Boost your journey with 24/7 access to skilled experts, offering unmatched basic mathematics homework help
Frequently Asked Questions
Q. 1) Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = x², y = 1 about y = 6
Volume of Solid Rotated about ???? = 6 y=6: Use the disk method. The volume ???? V is: ???? = ???? ∫ 0 1 ( ( 6 − ???? 2 ) 2 − ( 6 − 1 ) 2 ) ???? ???? V=π∫ 0 1 ((6−x 2 ) 2 −(6−1) 2 )dx Solve the integral for the exact volume.
Q. 2) Find the volume of the solid obtained by rotating the region bounded by the curves y=x2y = x^2y=x2, y=4y = 4y=4, about y=5y = 5y=5.
Volume of Solid Rotated about ???? = 5 y=5: Use the disk method: ???? = ???? ∫ 0 2 ( ( 5 − ???? 2 ) 2 − ( 5 − 4 ) 2 ) ???? ???? V=π∫ 0 2 ((5−x 2 ) 2 −(5−4) 2 )dx Solve the integral to get the volume.
Q. 3) Determine the volume of the solid formed by rotating the region bounded by y=x2y = x^2y=x2 and y=1y = 1y=1, about the line y=−2y = -2y=−2.
Volume of Solid Rotated about ???? = − 2 y=−2: Use the washer method: ???? = ???? ∫ 0 1 ( ( ???? 2 + 2 ) 2 − ( − 2 − 1 ) 2 ) ???? ???? V=π∫ 0 1 ((x 2 +2) 2 −(−2−1) 2 )dx Solve the integral to find the volume.
Q. 4) Compute the volume of the solid generated by rotating the region bounded by y=xy = \sqrt{x}y=x, y=0y = 0y=0, and x=4x = 4x=4, about the line y=6y = 6y=6.
Volume of Solid Rotated about ???? = 6 y=6: Use the washer method for rotation: ???? = ???? ∫ 0 4 ( ( 6 − ???? ) 2 − ( 6 − ???? ) 2 ) ???? ???? V=π∫ 0 4 ((6− x ) 2 −(6−x) 2 )dx Solve the integral for the volume.
Q. 5) Find the volume of the solid obtained by rotating the region enclosed by x=yx = \sqrt{y}x=y, x=0x = 0x=0, and y=9y = 9y=9, about y=10y = 10y=10.
Volume of Solid Rotated about ???? = 10 y=10: Use the washer method: ???? = ???? ∫ 0 9 ( ( 10 − ???? ) 2 − ( 10 − ???? ) 2 ) ???? ???? V=π∫ 0 9 ((10− y ) 2 −(10−y) 2 )dy Solve the integral to compute the volume.
Q. 6) Ashley and Ted left the mall at the same time. They traveled in opposite directions. Ted traveled 0 km/h slower than Ashley. After one hour, they were 40 km apart. Find Ashley's speed.
Ashley’s Speed: Let Ashley’s speed be ???? x. Then Ted's speed is ???? − 0 x−0. After 1 hour: ???? + ( ???? − 0 ) = 40 ⇒ 2 ???? = 40 ⇒ ???? = 20 km/h x+(x−0)=40⇒2x=40⇒x=20km/h Ashley’s speed is 20 km/h.
Q. 7) Given the polynomial function f(x) = x³ 4x²+x+6 How could we prove 2 is one of the zeros of this function? Choose ALL of the correct answers.
Proving 2 is a Zero of ???? ( ???? ) = ???? 3 + 4 ???? 2 + ???? + 6 f(x)=x 3 +4x 2 +x+6: Substitute ???? = 2 x=2 into the function: ???? ( 2 ) = 2 3 + 4 ( 2 ) 2 + 2 + 6 = 8 + 16 + 2 + 6 = 32 ≠ 0 f(2)=2 3 +4(2) 2 +2+6=8+16+2+6=32 =0 Therefore, 2 is not a zero of the function
Popular Subjects for Basic Mathematics
Boost your journey with 24/7 access to skilled experts, offering unmatched basic mathematics homework help