(a) Show that if a varies, then the polar equation raseco (π/2<02) describes a family of lines perpendicular to the polar axis. (b) Show that if b varies, then the polar equation r=besc0 (0<0<7) describes a family of lines parallel to the polar axis.

Q: Evaluate V = the double integral of (xy)dxdy D is bounded by y=x-1 and y2==2x+6

A:

Q: finr the exact solution 2*In(4x)=30

A:

Q: radioactive cesium-137 has a wide variety of uses and is commonly used in hospitals for diagnosis…

A: Given let a(t) represent the amount of cesium-137 left, measured in milligrams, after t yearsA(t) =…

Q: Write the expression in terms of first powers of cosine. Do not use decimals in your answer. Make…

A: Solve the following

Q: I. Find the intercepts, the critical points and point of inflection for each of the following…

A: we need to find out the intercepts, critical points, point of inflection, etc.

Q: A college food court surveyed students to gather information about the types of drinks they like.…

A:

Q: A box with an open top has vertical sides, a square bottom, and a volume of 4 cubic meters. If the…

A: A box with an open top has vertical sides, a square bottom, and a volume of 4 cubic meters. To be…

Q: Using the limit definition of the derivative, determine if the function f defined below is…

A: The given piecewise function is: f(t)=3,             t≤12t-6, 1&lt;t≤3t-3,t&gt;3

Q: d the equation of the surface in Cartesian coordinates, given the equation in cylindrical…

A: Given query is to find the equation in Cartesian coordinates.

Q: fraction Find the partial decomposition for the retionel expression. 5 x + 8 (X + 8) (8X-1) =

A: Solution ) ( 5x +8 ) / (x + 8 ) ( 8x - 1 ) ( 5x +8 ) / (x + 8 ) ( 8x - 1 ) = A/( x + 8 ) + B/( 8x -…

Q: Perform scaling on a triangle (1, 1), (8, 1) and (1, 9) with a scaling factor of 2 in both x and…

A:

Q: (c) x (1) Identify the critical numbers of f. (Enter your answers as a comma-separated list.) -1,0,1…

A: Given query is to find the interval where function increasing and decreasing.

Q: All edges of a cube are expanding at a rate of 2 centimeters per second. How fast is the volume…

A: Topic:- application of derivatives

Q: Find the points on the cone z² = x² + y² that are closest to the point (1, 5, 0). Please show your…

A: Consider A(x,y,z) to represent the point on cone z2=x2+y2---(1)The distance between (1,5,0) and…

Q: A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 600…

A: we need to find out the dimensions that will minimize the cost.

Q: 60° (a) Express the velocity of the river as a vector in component form. 12i (b) Express the…

A: Given query is to find the direction of the boat.

Q: How long will it take for the population of a certain country to double if its annual growth rate…

A: We are required to find the number of years it will take for the population of a certain country to…

Q: x² + y² lim (x,y) →(0,0) x² - y² Ignore "Give your reasons" below. There is no need to give a…

A: To find whether the limit exists or not

Q: Consider the function y= x Find y'.

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: 24 Write the expression (e-³)¯ in the former for a suitable constant k. Determine k. Give your…

A:

Q: A baseball team plays in a stadium that holds 58000 spectators. With the ticket price at $8 the…

A:

Q: If f(w) ) = cos¯¹(7w¹), find ƒ'(w). Use exact values and don't forget the chain rule. f'(w) =…

A:

Q: Find the extreme values of f(x,y) = y2 - x2

A: we can find extreme values.

Q: how do you shade 1/5 of a grid

A: The given data is: How do you shade 15 of a grid?

Q: after graduation, emily opens a saving account that offers a 6.25% annual percentage rate. she makes…

A:

Q: t²y' + 2ty - y³ = 0

A: To solve the following differential equation.t2y'+2ty-y3=0

Q: he population P (in thousands) of Orlando, Florida, from 1980 through 2013 can be modeled by P =…

A: Given query is to find the time when population reached to 390000.

Q: The fox population in a certain region has an annual growth rate of 7 percent per year. It is…

A: NOTE: Refresh your page if you can't see any equations. . the exponential function is given by…

Q: ulate each of the following derivatives using only th vative. f(x) = x³, f'(2); g(x)=x+2, g'(a) (for…

A: Topic:- application of derivatives Note :- as per our guideline if more than three subparts posted…

Q: 1) The rate of change of the concentration of a drug in a patient's bloodstream measured in mg/l per…

A: Given :- f't=-100e-0.25t f't=Rate of change of the concentration of a rug in a patient bloodstream…

Q: Find the particular solution. π x dy - (3y + x4 cos(x)) dx = 0, y = 8 X when x = |N 2

A:

Q: Sketch a possible graph of the function f given the graph of f' below. Assume that f is continuous…

A:

Q: Consider the following function. f(x)=x²-8x (a) Find the critical numbers of f. (Enter your answers…

A:

Q: Find the volume of the solid whose base is the semicircle y = √1 - x² where -1 ≤ x ≤ 1, and the…

A: To find:- Volume of solid whose base is the semicircle y=1-x2 where -1≤x≤1and the cross sections…

Q: Use Newton's method to approximate a root of the equation x³ + x +3 Let 1 = The second approximation…

A:

Q: solution is incorrect

A: We have to differentiate the series represented by the function fx=32-x6 term-by-term to find the…

Q: If f(x) = (7 sin x + 8 cos x)tan -1 x, find f'(x). Hint: Use the product rule! Question Help:…

A: Given; f(x)=(7sinx+8cosx)tan-1x.

Q: A projectile fired from the ground follows the trajectory given by the following equation, where is…

A:

Q: Consider the following function. f(x)= -8x3 + 24x + 7 (a) Find the critical numbers of f. (Enter…

A:

Q: Find the area of the shaded region. r2 = sin(2?) A coordinate plane is given. There is a closed…

A:

Q: Differentiate f(x) = tan-¹(5x). Use exact values, and don't forget the chain rule. f'(x) =

A:

Q: A fence 6 feet tall runs parallel to a tall building at a distance of 3 ft from the building as…

A:

Q: value of a car was $48000 in 2015. By 2020, the value of the car depreciated to $16226 a)Assume…

A: Given query is to find stue linear function for the value of the car.

Q: 5 0 x+√√(25-x²) dx

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: x+1 x-2 3 1. p(x) = 2. h(x) 3. g(x) = {x²2²2 = x; - x²-16 4. f(x) = x-4 = at x = 2 at x = 5 x-5 (x²…

A: (1).The given function is:p(x)=x+1x-2

Q: Find the value of the constant C' for which the integral converges. Evaluate the integral for this…

A:

Q: Let 5x³ - y³ + 52³ - 4xyz - 874 = 0. дz Use partial derivatives to calculate and ?х дz ?х дz ду…

A: To find the partial derivatives at a given point.

Q: Calculating First-Order Partial Derivatives In Exercises 1-22, find af/ax and af/av. 15. f(x, y) =…

A: Here is the solution:

Q: write the exponential function y=50(1.025)^t in the form of y=a(e)^kt, once you have rewritten the…

A:

Q: The population growth model of a city is given by: dP P(0) = 235. P = 0.34 P, The population size…

A: