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zimovet [89]
3 years ago
15

The surface area of a right cone is 400.2 m2. The radius of the cone is 6.0 m. Determine the height of the cone to the nearest m

etre.
Mathematics
1 answer:
svetoff [14.1K]3 years ago
8 0
                 S = πr(r + √(h² + r²))
          400.2 = 3.14(6)(6 + √(h² + 6²))
          400.2 = 18.84(6 + √(h² + 36))
          18.84                 18.84
        21¹⁰⁹/₄₇₁ = 6 + √(h² + 36))
        - 6         - 6
        15¹⁰⁹/₄₇₁ = √(h² + 36)
231²²¹⁰⁰⁵/₂₂₁₈₄₁ = h² + 36
- 36                       - 36
195²²¹⁰⁰⁵/₂₂₁₈₄₁ = h²
                14 ≈ h
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Find the x-coordinates where f '(x) = 0 for f(x) = 2x - sin(2x) in the interval [0, 2π].
Serggg [28]

Answer:

The x-coordinates where f '(x) = 0 for f(x) = 2x - sin(2x) in the interval [0, 2π] are: x=0, π, and 2π.


Step-by-step explanation:

f(x)=2x-sin(2x)

f'(x)=[f(x)]'

f'(x)=[2x-sin(2x)]'

f'(x)=(2x)'-[sin(2x)]'

f'(x)=2-cos(2x) (2x)'

f'(x)=2-cos(2x) (2)

f'(x)=2-2 cos(2x)


f'(x)=0, then:

2-2 cos(2x)=0

Solving for x. First solving for cos(2x): Subtracting 2 from both sides of the equation:

2-2 cos(2x)-2=0-2

-2 cos(2x)=-2

Dividing both sides of the equation by -2:

-2 cos(2x) / (-2)=-2 / (-2)

cos(2x)=1

If cos(2x)=1, then:

2x=2nπ

Dividing both sides of the equation by 2:

2x/2=2nπ/2

x=nπ


If n=-1→x=-1π→x=-π, and -π is not in the interval [0,2π], then x=-π is not in the solution.

If n=0→x=0π→x=0, and 0 is in the interval [0,2π], then x=0 is in the solution.

If n=1→x=1π→x=π, and π is in the interval [0,2π], then x=π is in the solution.

If n=2→x=2π, and 2π is in the interval [0,2π], then x=2π is in the solution.

If n=3→x=3π, and 3π is not in the interval [0,2π], then x=2π is not in the solution.


Solution: x=0, π, and 2π.

5 0
3 years ago
A record album is 3/16 of an inch thick. How many albums can be stacked to fit in a box 12 inches high? Please show me how you g
german
Hope this was helpful

5 0
3 years ago
2) The distance between Janet's home and her office is represented on the map with a scale factor of 1 inch = 5.6 miles. If the
SpyIntel [72]

Hey there! I"m happy to help!

We see that 1 inch is equal to 5.6 miles for this scale factor. If we have three inches, we simply multiply 5.6 by 3 to figure out how many miles this is!

5.6(3)=16.8

Therefore, Janet's home is 16.8 miles from her office.

Have a wonderful day! :D

5 0
2 years ago
The coordinates of point 7 are given. The midpoint of ST is (5. - 8). Find the coordinates of point S.
Mamont248 [21]

Answer:

S(0, 2)

Step-by-step explanation:

Midpoint Formula: (\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )

Step 1: Plug in known variables

5 = (10 + x)/2

-8 = (18 + y)/2

Step 2: Solve

10 = 10 + x

x = 0

-16 = 18 + y

y = 2

Step 3: Write coordinates

(0, 2)

4 0
3 years ago
Evaluate square root 16 minus x when x = 8. Write the answer in simplified radical form.
PtichkaEL [24]
Answer -4
___
-/ 16 = 4 X=8

4-8= -4
3 0
2 years ago
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