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Question 1191133: A school club makes and sells decorations to raise money. The materials for each decoration cost
$6, and the club sells them for $10 each. They sell 20 decorations per week. They are considering
raising the price, so they conduct a survey and find that for every dollar increase, they will lose 2
sales per week. Set up a function and solve to determine what price they should charge to maximize
profits.
Click here to see answer by Boreal(15235)

Question 1191207: The function f is of the form f(x) = (ax + b) / (2x + c), for x ≠ -(c/2), where a, b, and c ∈ ℤ. Given that the graph of y = f(x) has asymptotes x = -5 and y = 2, and that the point P(1, -1/12) lies on the graph, what are the values of a, b, and c?
Click here to see answer by math_tutor2020(3817)

Question 1190858: Find the derivative for y=6/(5x-4)^2 and 3√2x^3-x^2
Click here to see answer by Alan3354(69443)

Question 1191562: A car moving at a constant speed passed a timing device at t0. After seconds, the car has traveled ft. Write a linear function rule to model the distance in feet d the car has traveled any number of seconds t after passing the timing device.
Click here to see answer by ikleyn(52794)

Question 1191974: Let f(x) =2x-3 find f-1, ff-1(x), ff-1(4)
Click here to see answer by Solver92311(821)

Question 1191974: Let f(x) =2x-3 find f-1, ff-1(x), ff-1(4)
Click here to see answer by greenestamps(13200)

Question 1192069: 2x^2+x+5
Click here to see answer by ikleyn(52794)

Question 1192133: the parabola y=2x^2 is translated to a new parabola with x intercepts 4 and -3. The y-intercept of the new parabola is
a.12
b.-12
c.-0.5
d.-24
Click here to see answer by ikleyn(52794)

Question 1192281: Suppose y = a/√1+bx where a and b are constants. When x=3, y=1 and dy/dx = -1/8. Find a and b.
Click here to see answer by MathLover1(20850)

Question 1192279: The gradient/slope of a function of f(x) = (2x-b)^a is f'(x) = 24x^2-24x+6, find the constant a and b. I'm a confused on how to start on this.
Click here to see answer by ikleyn(52794)

Question 1192342: Find the values of such that f(x) = x^2y=√x^2+a and f'(-2) = -34/3
Click here to see answer by greenestamps(13200)

Question 1192341: Find the value for of x for which the tangent to f(x) = ax√1-x has gradient
a. 0
b. a
Click here to see answer by greenestamps(13200)

Question 1192340: Consider y=√x(3-x)^2.
Show that dy/dx = (3-x)(3-5x)/2√x
Next find the x-coordinates of all points on y=√x(3-x)^2. where the tangent is horizontal.
Click here to see answer by greenestamps(13200)

Question 1192374: Given the transformation (x,y) ⏩ (x,2x+y), determine the equation of the line 3x+5y-30=0 after it undergoes this transformation
Click here to see answer by greenestamps(13200)

Question 1192363: list all the ordered pairs in the relation r = (a,b)|a)^2 divides b} on the set {x|x is a positive integer less than or equal to 10}
Click here to see answer by greenestamps(13200)

Question 1192398: Find the values of a such that f(x) = x^2y(√x^2+a) and f'(-2) = -34/3
Click here to see answer by Solver92311(821)

Question 1192397: Find the value for of x for which the tangent to f(x) = ax(√1-x) has gradient
a. 0
b. a
Click here to see answer by Solver92311(821)

Question 1192465: Find another tangent to y=1-3x+12x^2-8x^3 which is parallel to the tangent at (1,2).
Click here to see answer by Alan3354(69443)

Question 1192491: Find the equation of the tangent to;
f(x) = e^-x at the point where x=2.
So I know dy/dx=-1/e^x, but don't understand how I can sub that x value in the original equation and find the y value.
Click here to see answer by ikleyn(52794)

Question 1192494: find where the tangent to the curve y=x^3 at the point where x=2, meets the curve again
Click here to see answer by greenestamps(13200)

Question 1192564: Two verticies of a rectangle are on the x-axis and the other two vertices on the curve y=8/(x^2+4). Find the maximum area of the rectangle.
I did find y'=-16x/(x^2+4)^2. I couldn't figure out what do afterwards, I did try setting this to zero, but that isn't correct.
Click here to see answer by ikleyn(52794)

Question 1192568: The height of the Pinus sylvestris is given by:
H=35-172.5/(t+5) meters, where t is the number of years after the tree was planted from an established seedling.
b. Find the height for the tree after 4 years.
Click here to see answer by ikleyn(52794)

Question 1192587: A stone is thrown vertically upward from a 20 foot platform at a rate of 160 ft per second. The height is the stone is modeled by the quadratic function f(x)=-16t^2+160t+20
a)how long will it take for the stone to reach its maximum height?
b)what is the maximum height of the stone?
c)how long will it take for the taco to hit the ground?
Click here to see answer by ikleyn(52794)

