F(x) is a piecewise function defined as:
f(x) = (3/2)x when 0 <= x <= 2
or
f(x) = -(3/2)x+6 when 2 < x <= 4
g(x) is defined as:
g(x) = -(1/4)x+1 when 0 <= x <= 4
Based on the graph or through the equations we can say:
f(1) = (3/2)*1 = 1.5
g(1) = -(1/4)*1+1 = 0.75
f(3) = (3/2)*3 = 4.5
g(3) = -(1/4)*3+1 = 0.25
And the derivative values are:
f ' (1) = 3/2 = 1.5
f ' (3) = -3/2 = -1.5
g ' (1) = -1/4 = -0.25
g ' (3) = -1/4 = -0.25
which are the slopes of each line
So...
h(x) = f(x)*g(x)
h ' (x) = f ' (x)*g(x) + f(x)*g ' (x) ... product rule
h ' (1) = f ' (1)*g(1) + f(1)*g ' (1)
h ' (1) = 1.5*0.75 + 1.5*(-0.25)
h ' (1) = 0.75
and,
h(x) = f(x)*g(x)
h ' (x) = f ' (x)*g(x) + f(x)*g ' (x)
h ' (3) = f ' (3)*g(3) + f(3)*g ' (3)
h ' (3) = -1.5*0.25 + 4.5*(-0.25)
h ' (3) = -1.5
Answer:
D 4/9 = 12/n
Step-by-step explanation:
sides that are 9 and n are hypotenuses of their triangles
sides that are 4 and 12 are bases of their triangles
Use the law of cosines to find the value of cos theta. round your answer to two decimal places.
The opposite side of the theta is 5.7. Adjacent to the theta is 9.8.
Hypotenuse is 10.2
A. 0.35
B. 0.23
☆☆☆☆☆☆☆☆☆☆☆☆☆☆C. 0.84
D. 1.23
Answer: the cost of 1 one-inch binder is $4
the cost of 1 three-inch binder is $7
Step-by-step explanation:
Let x represent the cost of 1 one-inch binder.
Let x represent the cost of 1 three-inch binder.
Jesse selected 3 one-inch binders and 3 two-inch binders, which cost a total of $33. This means that
3x + 3y = 33 - - - - - - - - - - 1
Luann selected 2 one-inch binders and 1 two-inch binder, which cost a total of $15. This means that
2x + y = 15 - - - - - - - - - - - 2
Multiplying equation 1 by 2 and equation 2 by 3, it becomes
6x + 6y = 66
6x + 3y = 45
Subtracting, it becomes
3y = 21
y = 21/3 = 7
Substituting y = 7 into equation 2, it becomes
2x + 7 = 15
2x = 15 - 7 = 8
x = 8/2 = 4
