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Question 366485: A parabola with an equation of the form y = ax^2 + bx + c has the point (-2, 1) as its vertex. If (-4, 5) also lies on the parabola, which of the following is
another point on this parabola?
(A) (-4, 3) (B) (-1, 3) (C) (0, 5) (D) (2, 1) (E) (4, 5)
Click here to see answer by Fombitz(32388)   |
Question 366556: Evening All,
Right its been a while since i have attempted maths, and have just gone back to further ed. I have attempted the following questions, which im sure should be simple, but of course like anything its just getting back into things after a number of years. i have listed the questions below, and my answers if anybody will take the time to have a quick look and correct me where neccessary i would appreciate this.
1)Find dy/dx by differentiating with respect to x the following expressions.
a) y=x^3-6x^2+9x-1 = 3x^2-12x+8
b) y=1/2x -sqrtx = 1/2-1/2x^-1/2
c) y=e^x-e^-x = e^x+e^-x
d) y=25cosx--sinx = -25sinx-cosx
e) y= 3sinhx-4coshx = 3hsinhx+4hsinhx
f) y= (x^2+1) sinhx = 1
2 Use product rule to obtain dy/dx for the following
a) y=x^2e^x = 2x(e^x)+x^2(e^x)
b) y= xtanx = 1(tanx)+x(sec^2x)
c) y= x^4ln(x)= 4x^3(ln(x))+x^4(1/x)
d) y= x^2sinx = 2x(sinx)+x^2(cosx)
e) y= e^-xcosx = -e^-x(cos x)+ e^-x (-sinx)
f) y=(x^2+1)sinhx = (2x +1) (sinhx)+(x^2+1)(cosh x)
Finally, use the quotient rule to differentiate with respect to x, simplifying as far as possible.
a) y= sinx/1+e^-x = 1+e^-x(cosx)-(1-e^x)sinx/(1+e^-x)^2
b) y= lnx/1+x^2 = 1+x^2(1/x)-1+2x(ln x)/(1+x^2)^2
Really this would be appreciated thank you
Click here to see answer by Alan3354(69443)  |
Question 366198: Evening All, Right its been a while since i have attempted maths, and have just gone back to further ed. I have attempted the following questions, which im sure should be simple, but of course like anything its just getting back into things after a number of years. i have listed the questions below, and my answers if anybody will take the time to have a quick look and correct me where neccessary i would appreciate this.
1)Find dy/dx by differentiating with respect to x the following expressions.
a) y=x^3-6x^2+9x-1 = 3x^2-12x+8
b) y=1/2x -sqrtx = 1/2-1/2x^-1/2
c) y=e^x-e^-x = e^x+e^-x
d) y=25cosx--sinx = -25sinx-cosx
e) y= 3sinhx-4coshx = 3hsinhx+4hsinhx
f) y= (x^2+1) sinhx = 1
2 Use product rule to obtain dy/dx for the following
a) y=x^2e^x = 2x(e^x)+x^2(e^x)
b) y= xtanx = 1(tanx)+x(sec^2x)
c) y= x^4ln(x)= 4x^3(ln(x))+x^4(1/x)
d) y= x^2sinx = 2x(sinx)+x^2(cosx)
e) y= e^-xcosx = -e^-x(cos x)+ e^-x (-sinx)
f) y=(x^2+1)sinhx = (2x +1) (sinhx)+(x^2+1)(cosh x)
Finally, use the quotient rule to differentiate with respect to x, simplifying as far as possible.
a) y= sinx/1+e^-x = 1+e^-x(cpsx)-(1-e^x)sinx/(1+e^-x)^2
b) y= lnx/1+x^2 = 1+x^2(1/x)-1+2x(ln x)/(1+x^2)^2
Really this would be appreciated thank you
Click here to see answer by user_dude2008(1862) |
Question 366198: Evening All, Right its been a while since i have attempted maths, and have just gone back to further ed. I have attempted the following questions, which im sure should be simple, but of course like anything its just getting back into things after a number of years. i have listed the questions below, and my answers if anybody will take the time to have a quick look and correct me where neccessary i would appreciate this.
1)Find dy/dx by differentiating with respect to x the following expressions.
a) y=x^3-6x^2+9x-1 = 3x^2-12x+8
b) y=1/2x -sqrtx = 1/2-1/2x^-1/2
c) y=e^x-e^-x = e^x+e^-x
d) y=25cosx--sinx = -25sinx-cosx
e) y= 3sinhx-4coshx = 3hsinhx+4hsinhx
f) y= (x^2+1) sinhx = 1
2 Use product rule to obtain dy/dx for the following
a) y=x^2e^x = 2x(e^x)+x^2(e^x)
b) y= xtanx = 1(tanx)+x(sec^2x)
c) y= x^4ln(x)= 4x^3(ln(x))+x^4(1/x)
d) y= x^2sinx = 2x(sinx)+x^2(cosx)
e) y= e^-xcosx = -e^-x(cos x)+ e^-x (-sinx)
f) y=(x^2+1)sinhx = (2x +1) (sinhx)+(x^2+1)(cosh x)
Finally, use the quotient rule to differentiate with respect to x, simplifying as far as possible.
a) y= sinx/1+e^-x = 1+e^-x(cpsx)-(1-e^x)sinx/(1+e^-x)^2
b) y= lnx/1+x^2 = 1+x^2(1/x)-1+2x(ln x)/(1+x^2)^2
Really this would be appreciated thank you
Click here to see answer by Fombitz(32388) |
Question 366578: We want to set up a business so that the minimum cost occurs when we make 13,000 items per hour at a cost of $21 per item. We also know that if we make 9,000 items per hour the cost per item is $24.
Create a quadratic equation that represents the situation. Give you final answer in the form y=ax^2+bx+c
I cannot figure out how to write anything in this form. I don't understand which each letter stands for.
Click here to see answer by jim_thompson5910(35256) |
Question 366738: I am doing quadratic equations, the problem is  I understand most of it except for when I get to where the problem says x = -1 sqrt(47)/2 I don't know what to do with the square root symbol. I know how to find the vertex but I don't have the roots to graph the parabola, If some one could help me with this I would be grateful.
Click here to see answer by Alan3354(69443) |
Question 366738: I am doing quadratic equations, the problem is I understand most of it except for when I get to where the problem says x = -1 sqrt(47)/2 I don't know what to do with the square root symbol. I know how to find the vertex but I don't have the roots to graph the parabola, If some one could help me with this I would be grateful.
Click here to see answer by jim_thompson5910(35256) |
Question 366613: a punter, punts the football at the 40 yard line at the equation of y=-0.008x^2+2.5x+1. I know how to graph a linear function starting at a cirtain point, how would you graph a quadratic function from the 40 yard line?
Click here to see answer by edjones(8007)  |
Question 366785: Suppose you are an event coordinator for a large performance theater. One of the hottest new Broadway musicals has started to tour and your city is the first stop on the tour. You need to supply information about projected ticket sales to the box office manager. The box office manager uses this information to anticipate staffing needs until the tickets sell out. You provide the manager with a quadratic equation that models the expected number of ticket sales for each day x. ( is the day tickets go on sale).
a. Does the graph of this equation open up or down? How did you determine this?
b. What is the number of tickets sold on the 10th day? The 20th day? The 40th day? The 50th day?
c. Use the quadratic equation to determine the last day that tickets will be sold.
Note. Write your answer in terms of the number of days after ticket sales begin.
d. After how many days will the maximum or minimum occur?
e. How many tickets will be sold on the day when the maximum or minimum occurs?
f. What are the coordinates of the vertex? How does this number relate to your answers in parts d and e?
g. How many solutions are there to the equation ? How do you know?
h. What do the solutions represent? Explain.
Click here to see answer by mananth(16946)  |
Question 366786: can you tell me if these are right if not can you help me out with them please.
Hint: Pay attention to the units of measure. You may have to convert from feet to miles several times in this assignment. You can use 1 mile = 5,280 feet for your conversions.
1. Many people know that the weight of an object varies on different planets, but did you know that the weight of an object on Earth also varies according to the elevation of the object? In particular, the weight of an object follows this equation: , where C is a constant, and r is the distance that the object is from the center of Earth.
a. Solve the equation for r, and then solve the equation for C.
Multiply both sides by r^2 to get:
wr^2 = C
r^2 = C/w
r = sqrt[C/w]
b. Suppose that an object is 160 pounds when it is at sea level. Find the value of C that makes the equation true. (Sea level is 3,963 miles from the center of the Earth.)
C=160*3963^2=40205744640
c. Use the value of C you found in the previous question to determine how much the object would weigh in
i. Death Valley (282 feet below sea level).
Distance from center = 3963 - (282/5280) = 3962.946591 miles = 20,924,358 ft
w=Cr^-2
w = 1570536900*3962.946591^-2= 100.0026954 miles
ii. The top of Mount McKinley (20,320 feet above sea level).
3963+ (20320/5280) = 3966.848484848485 miles
2. The equation gives the distance, D, in miles that a person can see to the horizon from a height, h, in feet.
a. Solve this equation for h.
1.2*Sqrt (h) = D
:
Sqrt(h) = ; Divided both sides by 1.2
h = ; Squared both sides
b. Mauna Kea in Hawaii is 13,796 feet in elevation. How far can you see to the horizon from the top of Mauna Kea? Can you see Waikiki beach, Honolulu (about 198 miles away)? Explain your answer.
13796/5280=2.6 miles
D=1.2 sprt (2.6)= 1.2*
Click here to see answer by stanbon(75887) |
Question 366798: The height (t) in feet above the ground, of a ball thrown into the air from the top of a building is given by the function of h(t)= -16(t-2)^2+264, where t is the number of seconds the ball has been in the air.
a. From what height was the ball thrown?
b. what height does the ball reach?
c. when does the ball strike the ground?
e. for what values of t does the function have meaning?
Click here to see answer by Alan3354(69443) |
Question 366861: The number of tickets sold each day for an upcoming performance of handel's Messiah is givn by N(x)=-0.4x^2+10.4x+10 where x is the number of days since the concert was first announced. When will daily sales peak and how many tickets will be sold that day? Pleas show work Thank you
Click here to see answer by josmiceli(19441)  |
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