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7nadin3 [17]
2 years ago
11

The traffic flow rate (cars per hour) across an intersection is r ( t ) = 400 + 800 t − 120 t 2 , where t is in hours, and t =0

is 6am. How many cars pass through the intersection between 6 am and 8 am?
Mathematics
1 answer:
Leto [7]2 years ago
3 0

Answer:

2080

Step-by-step explanation:

Given: r(t)=400+800t-120t^2

Looking for: \int\limits^{t_2}_{t_1} {r} \, dt

Solve:

\int\limits^{t_2}_{t_1} {r} \, dt= \int\limits^{2}_{0} ({400+800t-120t^2}) \, dt\\ =(400t+400t^2-40t^3)|^{2}_{0}

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Answer:

2 boxes

Step-by-step explanation:

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2 years ago
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A news organization previously stated that three of four people believed that the state of the economy was the country's most si
gizmo_the_mogwai [7]

Answer:

Option d)

H_{0}: p = 0.75\\H_A: p \neq 0.75

Step-by-step explanation:

We are given the following in the question:

Three of four people believed that the state of the economy was the country's most significant concern.

They would like to test the new data against this prior belief.

The null hypothesis will state that the three of four people believed that the state of the economy was the country's most significant concern.

The alternate hypothesis will state that this is not true. It states that people believed that the state of the economy was the country's most significant concern is not the same.

p =\dfrac{3}{4} = 0.75

We design the null and the alternate hypothesis  

H_{0}: p = 0.75\\H_A: p \neq 0.75

4 0
2 years ago
A bike wheel is 26 inches in diameter. What is the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters)?
ruslelena [56]

Answer:

Diameter of wheel in millimetres is 660.4

Step-by-step explanation:

Diameter of wheel in inches = 26

given

1 inch = 25.4 millimeters

multiplying RHS and LHS by 26

26*1 inch = 26*25.4 millimeters

=>26 inch = 660.4 mm.

Thus, diameter of wheel in millimetres is 660.4

3 0
2 years ago
the numbers below follow a pattern 0.006 0.06 0.6 6 what are the next two numbers in the pattern and what is the relationship be
aleksklad [387]
66, then 666, I am assuming cause of how it goes .006 ---> .06 --> .6 ---> 6
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Page:<br>If A+B+C=180 , then prove that:cosA+cosB+cosC= 1+4SINA/2SINB/2SINC/2​
lakkis [162]

Answer:

A + B + C = π ...... (1)

...........................................................................................................

L.H.S.

= ( cos A + cos B ) + cos C

= { 2 · cos[ ( A+B) / 2 ] · cos [ ( A-B) / 2 ] } + cos C

= { 2 · cos [ (π/2) - (C/2) ] · cos [ (A-B) / 2 ] } + cos C

= { 2 · sin( C/2 ) · cos [ (A-B) / 2 ] } + { 1 - 2 · sin² ( C/2 ) }

= 1 + 2 sin ( C/2 )· { cos [ (A -B) / 2 ] - sin ( C/2 ) }

= 1 + 2 sin ( C/2 )· { cos [ (A-B) / 2 ] - sin [ (π/2) - ( (A+B)/2 ) ] }

= 1 + 2 sin ( C/2 )· { cos [ (A-B) / 2 ] - cos [ (A+B)/ 2 ] }

= 1 + 2 sin ( C/2 )· 2 sin ( A/2 )· sin( B/2 ) ... ... ... (2)

= 1 + 4 sin(A/2) sin(B/2) sin(C/2)

= R.H.S. ............................. Q.E.D.

...........................................................................................................

In step (2), we used the Factorization formula

cos x - cos y = 2 sin [ (x+y)/2 ] · sin [ (y-x)/2 ]

Step-by-step explanation:

6 0
2 years ago
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