Find the tangential and normal components of the acceleration vector. r(t) = 4(3tt³)i + 12t²j aT an II

Q: find ℒ{f(t)}. (Write your answer as a function of s.) f(t) = (4t − 1)3 ℒ{f(t)} =

A:

Q: The Cartesian equation, x = 3, is equivalent to the polar equation, Or² = 3 cos 0 3 COS O r = r = 1…

A: We are given a Cartesian equation  x=3 and we have to which among the following is it's equivalent…

Q: Use multiple application of simpson's 1/3 rule to numerically in- tegrate: f(x) = 8 + 5 sin (x) 0 to…

A: We need to use Simpson's one third rule.

Q: Use the second fundamental theorem of calculus to evaluate the following: 1 1 + 1 + sin 0 5) de 1 -…

A: Value of definite integration is given.

Q: Let y = tan(5x + 2). Find the differential dy when x = 2 and dx = 0.3 Find the differential dy when…

A:

Q: 31 In how many ways can 9 math students be seated at a round table? 81 40,320 80,640

A: In how many ways can 9 math students be seated at a round table?

Q: Q4: Let y = √t and a) 2 b) 3 c) 4 t = x² then y(n) = 0 if n= d)5 e) others

A:

Q: Diffential Equation  Topic: First Order Linear DE and Bernoulli DE 4. Find the solution of the…

A:

Q: R is the region bounded by the functions f(x) = 2e - 1 and g(x)=x²-2. Find the area of the region…

A: R be the region bounded by the curves f(x)=2ex-1 and g(x)=x2-2 on the interval -1,1

Q: If g(x, y) = √√3xy - 7x, find gx and gy. 9x = gy =

A: partial derivatives

Q: Evaluate the integral. (Use C for the constant of integration.) 5 [BX 8x √√x + c dx

A:

Q: Find dy/dx:

A: We have to solve the dy/dx using fundamental theorem of calculus.

Q: give me the solution of   y'' - 2y'- 2y = 0

A: Topic:- differential equation

Q: Find the function that passes through the point (1,2) and whose derivative is dy/dx = (2/x^3) - 4

A: Topic:- application of integration

Q: On your phone you have 23 rap songs and 14 country songs. How many 6 song playlists (order atters)…

A: Recall:  Crn=n!r!(n-r)!

Q: A tire manufacturer estimates that the demand function for their radial tires will be given by P =…

A:

Q: Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider…

A:

Q: Identify the vertex of the parabola: y = -4(x - 2) 2 - 3. (2, 3) (-2, -3) (-2, 3) (2, -3)

A:

Q: 18. Find the partial sum. Σ128(4) n=1

A: Given problem:-

Q: In the process of calculating that: cos³ (112) de a substitution is made in the variable u, then it…

A: Given query is to find the integral after substitution.

Q: 1. Given the function f(x) = 20 √7-x find f (-9). "

A: The given function is: fx=207-x    ...1

Q: Determine the volume generated of the area bounded by y=√√x and y=-x rotated around x=5. 2

A:

Q: 29. Verify that the piecewise-defined function 1-x², x<0 x ≥ 0 is a solution of the differential…

A:

Q: Using double integral, the area of the region bounded by the lines y=x y=x/2 and y=2 equal :

A:

Q: a. (x-²)(x + xy) = 4 b. √√√xy=x-2y at (4,1) c. cos(x² + y²) = y²sinx² d. y² = ln(x² + y²)

A:

Q: 00 (-1) 22k+1 k! Determine whether the series converges absolutely, converges conditionally, or…

A:

Q: 3- show that the diff. equ. is homogeneous and Salve it (2x +34) dx +(y-x)dy = a

A: In this question we have to solve the differential equation.

Q: Write the equation of a circle with a center at (2, -3) and a radius of 4. ( x - 2) 2 + ( y + 3) 2…

A: To write the equation of a circle with a center at (2, -3) and a radius of 4.

Q: A tank contains 400 liters of fresh water. Brine containing 0.3 kg/L of salt runs into the tank at…

A:

Q: =

A:

Q: Q4: Let y = √t and a) 2 b) 3 c) 4 t = x² then y(") = 0ifn= d)5 e) others

A:

Q: 10x3, 5-x, = x < -2 x ≥ −2 Let f(x) 1. f(-2)= 2. lim f(x) = x→→2+ 3. lim f(x): = x→→→2 4. lim f(x) x…

A: The solution of 4 and 5 are given in the next steps.

Q: dx ex+e-x 2. S dx

A:

Q: 18. Evaluate § (9 − x² − y²) dV, where H is the solid hemi- sphere x² + y² + z² ≤ 9, z ≥ 0.

A:

Q: Find the general solution of the differential equation: (1 + cos(x))y' - (sin(x))y= 2x 2x Step zero,…

A:

Q: Evaluate the integral 2 ક્ષ ;-) Sa Say e dxdy

A:

Q: Use point-slope form to find the equation of a line that contains the points (100, -40) and (20,…

A: Given, (x1,y1)= (100,-40) (x2,y2)= (20,-5)

Q: In how many different, distinguishable orders can the letters of the word algebra be arranged?

A: We have to find the number of ways in which the letters of the word algebra be arranged in…

Q: 14. Solve for x. 2¯¾ = 8(x-3)

A: Given, 2-x2=8x-3

Q: Q5: If y=tant and x = cost then at t= is (not that these functions in N) dx a) -1 b) 0 c) d) 1 e)…

A:

Q: 1. Evaluate the given integral Q. /9-22 Q= - 1²³ 1²/³3 (№²=³² 0 0 0 Your answer (y - x) dx dy dz

A:

Q: Test the series for convergence O a. the series diverges O b. the series converges ∞ 3k k-1!

A: We need to evaluate the convergence of the series :

Q: Say whether the following statements is true or false 1 x = ²( ² ( ² + 2) = = = √( ²³ sin2t.dt 1. +4…

A: As per the company's guidelines, we are supposed to solve first three sub-parts for you, kindly…

Q: A 200 gallon tank initially contains 100 gallons of water with 20 pounds of salt. A salt solution…

A:

Q: If lim f(z) = 2 and lim g(x) = 7, then lim[3ƒ(z) — 4g(x)] = -22 G- *-b Ⓒ True O False

A:

Q: Solve 7 cos(5x) = 2 for the smallest positive solution. Give your answer accurate to at least two…

A:

Q: 3. Find the distance between points P₁ and P2. (a) P₁(-1,1,5), P₂ (2, 5,0) (b) P₁(3,4,5), P₂(2, 3,…

A:

Q: A particle moves along a line with a velocity v(t) = -21 +5, measured in meters per second. Find the…

A:

Q: Differential equation x² 2xln(y)dx + dy = 0 y

A: If the equation Mdx +Ndy =0 is exact i.e, ∂M∂y=∂N∂x , then the solution is      ∫y constant M dx…

Q: L 2 S 5 + 64

A: Laplace Inverse Transform of  function 5s2+64