What is an equation, in standard form, of the line through (1, 7) and (-2, -3)?

"A clock is positioned on an auditorium wall with its center 9 feet above the floor. The second hand is 10 inches long and conti

GenaCL600 [577]

Answer: f(x) = 10in*cos(x*2*pi/60s) + 10in*sin(x*2*pi/60s) + 108in.

Step-by-step explanation:

When we have a circular motion, we can write this as:

f(x) = A*sin(k*x + f) + A*cos(k*x + f) + C.

where:

k is a constant that depends on the period.

f is a phase shift.

C is the mean height of the circular motion, in this case will be equal to the height of the center, that is 9ft.

C = 9ft.

A is the amplitude of the motion, in this case is equal to the radius, that is equal to the lenght of the second hand

A = 10in

But we should write both quantities in the same units, so we have:

1ft = 12in

then:

C = 9ft = 9*12in = 108in

Then our equation is:

f(x) = 10in*cos(k*x + f) + 10in*sin(k*x + f) + 108in

now, x = 0s coincides with the noon

so at x = 0s, the second hand is pointint to the twelve, this means that is in the max height, so we have:

F(0s) = 10in*cos(0 + f) + 10in*sin(0 + f) + 108 in

Now, the maximum value will be when the value inside the sinusoidals is 0.

(because cos(0) = 1 and sin(0) = 0)

then we have that f = 0.

Now, we know that it takes 60 seconds to do a full revolution, and for the sinusodial functions the period is 2*pi

Then we have:

c*60s = 2*pi

c = 2*pi/60s.

Then the equation is:

f(x) = 10in*cos(x*2*pi/60s) + 10in*sin(x*2*pi/60s) + 108in.

4 0

3 years ago

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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room.

Gelneren [198K]

Answer:

B. y² – 5y = 750

C. 750 – y(y – 5) = 0

E. (y + 25)(y – 30) = 0

I'm assuming the 2 in the second option is supposed to be an exponent.

Step-by-step explanation:

Length = y

Width = y-5

Length × Width = Area

Area = y(y-5) = 750

Distribute.

y²-5y=750 (B is correct)

If you factor the equation above

(y + 25)(y – 30) = 0 (E is correct)

Area = y(y-5) = 750

Subtract y(y-5) from both sides.

750-y(y-5) = 0 (C is correct)

6 0

3 years ago

Kimberly and Mike have an equal amount of money. After Kimberly spent $50 and Mike spent $25, Mike's money is 50% more than Kimb

Paul [167]

Answer:

Kimberly and Mike had at first $100 each

Step-by-step explanation:

Assume that Kimberly and Mike each have $x

∵ Kimberly has $x

∵ Kimberly spent $50

- Find the reminder with Kimberly by subtracting 50 from x

∴ The money left with Kimberly = x - 50

∵ Mike has $x

∵ Mike spent $25

- Find the reminder with Mike by subtracting 25 from x

∴ The money left with Mike = x - 25

∵ Mike's money is 50% more than Kimberly's money

- That means Mike's money is more than Kimberly's money by

50% of Kimberly's money

∴ x - 25 = (x - 50) + 50%(x - 50)

∵ 50% = $\frac{50}{100}$ = 0.5

∴ x - 25 = (x - 50) + 0.5(x - 50)

- Simplify the right hand side

∴ x - 25 = x - 50 + 0.5x - 25

- Add the like terms in the right hand side

∴ x - 25 = 1.5x - 75

- Add 75 to both sides

∴ x + 50 = 1.5x

- Subtract x from both sides

∴ 50 = 0.5x

- Divide both sides by 0.5

∴ 100 = x

∵ x represents the amount of money that Kimberly and

Mike each had at first

∴ Kimberly and Mike had at first $100 each

7 0

3 years ago

How many roots does the equation 3x² = 1 - 7x have and what is the nature of the roots

AnnyKZ [126]

Answer:

Step-by-step explanation:

Rewrite this quadratic in standard form: 3x^2 + 7x - 1.

The coefficients of x are {3, 7, -1}, and so the discriminant is b^2 - 4ac, or

7^2 - 4(3)(-1), or 49 + 12, or 61. Because the discriminant is positive, this quadratic has two real, unequal roots

7 0

3 years ago

a hospital ward, there are 10 nurses and 6 doctors. 4 of the nurses and 3 of the doctors are male. If a person is randomly selec

stira [4]

The person has a 7/16 % chance.

3 0

3 years ago

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