A trough is 4 feet long and 1 foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of y = x° from x = - 1 to x = 1. The trough is full of water. Find the amount of work in foot-pounds required to empty the trough by pumping the water over the top. Note: In this problem, use 62 pounds per cubic foot as the weight of water. 10 Preview foot-pounds

Q: Given y=xx+4). Plot any stationary points, inflections points, and cusps which may or may not exist.…

A: Given, y=x23x+4 Used formulas, ddxxn=nxn-1ddxconstant=0Product rule of…

Q: Compared to the graph of y = 3 sin x, the graph of y = 3 sin(x + 1) – 2 is shifted %3D O 1 unit to…

A: Given : To compare the graph of y=3 sin x and y=3 sin (x+1)-2 and to identify where it has been…

Q: Find an equation for the line tangent to the graph of y=tan-1(x) at the point (1,π/4).

A: Given information:

Q: Find the equation of the line that is tangent to the curve y = 4x cos x at the point (T, -47). The…

A:

Q: Find the equation of the tangent line to the curve y = at 1+7e What is the equation of the line…

A:

Q: Find an equation for the tangent to the curve at the given point. y = (x^2)+2; (2,6)

A: Given:y=x2+2 (2,6)

Q: Start with the graph of y = ln x. Find an equation of the graph thatresults from reflecting about…

A: If a function is reflected over the y=x line then (x,y) → (y,x) This means y=ln(x) will become…

Q: Find the equation for the tangent to the curve at the given point.

A: First find slope using y'Slope=48

Q: Find the points on the curve xy2 = 54 nearest the origin.

A:

Q: Find the equation(s) of the tangent line(s)to the graph of the parabola y = x2 through the given…

A: Given, y=x2

Q: Find the equation of the line tangent to the graph of: y 6 at x = 1 Write your answer in the form y…

A:

Q: Match esch graph with its equation type: |- ♥| (ab* )sin(5æ) abř + sin(5r) v (mr t b)sin(5æ) sin(5z)…

A: Equation 1 and 2 has exponent function as well as sine function. So, the graph will be similar to c…

Q: Find the constant k so that the line with equation y = kx is tangent to the circle with equation (x…

A: Given:The line y = kx is tangent to the circle (x - 3)^2 + (y - 5)^2 = 4.

Q: Find the acute angle between the curves xy = -4 and y2 = 2x  If the correct answer is a =…

A: Given xy=-4 and y2=2x

Q: Find an equation of the tangent line to the parabola at the given point. y 15 10 x² = 8 y (7, 49/8)…

A:

Q: based on the period f(x)=3sin[2(x-30)]-4 how should the horizontal axis of the graph be scaled?

A: Let us plot the graph f(x)=3sin[2(x-30)]-4. Here, the period of the function f(x)=3sin[2(x-30)]-4…

Q: How does the value of b affect the behavior of the graph of the function y = a sin bx?

A: Consider the given function as y=asinbx

Q: Sketch the graph of y = sin (x − c) for c = −π/4, 0, and π/4. How does the value of c affect the…

A: Graph of y=sinx--π4

Q: 3.The diameter of a bicycle is 26 inches .If you are traveling at a speed of 35 miles per hour n the…

A: As per bartleby guidelines for more than one question asked only first is to be answered please…

Q: As television cable is pulled from a large spoolto be strung from the telephone poles along a…

A: Given: The truck pulling the cable moves at a steady  6 ft/sec. We have to find the rate the spool…

Q: Find an equation of the tangent to the curve at the point (1, 81) I = e', y = (t– 9)2

A: Given: x=et,y=(t-9)2   at (1,81)

Q: If f(x) = 2æ² – 6æ + 4, find f'( – 1). Use this to find the equation of the tangent line to the…

A: equation of the tangent line with slope m and point (x_1,y_1)  y-y_1 = m ( x- x_1)

Q: Start with the graph of y = ln x. Find an equation of the graph thatresults from shifting right 1…

A: To determine: Graph of y=lnx Also, to find an equation of the graph results from shifting the graph…

Q: Draw the graphs of y =x and y, = e* on the same coordinate's axes. Estimate the root of the equation…

A: To draw the graph of the given equations

Q: Question 2: The velocity of a dragster t sec after leaving the starting line is 100te -0.2t ft/sec.…

A:

Q: The point (2,1) is on the graph of x2 . y3 + 5· x² = y² + 23. Find the slope of the line tangent to…

A:

Q: The equation y? (y² – 4) = x² (x ² – 5) is known as the devil's curve. Give an equation for the…

A: Given  :

Q: Find the coordinates of all points where the tangent line to the graph below, given by y2 + cos(x) =…

A: For horizontal tangent the slope=0 So, dydx=0

Q: find the exact length of the curve of the equation below, show all work y = ln(sec(x)), with a range…

A: First, we find the dy/dx

Q: Find the equation of the tangent line to the parabola y = x^2 - 3 at point p(2,12)

A:

Q: A group of rowdy teenagers near a wind turbine decide to place a pair of pink shorts on the tip of…

A:

Q: Between two telephone poles that are 40 feet apart, there is a wire suspended in the shape of a…

A: we have to find slope of the curve and where the wire meets tha left pole

Q: 21 Find the equation of the tangent i ne OF the graph of yEra y= xe at the point ( ). y=? -2X

A: The objective is to find the equation of the tangent line.

Q: Consider the following. x1/2 + yl/2 = 8 dy Find dx () dy Find the slope of the graph of the equation…

A:

Q: Two curves with equations y = 6e¬* + 1 and y = 8 – e* are shown in the graphs below.

A:

Q: Sketch the figure of the described situation in the problem and then solve. Determine the equation…

A: Tangent and normal line: At the point of tangency, the normal line is defined as the line that is…

Q: Start with the graph of y = ln x. Find an equation of the graph thatresults from reflecting about…

A: Given: y=lnx equation of the graph that reflecting about y-axis will be y=ln-x

Q: Express the hupotenuse of h of a night triangle with an area of 25 m a function of its peri meter P.…

A: This question is based on Triangle.

Q: Find the equation of the line that is tangent to the curve y = 6x cos x at the point (T, -67). The…

A:

Q: Find the point (s) on the graph of the following equation that have horizontal or vertical tangent…

A:

Q: the curve x=l-5¢, y=4€²-1 (0=ts) lengin find the arcC kngth of the curve x=1-. (ux calculator to…

A: This question is based on length of a parametric curve calculated using definite integral.

Q: Find the rectangular coordinate equation for the curve x= cost and y=1-sin2t for 0 greater or equal…

A:

Q: Find the slope mm of the tangent line to the parabola f(x)=x^2+7x the point (5, 60) by using the…

A:

Q: . Find the points of inflection and comment on concavity for the graph y = r sin'

A:

Q: Find, correct to two decimal places, the coordinates of the point on the curve y =sin x that is…

A: Given that y=sinx So coordinate point is x, sinx.

Q: Find the equation of the family of curves whose slope at any point (x, y) is -4e-2ª sin 2x. Find the…

A:

Q: Find the equation of a tangent line that is tangent to the graph as stated below 3x 5y = -17 at (-1…

A:

Q: go Find the equations of the tangent lines to the graph of y=x²+6 graph of a to 197 +6 that through…

A: To find out the equation of tangent line and also graph it.

Q: , The equation y2(y? – 4) = x²(x² – 5) is known as the devil's curve. Give an equation for the…

A: