Simplify the ratio.<br><br> 14 ft to 21 ft

Given the system of linear equations. -x+y=3 and 2x+y=6 Part A: Use substitution to find the solution to the systems of equation

Juli2301 [7.4K]

-x+y=3
y=x+3

2x + x + 3 =6
3x + 3 = 6
3x = 3
x = 1

-1 + y = 3
y = 4

2(1) + y = 6
2 + y = 6
y = 4

Solution: (1, 4)

8 0

2 years ago

The population of Chicago, Illinois, in 2003 was 2,869,121. The area of Chicago was 227.1 square miles. What was the average num

ValentinkaMS [17]

Answer:

12,633.7

Step-by-step explanation:

population of Chicago, in 2003 = 2,869,121

The area of Chicago = 227.1 square miles.

What was the average number of people living in 1 square mile?

Average number of people living in 1 square mile also refers to the population density of Chicago

Average number of people living in 1 square mile = Total population / total square miles

= 2,869,121 / 227.1

= 12633.734037868

Approximately

12,633.7

5 0

2 years ago

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>

7 0

2 years ago

MATH1314-1043,1044 16wks SPR21

Brilliant_brown [7]

Step-by-step explanation:

how where is the graph cause I don't understand that

6 0

2 years ago

4 (×+3)<44. Solve each inequality

mel-nik [20]

X+3<11
x<8

thatll be your answer

4 0

2 years ago

Simplify the ratio. 14 ft to 21 ft