Equation of a sphere For constants a , b , c , and d , show that the equation x 2 + y 2 + z 2 − 2 a x − 2 b y − 2 c z = d describes a sphere centered at ( a , b , c ) with radius r , where r 2 = d + a 2 + b 2 + c 2 , provided d + a 2 + b 2 + c 2 > 0.
Equation of a sphere For constants a , b , c , and d , show that the equation x 2 + y 2 + z 2 − 2 a x − 2 b y − 2 c z = d describes a sphere centered at ( a , b , c ) with radius r , where r 2 = d + a 2 + b 2 + c 2 , provided d + a 2 + b 2 + c 2 > 0.
Solution Summary: The author describes the equation of the sphere centered at (a,b,c) with radius r.
Do the Laplace Transformation and give the answer in Partial Fractions. Also do the Inverted Laplace Transformation and explain step-by-step.
12. [-/1 Points]
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SESSCALCET2 6.3.508.XP.
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Make a substitution to express the integrand as a rational function and then evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
x + 16
dx
X
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13. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.3.512.XP.
ASK YOUR TEA
Make a substitution to express the integrand as a rational function and then evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
dx
8)(2x + 1)
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14. [-/1 Points]
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SESSCALCET2 6.3.518.XP.
Find the area of the region under the given curve from 1 to 5.
y =
x² +7
6x - x²
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SESSCALCET2 6.3.012.
6. [-/1 Points]
Evaluate the integral.
x-4
dx
x²
- 5x + 6
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7. [-/1 Points]
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SESSCALCET2 6.3.019.
Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
x²+1
(x-6)(x-5)²
dx
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8. [-/1 Points] DETAILS
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SESSCALCET2 6.3.021.
Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
✓
x²
4
+4
dx
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