The total sales of a company (in millions of dollars) t months from now are given by S(t) = 0.01t° +0.2t + 8t + 2. (A) Find S'(t). (B) Find S(6) and S'(6) (to two decimal places). (C) Interpret S(13) = 161.77 and S'(13) = 18.27. S'(6) = (C) Choose the correct interpretation of S(13) = 161.77. A. In approximately 162 months the sales will be $13 million dollars. B. The total sales 13 months from now will be $161.77 million dollars. C. In approximately 162 months the sales will be increasing by $13 million per month. D. In 13 months the sales will be increasing at a rate of $161.77 million per month. Click to select vour answer(s)

Q: Sketch the surfaces 1. 9x2 + y2 + z2 = 9  2. 4x2 + 9y2 + 4z2 = 36

A: Using graphing calculator to graph them. 9x^2 + y^2 + z^2 = 9 

Q: a khanacademy.org Dashboard ( Khán A. Spanisn Il (8-9 B) Differentiation: defi.. Blended Playlist: C...

A: Given the table value of the differentiable function g.

Q: Use the factor theorem to decide whether or not the second polynomial is a factor of the first. 4) 7...

A:

Q: Consider the following. -9x, f(x)=. lx² - 6x + 9, Find the x-value at which f is not continuous. Is ...

A: We need to find the x-value for which the given function is not continuous.

Q: In this section, we used the product-to-sum formulas to write sums and differences of trigonometric ...

A: We are given the Fourier series (later we are writting y = f(x) )

Q: How do you define and calculate the length of a segment of a smooth space curve? Give an example. Wh...

A: Description:

Q: Find each x-value at which fis discontinuous and for each x-value, determine whether fis continuous ...

A: Given:

Q: Which of the following are equations for the plane through the points P(1, 1, -1), Q(3, 0, 2), and R...

A: First find PQ and PR , two lines on the plane

Q: The cost for an animal shelter to spay a female cat is $82 and the cost to neuter a male cat is $55....

A: Given that, the cost to spray a female cat is $82 and the cost to neuter a male cat is $55.

Q: How can you tell when two planes A1 x + B1 y + C1 z = D1 and A2 x + B2 y + C2 z = D2 are parallel? P...

A: Two planes are parallel if their normal vectors are parallel.Normal vector of A1 x + B1 y + C1 z = D...

Q: 10)Guess the values of the limit (if it exists) by evaluating the function at the given numbers ( co...

A:

Q: find the antiderivative of the function h(x)=5/x

A: Recall the fact that the antiderivative of a function is the integration of that function.

Q: n Exercises 39–41, find the distance from the point to the plane. 39. (2, -3, 4), x + 2y + 2z = 13 4...

A: Given, (2, -3, 4), x + 2y + 2z = 13.

Q: x3 :/ V? +3 dt then If f(x) = 3

A: According to the given information it is required to calculate the definite integral of the followin...

Q: Which of the following are always true, and which are not always true? Give reasons for your answers...

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

Q: | 12f(x) + 3g(x)]dX 0. 50. Find f(x) dx if for x 3 51. For the function f whose graph is shown, li ...

A: Break the integration in two parts.One from 0 to 3, other from 3 to 5.

Q: Find the acute angle between the planes x = 7 and x + y + sqrt(2)z =-3.

A: We know that cosine of angle between plane a1x+b1y+c1z=d1 and a2x+b2y+c2z=d2 is given by

Q: In Exercises 9–14, sketch the coordinate axes and then include the vectors u, v, and u * v as vector...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: Find the acute angles between the intersecting lines in Exercises 49 and 50. 49. x = t, y = 2t, z =-...

A: Note: We’ll answer the 49th question since we answer only one question at a time. Please submit a ne...

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the d...

A: The given function is,

Q: where is the function (5+x) / (x(x-2)) discontinuous?

A:

Q: Please solve and show your work

A: Given:

Q: How do you find a vector’s magnitude and direction?

A: If a vector is given. For example: ai+bj+ckThen to find the magnitude we need: 

Q: Suppose r(t) = (et cos t)i + (et sin t)j. Show that the angle between r and a never changes. What is...