Question 1192588: A stone is thrown vertically upward from a 20 foot platform at a rate of 160 ft per second. The height of the stone is modeled by the quadratic function f(t)=-16t^2+160t+20
a)how long will it take for the stone to reach its maximum height?
b)what is the maximum height of the stone?
c)how long will it take for the stone to hit the ground
Click here to see answer by ikleyn(52794)

Question 1192589: A stone is thrown vertically upward from a 20 foot platform at a rate of 160 ft per second. The height of the stone is modeled by the quadratic function f(t)=-16t^2+160t+20
a)how long will it take for the stone to reach its maximum height?
b)what is the maximum height of the stone?
c)how long will it take for the stone to hit the ground
Click here to see answer by ikleyn(52794)

Question 1192565: Find the stationary point on the curve y = sinx-0.5x for o < x < π and justify that it is a local maximum.
Click here to see answer by ikleyn(52794)

Question 1192490: Consider the curve (a√1-bx) where a and b are constants. The tangent to this curve at the point where x=-1 is 3x+y=5. Find the values of a and b.
Click here to see answer by KMST(5328)

Question 1192640: The volume of water, v million cubic meters in a lake t ours after a storm is modelled by V = 2te^-t+5
a. What is the initial volume of the lake and he maximum volume of the lake.
b. When is the lake emptying the fastest.
Click here to see answer by Alan3354(69443)

Question 1192678: A curve has gradient function f'(x) = ax+1 where a is constant. Find f(x) given that f(0) = 3 and f(3) = -3.
Click here to see answer by ikleyn(52794)

Question 1192700: The volume of water, v million cubic meters in a lake t ours after a storm is modelled by V = 2t(e^-t)+5
a. What is the initial volume of the lake and he maximum volume of the lake.
b. When is the lake emptying the fastest.
Click here to see answer by Alan3354(69443)

Question 1192762: y=4x^2+4x+9
Click here to see answer by josgarithmetic(39618)

Question 1192803: The first three terms of a geometric sequence are lnx^16, lnx^8, lnx^4, for x>0. Find the common ratio.
Click here to see answer by ikleyn(52794)

Question 1192803: The first three terms of a geometric sequence are lnx^16, lnx^8, lnx^4, for x>0. Find the common ratio.
Click here to see answer by greenestamps(13200)

Question 1192812: A ball is thrown from 1 m above ground level. It's velocity is v(t) = 29.4-9.8t ms^-1.
a. Find the displacement function s(t) (I found this: 29.4-4.9t^2+1
b. Find the maximum height reached by the ball (need help in this).
Click here to see answer by Boreal(15235)

Question 1192910: Let x ⧪ y = 2x/y . Suppose (a ⧪ b)⧪c − a ⧪ (b ⧪ c) = a, where a, b and c are
nonzero integers. What is the sum of all possible positive values of c?
Can I get help on this please? Trying to understand how to solve this? Thank you for your help and time.
Click here to see answer by math_tutor2020(3817)

Question 1192924: Given that f(x)=-3x+7
Find (f+h)-f(x)/h
Click here to see answer by math_tutor2020(3817)

Question 1192924: Given that f(x)=-3x+7
Find (f+h)-f(x)/h
Click here to see answer by josgarithmetic(39618)

Question 1192944: For a certain company, the cost function for producing x items is C(x)=50x+100 and the revenue function for selling x items is R(x)=−0.5(x−110)2+6,050. The maximum capacity of the company is 170 items.
Click here to see answer by ikleyn(52794)

Question 1192968: Find f[f(-3)] when f(x) = x^2 + 1. Is this the same as f(f(x))?
Click here to see answer by josgarithmetic(39618)

Question 1192968: Find f[f(-3)] when f(x) = x^2 + 1. Is this the same as f(f(x))?
Click here to see answer by ikleyn(52794)

Question 1192948: For a certain company, the cost function for producing x items is C(x)=50x+100 and the revenue function for selling x items is R(x)=−0.5(x−110)2+6,050. The maximum capacity of the company is 170 items.

The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost function C(x) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit!

Answers to some of the questions are given below so that you can check your work.

Assuming that the company sells all that it produces, what is the profit function?
P(x)=
Preview Change entry mode .
Hint: Profit = Revenue - Cost as we examined in Discussion 3.
What is the domain of P(x)?
Hint: Does calculating P(x) make sense when x=−10 or x=1,000?
The company can choose to produce either 60 or 70 items. What is their profit for each case, and which level of production should they choose?
Profit when producing 60 items =
Number

Profit when producing 70 items =
Number

Can you explain, from our model, why the company makes less profit when producing 10 more units?
Click here to see answer by ikleyn(52794)

Question 1193172: Find the domain of the function f(x)=4/(x-9)-√(x^2-36)

Click here to see answer by MathLover1(20850)

Question 1193178: A rectangle is inscribed in a circle of radius r. If the rectangle has a length of 3x, write the area of the rectangle as a function of both x and r
Click here to see answer by greenestamps(13200)

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