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3 years ago

Steve built a square dog pen that has a perimeter of 240 inches. What is the length of one side of Steve's dog pen?

Mathematics

2 answers:

Anettt [7]3 years ago

7 0

Answer:

60 in

Step-by-step explanation:

We are given that

Steve built a square dog pen of perimeter=240 in

We have to find the length of one side of Steve's dog pen.

To find the value of length of Steve's side we will use the formula of perimeter of square.

We know that

Perimeter of square= $4\times side$

Substitute the values in the given formula

$240=4\times side$

$Side=\frac{240}{4}=60$

Length of Steve' s dog pen=60 in

Hence, the length of one side of Steve's dog pen=60 in

Liono4ka [1.6K]3 years ago

6 0

240 divided by 4 equals 60

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3 years ago

The dye dilution method is used to measure cardiac output with 3 mg of dye. The dye concentrations, in mg/L, are modeled by c(t)

Lemur [1.5K]

Answer:

Cardiac output: $F=0.055 L\s$

Step-by-step explanation:

Given : The dye dilution method is used to measure cardiac output with 3 mg of dye.

To Find : Find the cardiac output.

Solution:

Formula of cardiac output: $F=\frac{A}{\int\limits^T_0 {c(t)} \, dt}$ ---1

A = 3 mg

$\int\limits^T_0 {c(t)} \, dt =\int\limits^{10}_0 {20te^{-0.06t}} \, dt$

Do, integration by parts

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[20t\int{e^{-0.6t} \,dt}-\int[\frac{d[20t]}{dt}\int {e^{-0.6t} \, dt]dt]^{10}_0$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20}{0.6}\int {e^{-0.6t} \,dt]^{10}_0$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20e^{-0.6t}}{(0.6)^2}]^{10}_{0}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-200e^{-6}}{0.6}+\frac{20e^{-6}}{(0.6)^2}]+\frac{20}{(0.60^2}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0=\frac{20(1-e^{-6}}{(0.6)^2}-\frac{200e^{-6}}{0.6}$

$[\int{20te^{-0.6t}} \, dt]^{10}_0\sim {54.49}$

Substitute the value in 1

Cardiac output: $F=\frac{3}{54.49}$

Cardiac output: $F=0.055 L\s$

Hence Cardiac output: $F=0.055 L\s$

4 0

2 years ago

You split $1500 between two savings accounts one pays 4%interest and the other pays 5% after one year you have earned $69.50 in

ANTONII [103]

Answer:

Step-by-step explanation:

Use the basic simple interest formula:

P * r * t = I and put the info into a table with those variables along the top, formig the columns we need:

P * r * t = I

Acct 1

Acct 2

If we have a total of 1500 to split up between 2 accounts, we put x amount of money into one and then have 1500-x left to put into the other. We will fill those in along with the interest rates in decimal form and the time of 1 year:

P * r * t = I

Acct 1 x .04 1

Acct 2 1500-x .05 1

Looking at the formula we are told that Prt = I, so we will multiply P times r times t and fill in the I column:

P * r * t - I

Acct 1 x .04 1 .04x

Acct 2 1500-x .05 1 .05(1500-x)

The total Interest earned by the addition of the interest earned from both accounts is 69.50. So we add the interest column together and set it equal to 69.50:

.04x + .05(1500 - x) = 69.50 and

.04x + 75 - .05x = 69.50 and

-.01x = -5.5 so

x = 550

That's how much money is in the account earning 4% interest.

7 0

3 years ago