle 1 you can subtract angle 1 from 180 to get angle 2.
Answer:
D $1.50
Step-by-step explanation:
240/8 = 30p or 30 cents in America
30 x 5 = 150 cents = $1.50
Answer:
-3.9% I.e there is decrease in the population
Step-by-step explanation:
Population @ 1990 = 1585577
Population @ 2010 = 1526006
% change =
(1526006-1585577)/1526006 × 100%
= -59571/1526006 ×100%
= -3.9%