equation of any straight line is ... y=mx+b ... m=slope, b=y intercept
dy/dx = f'(x) is the slope at any point and is also the slope of the tangent line. Thus m = f'(x). Now if you know the point (x1,y1) and the slope you can find b by substituting the x1,y1 values of...

d/dx etanx= sec2x *etanx

Draw a horizontal line representing a level plane. Draw another line at an incline to the first and label the angle between the horizontal and the incline as
Theta.
Draw a box on the incline representing the car, add a vertical arrow from the centroid of the box pointing down...

From the given information, one way to proceed is to calculate the slope between each of the four points. If the slope is a constant then look for a constant y-intercept among the four points. If both the slope and y-intercept is constant, the points are all on the same line.
slope = (y2-y1)/(x2-x1)...

Since the area of a rectangle is related to it's length times width (A = L*W), then that formula can be rearranged to show that the width is the Area divided by the Length (W=A/L). So:
W = 20r5s7t4/4r2s5t2 (substitute the given expressions for A and L)
W = 20*5*7*4*r*s*t / 4*2*5*2*r*s*t...

There is missing information for this problem. We need information regarding the initial line in order to compare the final line and the initial line.
a) If I were to create some information about the initial line so that the (slope, y-intercept) is (0,0), then we can say that the initial...

It seems like some of the question has been lost as there is not enough information to establish an appropriate response. However, if I take the liberty of adding to the problem statement the below formula:
V = pi * r^2 *h
then we can say that V (volume) is dependent upon radius and height...

Just taking the wording of the question and breaking it apart will lead you to the right answer.
1) If rain is causing car washes, rain is related to the INDEPENDENT VARIABLE and "... the more
often it rains ... ", the word often is indicating a frequency of rain. So,...

The best way to deal with these problems is to first make a sketch. The sketch should look like a triangle with the wall on the left of height (h), the ground at the bottom with the ladder forming the diagonal starting at the top of the wall and touching the ground at distance (d) from the wall. The...

Let's define some variables
1) V = volume of water the radiator can hold = 3.6L
2) CWinter = concentration of antifreeze for Winter = 65% = .65*3.6 = 2.34L
2a) Concentration of water in Winter = 100-65 = 35% = .35*36 = 1.26L
3) CSummer = concentration of antifreeze for Summer = 50% = .50*3.6 = 1...

Proportions are ratios. A ratio is simply one dimension divided by another. Example is Width/Length. Mrs. Stearns most likely wishes the Width/Length ratio for her new photocopy to stay the same as old one.
1) Width (old)/Length (old)= Width (new)/Length (new)...this is the form of the calculation...

1) Given: 2x-2= 4x+6
a) Add 2 to both sides of equation.
b) 2x-2+2=4x+6+2
c) Simplify to get 2x=4x+8
d) Now get rid of the 4x on the right by subtracting 4x from both sides.
e) 2x-4x=4x+8-4x
f) Simplify to get -2x=8
g) Now get rid of the -2...

Use a step by step approach and it helps to number the lines.
1) Given:4x + 13y = 40
2) Given:4x + 3y = -40
3) Modify one of the equations to express one of the variables (x or y) in terms of the other. Line 1) can be re-arranged to the form below.
4) x=10-13/4y
5) Substitute the expression for x...

The quadratic formula provides a step by step means to find the roots of a second order polynomial of the form Ax^2+Bx+C=0. It always works the same way and is easy to follow. The quadratic formula calculates 2 roots x1 & x2, often written x1,2 x1=(-B+SQRT(B^2-4AC))/2A. X2=(-B-S...

This can be simplified by first multiplying through with -2 changing the expression to -2x+18-x. This can be further simplified by adding the -2x term to the -x term forming -3x thus changing the entire expression to 18-3x. Much easier to use!

It would look like a house from the front with a peaked roof and two parallel walls. The roof is two lines, the floor a third, the two walls totalling five.

The A=bh looks like Area = Base X Height which is the formula for the area of a rectangle (or parallelogram). Assuming that then the Area is given as 45 and the Base is given as 15, the Height could then be found as 45/15=3.