A roofer requires 10 h to shingle a roof. After the roofer and an apprentice work on a roof for 5 h, the roofer moves on to another job. The apprentice requires 13 more hours to finish the job. How long would it take the apprentice, working alone, to do the job?
In: Math
Calculate the arc length of the indicated portion of the curve r(t).
r(t) = i + (9t sin t)j + (9t cos t)k ; -3 ≤ t ≤ 7
In: Math
The motion of a particle in space is described by the vector equation
⃗r(t) = 〈sin t, cos t, t〉
Identify the velocity and acceleration of the particle at (0,1,0) How far does the particle travel between t = 0 & t= pi
What's the curvature of the particle at (0,1,0) & Find the tangential and normal components of the acceleration particle at (0,1,0)
In: Math
Solve each inequality and graph the solution. Thank you!
1. -3/8(x) - 20 +2x > 6
2. 2/3(x) + 14 - 3x > -7
3. 0.5x - 4 - 2x ≤ 2
4. 4x + 1 + 2x ≥ 5
In: Math
Consider the linear transformation T : P2 ? P2 given by T(p(x)) = p(0) + p(1) + p 0 (x) + 3x 2p 00(x). Let B be the basis {1, x, x2} for P2.
(a) Find the matrix A for T with respect to the basis B.
(b) Find the eigenvalues of A, and a basis for R 3 consisting of eigenvectors of A.
(c) Find a basis for P2 consisting of eigenvectors for T.
In: Math
Determine the amplitude, the period and the phase shift of the function
1. y = -3 cos ( 4 x - PIE ) + 2
2. y = 2 + 3 cos ( PIEx - 3 )
3. y = 5 - 2 cos ( PIE/2 x + PIE/2 )
4. y = - 1/2 cos (2 PIE x ) + 2
5. y = - 2 sin ( - 2 x + PIE ) - 2
6. y = - sin ( ( ½ x - PIE/2 ) + 1/2
Thank you.
In: Math
12a Find an equation of the tangent plane to the surface ? = 2? 2 + ? 2 − 5?, ?? (1, 2, −4).
12b If ? = ? 2 − ?? + 3? 2 and (?, ?) changes from (3, −1) to (2.96, −0.95), compare ∆? and ??.
Calculus 3 question. Please help.
In: Math
Suppose products A and B are made from plastic, steel, and glass, with the number of units of each raw material required for each product given by the table below.
| Plastic | Steel | Glass | |
| Product A | 3 | 1 | 0.50 |
| Product B | 5 | 0.50 | 2 |
Because of transportation costs to the firm's two plants, X and Y, the unit costs for some of the raw materials are different. The table below gives the unit costs for each of the raw materials at the two plants.
| Plant X | Plant Y | |
| Plastic | 11 | 9 |
| Steel | 22 | 27 |
| Glass | 15 | 14 |
Using the information just given, find the total cost of producing each of the products at each of the factories.
A)
B)
C)
D)
In: Math
5. Given the function y = q(x) = (x^2)/(x-1)
a. What is the domain of q(x)?
b. What are the vertical asymptotes?
c. What are the horizontal asymptotes?
d. Where is q(x) increasing/decreasing (draw a line and specify by intervals – be sure to include points where q isn’t defined)?
e. Where is q(x) concave up/down ((draw a line and specify by intervals – be sure to include points where q isn’t defined)?
f. Find rel max/min.
g. Find inflection points.
h. Sketch the curve.
In: Math
Westside Energy charges its electric customers a base rate of $4.00 per month, plus 12¢ per kilowatt-hour (kWh) for the first 300 kWh used and 3¢ per kWh for all usage over 300 kWh. Suppose a customer uses x kWh of electricity in one month.
(a) Express the monthly cost E as a piecewise defined function of x. (Assume E is measured in dollars.)
E(x) =
A. if 0 ≤ x ≤ 300
B. if 300 < x
C. (b) Graph the function E for 0 ≤ x ≤ 600.
In: Math
f(x)=e^x/(x+1)
Find the vertical and horizontal asymptotes using limits. Also, intervals of increase and decrease, local extrema. Finally, find the intervals of concavity and points of inflection.
In: Math
find the volume of the region bounded by y=sin(x) and y=x^2 revolved around y=1
In: Math
Use the given function, its first derivative, and its second derivative to answer the following:
f(x)=(1/3)x^3 - (1/2)x^2 - 6x + 5
f'(x)= x^2 - x - 6 = (x+2)(x-3)
f''(x)= 2x - 1
a) What are the intervals of increase and the intervals of decrease
b) Identify local min and max points
c) What are the intervals where the function is concave up, concave down and identify the inflection points
In: Math
Use a software program or a graphing utility to solve the system of linear equations. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set x5 = t and solve for x1, x2, x3, and x4 in terms of t.) x1 − x2 + 2x3 + 2x4 + 6x5 = 16 3x1 − 2x2 + 4x3 + 4x4 + 12x5 = 33 x2 − x3 − x4 − 3x5 = −9 2x1 − 2x2 + 4x3 + 5x4 + 15x5 = 34 2x1 − 2x2 + 4x3 + 4x4 + 13x5 = 34 (x1, x2, x3, x4, x5) =
In: Math
S = {(2,5,3)} and T = {(2,0,5)} are two clusters. Two clusters that S and T spans are L(S) and L(T) . Is the intersection of L (S) and L (T) a vector space? If yes, find this vector space. If no, explain why there is no vector space.
In: Math