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3 years ago

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a guy wire 15 ft long runs from the top of a pole to spot on the ground. if the height of the pole is 3 ft more than the distanc

e from the base of the pole to the spot where the guy wire is anchored, how tall is the pole?

1 answer:

Murrr4er [49]3 years ago

6 0

18. The answer is 18 because the wire is 15ft and the pole is 3ft taller than the wire

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Question 3(Multiple Choice Worth 2 points)

Lilit [14]

The equivalent expression is seven-fifths squared times one-third cubed. Then the correct option is D.

<h3>What is an equivalent expression?</h3>

The equivalent is the expression that is in different forms but is equal to the same value.

Five-sevenths squared times one-third raised to the power of negative three all raised to the power of negative one.

Convert the sentence into numerical form.

$\rm \rightarrow \left [ \left (\dfrac{5}{7} \right )^2 \times \left ( \dfrac{1}{3}\right )^{-3} \right ] ^{-1}$

Simplify the expression, then we have

$\rm \rightarrow \left [ \left (\dfrac{7}{5} \right )^{2} \times \left ( \dfrac{1}{3}\right )^{3} \right ]$

The equivalent expression is seven-fifths squared times one-third cubed. Then the correct option is D.

More about the equivalent link is given below.

brainly.com/question/889935

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6 0

1 year ago

The radius of a circle is 12.1 ft. Find the circumference to the nearest tenth}to the nearest tenth

Gnoma [55]

Answer:

76 ft

Step-by-step explanation:

Use the circumference formula, C = 2 $\pi$ r

Plug in the radius:

C = 2 $\pi$ r

C = 2 $\pi$ (12.1)

C = 76.0

So, the circumference is 76 ft

3 0

3 years ago

Read 2 more answers

13. Find the range of the function on the graph<br> below.

aliina [53]

Range is ] -20 , -10 [

both points are disclude according to the empty circle

4 0

1 year ago

What is the missing angle?

murzikaleks [220]

a straight line = 180 degrees

so the missing angle is 180 - 130 = 50 degrees

8 0

3 years ago

Read 2 more answers

The Department of Agriculture is monitoring the spread of mice by placing 100 mice at the start of the project. The population,

uranmaximum [27]

Answer:

Step-by-step explanation:

Assuming that the differential equation is

$\frac{dP}{dt} = 0.04P\left(1-\frac{P}{500}\right)$ .

We need to solve it and obtain an expression for $P(t)$ in order to complete the exercise.

First of all, this is an example of the logistic equation, which has the general form

$\frac{dP}{dt} = kP\left(1-\frac{P}{K}\right)$ .

In order to make the calculation easier we are going to solve the general equation, and later substitute the values of the constants, notice that $k=0.04$ and $K=500$ and the initial condition $P(0)=100$ .

Notice that this equation is separable, then

$\frac{dP}{P(1-P/K)} = kdt$ .

Now, intagrating in both sides of the equation

$\int\frac{dP}{P(1-P/K)} = \int kdt = kt +C$ .

In order to calculate the integral in the left hand side we make a partial fraction decomposition:

$\frac{1}{P(1-P/K)} = \frac{1}{P} - \frac{1}{K-P}$ .

So,

$\int\frac{dP}{P(1-P/K)} = \ln|P| - \ln|K-P| = \ln\left| \frac{P}{K-P} \right| = -\ln\left| \frac{K-P}{P} \right|$ .

We have obtained that:

$-\ln\left| \frac{K-P}{P}\right| = kt +C$

which is equivalent to

$\ln\left| \frac{K-P}{P}\right|= -kt -C$

Taking exponentials in both hands:

$\left| \frac{K-P}{P}\right| = e^{-kt -C}$

Hence,

$\frac{K-P(t)}{P(t)} = Ae^{-kt}$ .

The next step is to substitute the given values in the statement of the problem:

$\frac{500-P(t)}{P(t)} = Ae^{-0.04t}$ .

We calculate the value of $A$ using the initial condition $P(0)=100$ , substituting $t=0$ :

$\frac{500-100}{100} = A}$ and $A=4$ .

So,

$\frac{500-P(t)}{P(t)} = 4e^{-0.04t}$ .

Finally, as we want the value of $t$ such that $P(t)=200$ , we substitute this last value into the above equation. Thus,

$\frac{500-200}{200} = 4e^{-0.04t}$ .

This is equivalent to $\frac{3}{8} = e^{-0.04t}$ . Taking logarithms we get $\ln\frac{3}{8} = -0.04t$ . Then,

$t = \frac{\ln\frac{3}{8}}{-0.04} \approx 24.520731325$ .

So, the population of rats will be 200 after 25 months.

6 0

3 years ago