A: Given information:

Q: Find the length of the curve r(t) = (sqrt(2)t)i + (srqt(2)t)j + (1 - t2)k from (0, 0, 1) to (sqrt(2)...

A: Given curve

Q: please solve and show your work

A: Two end points of the line segment are: (0,4) and (-5,-3)

Q: Can someone show me how to reach this answer shown in the problem?

A: Given,

Q: Find the limit, if it exists.

A: For the given function, we get an indeterminate form 0/0 then apply L’Hospital’s Rule

Q: Show that a projectile attains three-quarters of its maximum height in half the time it takes to rea...

A: Show that a projectile attains three-quarters of its maximum height in half the time it takes to rea...

Q: generate a parametrization of the line through P(2, -4, 7) parallel to v1 = 2i - j + 3k. Then genera...

A: We know that equation of line through (x1,y1,z1)  and parallel to ai+bj+ck is

Q: Find the measures of the angles between the diago-nals of the rectangle whose vertices are A = (1, 0...

A: The given vertices of the rectangle is A = (1,0), B = (0,3), C = (3,4), and D = (4,1).Use the given ...

Q: 50. Fungal Growth As a fungus grows, its rate of growth changes. Young fungi grow exponentially, whi...

A: We are given the model :

Q: Find the distance between the line through A(4, 0, 2) and B(2, 4, 1) and the line through C(1, 3, 2)...

A: Find the distance between the line through A(4, 0, 2) and B(2, 4, 1) and the line through C(1, 3, 2)...

Q: Find the limit "L" The prove how the limit is "L"

A: Given function is

Q: The Union Pacific’s Big Boy locomotive could pull 6000-ton trains with a tractive effort (pull) of 6...

A: given  The Union Pacific’s Big Boy locomotive could pull 6000-ton trains with a tractive effort (pul...

Q: Show that v = ai + bj is perpendicular to the line ax + by = c by establishing that the slope of the...

A: Given: Show that v = ai + bj is perpendicular to the line ax + by = c by establishing that the slope...

Q: Find an equation of the plane. The plane that passes through  (6, 0, −3)  and contains the line  x =...

A: The plane passes through a point P=(6,0,-3) and contains the line x=2-4t, y=1+5t, z=6+4t. Hence, we ...

Q: In Exercises 37 and 38, find an equation for the plane through points P, Q, and R. 37. P(1, -1, 2), ...

A: Given, the points P(1, -1, 2), Q(2, 1, 3), R(-1, 2, -1)The vector

Q: Find the acute angles between the lines and planes in Exercises 51 and 52. 51. x = 1 - t, y = 3t, z ...

A: Given:The line equations x = 1 - t, y = 3t, z = 1 + t.

Q: Let f (x) = 10x and g(x) = x2 + 7x, and let R be the bounded region between the graphs of f and g. S...

A: We draw the graphs using graphing calculator and shade the region bounded by y=10x and y=x^2+7xThey ...

Q: #19

A: Consider the function.

Q: Can you help me step by step with this problem please

A: Given,  

Q: Find the x-values ( if any) at which f is not continuous. Which of the discountinuities are removabl...

A: Given:

Q: Solve the equation for all solutions in the interval [0,2π). cos(x/2)=√3/2 Express answer in radians...

A: Find x/2 using  cos inverse.

Q: Show that the diagonals of a rhombus (parallelogram with sides of equal length) are perpendicular.

A: Show that the diagonals of a rhombus (parallelogram with sides of equal length) are perpendicular

Q: Draw the region bounded by the curves y=2x^2, y=2, and x = 0. Use the disk method to find the volume...

A: Given:

Q: Assume a quantity decreases by 5.1% in 7.5 hours.What is the half-life of the substance?

A: Find half – life substance.

Q: Can you please explain and solve this using the concept of limits? Our topic right now is all about ...

A: Given : find the interval on which the following function is continuous.

Q: Find T, N, and k for the plane curves in Exercises 1–4. 1. r(t) = t i + (ln cos t)j, -pai/2<t<...

A: NOTE: Hello there! You seem to have uploaded multiple questions. As per our guidelines, we are provi...

Q: Find the limit, if it exists.

A: Given expression is,