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ohaa [14]
2 years ago
7

A truck driver travels at 59 miles per hour. The truck tires have a diameter of 30 inches. What is the angular velocity of the w

heels in revolutions per minute (rpm)?
Mathematics
1 answer:
Misha Larkins [42]2 years ago
5 0

Answer:

661.4\ rpm

Step-by-step explanation:

we know that

1 mile=63,360 inches

step 1

Find the circumference of the wheels

C=2\pi r

we have

r=30/2=15\ in -----> the radius is half the diameter

substitute

C=2\pi(15)

C=30\pi\ in

assume

\pi =3.14

C=30(3.14)=94.2\ in

Remember that    

The circumference of the wheels represent one revolution

Convert 59 miles per hour to inches per minute

59\ mi/h=59*63,360/60=62,304\ in/min

using proportion find the number of revolutions  

\frac{1}{94.2}\frac{rev}{in}=\frac{x}{62,304}\frac{rev}{in}\\ \\x=62,304/94.2\\ \\x=661.4\ rev

therefore

substitute

62,304\ in/min=661.4\ rev/min=661.4\ rpm

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Allison is working two summer jobs, making $12 per hour lifeguarding and $8 per hour washing cars. Last week Allison worked 3 mo
timama [110]

Answer:

Allison worked 6 hours lifeguarding and 3 hours washing cars.

Step-by-step explanation:

Let

Number of hours Allison worked lifeguarding last week = x

Number of hours Allison worked washing cars last week = y

1. Last week Allison worked 3 more hours lifeguarding than hours washing cars hours, then

x-y=3

<u>Lifeguarding:</u>

$12 per hour

$12x in x hours.

<u>Washing cars:</u>

$8 pere hour

$8y in y hours.

2. Allison earned a total of $96, hence

12x+8y=96

You get the system of two equations:

\left\{\begin{array}{l}x-y=3\\ \\12x+8y=96\end{array}\right.

Plot the graphs of these two equations (see attached diagram). These line intersect at point (6,3), so Allison worked 6 hours lifeguarding and 3 hours washing cars.

3 0
3 years ago
Aaron and Belinda went swimming. Aaron swam 575 meters. This is 150 more meters than Belinda swam. Write and solve an addition e
creativ13 [48]

Answer:

Belinda swam 425 meters

Step-by-step explanation:

575=150+x

575-150=x+150-150

425=x

0 0
3 years ago
Jodi is cutting out pieces of paper that measure 8 1/2ninches by 11 inches from a large sheet of paper that has a area of 1,000
Tasya [4]

Answer:

93.5 in^2

Step-by-step explanation:

we know that


Jodi is cutting out pieces of paper that measure  inches by  inches


The area of each piece that jodi is cutting out is equal to the area of a rectangle


5 0
3 years ago
Better quality version of last question
nadya68 [22]
Not sure at all but i think the 18 one
3 0
3 years ago
Find a1 and d for an arithmetic sequence with these terms. a3=-8 and a7=32
Arte-miy333 [17]
We know that
the formula for the <span>arithmetic sequence is
</span><span>an = a1 + (n - 1)*d
where
a1  is the first term
n is the numbers of terms

for n=3   a3=-8
-8=a1+(3-1)*d-----> -8=a1+2*d-----> equation 1

for n=7   a7=32
-32=a1+(7-1)*d----> -32=a1+6*d----> equation 2

multiply equation 2 by -1-----> 32=-a1-6*d------> equation 3

add equation 1 and equation 3
</span>-8=a1+2*d
32=-a1-6*d
----------------
24=-4*d------> d=-6
-8=a1+2*(-6)    (substitute the value of d in equation 1)
-8=a1-12-----> a1=-8+12-----> a1=4

the answer is
a1=4
d=-6

<span>

</span>
4 0
3 years ago
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