Show that the lines L₁ : x = 5-t, y = 2t, z = 5+t and L₂: x = 1 + 4t, y = 3 - 8t, z = 5 - 4t are parallel and find the distance between them. NOTE: Enter the exact answer. L₁ and L2 are parallel because they are parallel to vectors v₁ and v₂ that satisfy: Choose one Ch

Q: t (seconds) 0 481216 Velocity (ft/sec) 048 1725 Shown in the table is the velocity of a car at…

A:

Q: n k=1 (3 + 2k)² = Hint: Start by multiplying out (3 + 2k)². fra

A:

Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

A:

Q: Which curve does it need to be label and what area are we shading in?

A: Labeled graph is given below,

Q: From the figure consider the representative rectangle. The radius of the solid of revolution…

A: From the figure    Disk method

Q: Given f(x, y, z)=√x+6y-52, find fz(x, y, z)= 1₂(x, y, z)= f.(x, y, z)=

A: Partial Derivative

Q: Find the linearization L(x,y) of the function f(x,y) = 5x cos (y) at the points (0,0) and The…

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) 7xeox dx 6x [7xe 7…

A:

Q: For a rectangle with a perimeter 24 to have the largest area, what dimensions should it have? (Enter…

A: According to question, Given Perimeter, Perimeter of a rectangle = 24 units

Q: Jump to level 1 Order the functions by growth rate. a(x) = 9ª + 9x c(x) = x log₂ (x) +20x! Select…

A: Please see the below picture for detailed solution.

Q: Find the limit by evaluating the derivative of a suitable function at an appropriate point. Hint:…

A: According to question,Given Limit,limh→048+h2-8+h-248h

Q: Drives Co. sells portable hard drives. They can sell 400 drives when the price is $85/drive, and…

A:

Q: Determine which value best approximates the area of the region bounded by the graphs of f and g.…

A: Topic = Area

Q: 58. y = x³ - 24 ln x, [2,3]

A:

Q: Evaluate the following integrals and/or determine whether the integral is convergent or divergent…

A: Note:- Since you asked multiple question, as per policy we can solve only first question for you…

Q: (c) 1 So ²2-²32 3z ² dz.

A:

Q: 1 Graph the function by using transformations of the graph of y = Plot all necessary asymptotes. For…

A:

Q: A company determined that the marginal cost, C'(x) of producing the xth unit of a product given by…

A: A company determined that the marginal cost, C'x of producing the  xth unit of a product is given by…

Q: If h(x) = (1 + 4) 4) 7x I find lim h(x). X→∞

A: Given :hx=1+4x7x

Q: 8 2 SO SATY 4 Te dxd

A:

Q: Given z=f(x,y)=5-8 (5x-y) find and ax ay पेर 一

A:

Q: Find the directional derivative of f at the given point in the direction indicated by the angle 8.…

A: Given, 4. f(x,y) =xy3 - x2, (1,2) , θ = π/3

Q: Grade A and Grade B) in each department. In department 1, Grade A and Grade B workers are paid $14…

A: As per our guidelines we are supposed to answer only three subparts of a question. So first three…

Q: Sta tan³ xsec³ x dx

A:

Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the…

A: The revenue function is R(x)=40x-0.5x2 Cost of producing x units is C(x)=6x+10 Profit function is…

Q: Write the expression as the logarithm of a single quantity. 1/2 ln(x) + 6 ln(y) − 3 ln(z)

A:

Q: Suppose that in the interval 15 ≤ x ≤ 20 you know that the graph of y = f(x) rises as you move from…

A: The given data is: y=f(x), 15≤x≤20 The graph of y=f(x) is concave down.

Q: 2. Sketch a function, g(x), where lim g(x) = 0 and lim_g(x) = 3. = x→2+ x→2- 3 HH 2

A: Using limits

Q: is there no step 3 to this solution? and why does it end like that like what exactly would be the…

A: There is no any step 3. i am going to derive equation again.

Q: Use differentials to estimate the value of 1.5. Compare the answer to the exact value of $1.5. Round…

A: By using differential to estimate the value of 1.54.  To compare the answer to exact value of 1.54.…

Q: Marginal Revenue The demand function for a certain boat company's 34 ft Sundancer yacht is p=…

A:

Q: Mike and John take the same math class. The probability that Mike will attend the class today is…

A:

Q: Use the model to estimate the monthly inflation rate in January 2007 (t = 1).  Recall that the…

A:

Q: 20. A farmer has 6000 m of fencing and wants to create a rectangular field subdivided into four…

A:

Q: For the matrix Determine: (i) (ii) (iii) the eigenvectors. (iv) Diagonalize A. the characteristic…

A:

Q: sketch the curve, Find :  a) domain  b) intercepts (x and y)  c) symmetry

A: As per rule I need to solve only first 3 subparts.

Q: Find the area of the region under the curve y = f(x) over the indicated interval. 6 1) 5/2 i f(x): =…

A:

Q: Description suppose f(x) is given: 1- explain steps you take to find out where Min and Max points…

A: (1) To find the minimum and maximum points of a function f(x), we need to find the values of x that…

Q: Find the absolute maximum f(x, y) = xy² + 1, absolute maximum value absolute minimum value and…

A: Given function:- fx,y=xy2+1

Q: Find the absolute maximum and absolute minimum values of f on the given interval. X x²4 [0, 5] +…

A:

Q: Consider the function g(x)=√x + x² where g'(x) = ₂ + 2x 2 3x3

A:

Q: Exercises In Exercises 1-8, find a point c satisfying the conclusion of the MVT for the given…

A: As we know from the Mean value theorem: If the function fx is real-valued function is defined on a,b…

Q: How long, rounded up to the nearest year, will it take me to become a millionaire if I invest $3,000…

A: Given data Principle, P= $ 3000 Interest rate, R = 12 % Time in years = t Amount, A = $ 10,00,000

Q: A car dealership advertises a 10% discount on all its new cars. In addition, the manufacturer offers…

A: Given function f( x ) = 0.9x g( x ) = x - 1750

Q: Let g(x)=2tan(x). Using what you learned from your answer in (a), give the particular antiderivative…

A: We have to find the antiderivative of g(x).

Q: Find the area of the shaded region. y=0 square units y 9|2 9|2 y=x√√9-x² y=0 3 - X

A: Area

Q: Use the additivity of moments to find the COM of an ice cream cone consisting of a semicircle of…

A:

Q: A wire 10 cm long is cut into two pieces, one of length x and the other of length 10 - x, as shown…

A:

Q: You plan to build a cylindrical container with no top. The material used for the lateral sides costs…

A:

Q: Graph the system of inequalities. x≤2 y≥3-3x Use the graphing tool to graph the system of…

A: x≤2 line x=2     y≥3-3x draw line y=3-3x x y 0 3 1 0 check for orgin y≥3-3x0≥3-3(0)0≥3…