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makkiz [27]
3 years ago
7

a car is traveling at a rate of 75 miles per hour. what is the car rate in miles per minute? how many miles will the car travel

in 15 minutes? do not round your answers.
Mathematics
1 answer:
Nuetrik [128]3 years ago
5 0

\dfrac{75 miles}{hour} * \dfrac{1 hour}{60 minues} = \dfrac{1.25 miles}{minute}

Now you want to set up a proportion.

1.25 miles:1 minute :: x : 15 minutes  Set up the proportion

\dfrac{1.25 miles}{1 minute}= \dfrac{x }{15 minutes}  Cross multiply

1.25 miles * 15 minutes = x * 1 minute

18.75 miles * minutes = x * 1 minute. Divide by minutes

x = 18.75 miles. Answer



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On a circle of radius 10 feet, what angle would subtend an arc of length 1 feet?
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7 0
3 years ago
(a) By inspection, find a particular solution of y'' + 2y = 14. yp(x) = (b) By inspection, find a particular solution of y'' + 2
SOVA2 [1]

Answer:

(a) The particular solution, y_p is 7

(b) y_p is -4x

(c) y_p is -4x + 7

(d) y_p is 8x + (7/2)

Step-by-step explanation:

To find a particular solution to a differential equation by inspection - is to assume a trial function that looks like the nonhomogeneous part of the differential equation.

(a) Given y'' + 2y = 14.

Because the nonhomogeneus part of the differential equation, 14 is a constant, our trial function will be a constant too.

Let A be our trial function:

We need our trial differential equation y''_p + 2y_p = 14

Now, we differentiate y_p = A twice, to obtain y'_p and y''_p that will be substituted into the differential equation.

y'_p = 0

y''_p = 0

Substitution into the trial differential equation, we have.

0 + 2A = 14

A = 6/2 = 7

Therefore, the particular solution, y_p = A is 7

(b) y'' + 2y = −8x

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = -8x

2Ax + 2B = -8x

By inspection,

2B = 0 => B = 0

2A = -8 => A = -8/2 = -4

The particular solution y_p = Ax + B

is -4x

(c) y'' + 2y = −8x + 14

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = -8x + 14

2Ax + 2B = -8x + 14

By inspection,

2B = 14 => B = 14/2 = 7

2A = -8 => A = -8/2 = -4

The particular solution y_p = Ax + B

is -4x + 7

(d) Find a particular solution of y'' + 2y = 16x + 7

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = 16x + 7

2Ax + 2B = 16x + 7

By inspection,

2B = 7 => B = 7/2

2A = 16 => A = 16/2 = 8

The particular solution y_p = Ax + B

is 8x + (7/2)

8 0
3 years ago
Which relation is a function?
zimovet [89]

Answer:

D

Step-by-step explanation:

A relation is a set of related points. A function is a set of related points where no inputs repeat.

A. {(1, 2), (2, 3), (3,  2), (2, 1)}

This repeats (2,3) and (2,1). Not a function.

​B. {(4, 2), (3, 3), (2,  4), (3, 2)}  

This repeats (3,3) and (3,2). Not a function.

C. {(1, −1), (−2, 2), (−1,  2), (1, −2)}

This repeats (1,-1) and (1,-2). Not a function.

D. {(1, 4), (2, 3), (3,  2), (4, 1)}

This doe NOT repeat. Function.

6 0
3 years ago
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