Ice is forming on a pond at a rate given by k√t where y is the thickness of the ice in inches at time t measured in hours since the ice started forming, and k is a positive constant. Find y as a function of t. Assume there is no ice initially. y(t) =

Q: Evaluate the indefinite integral 3y¹4 √5 + 3 dy

A: ∫3y14y5+5dyLet y5+5=x2on differentiating5y4dy=2xdxon substituting the value in above…

Q: Determine the sum of the following series. -2- (-2)¹-1 8n

A:

Q: The spacing on the steps are spaced a bit strangely and is a little confusing, may i get the steps…

A: we use substitution method to evaluate the integral

Q: Evaluate the surface integral. √(x²z+ y²z) ds S is the hemisphere x² + y² + z² = 4, z ≥ 0

A:

Q: Let f(x) = -x4-9x³+2x+8. Find the open intervals on which is concave up (down). Then determine the…

A: For a given function f( x ) ( a ) inflection points by f''( x ) = 0 ( b ) For concave up , f''( x )…

Q: A trapezoidal plate with height h and bases a and 2a is submerged vertically in water as shown.…

A: Given that, a trapezoidal plate with height = h, Bases = a, 2a, and the weight density constant = δ.…

Q: Find the interval of convergence of n=2 (x-4)" In (5n) (Use symbolic notation and fractions where…

A:

Q: 3. The axes of two right circular cylinders of equal radius 36 cm intersect at right angles. Find…

A:

Q: Find the general solution of the differential equation. Use C for the constant of integration. 3 X…

A:

Q: Question 9 Find slope of tangent line to y = 2x² -3 at x = -1 O-4 0-7 01

A: given y=2x3-3

Q: Show that the value of f(x) approaches the value of g(x) as x increases without bound graphically…

A: f(x)=(1+3x)x and g(x)=e3

Q: Let g(x) = sin(x). Use Addition or Subtraction Formulas to show the following. g(x + h) − g(x) =…

A:

Q: Find f(x) if f'(x) = 5/1-x² and f ¹ f(²)=7 7. f(x) =

A: Given f'( x ) = 51 - x2f( 12 ) = 7

Q: Match the polar equation with the graphs labeled I-VI. r 18 3 + 2 sin(0)

A: The answer is in step2.

Q: Use the midpoint rule with the given value of n to approximate the integral. 4ex dx, n=6 VE Find the…

A:

Q: Evaluate the indefinite integral 27x8 √(3x³ - 2) dx

A:

Q: SS₂ D = {(x,y)10≤x≤1, 0<x<√x E 1 + x3dA

A:

Q: ind the amount of money that will be accumulated in a savings account if $5050 is invested at 6.0%…

A: To find out the amount of money accumulated after 19 years when it is compounded continuously.

Q: Find the integral. Assume m + 0. Use c for the constant of integration. [ (mx+b) ³dx

A:

Q: f(x, y) = −5x – 9y, (-4,9), A=4i-3j A) - 13 B) 5 C) -47 N D) //

A:

Q: Use spherical coordinates. Evaluate JL. (x (x² + y²) dv, where E lies between the spheres x² + y2 +…

A:

Q: 55 **-2'2 The expression 22-55 simplifies to 2x+5, where x + 4x²-25 O True O False

A:

Q: Find the integral. Use C for the constant of integration. 1 (2² (y² + 6)² dy

A:

Q: Find the rectangular coordinates of the point, whose cylindrical coordinates are given. (a) (8, π/4,…

A:

Q: Find all points on the graph of f(x) = 9x² -33x+28 where the slope of the tangent line is 0. The…

A: fx=9x2-33x+28 Differentiating equation with respect to x  f'x=ddxfx f'x=9ddxx2-33ddxx+ddx28…

Q: Write a derivative formula for the function. f(x) = 8x√5x + 4 + 93 f'(x) = = 52x + 32 √5x + 4 X

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

Q: the series Σ(-1)n-1 ln(n) n n=1 absolutely convergent, conditionally convergent, or divergent? Make…

A:

Q: Draw a picture of the following vectors, then calculate them algebraically. Make sure you label the…

A:

Q: Identify which step is incorrect in graphing g(x) = -2(x-1)4-1 Step 1: Shift right 1 unit Step 2:…

A: Given that, the function             g(x) = -2x-14 - 1

Q: Use the given transformation to evaluate the integral. JJ₁50 5(x + y) ex² - y² da, where R is the…

A: We have given an integral and using transformations we have to evaluate it.

Q: Describe how you would sketch a quick graph of a polynomial if it was given in factored form (…

A: The factored form of the polynomial p(x)=(x-a)(x-b)(x-c)........ The standard form of the polynomial…

Q: Consider the indefinite integral The integrand decomposes into the form ax+b+ + where a = b = C = d…

A:

Q: Consider the following. x = e-5t, y = est (a) Eliminate the parameter to find a Cartesian equation…

A: The Given Parametrization of the curve is x=e-5t and y=e5t

Q: Find the general antiderivative. Use C for the constant of integration. 1 4 cos² (3x) F(x)= = f(x) =

A:

Q: Find the function's relative maxima, relative minima, and saddle points, if they exist. z = 19 x² +…

A:

Q: 1 1. y= 2. g(x) = x² + √ 3. Evaluate 12 - sin x 1² x² sin x³ dr

A:

Q: Use the derivative to find the vertex of the parabola. y = -x² - 4x +4

A: y=-x2-4x+4

Q: A box with a square base and open top must have a volume of 442368 cm³3. We wish to find the…

A:

Q: (2) Graph the polynomial P(x) = x³ + x² − 5x+3 using calculus by showing the given steps: (a) Find…

A: We need to solve function and draw graph.

Q: Problem #8: Demand for a certain kind of SUV obeys the following equation, D(x, y) =…

A: Given demand functionD( x, y ) = 22000 - 12x - 12( 0.9y - 10 )32 Also given x = 58200 + 300t y = 127…

Q: The price of a double-dip ice cream cone is increasing at the rate of 18e0.06t cents per year, where…

A: GIVEN: The increasing rate of ice cream is  dPdt=18e0.06t Where t=0 in 2000 To find: Total change in…

Q: 9 Calculate To, So as indicated. Do not round. any intermediate calculations. Round ( your final…

A: As per the instruction, we will be answering only the first question.  Given: Now, we need to find…

Q: Use the figure, which shows the graph of y=f(x) , to answer the following questions. Estimate the…

A: The graph of fx is given as , Evaluate ∫-33fxdx=?

Q: Use the Ratio Test to determine the radius of convergence of M8 Σ √n. 12" Then determine whether the…

A:

Q: Use the Leading Coefficient test to determine the right and left end behavior of the following…

A: fx=2x5+x-1 Comparing this with equation  fx=anxn+an-1xn-1+.......... We get, n=5 , an=2 n=5 (odd)…

Q: 3. a. What is the domain of the function g(x)? Write the answer in interval notation. g(x) = log₂…

A:

Q: Find dx dy dx 11 d²y dx² x = t² + 3, y = t² + 9t = and d²y dx² For which values of t is the curve…

A: x=t2+3 , y=t2+9t

Q: 1.Given the series 3+4.5+10.125+......., Find S↓10 to the nearest hundredth

A: As per as our guideline i am supposed to answer only only one question please repost all remaining…

Q: dd cos² x. tan x, and use u = tan x. Split off sec x tan x, rewrite the rem terms of sec x, and use…

A:

Q: Find the limit: lim1 [(x-1)(x+2)/(x-1)]

A: