4. The diagram is a rectangular prism. Let u = AB, v = AD and w = AE. Express each vector as a linear combination of u, v and w. a) AG = b) EC = E H A B C

Q: (SHORT BOND PAPER) Find the slope and equation of the tangent line to the graph of the equation at a…

A: since you have posted multiple questions in this question which are not interlinked so i have solved…

Q: 3. s) Determine whether the equation is exact. If it is, then solve it. 1 (2xy + 2)dx + (x² + y3)dy…

A:

Q: Each week, you have a total of 80 hours to split between x hours of work and y hours of leisure. The…

A:

Q: f'(x) = Let f(x)= = I cos ³

A:

Q: Let f(x, y, z) = x^2 + y^3 + z^5 and let u =. Find the directional derivative Du f(x, y, z).

A: The directional derivative Du​f(x,y,z) is 64/81​.Explanation:Step 1: To find the directional…

Q: pesticides is to introduce into the population a number of sterile males that mate with fertile…

A:

Q: Let f(x) = x²e19x (a) Find the critical values of f(x). (Enter your answers as a comma-separated…

A:

Q: a) The function and its derivative always have the same domains. (b) To find the derivative of h(x)…

A:

Q: Consider the equation ex+3y+4x+9y+ sin(xyz) + 12z = 1 The implicit function theorem implies that…

A:

Q: I need the equation of the tangent line to the curve at (1,3)

A: Slope is given by as calculated m=3

Q: Approximate the area under the curve by evaluating the function at the left-hand endpoints of the…

A:

Q: pls solve using differential equation thank you so much

A: The rate at which the flow velocity is changing halfway between the center line is…

Q: d) - dx = (x-1)² √x

A: To evaluate the following integral by using chain rule.

Q: Let f(x) = x²15x (a) Find the critical values of f(x). (Enter your answers as a comma-separated…

A: Given:a function To find:critical points, monotone intervals and extreme points of function f(x).

Q: Find by implicit differentiation, where 3x5 + 7x¹y - 6xy5 = 2. dy dx

A:

Q: Let f(t) = 3t2/3 + 5/3 (a) Find all partition numbers of f'(t). (Enter your answers as a…

A: Note:As per our guidelines we are supposed to answer only first 3 subparts if there are multiple…

Q: Biologists stocked a lake with 500 fish and estimated the carrying capacity (the maximal population…

A:

Q: what does f'(m) = ?

A: We need to provide meaning of f'(m).

Q: Find the logical value of the proposition and the domain of discourse is R(real)

A: The logical value of the proposition ∀x∃y∃zxyz=1 is true for all x∈R except x = 0.Explanation:Step…

Q: A spherical balloon is inflating with helium at a rate of 400x ft3/min. How fast is the balloon's…

A:

Q: A price p (in dollars) and demand x (in items) for a product are related by  2x2 − 5xp + 70p2 =…

A: The demand is decreasing at a rate of approximately 71.43  dollars per month.Explanation:Given A…

Q: Please solve this vector calculus problem step by step. Thanks!

A: ANSWER IS GIVEN BELOW.Explanation:

Q: If consumption is $7.9 billion when income is $1 billion and if the marginal propensity to consume…

A: Given marginal propensity  (in billions of dollars)

Q: Find the equation of the tangent line to y = 7e* at x = 8. (Use symbolic notation and fractions…

A:

Q: Let Compute dw Əs dw Ət (−3,−4) = 12 4e¹2 +64 w = -5xy + 4yz - xz, x = st, y = est, z = ²

A: The answer is in the explanation section Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Assume that f'(4)= -9, g'(3)= 9(3)=4, and y=f(g(x)). What is y' at x=3? Atx=3, y'= (Simplify your…

A:

Q: λ x²y"+2xy+(3x² + y= 0, y(-1)= y(1) = 0, (x2+1)3 with eigenvalue A, can be written as a constrained…

A: λ1​≤7π32​Explanation:To show that λ1​≤7π32​ using the trial function z(x;A)=A(1−x2), we'll use the…

Q: In this problem, we'll evaluate (b) Now evaluate X X J (a) Use the trigonometric substitution x = -…

A:

Q: 8. Use the Product Rule to find the derivative of f   f(x)=cot(x)sec(x)

A: Use the Product Rule to find the derivative of the following function.

Q: ints Find the general solution to the equation in implicit form dy 1 dx yey+x =

A: The given differential equation is

Q: At an Oregon fiber-manufacturing facility, an analyst estimates that the weekly number of pounds of…

A:

Q: Find all max and mins on the given intervals using the first derivative test. Make sure to show all…

A:

Q: Given the following functions: f(u) = u7/2 and g(x) = 8 + 1. Find: f(g(x)) = f' (u) = f' (g(x)) =…

A:

Q: A vehicle purchased for $22,400 depreciates at a constant rate of 4%. Determine the approximate…

A: $12142.73Explanation:The given values are as follows-Vehicle purchased for $22,400Depreciates at a…

Q: Let f be the function defined by f(x) = 2x + 3e-5, and let g be a differentiable function with…

A:

Q: The rate of vocabulary memorization of the average student in a foreign language course is given by…

A:

Q: Зп 4 6п Зп 8 П 4. Find Ax in the Riemann Sum k=1 Зп f(x1)∆x on the interval |0, 0,3 2 using 4…

A: The Riemann sum  is given on the interval .

Q: what does z equal?

A:

Q: Find the tangent vector for the position vector r(t)=ln(1-t)i+(t-t^3)j+e^-3t k

A: Explanation of the answer is as follows

Q: Find the arclength of the curve y x2 28 -In x where 4 < x < 9 72

A:

Q: A contour map for a function f is shown. Estimate the value of f₁(4, 18) 20 15 10 5 70 fy(4, 18) ~…

A: Given:a contour map for a function f is shown.To find:Estimate the value of fy(4, 18).

Q: Find the centroid of the region lying underneath the graph of the function f(x)=√ over the interval…

A: f(x) =

Q: what does f'(m) = ?

A: We need to provide meaning of f'(m).

Q: π-2 2π - 15/10 05 Multiple Choice A particle is moving on the x-axis with a velocity of v (t) = t² -…

A: The objective of this question is to find the values of time (t) for which the speed of the particle…

Q: The area of a circle is increasing at a constant rate of 88 square meters per second. At the instant…

A: The area of a circle is increasing at a constant rate of 88 square meters per second.dAdt=88 square…

Q: 16. Find an equation of the line tangent to the curve defined by x3+3xy+y3 = 28 at the point (2,2

A:

Q: Solve the separable differential equation for. dy 1 + x ; x > 0 dx xy³ Use the following initial…

A: Given Differential Equation is as follows Given Initial condition

Q: Write out the form of the partial fraction decomposition of the function. Do not determine the…

A:

Q: f(x) = = -9x 1- x

A: f(x)=−9x1−x

Q: For each pair of integers m and n, use the division algorithm to divide m by n. Write the result in…

A: Given:pair of integers m and n.To find:Use the division algorithm to divide m by n.