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2 years ago

9

Jack and Jill are walking to school. After 20 minutes, Jack walked 4/5 mile. After 25 minutes, Jill walked 5/6 mile. What is the

ir speed in miles per hour?

1 answer:

Zinaida [17]2 years ago

5 0

Answer: Jill: 2mph and jack: 2 2/5 I had this in my test lol and tell me if it was right for you all

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Oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. Initially there were millio

JulijaS [17]

Answer:

The amount of oil was decreasing at 69300 barrels, yearly

Step-by-step explanation:

Given

$Initial =1\ million$

$6\ years\ later = 500,000$

Required

At what rate did oil decrease when 600000 barrels remain

To do this, we make use of the following notations

t = Time

A = Amount left in the well

So:

$\frac{dA}{dt} = kA$

Where k represents the constant of proportionality

$\frac{dA}{dt} = kA$

Multiply both sides by dt/A

$\frac{dA}{dt} * \frac{dt}{A} = kA * \frac{dt}{A}$

$\frac{dA}{A} = k\ dt$

Integrate both sides

$\int\ {\frac{dA}{A} = \int\ {k\ dt}$

$ln\ A = kt + lnC$

Make A, the subject

$A = Ce^{kt}$

$t = 0\ when\ A =1\ million$ i.e. At initial

So, we have:

$A = Ce^{kt}$

$1000000 = Ce^{k*0}$

$1000000 = Ce^{0}$

$1000000 = C*1$

$1000000 = C$

$C =1000000$

Substitute $C =1000000$ in $A = Ce^{kt}$

$A = 1000000e^{kt}$

To solve for k;

$6\ years\ later = 500,000$

i.e.

$t = 6\ A = 500000$

So:

$500000= 1000000e^{k*6}$

Divide both sides by 1000000

$0.5= e^{k*6}$

Take natural logarithm (ln) of both sides

$ln(0.5) = ln(e^{k*6})$

$ln(0.5) = k*6$

Solve for k

$k = \frac{ln(0.5)}{6}$

$k = \frac{-0.693}{6}$

$k = -0.1155$

Recall that:

$\frac{dA}{dt} = kA$

Where

$\frac{dA}{dt}$ = Rate

So, when

$A = 600000$

The rate is:

$\frac{dA}{dt} = -0.1155 * 600000$

$\frac{dA}{dt} = -69300$

<em>Hence, the amount of oil was decreasing at 69300 barrels, yearly</em>

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2 years ago

HELP ME AS FAST AS POSSIBLE! 95 POINTS!!!

Likurg_2 [28]

Answer:

B

Step-by-step explanation:

4 (x - 7) - 2 (x + 1) = 10

x = 10

B. -2 (x - 7) + (x + 1) = 5

x = 10

your equation is equivalent to B!

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2 years ago

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Annette is surveying people in the city about their interest in a new shopping mall. She found that 180 people, or 30% of those

Vesna [10]

Answer:

306 people were surveyed

Step-by-step explanation:

180 people + 70% = 306 people surveyed

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2 years ago

Hello, I need assistance with the attached problem. My answer was incorrect

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Answer:

(a) 480 + 1640

Step-by-step explanation:

I don't really know what (b) is

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2 years ago

Based on the table of values below find the slope between points where x=2 and where x=6

kobusy [5.1K]

Slope=(12-4)/(2-6)=-2

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3 years ago