Consider the plane curve given by the parametric equations x = t² + 3t - 26 y = t² + 3t - 28 - What is the arc length of the curve determined by the above equations between t and t = 5? 0

Q: 4 P = 80x-2x²-xy-3y² +100y + X(12-X-Y) FinD Px, Pxx, Py, Pyy, Pxy = Pyx, fino x And y Fine Fine P

A: Here's the solution.... please have a look at it...

Q: A piece of wire is with a length of 4 m is cut into two pieces, and the resulting two pieces are…

A: According to given,    Let x be length of the portion that is bent into a circle   Therefore, 4-x=…

Q: S ex √1-e²x dx

A:

Q: 3. A snowball is rolling down a hill, getting bigger as it goes. Assume the snowball remains a…

A:

Q: Identify and sketch the graph of the equation in R³. Identify and sketch the graph of the traces as…

A: An equation is given                         -x+y2+z29=0We will name and sketch the graph of the…

Q: The position of an object attached to a spring is given by s (t) = cos(4t) — —sin(4t), - where t is…

A: The position of an object,st=14cos4t-16sin4t on the interval 0<t<3

Q: dx 6x + x² V

A: To integrate by using the trigonometric substitution.

Q: Let f(x) = 3x5 - 5x³.

A: The given function,   f(x)=3x5-5x3

Q: Find the length of the part of the curve y = = between x = 1 and x = 2.

A:

Q: ∫(4x3−12x)(x4−6x2)−3 dx Evaluate the following integral using substitution rule or integration by…

A:

Q: 7) Two ships are leaving port at the same time. The first ship sails due east at 20 km/h, the second…

A:

Q: Solve the following a) 2d²y_dy 3y = 25 sin 2x dx² dx d²y b) - 4 - 3y = 25 sin 2x dx² dx c) d²y dx² +…

A:

Q: 2 Σ(-1)". n+1 n=1

A:

Q: dw the functions w= -5x²-3y².x= cost, and y=sint, express as a function of t, both by using the…

A: Use chain rule for derivative

Q: The average cost function for the weekly manufacture of retro portable CD players is given by C(x)…

A:

Q: 4. Elizabeth needs 2 1/3 cups of sugar for vanilla cake and 1 3/4 cups of sugar for chocolate cake.…

A:

Q: Confirm that the force field F(x, y) = yeyi+ xey j is conservative in some open connected region…

A: We have to find the work.

Q: Write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 9x²,…

A: Given query is to find the equation of the parabola.

Q: f sin √x dx

A:

Q: f(x)= = x+1 1³ - 2x² + 1

A:

Q: хр. e X О

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

Q: Plot the curve c(t)=(2t−1,²+3). Then find the length of the curve for 1<t≤2 to two decimal places.

A: Curve is ploted and length of curve is obtained.

Q: Ultrasound is often used to make images of developing fetuses. In particular, by measuring the size…

A: Given query is to find the rate of change.

Q: Find the exact value of the logarithmic expression without using a calculator. (If not possible,…

A:

Q: -8 27 -6 -5 -4 -3 -2 ਆਰਡਰ 41 3 1 -2 -3 The curve above is the graph of a sinusoidal function. It…

A: Given query is to find the graph of the function.

Q: Find the equation for the tangent and normal lines for f(x) at the specified points. Show your…

A:

Q: 7. Find the flux of F(x, y, z) = x î+ y ĵ+ z² k across the sphere of radius 1 centered at the origin…

A:

Q: Find the limit. lim (ti – 4 · 4 j + t² k) t→7 lim (t i − 4 j + t² k) = i 1→7 i+ i j+ i k

A:

Q: x5 (2 – x²) 5 dx

A:

Q: Find the critical number of the function defined by f(x) = x² + 4x O-1 and 0 are the critical…

A:

Q: Consider the curve parametrized by x www = 1 + ln(t) and y = t¹ + 2t. dy a) First eliminate the…

A: topic - derivatives

Q: d³y d²y dy+y=0 dx3 dx² dx

A: d3ydx3-d2ydx2-dydx+y=0                (1)LetD=ddxTherefore   equation (1)…

Q: ∫12v (7+6v2)9 dv Evaluate indefinite anti-differentiation

A:

Q: 2. Using the graph and its labeled points shown below, calculate the Left Riemann sum over the…

A:

Q: Evaluate the definite integral. NOTE: Enter the exact answer. 12 ti + t²idt = 0

A: To evaluate: ∫012t i+t2jdt

Q: Find the exact area under the graph of f(x)=1 between r=0 and r = 2. Area =

A:

Q: 0 2 4 Let A = -2 2 5 and B= 7 -1 1 Find A-B. A - B = 0 1 -6 -35 25 6 3 8 [000) X 00 000 5 [00]…

A: Given A=   0   2   4-2   2   5   7-1  1 and B=   0-3   5   1   2   5-6   6   3.

Q: The supply function for a product is given by p = 50+ 100√2x + 5, where x is the number of units…

A: The supply function for a product is given by p=50+1002x+5, where x is the number of units supplied…

Q: Calculate the definite integral by referring to the figure with the indicated areas. [f(x)dx a Area…

A: topic - definite integral area above the x axis is taken as positive in definite integral when…

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: We have to find the value

Q: 3) f cost x dx بعة

A:

Q: define gradient of a function.

A: The gradient of a function f(x,y) in two dimension is defined as:

Q: Consider the following. (1, 1) 2 6 10 X 4 X=8 -4 y = 2-x -6 -8F (a) Form the integral that…

A:

Q: مرده X dx (3x²-1)³

A: This question is based on definite integral.

Q: Find the exact area under the graph of f(x) = = and x = 2. Area = 1 x+1 between r=0

A:

Q: The Smith's borrow $45,000 to purchase a new home. They finance the amount through a 25-yr mortgage…

A: Given problems:- 1. The Smith's borrow $45.000 to purchase a new home. They finance the amount…

Q: Find dy dx 1. y = (3-2x)³ (x² − 2)

A:

Q: Find the sum of the series, if it converges. Otherwise, enter DNE. 6 Σ n(n + 2)

A: Given problem:-

Q: For the right triangles below, find the exact values of the side lengths b and If necessary, write…

A:

Q: 2. If the Profit function for producing x units is P(x) = 0.0035x³ + 120x, then the marginal profit…

A: