A light is to be placed on top of a pole with height h feet to keep a busy traffic circle illuminated, which has a radius of 40 ft. The intensity of illumination I at any point P on the circle is directly proportional to the cosine of the angle 0 and inversely proportional to the square of the distance d from the source. At what height should the pole be in order to maximize the illumination of the light? [HINT: Use the figure below as a guide.] d h 40 D 22.28 feet O 28.28 feet 55.67 feet

Q: f(x + h) – f(x) -2h(x + 3) – h? h(x +h + 3)2(x + 3)2 se that . Find the slope m of the tangent lir h

A:

Q: 31. Table 1 lists the population density (in people per square kilometer) as a function of distance…

A:

Q: a. Determine the point (a, la)) for which f'(a) = a, given that Ax) = -x + 3x-7. b. Write the…

A: For (a), Given: We need to find the point a for which f'(a)=a. Here, f'(x)=-2x+3. So,…

Q: the line 3x+ y=l is the tangent line for the graph of y= f(x) at x=1, then f'(1)= 1 (C) 1 (D) 3 A) 3…

A: The slope of the line y=mx+c is m. The slope is equal to the derivative of y i.e., f'y=m

Q: Find the indicated quantities for f(x) = 2x². (A) The slope of the secant line through the points…

A:

Q: Consider the curve defined by y? x3 – 3x + 3 for x > 0. At what value of x does the curve have a…

A:

Q: Find the area A of the largest rectangle that can be inscribed under the curve of the equation below…

A: Given y=e-x2

Q: The graph below shows the total distance s, in miles, traveled by a bicyclist after t hours. 40 mi…

A: To answer the given question about the average velocity and instantaneous velocity from the graph.

Q: f(a +h) – f(a), Which of the following is/are equivalent to h I. The slope of the tangent line at 2…

A:

Q: 2. A Ferris wheel of diameter 18.5 m rotates at a rate of 9.2 rad/s. If passengers board the lowest…

A:

Q: Example 3: A balloon rising from ground at 140 ft/min is traced by a range finder at point A located…

A:

Q: The slope-intercept form of a linear equation is: y = kx + q The gradient k equals to tan a. a. show…

A:

Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

A: Given that: The height of the tank is 20 feet, radius is 8 feet and the radius of the circular hole…

Q: Consider the curve defined by x? = e-y for æ > 0. At what value of x does the curve have a…

A: Given x2=ex-y, x>0

Q: Consider the following figure. Dilate the figure about the origin with a scale factor of and then…

A: Hey, since there are multiple subparts posted, we will answer first question. If you want any…

Q: Find the indicated quantities for f(x) = 2x. (A) The slope of the secant line through the points…

A:

Q: A 5-foot-lall person is walking towards a 7-foot-tall lamppost at au niform rate of 2 feet per se…

A:

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: GH is tangent to OF at point G. What is the value of x? 2х-1 H. x + 2 O A. 2 В. 3 о с. 4 O D. 5 2.

A: Since, FG is the radius and GH is the tangent, it can be written that ∆FGH is a right-angled…

Q: Find the indicated quantities for f(x)=5x2 (A) The slope of the secant line through the points…

A: Given function fx=5x2To find the slope of this secant line , we first need to find the values at…

Q: JF and GF are tangent to OH. What is HJ? 3x-5 H X+1 2x G HJ =| (Type an integer or a decimal.)

A:

Q: On the graph of the curve defined by X = 9t? + 5 t3 - 8 V = a tangent line at the point p(x,y) has a…

A: Explanation of the answer is as follows

Q: Find the slope of the tangent line to the curve 3xy- 5y 4 at = 1. ECAD Hint: what is the y-value at…

A: Differentiate at given point

Q: The slope of the tangent line x= e, y= In e3x %3D 3er 3e-3r K OR 3e none of the above

A: Given:    x = ex , y = ln e3x

Q: O Find the coordinate of the point under the root function y=Jx en the interval (o,3) into equal…

A:

Q: (a) (i) Find the equation of the tangent to the graph of f(x) = e² at x = 0. (ii) Show that the…

A: NOTE: As per our guidelines, I have solved three parts. If you want the answer of other, kindly post…

Q: At a given moment, a plane passes directly above a radar station at an altitude of 6 miles and a…

A: Let's find.

Q: The x- coordinate of the point on the graph of y = Vx-1 at which the tangent line is perpendicular…

A: slope of tangent of the curve y=x-1 is dydx=12x-1 slope at (x1, y1)dydx=12x1-1=m1if (x1, y1) is the…

Q: u(x, y) = arctan a = (-1,0)

A:

Q: A tank in the form of a right circular cylinder standing on end is leaking water through a circular…

A: We begin by combining all the constants as follows: Ah=π·0.52=0.785 ft2Aw=π·(2)2=12.566 ft2…

Q: f (x) X - 9 ) (smaller x-v (x, y) = ([ (x, y) = (C ) (larger x-va %3D

A:

Q: If cost = - and t is in the 3rd quadrant, then sint V52 6 20 4 20 6 V20 4 V20

A:

Q: Find the indicated quantities for f1(x) 3x (A) The slope of the secant line through the points…

A:

Q: If a is a positive integer, then the slope of the tangent to the graph of y = a? + In(az + 1) at a =…

A: To find the slope of the tangent to the graph of the given equation

Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

A:

Q: The slope of the tangent line to the graph of y =; I+1 when x = 1 is %3D %3D - 4 3/4 O 1 4. 1/2

A: y=xx+1 Slope of the tangent line is the derivative of the given function at the given point. So…

Q: Find the indicated quantities for f(x) = 2x. (A) The slope of the secant line through the points…

A:

Q: Find the indicated quantities for f(x) = 2x². (A) The slope of the secant line through the points…

A: note : According to our guidline i can solve only first 3 , please reroute remaining question.

Q: 2. Determine whether the following statements are true and give an explanation or counterexample.…

A:

Q: Q2. Rope. To tie a boat in a harbor, how many times must a rope be wound around a bollard (a…

A:

Q: (b) (i) A wire of length 200m is used to form a rectangle. If the length is x meters and width is y…

A: Here I am attaching image so that you understand each and every step.

Q: Question 2. Find from the origin (0, 0) the direction of steepest increase of the function f (x, y)…

A:

Q: Can i get help step by step please

A:

Q: d an equation of the tangent plane to the given surfa (-1, 1, –9). %3=

A:

Q: Based on the data shown on the scaller plot at the right, which type of function would describe a…

A: We have to choose the correct answer

Q: Find an equation of the tangent plane to the graph of F (r,s) at the given point: F (r,s) =…

A:

Q: The slope of the tangent line to the graph of y? = In(xy) at the point (e, 1) is :Select one -e-1.a…

A:

Q: If the tangent line to the curve f(x)= x² + ar at (1, f(1)) is tangent to the curve g(z) = bz at…

A: tangent line's slope is given by the first derivative