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3 years ago

A rectangular flower garden has an area of 75 square feet. It is 15 feet long. How wide is the garden? *

Mathematics

1 answer:

nlexa [21]3 years ago

3 0

A. 5 feet

To find the area of a rectangle, multiply length by width. Since the length is 15, you divide 75 by 15, so the width would be 5 feet.

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Find the perimeter of this complex figure

denpristay [2]

Answer:

Step-by-step explanation:

9 + 10 + 2 + 6 + (9 - 2) + (10 - 6) = 38

6 0

2 years ago

During optimal conditions, the rate of change of the population of a certain organism is proportional to the population at time

Lana71 [14]

Answer:

The population is of 500 after 10.22 hours.

Step-by-step explanation:

The rate of change of the population of a certain organism is proportional to the population at time t, in hours.

This means that the population can be modeled by the following differential equation:

$\frac{dP}{dt} = Pr$

In which r is the growth rate.

Solving by separation of variables, then integrating both sides, we have that:

$\frac{dP}{P} = r dt$

$\int \frac{dP}{P} = \int r dt$

$\ln{P} = rt + K$

Applying the exponential to both sides:

$P(t) = Ke^{rt}$

In which K is the initial population.

At time t = 0 hours, the population is 300.

This means that K = 300. So

$P(t) = 300e^{rt}$

At time t = 24 hours, the population is 1000.

This means that P(24) = 1000. We use this to find the growth rate. So

$P(t) = 300e^{rt}$

$1000 = 300e^{24r}$

$e^{24r} = \frac{1000}{300}$

$e^{24r} = \frac{10}{3}$

$\ln{e^{24r}} = \ln{\frac{10}{3}}$

$24r = \ln{\frac{10}{3}}$

$r = \frac{\ln{\frac{10}{3}}}{24}$

$r = 0.05$

$P(t) = 300e^{0.05t}$

At what time t is the population 500?

This is t for which P(t) = 500. So

$P(t) = 300e^{0.05t}$

$500 = 300e^{0.05t}$

$e^{0.05t} = \frac{500}{300}$

$e^{0.05t} = \frac{5}{3}$

$\ln{e^{0.05t}} = \ln{\frac{5}{3}}$

$0.05t = \ln{\frac{5}{3}}$

$t = \frac{\ln{\frac{5}{3}}}{0.05}$

$t = 10.22$

The population is of 500 after 10.22 hours.

7 0

2 years ago

Her 6. Karen buys a sweatshirt for $30. The sales

Fynjy0 [20]

Answer:

32.1

Step-by-step explanation:

you take 30 times .07 (this was 7% but since you need it to be a decimals you move it over 2 places left). You should get 2.1 and then you add the 2.1 and 30 to get 32.1

7 0

2 years ago

Simplify the polynomial. Then find its value for the given value of the variable.

vekshin1

Answer:

Step-by-step explanation:

Simplified expression:

$3x^3 -x^3 +5x^3-9x^3$

$2x^3 +5x^3-9x^3$

$7x^3 -9x^3$

$-2x^3$

If x = -1, the value of the expression is:

$-2x^3$

$-2(-1^3)$

$-2(-1)$

$2$

Hope this helps!

3 0

2 years ago

Solve the following simultaneous equations : with the help of steps 1. x + 2y = 1, 3x - y = 17

IRISSAK [1]

Answer:

x = 5, y = -2

Step-by-step explanation:

Given equations:

x + 2y = 1
3x - y = 17

From the first equation we get:

x = 1 -2y

Substitute x in the second equation, find y:

3x - y = 17
3*(1-2y) - y = 17
3 - 6y - y = 17
-7y = 17 - 3
-7y = 14
y = -14/7
y = -2

Find x:

x = 1 - 2y
x = 1 - 2*(-2)
x = 1 + 4
x = 5

6 0

2 years ago