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snow_lady [41]
3 years ago
5

a car leaves a town by traveling at 40 mph and two hours later,a second car left the same time in the same road,and the same dir

ections at 60 mph,the question is in how many hours the second car passes the first car????
Mathematics
1 answer:
Shkiper50 [21]3 years ago
3 0
\bf \begin{array}{ccccllll}
&distance&rate&time(hrs)\\
&\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\\
\textit{first car}&d&40&t\\
\textit{second car}&d&60&t+2
\end{array}
\\ \quad \\\\\\
d=d\implies (40)(t)=(60)(t+2)

"t", is the time the first car has travelled when reaching "d" distance,
whatever that is, at that point, the second car is passing it
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In quadratic drag problem, the deceleration is proportional to the square of velocity
Mars2501 [29]
Part A

Given that a= \frac{dv}{dt} =-kv^2

Then, 

\int dv= -kv^2\int dt \\  \\ \Rightarrow v(t)=-kv^2t+c

For v(0)=v_0, then

v(0)=-kv^2(0)+c=v_0 \\  \\ \Rightarrow c=v_0

Thus, v(t)=-kv(t)^2t+v_0

For v(t)= \frac{1}{2} v_0, we have

\frac{1}{2} v_0=-k\left( \frac{1}{2} v_0\right)^2t+v_0 \\  \\ \Rightarrow \frac{1}{4} kv_0^2t=v_0- \frac{1}{2} v_0= \frac{1}{2} v_0 \\  \\ \Rightarrow kv_0t=2 \\  \\ \Rightarrow t= \frac{2}{kv_0}


Part B

Recall that from part A, 

v(t)= \frac{dx}{dt} =-kv^2t+v_0 \\  \\ \Rightarrow dx=-kv^2tdt+v_0dt \\  \\ \Rightarrow\int dx=-kv^2\int tdt+v_0\int dt+a \\  \\ \Rightarrow x=- \frac{1}{2} kv^2t^2+v_0t+a

Now, at initial position, t = 0 and v=v_0, thus we have

x=a

and when the velocity drops to half its value, v= \frac{1}{2} v_0 and t= \frac{2}{kv_0}

Thus,

x=- \frac{1}{2} k\left( \frac{1}{2} v_0\right)^2\left( \frac{2}{kv_0} \right)^2+v_0\left( \frac{2}{kv_0} \right)+a \\  \\ =- \frac{1}{2k} + \frac{2}{k} +a

Thus, the distance the particle moved from its initial position to when its velocity drops to half its initial value is given by

- \frac{1}{2k} + \frac{2}{k} +a-a \\  \\ = \frac{2}{k} - \frac{1}{2k} = \frac{3}{2k}
7 0
3 years ago
Jason owes the bank a little more than $10. Which could be his balance?
nadezda [96]
I would say C seeing that he owes the bank a little more than $10, but im not sure it could also be A. I chose the negative number because if he owes them that would be money coming out of his account.
Hope This Helps!
5 0
3 years ago
!!!!!!!! Please help!!!!!!!!
liberstina [14]
Answer : 300

30% of 1000 is 300
5 0
2 years ago
Find the values of x and y in the diagram below.<br> 86°<br> (4x - 7)°<br> (7y - 1)<br> (9x + 4)
Aneli [31]

The value of x in the diagram is 15° and the value of y is 6°

Please find attached the diagram used in answering this question

The figure given is a triangle. A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees

The first step is to determine the value of x.

The value of x can be determined using the exterior angle.

The sum of the two interior opposite angles in a triangle is equal to the external angle

(4x - 7)° + 86° = (9x + 4)°

Combine similar terms

9x - 4x = 86 - 7 - 4

5x = 75

x = 15°

To determine the value of y, first substitute for the value of x in the angle (4x - 7)°

(4x - 7)° = (4x15) - 7 = 53°

The sum of angles in a triangle add up to 180°

53° + 86 + (7y - 1) = 180°

add like terms

138 + 7y = 180

7y = 42

y = 6°

To learn more, please check: brainly.com/question/23688688?referrer=searchResults

8 0
2 years ago
The distance to the sun is approximately 93,000,000 mi. A firefly is about 0.04 in. long. (a) What is the distance to the sun wr
stiks02 [169]
A) The answer is 9.3 * 10⁷ mi

First, represent the number as the product of a number in the range 1 up to 10 and a number divisible by 10:
93,000,000 mi = 9.3 * 10,000,000 mi

10,000,000 = 10 * 10 * 10 * 10 * 10 * 10 * 10 = 10⁷

 93,000,000 mi = 9.3 * 10,000,000 mi = 9.3 * 10⁷ mi


b) The answer is 4 * 10⁻² in

Represent the number as the product of a number in the range 1 up to 10 and a number divisible by 10.
0.04 in = 4 * 0.01 in

0.01 = 10⁻²

0.04 in = 4 * 0.01 in = 4 * 10⁻² in


c) The distance to the sun in inches is  5,892,480,000,000 in

1 mi = 63,360 in
93,000,000 mi = 93,000,000 * 63,360 in = 5,892,480,000,000 in

<span>How many fireflies would it take to reach the sun if they were put end to end:
</span>147,312,000,000,000<span>

x - number of fireflies
x * 0.04 in = </span>5,892,480,000,000 in
x = 5,892,480,000,000 in / 0.04 in
x = 147,312,000,000,000
3 0
3 years ago
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