Thinking about the graph of f(x), the rate of change is zero whenever there is an extremum.
First, differentiate f(x)
Next, find the zeros of f'(x) by factoring.
Now, we substitute these x-values into the
original equation to find the coordinates.
(-2.667, 11.481), (0, 2)
Sin³ x-sin x=cos ² x
we know that:
sin²x + cos²x=1 ⇒cos²x=1-sin²x
Therefore:
sin³x-sin x=1-sin²x
sin³x+sin²x-sin x-1=0
sin³x=z
z³+z²-z-1=0
we divide by Ruffini method:
1 1 -1 -1
1 1 2 1 z=1
-------------------------------------
1 2 1 0
-1 -1 -1 z=-1
--------------------------------------
1 1 0 z=-1
Therefore; the solutions are z=-1 and z=1
The solutions are:
if z=-1, then
sin x=-1 ⇒x= arcsin -1=π+2kπ (180º+360ºK) K∈Z
if z=1, then
sin x=1 ⇒ x=arcsin 1=π/2 + 2kπ (90º+360ºK) k∈Z
π/2 + 2kπ U π+2Kπ=π/2+kπ k∈Z ≈(90º+180ºK)
Answer: π/2 + Kπ or 90º+180ºK K∈Z
Z=...-3,-2,-1,0,1,2,3,4....
25 ÷ (6 - 1) = 25 ÷ 5 = 5, she saved 5 nickels,
5 nickels = 5 × 5 = 25 cents = $0.25
5 + 25 = 30, she saved 30 dimes, 30 dimes = 300 cents = 3 dollars.
3 + 0.25 = $3.25, she saved $3.25 in all.
Answer:
135 square feet.
Step-by-step explanation:
A triangular prism. The rectangular sides are 8 feet by 2.5 feet, 8 feet by 6 feet, and 8 feet by 6.5 feet. The triangular sides have a base of 2.5 feet and a height of 6 feet.
The prism has two triangular faces and three rectangular faces.
So, the surface area of the prism will be
= 15 + 20 + 48 + 52
= 135 square feet. (Answer)
Segment JI is a midsegment (given). So that means point J is a midpoint of segment HF. The midpoint cuts HF into two equal pieces. Those two pieces are HJ and JF. Therefore, HJ = JF
Using substitution, we can plug in the given expressions that the diagram shows. Then we can solve for x
HJ = JF
2x-3 = x+2
2x-3+3 = x+2+3
2x = x+5
2x-x = x+5-x
x = 5
Now that we know x = 5, use this to find the length of HG
HG = 11*x + 5
HG = 11*5 + 5
HG = 55 + 5
HG = 60
So HG is 60 inches long, which is the final answer
Note: 60 inches = 5 ft
