Find the cross product a x b. a =j+ 6k, b = 2i -j + 5k Verify that it is orthogonal to both a and b. (a x b) a = (a x b) b =

Q: Find the point of intersection (xo, Yo, Zo) of the lines given as: L₁: y = 7+8t, x=6+t, x=6+t, L₂: y…

A:

Q: ind the Laplace Transform of the following functions, using the definition of t _aplace transform 1)…

A:

Q: Sketch the region of integration and evaluate the integral. 3 x² S S - 2x dy dx

A:

Q: . Graph the Polar function r = f(0) = 1-2 cos

A:

Q: Karl Yates needs $6,000 to pay for the remodeling work on his house. A contractor agrees to do the…

A:

Q: A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium…

A: The given data is: A common inhabitant of human intestines is the bacterium Escherichia coli

Q: Write out the form of the partial fraction decomposition of the function appearing in the integral:…

A:

Q: The graph of f(x) is given on the grid. Graph ƒ'(x), its derivative. 5- -5 -4 -3 -2 -1 3 2 1 -1 -2…

A:

Q: evaluate using integration by parts

A:

Q: Graph the Polar function r = f(0) = 2 - 3 cos 0

A:

Q: In 1997, researchers at Texas A&M University estimated the operating costs of c sizes. A quadratic…

A: Given: c(q)=0.021q2+26.9q+313

Q: Find the volume of the solid generated when the area bounded by the curves y = x² and y = x³around…

A: To find the volume of the solid generated when the area bounded by  the curves y=x2 and y=x3 around…

Q: Find an equation of the line tangent to the curve defined by a³ + 5xy + y = 7 at the point (1, 1). Y

A:

Q: SET UP the double integral to find the area of e right by the parabola y = x², on the left by the…

A: Given  Area is bounded by parabola (y=x^2) from right and line x+y=2 from left and y=4 from above

Q: A rectangular field adjacent to a river is to be enclosed. Fencing along the river costs $5 per…

A: A rectangular field adjacent to a river is to be enclosed. Fencing along the  river costs $5 per…

Q: Find a function of the form y= A sin(kx) + C or y= A cos(kx) + C whose graph matches this or -6 5₁…

A: We are asked to find the equation of the graph

Q: Estimate the area between the x-axis and the graph of f(x) = 9 - x² over the interval [-1,2] by…

A:

Q: Let f(x) = 9x² - 4x + 8. Determine f(a+h). Simplify completely. f(x+h) = Determine f(x+h)-f(x) h…

A:

Q: Write an integral that represents the area of the shaded region of the figure. Do not evaluate the…

A:

Q: Find the region generated by rotating the region bounded by xy=1, x=1, x=2 and y=0 around the y-axis

A: Given :- The region bounded by xy=1, x=1, x=2 and y=0 To find :- The region

Q: 18 > (a) Find the direction for which the directional derivative of the function f (x, y) = 7xy² +…

A:

Q: Use implicit differentiation to find y' for 4x³y² + ln(xy³) Answer exactly. y' (1, 1) = 4 and then…

A:

Q: Evaluate the iterated integral ] [18x²y³ 18x²y³dy dx.

A: A detailed solution is given below.

Q: Calculate the integral of f(x, y, z) = z(x² + y² + z²)−³¹2 over the part of the ball x² + y² + z² ≤…

A:

Q: If f(x)=√ sinx, find f'(x). f'(x) =

A:

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A:

Q: Let a = 1 and b = 4. 0 16 S.L. ㅠ -√a²-x² If you need to use π for your answer, just type pi.…

A:

Q: How many critical points does the function f(x) = 8sin2 (3x) have on the interval (0, π)? Provide…

A:

Q: A drug is administered to a patient through an IV drip. The drug concentration (in milligrams/…

A:

Q: so whats the answer

A: So what's the answer.

Q: 8. A bead slides down the curve xy 10. Find the bead's horizontal velocity at time t = 2 s if the…

A:

Q: Find parametric equations of the line through (-3, 1,6) that is parallel to 4i-8j+ k. x(t) = y(t) =…

A:

Q: E) y = 3x² ln(x)

A: Given :

Q: Find the point of intersection (xo, Yo, Zo) of the lines given as: L₁: L₂: Xo = Yo = Zo = M i x=…

A: Given lines equation:- L1: x=3+t,y=5+6t,z=5+tL2: x=3+t, y=6+7t,z=6+2t

Q: Differentiate the function, and find the slope of the tangent line at the given value of the…

A: As we know that, The slope of the tangent line to the given curve is equal to the derivative of the…

Q: - The cost function for a product is C(q) = q³ −— 66q² + 1452q + 1110 for 0 ≤ q ≤ 50 and a price per…

A: Given cost function:- Cq=q3-66q2+1452q+1110

Q: Find the distance between the skew lines: z=8-9t x = 5+7t, y=3+7t, x = 1-t, y = 6, z = 5+8t NOTE:…

A: Solution:  To find the distance between the following skew lines. x=5+7t, y=3+7t,  z=8-9tx=1-t, y=6,…

Q: 42. Use cylindrical coordinates to find the volume of the region bounded below by the plane z = 1…

A: The solution is shown below-

Q: For each function a) find the critical points/numbers, b) intervals of increasing/decreasing c)…

A: Given function:- fx=3x2-4x+6

Q: Compute sin((t + 2))dt. 0-1/1/12 01/1/12 3 2πT O O- cold 3 2πT ONone of above

A: Given integral:- ∫01sinπ3t+2dt

Q: For the given function, compute the missing values in the following table. f(x) = 2−x x −3 −2…

A: We have given f(x) = 2-x

Q: Find the volume of the solid generated by revolving the region bounded by the given curve and lines…

A:

Q: Consider the function f(x, y) = 2ye7 and the region R = {(x, y)|0 ≤ x ≤ 1, 0 ≤ y ≤ x³}. (a) Find the…

A: The solution is shown below-

Q: woman deposits $6000 at the end of each year for 10 years in an account paying 8% interest…

A:

Q: 2 Find the average rate of change of g(x) = 7x² + on the interval [-3,4]

A:

Q: 1. Let v (4, -2,-4) be a vector in R³. (a) Find a unit vector in the direction of v. (b) Find a…

A: Given vector v→ = 4i -2j -4k

Q: Match each of the following conditions with an equation. f(x) = 24x - 4 fil(0) f(0) = f(0) = 0 = y =…

A:

Q: Show that the lines L₁ : x = 3-t, y = 2t, z = 2+t and L₂: x = 1 + 4t, y = 3-8t, z = 5 - 4t are…

A: Solution is given below:

Q: 8. 5x³43x²+72x+36> 0 10. 2x²-x-4

A:

Q: Find y' a) y = 2 tan (x) + 9 cos (x) y'= (b) y = 5 cos (x)= 4 x ² 'y'= c) y = y sin (x) = tan (x) -…

A: