Questions on Algebra: Introduction to vectors, addition and scaling answered by real tutors!

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Question 199662: Given f(x)=(ax)/(x^2+b), a≠0, b≠0. Find a and b such that f’(1)=0 and f’(0)=2.
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Question 199657: Differentiate each function. Express all final answering simplified factored form, positive exponents, and with radical notation where possible.
a) y=log_7(4x^2+2)^4
b) f(t)=-3t^(2pi-1)
c) y=x^(√x)
d) y=(3x^7)e^(7x)
e) y=(3x)^(2x)
f) y=(cosx)/(4+sinx)
g) y=In(x^3+e^x)

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Question 199655: The polynomial function f(x)=(0.001x^3)-(0.12x^2)+3.6x+10, 0≤x≤75, models the shape of a roller coaster track, where f is the vertical displacement of the track and x is the horizontal displacement of the track. Both displacements are in meters. Determine the absolute maximum and minimum heights along this stretch of track.

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Question 199962:
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Question 203575: I am in summer school and i was wondering how you would do this problem..
The directions are to simplify:
(xy^7)(x^4y)/(x^5y^2)^2
and how would i add this equation:
x-3/x^2+7x+12 + x-5/x^2-16
please and thank you in advance!

Click here to see answer by stanbon(75887) About Me 

Question 204887: Hi all, Im still having trouble with these vector problems, I cant solve the problems listed below for the following:
Let ~u = 3~i - ~j - 2~k and ~v = 2~i + ~j + ~k.(Again, the ~ symbols mean that there is and arrow symbol above the value in the positive direction)
I need to:
a) Find the corresponding unit vectors for ~u and ~v
b) Calculate the dot product of the angle between ~u and ~v.
Some help with steps and explanations on how to solve would be great.
Thanks, -Nick.

Click here to see answer by Alan3354(69443) About Me 

Question 205178: Hi all, can anyone please show me how to; Find the equation of the line that contains points (2,1,-3) and (-1,4,1)
Would really appreciate if someone could show me with steps and notes.
Thanks, -Nick

Click here to see answer by Edwin McCravy(20054) About Me 

Question 205201: Hi all, I dont quite understand what this questions is asking:
Determine whether the following functions y = xsin3x, y+=+x%2Asin%283x%29, y+=+x%5E2+%2B+e%5Ex, y+=+x%5E3%2Acosx are even, odd or none of these.
Can anyone help me with solving it and explain how to do it please?
Thanks, -Nick.

Click here to see answer by Edwin McCravy(20054) About Me 

Question 205587: Hi all, I am still struggling a bit with this vectors stuff, hopefully I willahve it sorted after learning how to solve the following:
I need to calculate 2~u + ~v - 5~w, if ~u = 3~i + 2~j - 7~k, ~v = 5~i - 2~j + 4~k and ~w = 3~i + 2~j - 4~k.
(Agian the ~ symbols refer to arrows in the positive direction above the values shown)
Thnaks, -nick.

Click here to see answer by Alan3354(69443) About Me 

Question 205585: Hi all, I cant seem to get this next problem sorted. I need to find the direction cosines of the vector:
~w = 2~i - ~j + 5~k.
(Again, the ~ symbols refer to arrows in the positive direction above each value, with ~ in-between referring to the arrow being above both values together)
Any help with notes would be really good.
Thanks, -Nick.

Click here to see answer by Alan3354(69443) About Me 

Question 205755: 12x + 71 > 27
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Question 206221: Hi all, can anyone please show me how to do the following question?
Determine whetherher the following line [(x-3)/5] = [(y+1/-2] = [(x-3)/4] contains the point (3, -1, 1).
Steps and notes on how to solve would be really helpful.
Thanks, -nick

Click here to see answer by Alan3354(69443) About Me 

Question 206228: Hi all, can anyone help me with the following?;
Find a unit vector in the direction of (3,1,2) and one in the opposite direction. How do you do this?
Thanks, -nick

Click here to see answer by Theo(13342) About Me 

Question 206224: Hi again, hopefully someone can help me with the follwoing question,
Find an equation of the line intersection of the two planes:
x+2y-z = -1 and 3x-2y+5z = 5
Any help would be most appreciated.
-nick

Click here to see answer by Alan3354(69443) About Me 

Question 206220: Hi all, I was hoping someone could help me answer the followingl; I need to show that the lines:
[(x-2)/5] = [(y+3)/-3] = [(x-5)/2] and [(x-3)/4] = [(y-2)/6] = [(z-10)/-1] are orthagonal.
Im not sure how to do this so some help with steps and explanations would most appreciated.
Thanks, -nick

Click here to see answer by Alan3354(69443) About Me 

Question 206413: Hi all, I was hoping someone could show me how to solve the following,
Find the equation of the line that contains points (2,1,-3) and (-1,4,1)
Help with steps on how to solve would be great,
Thanks, -nick.

Click here to see answer by Edwin McCravy(20054) About Me 

Question 206412: Hi all, can anyone show me how to do the following? Show that the lines
[(x-2)/5] = [y+3/-3] = [(z-5)/2] and [(x-3)/4 = [(y-2)/6] = [(z-10)/1]
are orthagonal.
Would be very hwlpful,
Thnaks, -nick.

Click here to see answer by Alan3354(69443) About Me 

Question 206411: Hi all, I am still having trouble with the following problem.
An object travels which velocity (3,1,2)
a) What is the speed of the object?
b) The object slows to speed 2 without changing direction. Give its velocity vector.
Thanks, -Nick.

Click here to see answer by Alan3354(69443) About Me 

Question 207531: Given the vectors v = -2i + 5j and w = 3i + 4j, determine
#1 1/2 v
#2 w - v
#3 length of w
#4 the unit vector for v

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Question 210653: Hi I am having trouble with the following problem.
Determine whether the following two planes 4x+y-z=3 and 2x-5y+3z=2 are parallel, orthogonal, coincident (that is, the same) or none of these?
Help with this would be much appreciated.
Thanks, Judy

Click here to see answer by Alan3354(69443) About Me 

Question 210652: Hi I am having trouble with the following problem.
Determine whether the following two planes 4x+y-z=3 and 2x-5y+3z=2 are parallel, orthogonal, coincident (that is, the same) or none of these?
Help with this would be much appreciated.
Thanks, Judy

Click here to see answer by DRichardson(63) About Me 

Question 211420: could anyone help me with this qustion please.
find delta y/delta x, give the following iformation.
a) y=1/x, x=3, delta x=0.01
b) y=squrut x, x=9, delta x=0.9

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Question 212412: please could someone help me with this question?
A tea connoisseur has a collection of teapots that are scaled versions of the same design. The one-cup teapot is 10cm high. Choose the TWO options that are true statements.
A The two-cup teapot is 20cm high
B The eight-cup teapot is 20cm high.
C The nine-cup teapot is 30cm high.
D The 25cm high teapot is appropriate to make 20 cups of tea.
E The 16cm teapot is appropriate to make 4 cups of tea.
Thank you very much
Dawn

Click here to see answer by vleith(2983) About Me 

Question 212712: Wrongly called for a foul, an angry basketball player throws the ball straight down to the floor. If the ball bounces straight up and returns to the floor 2.7 after first striking it, what was the ball's greatest height above the floor?
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Question 214134: Use pythagorean therom to find the distance between (5,3) and(-2,-3).
Can you give me a step by step of this promblem

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Question 220585: My algebra 2 review sheet has problems and there directed as. Add, Subtract or Multiply as indicated
this is one of the problems
1.(9x3-4+x2+8)-(7x3-3x+7)
The x's in in the first equation is x to the qubed and x squared, on the second equation 7x, that suppose to be qubed too.
sorry this maybe confusing and im soooo sorry! i just dont understand.

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Question 227431: Let v=3i+2j-2k
Find the equation of the plane containing vector v and point (0,3,2).

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Question 227981: Let u=i-2j+4k
Find the equation of the plane that has a normal u and contains a point (2,3,4).
Thanks, Judy

Click here to see answer by Alan3354(69443) About Me 
Question 227981: Let u=i-2j+4k
Find the equation of the plane that has a normal u and contains a point (2,3,4).
Thanks, Judy

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Question 232927: solve by substitution 4x+5y= -9
-2x+y=15 what is the solution set , I came up with (-2,4) am I right

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Question 232929: solve by substitution 5x-3y= -43
-8x+y=66 what is the solution set I came up with ( -8,3) am I right

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Question 204119: Find the component form of v given its magnitude and the angle it forms with the positive x axis. Magnitude of v is 3, and the direction is 3i+4j.

Steps would be appreciated as well

Click here to see answer by Alan3354(69443) About Me 

Question 184782: Differentiate
+h%28x%29+=+%281%2F%28%28SQRTx%29%2B1%29%29+

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Question 244229: 10x-25+10x+3x^2+2x^2=360
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Question 252815: How do u find the resultant vector's magnitude as well as anlge using 5.0 m/s, 45 deg + 2.0 m/s, 180 deg
the ansner is = 3.85m/s, 66.5 deg but i would like to know how to do it and the formula you have used

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Question 253096: 1.Determine whether -3.5 is a solution of the inequality. x>-6.

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Question 258177: how do you figure 3-4(x-2)=3(3-x)
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Question 259557: the area of a square, expressed in square inches, is 165 in inches greater than its perimeter, expressed in inches. what is the length of a side of the square?
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Question 261228: -6=-(x-5)-3(5+2x)-4(2x-4)
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Question 261383: Problem Solving:

In the excercise 33-50 (a) translate the argument into symbolic form and (b) determine if the argument is valid or invalid. You may compare the argument to a standard form or use a truth table.

#38
We will go for a bike ride or we will go shopping.
We will not go shopping.
--------------------------------------------------------------------------
.
.. We will go for a bike ride.

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Question 265926: can you slove 5x-2y=-20
-4x+y=7?
please.

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Question 275163: What is the magnitude of the vector: v = 5i + 6j ?
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Question 278382: Give the rectangular coordinates: (-3, -120°).
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Question 278382: Give the rectangular coordinates: (-3, -120°).
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Question 278381: Give the polar coordinates: (4, 0).
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