Question 1

Find the area of the region that is bounded by the given curve and lies in the specified sector. $r = 9 \sqrt { \sin 2 \theta } , 0 \leq \theta \leq \pi / 2$

Accepted Answer

The answer of Find the area of the region that...

Question 2

Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.  x=t−2sin⁡t,y=t−2cos⁡t,0≤t≤4πx = t - 2 \sin t , \quad y = t - 2 \cos t , \quad 0 \leq t \leq 4 \pix=t−2sint,y=t−2cost,0≤t≤4π

Accepted Answer

A)    28.729828.729828.7298 
B)    26.729826.729826.7298 
C)    25.729825.729825.7298 
D)    24.729824.729824.7298 
E)    27.729827.729827.7298F) B) and D)
G) C) and D)

Question 3

Solve the initial-value problem. $\frac { d r } { d t } + 2 t r - r = 0 , r ( 0 ) = 3$

Accepted Answer

The answer of Solve the initial-value problem. \(\frac { d...

Question 4

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.  y=5(x2+4) ,y=5(12−x2) ; about y=−5y = 5 \left( x ^ { 2 } + 4 ight)  , y = 5 \left( 12 - x ^ { 2 } ight)  ; 	ext { about } y = - 5y=5(x2+4) ,y=5(12−x2) ; about y=−5

Accepted Answer

A)    9525π9525 \pi9525π 
B)    9575π9575 \pi9575π 
C)    9550π9550 \pi9550π 
D)    9600π9600 \pi9600π 
E)   None of these F) A) and E)
G) B) and C)

Exam 18: Final Exam

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. $y = 5 \left( x ^ { 2 } + 4 \right) , y = 5 \left( 12 - x ^ { 2 } \right) ; \text { about } y = - 5$

Correct Answer
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Solve the initial-value problem. $\frac { d r } { d t } + 2 t r - r = 0 , r ( 0 ) = 3$

Correct Answer
verified

Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places. $x = t - 2 \sin t , \quad y = t - 2 \cos t , \quad 0 \leq t \leq 4 \pi$

Correct Answer
verified

Find the area of the region that is bounded by the given curve and lies in the specified sector. $r = 9 \sqrt { \sin 2 \theta } , 0 \leq \theta \leq \pi / 2$

Correct Answer
verified

Exam 18: Final Exam

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=5(x2+4) ,y=5(12−x2) ; about y=−5y = 5 \left( x ^ { 2 } + 4 \right) , y = 5 \left( 12 - x ^ { 2 } \right) ; \text { about } y = - 5y=5(x2+4) ,y=5(12−x2) ; about y=−5

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Solve the initial-value problem. drdt+2tr−r=0,r(0)=3\frac { d r } { d t } + 2 t r - r = 0 , r ( 0 ) = 3dtdr​+2tr−r=0,r(0)=3

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Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places. x=t−2sin⁡t,y=t−2cos⁡t,0≤t≤4πx = t - 2 \sin t , \quad y = t - 2 \cos t , \quad 0 \leq t \leq 4 \pix=t−2sint,y=t−2cost,0≤t≤4π

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Find the area of the region that is bounded by the given curve and lies in the specified sector. r=9sin⁡2θ,0≤θ≤π/2r = 9 \sqrt { \sin 2 \theta } , 0 \leq \theta \leq \pi / 2r=9sin2θ​,0≤θ≤π/2

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Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. $y = 5 \left( x ^ { 2 } + 4 \right) , y = 5 \left( 12 - x ^ { 2 } \right) ; \text { about } y = - 5$

Correct Answer
verified

Solve the initial-value problem. $\frac { d r } { d t } + 2 t r - r = 0 , r ( 0 ) = 3$

Correct Answer
verified

Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places. $x = t - 2 \sin t , \quad y = t - 2 \cos t , \quad 0 \leq t \leq 4 \pi$

Correct Answer
verified

Find the area of the region that is bounded by the given curve and lies in the specified sector. $r = 9 \sqrt { \sin 2 \theta } , 0 \leq \theta \leq \pi / 2$

Correct Answer
verified