Calculus Answers

Real life applications of Hyperbole

B.   Read and analyze the problem below. Solve and show complete solution. (5 points)

Two stations, located at M(1.5, 0) and N(1.5, 0) (units are in km), simultaneously send sound signals to a ship, with the signal traveling at the speed of 0.33 km/s. If the signal from N was received by the ship four seconds before the signal it received from M, find the equation of the curve containing the possible location of the ship.  

Find the standard equation of the parabola which satisfies the given conditions.

1. Focus(-2, -5), directrix x=6
2. Vertex(-4, 2), focus(-4,-1)
3. Vertex(-8,3), directrix x= -10.5
4. Focus(7, 11), directrix y=4

if A = cos(xy)i + ( 3xy + 2x ^2 )j - (3x + 2y )k find d^2A/dy^2 and d^2A/dxdy

 If A, B are differentiable vector point function of scalar variable f over domain S, then prove that d/dt( AxB) = (dA/dt x B) + (A x dB/dt) 

A. Find the area underneath the given curve.

1.) y= -2x² + 8

from x=0 to x=1

2.) y= -x² + 7

from x=0 to x=1

B. Find the area enclosed by the given curve, the x-axis, and the given lines.

1.) y= -1/3x² + 10

from x=1 and x=3

2.) y= x³ - 8

from x= -1 to x =2

C. Find the area bounded by the given curve and line.

1.) y= x² + 3 and y= 7

2.) y= 2x² and y= 4x + 6

3.) y= -x² + 4x and y= x²

4.) y= x³ -6x² + 8x and y= x² -4x

D. Find the area bounded by y=2; y=√x+2; and y=2 - x.

A. Find the area underneath the given curve.

1.) y= -2x²+8

from x=0 to x=1

2.) y= -x²+7

from x=0 to x=1

B. Find the area enclosed by the given curve, the x-axis , and the given lines.

1.) y=-1/3 x² + 10,

from x=1 and x=3

2.) y= x³-8

from x=-1 to x=2

C. Find the area bounded by the given curve and line.

1.) y= x² + 3 and y=7

2.) y= 2x² and y= 4x + 6

3.) y = -x² + 4x and y= x²

4.) y= x³ - 6x² + 8x and y= x² - 4x

D. Find the area bounded by y= 2; y=√x+2; and y=2-x.

Use the graph of F to find the given limit. When​ necessary, state that the limit does not exist. lim F(x)= 5

A cylindrical can without a top is to be made from 27cm^2

of sheet metal. Find the dimensions of the can with

the greatest volume. Be sure to formally introduce any new variables and their domains. Confirm you have a maximum

e) lim_((x y) to (0 0)) (sin x)/(y) exists.

While walking on one bank of a 25 m wide canal you see a child 50m down the canal on the far bank slip, hit his head, and fall into the water. If you can swim 1.5m/s through the water and can run 5.0m/s along the side of the pool, what distance should you swim through the water to minimize the time to get to the child?