Answer:
Step-by-step explanation:
If y = 2x + 1, then dy/dt = 2(dx/dt).
If y = 2x + 1, then y = 2(40) + 1 when 40 is substituted for x. y = 81.
(a) if dx/dt = 3, find dy/dt when x = 4:
Replacing dx/dt with 3 in dy/dt = 2(dx/dt) yields dy/dt = 2(3) = 6.
(b) if dy/dt = 2, find dx/dt when x = 40:
Replacing dy/dt with 2 in dy/dt = 2(dx/dt) results in 2 = 2(dx/dt), so dx/dt must be 1.
The graph has a y-intercept of 2 and is shifted to the right 6 from the parent function.
The parent function, y=√x, looks like a parabola laid on its side. We generally only consider the positive square root unless told otherwise. Since we have √(x-6) instead of just √x, the graph is shifted to the right 6 units. The +2 at the end of the equation shifts the graph up 2.
The values of x are 2 and -1.
Solving the equation created by substitution listed in the question:
-2x+14=x²-3x+12
Add 2x to both sides:
-2x+14+2x=x²-3x+12+2x
14=x²-1x+12
Subtract 14 from both sides:
14-14=x²-1x+12-14
0=x²-1x-2
Factoring this, we want factors of -2 that sum to -1; -2(1) = -2 and -2+1=-1:
0=(x-2)(x+1)
Using the zero product property, we know that either x-2=0 or x+1=0:
x-2=0
x-2+2=0+2
x=2
x+1=0
x+1-1=0-1
x=-1
Answer:
A) (-3, 5)
General Formulas and Concepts:
<u>Algebra I</u>
- Solving systems of equations by graphing
Step-by-step explanation:
The solution set to any systems of equations is where the 2 lines intersect. According to the graph, we see that the 2 lines intersect at (-3, 5). Therefore, our answer is A.
Answer:
Step-by-step explanation:
We use trig to answer these questions:
sin x = opposite side of a triangle / hypotenuse
cos x = adjacent side / hypotenuse
Construct a right triangle with hypotenuse 4 m and lower angle 68 degrees.
The height of the top of the ladder is then defined by:
sin 68 degrees = height / 4 m, which yields (4 m)(sin 68) = height =
3.71 m
and the distance of the bottom of the ladder from the wall as follows:
cos 68 degrees = horizontal distance / hypotenuse =
1.50 m
