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skad [1K]
3 years ago
14

If a sports car is traveling at 95 miles per hour, how long would it take the sports car to overtake a family car traveling at 3

5 miles per hour that left the same starting point 4.5 hours earlier?
Mathematics
1 answer:
levacccp [35]3 years ago
3 0
Distance = speed * time
d = st

The sports car travels d distance for t time at speed, s, 95 mph until it overtakes the family
car.
The equation for the sports car is
d = 95t

The family car travels the same distance, d, but since it left 4.5 hours earlier  than the sports car, it travels for t + 4.5 time until it is overtaken. It travels at speed, 35 mph.
The equation for the family car is
d = 35(t + 4.5)

We solve the two equations as a system of equations.

d = 95t
d = 35(t + 4.5)

Since d = d, set the right sides of the equations above equal to each other.

95t = 35(t + 4.5)

95t = 35t + 157.5

60t = 157.5

t = 2.625

The answer is 2.625 hours, or 2 hours, 37 minutes, and 30 seconds.

Check:
In 2.625 hours, the sports car travels: 95 mph * 2.625 h = 249.375 miles
The family car traveled 2.625 hours plus the extra 4.5 hours, or 7.125 hours.
In 7.125 hours, the family car travels 35 mph * 7.125 h = 249.375 miles.
The cars have traveled the same distance 2.625 hours after the sports car left, so our answer is correct.
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2 (Picture) CONVERGENT AND DIVERGENT SERIES PLEASE HELP!!
Ivanshal [37]

Answer:

This series is divergent

F

Step-by-step explanation:

we are given a series

Firstly, we will find nth term

Numerator:

3, 4, 5,...

so, nth term will be

a_n=n+3

Denominator:

4,5,6,....

so, nth term will be

b_n=n+4

so, we can find it's nth term as

c_n=\frac{n+3}{n+4}

we can use divergent test

\lim_{n \to \infty}  c_n=\lim_{n \to \infty} \frac{n+3}{n+4}

we can divide top and bottom by n

\lim_{n \to \infty}  c_n= \lim_{n \to \infty} \frac{n/n+3/n}{n/n+4/n}

\lim_{n \to \infty}  c_n= \lim_{n \to \infty} \frac{1+3/n}{1+4/n}

now, we can plug n=inf

\lim_{n \to \infty}  c_n= \frac{1+0}{1+0}

\lim_{n \to \infty}  c_n=1

Since, it is non-zero value

so, this series is divergent


8 0
3 years ago
Question is in the picture please help
kotykmax [81]

Answer:

1808.64

Step-by-step explanation:

Area of a circle: Pi(r²)

3.14(24²)

1808.64

5 0
3 years ago
in an experiment, the temperature dropped 2 degrees each day until the temperature reaches negative 5.5 degrees. if the starting
WITCHER [35]
32.9-(-5.5)=38.4
38.4/2=19.2
around 19 days
3 0
3 years ago
A jetski rental company charges a $50 deposit, plus $25 per hour to rent a jetski. This can be represented by the formula T = 25
loris [4]

Answer:

None, the answer will be the same

Step-by-step explanation:


4 0
3 years ago
1) A basket of apples are given to a group of students. If 3 apples are given to each student, there will be 8 apples left. If 5
sattari [20]

Answer:

1) either 5 or 6 students in the group

2) 6 rooms are booked

Step-by-step explanation:

1) x students  

3x + 8 = apples

5 (x-1) + y (the one get less than 5 apples)

3x + 8 = 5 (x - 1) + y

3x + 8 = 5x - 5 + y

2x + y = 13

X       1       2      3      4      5      6

Y       11      9      7      5      3       1

because y < 5 so x = 5 or x = 6

2) x rooms are booked

4x + 20   total students

8 (x-1) + y (the students in room not full))

4x + 20 = 8 (x-1) + y

4x + 20 = 8x - 8 + y

4x + y = 28

X       1       2      3      4      5      6

Y       24    20    16    12     8      4

y < 8 answer is 6 rooms

4 0
3 years ago
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