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2 years ago

A seat on a Ferris wheel is level with the center of the wheel. The diameter of the wheel is 210 feet (ft). If the wheel

Mathematics

1 answer:

frutty [35]2 years ago

6 0

Answer:

The change in the height of the seat of the Ferris wheel is a reduction in height of approximately 74.25 feet

Step-by-step explanation:

The given information are;

The position of the seat on the Ferris wheel = The center level of the wheel

The diameter of the Ferris wheel = 210 feet

The angle of rotation of the wheel = 45° counterclockwise

The height of a point on the Ferris wheel is given by the relation;

h = A·cos(b·x + c) + d

With regards to the question, we have;

h = The height of the seat of the Ferris wheel

A = The amplitude = 1/2 × The diameter of the wheel = 210/2 = 105 feet

360/b = The period

c = The phase shift = 90°

d = The mid line = 0

For a rotation of 45° counterclockwise or-45° clockwise, we have;

b·x = 45°, therefore;

h = 105 × cos(45° + 90°) + 0 = 105 × cos(135°) + 0

h = 105 × cos(135°) ≈ -74.25 feet

Therefore, the height of the seat of the Ferris wheel reduces by 74.246 feet.

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Henri has $24000 invested in stocks and bonds. The amount in stocks is $6000 more than three times the amount in bonds. Call the

andrey2020 [161]

Answer:

Henri invested $ 4,500 in bonds and $ 19,500 in stocks.

Step-by-step explanation:

Given that Henri has $ 24000 invested in stocks and bonds, and the amount in stocks is $ 6000 more than three times the amount in bonds, to determine the amount that Henri invested in stocks (S) and the amount he invested in bonds (B), the following calculations must be performed:

6000 + 3B + B = 24000

3B + B = 24000 - 6000

4B = 18000

B = 18000/4

B = 4500

S = 6000 + 3x4500

S = 6000 + 13500

S = 19500

Thus, Henri invested $ 4,500 in bonds and $ 19,500 in stocks.

7 0

3 years ago

The first three steps in determining the solution set of the system of equations algebraically are shown in the table. y = −x2 +

lianna [129]

You have a system of equations $\left \{ {{y = -x^2+2x-9} \atop {y =-6x+6}} \right.$ .

1. Substitude right side of second equation into the left side of the first equation: $-6x+6=-x^2+2x-9$ .

2. Solve this equation:
$x^2-2x+9-6x+6=0, \\ x^2-8x+15=0, \\ D=(-8)^2-4\cdot 1\cdot 15=64-60=4, \\ \sqrt{D}=2, \\ x_{1,2}=\dfrac{8\pm 2}{2 } =3,5$ .

3. Find y:
for $x_1=3, y_1=-6\cdot 3+6=-18+6=-12$ ,
for $x_2=5, y_2=-6\cdot 5+6=-30+6=-24$ .

4. The solutions of the system are: (3,-12) and (5,-24).
Answer: Correct choice is A.

7 0

3 years ago

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ou buy a gallon of milk that costs $3.50. The milk is discounted for 10% off. You also have to pay tax of 6.25% on the discounte

Alchen [17]

Answer:

3.35.

Step-by-step explanation:

very simple!

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2 years ago

Which of the following transforms this non-statistical question into a statistical question? How much food does your dog eat?

kozerog [31]

Answer:

A) Not statistical /this question is answered by counting the number of days in March. This produces a single number. This number is not answered by collecting data that vary.

B) Not Statistical/ this question is answered by a single number. It is not answered by collecting data that vary.

C) Statistical/ this question would be answered by all collecting data, and there would be variability in that data.

D) statistical/ this question would be answered by collecting data, and there would be variability in that data

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2 years ago

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What is the first quartile of the following data set?<br> 15, 18, 20, 21, 23, 24, 26, 29, 34, 37, 40

nikklg [1K]

Answer:

20.5

Step-by-step explanation:

20 + 21 = 41. Divide 41 by 2 than you get 20.5.

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2 years ago