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Annette [7]
3 years ago
6

A bicycle wheel is rotating about a fixed axis at 10 rev/s in a clockwise sense. Five seconds later the wheel is rotating at 50

rev/s also in a clockwise sense. What is the average angular acceleration in this 5 second interval
Mathematics
1 answer:
Sedaia [141]3 years ago
8 0

Answer:

the average angular acceleration is 50.265 rad/s²

Step-by-step explanation:

since the angular acceleration represents the rate of change of the angular velocity ω with respect to the time t , then:

average angular acceleration = (ω₂-ω₁)/(t₂-t₁)

where 2 represents the final state and 1 the initial one. Also the angular velocity is related with the frequency f through :

angle covered / time = angle covered / revolution * revolutions/ time

ω= 2π*f

therefore

average angular acceleration = 2π*(f₂-f₁)/(t₂-t₁)

replacing values

average angular acceleration = 2π*(f₂-f₁)/(t₂-t₁) = 2π rad/rev *(50 rev/s-10 rev/s)/(5 s - 0 s) = 16*π rad/s² = 50.265 rad/s²

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Brrunno [24]

Answer:

- 3(x + 4) {}^{2}  - 4

Step-by-step explanation:

Vertex form is

a(x - h) {}^{2}  + k = f(x)

We know that h and k are both -4. Let x be -2 and y be -16.

a( - 2  + 4) {}^{2}   - 4 =  - 16

a(2) {}^{2}  - 4 =  - 16

4a - 4 =  - 16

4a =  - 12

a =  - 3

So the equation in vertex form is

- 3(x  + 4) {}^{2}  - 4

5 0
3 years ago
What is the sum? 3 y / Y 2 + 7 y + 10 + 2 / y + 2​
kap26 [50]

Answer:

  5/(y+5)

Step-by-step explanation:

Perhaps you want the sum ...

  \dfrac{3y}{y^2+7y+10}+\dfrac{2}{y+2}\\\\=\dfrac{3y}{(y+2)(y+5)}+\dfrac{2(y+5)}{(y+2)(y+5)}=\dfrac{3y+2(y+5)}{(y+2)(y+5)}\\\\=\dfrac{5y+10}{(y+2)(y+5)}=\dfrac{5(y+2)}{(y+2)(y+5)}=\boxed{\dfrac{5}{y+5}}

_____

<em>Comment on rational expressions</em>

When writing ratios in plain text, it is imperative to put parentheses around numerators and denominators. (If the numerator is a product only, then parentheses are optional.)

Your expression might be properly written as ...

  3y/(y^2 +7y +10) +2/(y+2)

As you have written it, it simplifies to ...

  3(y/y)2 +7y +10 +2/y +2 = 3·2 +7y +2/y +12

  = 7y +2/y +18

Please note, too, the exponentiation symbol (^).

6 0
3 years ago
Rent-Me Rent-A-Car charges $25.00 per day plus $0.14 per mile to rent an economy car. Better Deal Rental Car charges $23.00 per
zalisa [80]

Answer:

The number of miles at which a car rented from either company cost the same amount is <u>50 miles</u>.

Step-by-step explanation:

Let x represents the number of miles at which a car rented from either company cost the same amount. Therefore, we can have the following equation:

RC = 25 + 0.14x ....................... (1)

BC = 23 + 0.18x ...................... (2)

Where;

RC = Total cost of Rent-Me Rent-A-Car

BC = Total cost of Better Deal Rental Car

The the cost of the two companies equal where RC = BC. Therefore, we equate equations (1) and (2) and solve for x as follows:

25 + 0.14x = 23 + 0.18x

25 - 23 = 0.18x - 0.14x

2 = 0.04x

x = 2 / 0.04

x = 50

Therefore, the number of miles at which a car rented from either company cost the same amount is <u>50 miles</u>.

<u>Note:</u>

This can be confirmed for equations (1) and (2) individually by substituting for x = 50 as follows:

For equation (1):

RC = 25 + 0.14(50)

RC = 25 + 7

RC = 32

For equation (2):

BC = 23 + 0.18(50)

BC = 23 + 9

BC = 32

Therefore, RC = BC = 32 confirms the answer.

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3 years ago
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Answer:

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Step-by-step explanation:

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