Two spacecraft are following paths in space given by r₁ = (sin(1),1,1) and r₂ = (cos(1), 1-1,r). If the temperature for the points is given by T(x, y, z) = xy(9- 2), use the Chain Rule to determine the rate of change of the difference D in the temperatures the two spacecraft experience at time t = 3. (Use decimal notation. Give your answer to two decimal places.) dD dt 80.99 Incorrect

Q: Find all the possible rational zeros of the following polynomial: f(x) = x³ - 5x² - 3x+14 O #1, #2,…

A:

Q: The following complex number is a pure imaginary number. i√3 O True O False

A: An imaginary number of the form a+ib where a=0 i.e. the real part is 0 is called a pure imaginary…

Q: Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round…

A: Let us find the value of θ in the equation 4 sin (2θ)-2sin θ= 0 we know that sin(2θ)= 2sin θ Cos θ 4…

Q: Locate and classify all the critical points of the function. (If an answer does not exist, enter…

A:

Q: On a sketch of y = ln(x), represent the left Riemann sum with n = 2 approximating ſå ln(x) dx. Write…

A:

Q: Use Lagrange multipliers to find the maximum or minimum values of the function subject to the given…

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

Q: Consider the function f(x) whose second derivative is f"(x) = 2x + 10 sin(x). If f(0) = 4 and f'(0)…

A:

Q: Sketch a right triangle corresponding to the trigonometric function of the acute angle ?. Use the…

A: cotθ=4 As we know ⇒cotθ=BasePerpendicular=BP=41⇒B=4,P=1

Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = tan(4x + 5y+z) . F(x, y, z) =

A: given  f(x,y,z)=tan(4x+5y+z)we know that formula of gradient field is→gradient…

Q: Evaluate the integral. (Remember the constant of integration. Remember to use absolute values where…

A: ∫9x33x4+7dx

Q: d) Critical points from the g'(x). Show all the derivative steps. e) Intervals of…

A:

Q: Simplify √√-225.

A: We need to simplify the value.

Q: 3) Approximate *In(y + 1)dy with a midpoint Riemann sum using three equal subintervals.

A:

Q: Find the surface area of the solid generated by revolving y = 1,0 ≤ x ≤ 6 about the y-axis.

A: y=x/2, [0,6]

Q: 2) Approximate tanede with a right-endpoint Riemann sum using four equal subintervals. 0

A:

Q: Use a finite sum to estimate the average value of f on the given interval by partitioning the…

A:

Q: 0 10 a

A:

Q: Evaluate the double integral where D is the region with vertices (1, 0), (1, 2), (1, 2) and (3,0).…

A:

Q: This is a matching problem. For the problem I would recommend the following approach: first…

A: As per guidelines,  I can answer maximum three subparts of a question. So, I did first three…

Q: Prove that if x, y, z is a Pythagorean triple, then at least one of x and y is divisible by 3, and…

A:

Q: Evaluate the following indefinite integral. + 6t5 ¹ 5t [1+615 5t -dt = dt (Type an exact answer.)

A:

Q: Set up a triple integral as an iterated integral (but do not compute it) for the following solid:…

A: The given spheres are:x2+y2+z2=1      and        z=x2+y2+z2

Q: use integral test to determine the convergence or divergence of the series, but assume that all…

A:

Q: a. Locate the critical points of the given function. b. Use the First Derivative Test to locate the…

A:

Q: Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round…

A:

Q: Calculate the definite integral. 2 S- 0 -9e8x dx

A:

Q: Find the indicated second-order partial derivative for f(x,y), shown below. 5 Inx y fyy(x,y) if…

A: given  f(x,y)=5lnxy

Q: 0 1 2 3 4 where p = 4. Left sum = Right sum = 0 1234

A: p=4

Q: find dy/dx Yztan √x + √x

A: Given equation,

Q: e) 2t² +4 5t dt f) 5t $²,250 dt t²+4

A:

Q: Find the line integral along the path C shown in the figure on the right. [6x² + y²) dy (0,0)

A:

Q: I the curl of the vector field F = ■ F = j+ k

A:

Q: ✓ J Esc 78°F Clear ! Evaluate for the function: f(x) = 4x+12 O 20 F2 14 2 16 28 F3 #M 3 F4 $ 4 F5 28…

A: We need to find value of f(1/2)

Q: For a certain drug, the rate of reaction in appropriate units is given by 6 4 R'(t)=- + t+1 √√t+1…

A:

Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

A:

Q: π Let f(x) = 9sin x for 0 ≤ x ≤ Compute Lf (P) and Uf (P) for the function f and the partition P =…

A:

Q: Use a double integral in polar coordinates to find the volume V of the solid bounded by the graphs…

A: The region of integration is a cylindrical shell bounded by two circles with radii of 3 and 5, and a…

Q: Evaluate f(4) for the function f(x)= O 16 32 **-** (9) O 16 O 32

A: f(x) = (1/4)x-2 We have to find the function at x = 4

Q: find dy/dx у= sint cos2 хосод cesc

A:

Q: x - 2 (x² - 4x + 3)² dx

A: we have given integration ∫x-2x2-4x+32dx

Q: Let y = sin(5x). If Ax = 0.4 at x = 0, use linear approximation to estimate Ay Ay~= Find the…

A: y=sin5x If ∆x=0.4 at x=0

Q: 4. The sum of two positive numbers is 16. What is the smallest possible value of the sum of their…

A: The sum of two positive numbers is 16.

Q: =-xi-jaroun j around and across the closed semicircular path that consists of the semicircular arch…

A: Given the field is:  F= -x2i-y2j We need to find the circulation and flux of the field F.

Q: The terminal point P is determined by a real-value and lies on the unit circle with coordinates P…

A:

Q: Find the area of the shaded region. f(x)=x² - 4x³ +9x², g(x) = 2x + 16 The area is (Type an integer…

A:

Q: 5. Find the dimensions of a rectangle with perimeter 100 m whose area is as large as possible.

A:

Q: Evaluate the iterated integral by converting to polar coordinates. 32 - y² БГ √x² + y² dx dy

A:

Q: f(x, y) = 2x + 4y x ≥ 0 y≥ 0 x + y ≤ 6

A:

Q: 17. f(u) u¹ + 3√/u

A: question no-17

Q: r³ 36. f'(x) = 2x - 3/x¹, x>0, f(1) = 3 37. f"(0) = sin 0 + cos 0, f(0) = 3, f'(0) = 4 ƒ'(1) = 8 38.…

A: