Refer to the diagram below. If m

A Ferris wheel has a radius of 10 m, and the bottom of the wheel passes 1 m above the ground. If the Ferris wheel makes one comp

Morgarella [4.7K]

Answer:

$y = 11 - 10cos(0.1\pi t)$

Step-by-step explanation:

Suppose at t = 0 the person is 1m above the ground and going up

Knowing that the wheel completes 1 revolution every 20s and 1 revolution = 2π rad in angle, we can calculate the angular speed

2π / 20 = 0.1π rad/s

The height above ground would be the sum of the vertical distance from the ground to the bottom of the wheel and the vertical distance from the bottom of the wheel to the person, which is the wheel radius subtracted by the vertical distance of the person to the center of the wheel.

$y = h_g + d_b = h_g + R - d_c$ (1)

where $h_g = 1$ is vertical distance from the ground to the bottom of the wheel, $d_b$ is the vertical distance from the bottom of the wheel to the person, R = 10 is the wheel radius, $d_c$ is the vertical distance of the person to the center of the wheel.

So solve for $d_c$ in term of t, we just need to find the cosine of angle θ it has swept after time t and multiply it with R

$d_c = Rcos(\theta(t)) = Rcos(\omega t) = 10cos(0.1\pi t)$

Note that $d_c$ is negative when angle θ gets between π/2 (90 degrees) and 3π/2 (270 degrees) but that is expected since it would mean adding the vertical distance to the wheel radius.

Therefore, if we plug this into equation (1) then

$y = h_g + R - d_c = 1 + 10 - 10cos(0.1\pi t) = 11 - 10cos(0.1\pi t)$

7 0

3 years ago

REASONING IN ALGEBRA AND GEOMETRY Fill in the reason that justifies each step

pantera1 [17]

9514 1404 393

Answer:

1a. multiplication property of equality

1b. distributive property

1c. subtraction property of equality

1d. division property of equality

2a. distributive property

2b. addition property of equality

2c. division property of equality

Step-by-step explanation:

The properties that let you do the same thing to both sides of an equation are the properties of equality. These are usually given an additional qualifier according to the operation being performed: addition property ..., subtraction property ..., multiplication property ..., division property .... The property that lets you add or eliminate parentheses is the distributive property (of multiplication over addition).

To answer these questions, you need to compare each line to the previous to see what operation was performed. It will generally be use of one of the properties described above, or "simplification," in which like terms are combined.

1a. both sides are multiplied by 3: multiplication property of equality

1b. parentheses are eliminated: distributive property

1c. 18 is subtracted from both sides: subtraction property of equality

1d. both sides are divided by 2: division property of equality

__

2a. parentheses are eliminated: distributive property

2b. 24 is added to both sides: addition property of equality

2c. both sides are divided by 2: division property of equality

5 0

3 years ago

GET 15 POINTS NOWWWWWWWWW!!!!

anzhelika [568]

Slope = 2/5 ; Passes through (-4, -7) ; Point-slope form

point-slope form : y-y₁=m(x-x₁)

Simply plug everything in :)

Remember !! m=slope

y - (-7) = 2/3(x - (-4))

Simplify.

y + 7 = 2/3(x + 4)

*Some teachers want this simplified more so here's the simplest answer :

y + 7 = 2/3x + 8/3 *

~Hope I helped!~

3 0

3 years ago

The population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time t. After 3 hours

ella [17]

Answer:

137

Step-by-step explanation:

Use the model A = Pe^(kt), where P is the initial number and k is the growth constant. Then, in case 1,

300 = Pe^(k*3)

and in case 2,

4000 = Pe^(k*10). We need to find P and e^k.

300 = Pe^(k*3) can be rewritten as (300/P) = [e^k]^3, which in turn may be solved for e^k:

∛(300/P) = e^k

Now we go back to 4000 = Pe^(k*10) and rewrite it as (4000/P) = [e^k]^10. Substituting ∛(300/P) for e^k, we obtain:

(4000/P) = (300/P )^(10/3)

which must now be solved for P. Raising both sides by the power of 3, we get:

(4000/P)^3 = (300/P)^10. Therefore,

4000^3 300^10

------------- = -------------

P^3 P^10

which reduces to:

4000^3 300^10

------------- = -------------

1 P^7

or

1 P^7

------------ = -----------

4000^3 300^10

or:

300^10

P^7 = ---------------- = 9.226*10^13 = 92.26*10^12

4000^3

Taking the 7th root of both sides results in P = (92.26*10^12)^(1/7), or

P = 137.26

The initial number of bacteria was 137.

7 0

3 years ago

A company plans to sell a new type of cleaner for $280 each. The estimated cost, y, of manufacturing the cleaners is a function

Minchanka [31]

Suppose x is sold, $280 each , and y is the total financial cost. The first equation in the system is then certainly y = 280x.

The vertex form y-k = a(x-h)^2 where (h,k) is the vertex, and y is the y-intercept.

So, plug the values in.
11,000-24,000 = a(0-500)^2
-13,000=250,000a
a=-0.052

y-24,000 = -0.052(x-500)^2
y= -0.052(x-500)^2 + 24,000
This is the second equation in the system.

The answer is then A, which contain the system of equations which can be used to determine must be sold for the company to make a profit.

4 0

3 years ago