In: Math
Consider the graph of f(x) = |x|. Use your knowledge of rigid and nonrigid transformations to write an equation for the following description. Verify with a graphing utility.
The graph of f is reflected in the x-axis, shifted three units to the left, and shifted eleven units upward.
| STEP 1: | Reflect |x| about the x-axis. g(x) = |
|---|---|
| STEP 2: | Reflect |x| about the x-axis and shift three
units to the left. g(x) = |
| STEP 3: | Reflect |x| about the x-axis, shift three
units to the left, and shift eleven units upward. g(x) = |
Consider the graph of g(x) = √x. Use your knowledge of rigid and nonrigid transformations to write an equation for the following description. Verify with a graphing utility.
The graph of g is vertically stretched by a factor of 7, reflected in the x-axis, and shifted four units upward.
h(x) =
Consider the graph of f(x) = |x|. Use your knowledge of rigid and nonrigid transformations to write an equation for the following description. Verify with a graphing utility.
The graph of f is vertically shrunk by a factor of 1/9 and shifted three units to the left.
g(x) =
Consider the graph of f(x) = x3. Use your knowledge of rigid and nonrigid transformations to write an equation for the following description. Verify with a graphing utility.
The graph of f is shifted twelve units to the left.
y =
In: Math
Use synthetic division to divide (-3x3-4x4− 20 − 2?) ÷ (? + 2).
Write your answer in the form ???????? ÷ ??????? = ???????? + remainder/divisor
In: Math
Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
f(x) =
| x2 | if −1 ≤ x ≤ 0 |
| 2 − 3x | if 0 < x ≤ 1 |
| absolute maximum value | |
| absolute minimum value | |
| local maximum value(s) | |
| local minimum value(s) |
In: Math
Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)
f(x) =
| 9 |
| x8 |
f(x)=
f '(t) = sec(t)(sec(t) + tan(t)), −− π/ 2 < t < π/ 2 , f ( π/ 4) = −3
f(t)=
Find f. f '''(x) = cos(x), f(0) = 2, f '(0) = 3, f ''(0) = 5
f(x)=
A company estimates that the marginal cost (in dollars per item) of producing x items is 1.67 − 0.006x. If the cost of producing one item is $550, find the cost of producing 100 items. (Round your answer to two decimal places.)
$=
What constant acceleration is required to increase the speed of a
car from 28 mi/h to 50 mi/h in 2 seconds? (Round your answer to two
decimal places.)
ft/s^2
A particle is moving with the given data. Find the position of the particle.
a(t) = 17 sin(t) + 9 cos(t), s(0) = 0, s(2π) = 12
s(t)=
In: Math
1).Find an equation for the conic that satisfies the given conditions.
ellipse, foci
(0, −3), (8, −3),
vertex
(9, −3)
In: Math
A couple who borrow $50,000 for 20 years at 6%, compounded monthly, must make monthly payments of $358.22. (Round your answers to the nearest cent.) (a) Find their unpaid balance after 1 year. $ (b) During that first year, how much interest do they pay?
In: Math
1) Find the radius of convergence and interval of convergence of the given series Σ x^2n/n!
2) Find the power series representation of f(x)=(x-1)/(x+2) first then find its interval of convergence.
In: Math
Find the equation of the line goes through (1,0,-1) that is perpendicular to the lines x = 3+2t,y = 3t,z = −4t and x = t,y = t,z = −t. Write it in parametric and the vector equation form.
In: Math
The effect of applying x milligrams of drug A and y milligrams of drug B is measured by
f(x, y) = xy - 2x2 - y2 + 120x + 40y + 25
What amounts of each drug should be used to get the biggest effect?
In: Math
The pressure exerted by a certain liquid at a given point varies directly as the depth of the point beneath the surface of the liquid. The pressure at 80 feet is 320 pounds per square inch. What is the pressure at 30 feet?
Find a polynomial of degree 3 with real coefficients and zeros of −3, −1, and 4, for which f(−2)=18.
In: Math
Maximizing Profits The quantity demanded each month of the Walter Serkin recording of Beethoven's Moonlight Sonata, produced by Phonola Media, is related to the price per compact disc. The equation p = −0.00044x + 10 (0 ≤ x ≤ 12,000) where p denotes the unit price in dollars and x is the number of discs demanded, relates the demand to the price. The total monthly cost (in dollars) for pressing and packaging x copies of this classical recording is given by C(x) = 600 + 2x − 0.00004x2 (0 ≤ x ≤ 20,000). To maximize its profits, how many copies should Phonola produce each month? Hint: The revenue is R(x) = px, and the profit is P(x) = R(x) − C(x). (Round your answer to the nearest whole number.) discs/month.
In: Math
√xy+2x=√y . Use implicit differentiation to find y’.
In: Math
A rectangular storage container with an open top is to have a volume of 22 cubic meters. The length of its base is twice the width. Material for the base costs 11 dollars per square meter. Material for the sides costs 6 dollars per square meter. Find the cost of materials for the cheapest such container.
Total cost = (?)
(Round to the nearest penny and include monetary units. For example, if your answer is 1.095, enter $1.10 including the dollar sign and second decimal place.)
In: Math
Solve the c, d, e, f from the given equations.
e+2f=-1
2d+e=-0.2
2c+d+3e+4f=-0.5
-e-2f=1
In: Math