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The sides of a triangle are 3 consecutive odd integers and the shortest side is 20% of the perimeter of the triangle. What is th

AysviL [449]

Answer:

15 units

Step-by-step explanation:

The terms of an odd integer are given by 2n - 1. Since the sides of the triangle are three consecutive odd integers, let them be 2n - 1, 2(n + 1) - 1 and 2(n + 2) - 1 respectively, where 2n - 1 is the shortest side

Let P = perimeter of triangle = 2n - 1 + 2(n + 1) - 1 + 2(n + 2) - 1

= 2n - 1 + 2n + 2 - 1 + 2n + 4 - 1

= 2n - 1 + 2n + 1 + 2n + 3

= 2n + 2n + 2n - 1 + 1 + 3

= 6n + 3

Since the shortest side is 20% of the perimeter of the triangle, we have that

2n - 1 = 20%(6n + 3)

2n - 1 = 0.2(6n + 3)

expanding the bracket, we have

2n - 1 = 1.2n + 0.6

subtracting -1.2n and adding +1 to both sides, we have

2n - 1.2n = 1 + 0.6

0.8n = 1.6

dividing both sides by 0.8, we have

n = 1.6/0.8

n = 2

Since P = 6n + 3, substituting n = 2, we have

P = 6(2) + 3 = 12 + 3 = 15 units

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3 years ago

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Read 2 more answers

Find the general solution to the differential equation modeling how a person learns:

Luda [366]

Here we want to solve differential equations, we will see that the general solution is:

$y = A*e^{-t} + 100$

We want to solve the differential equation:

$\frac{dy}{dt} = 100 - y$

From this is pretty clear that y is an exponential function, with an exponent of -1*t.

We can write it generally as:

$y = A*e^{-t} + B\\\\\frac{dy}{dt} = -A*e^{-t}$

Then if we set B = 100 we get:

$y = A*e^{-t} + 100\\\\\frac{dy}{dt} = -A*e^{-t} \\\\\frac{dy}{dt} = -A*e^{-t} - 100 + 100 = -y + 100$

So we just found the general form of the function.

Now we have two cases:

A) y(0) = 35

$y(0) = A*e^{-0} + 100 = 35\\= A + 100 = 35\\\\A = 35 - 100 = -65$

In this case, the function is:

$y = -65*e^{-t} + 100$

B) y(0) = 125

$125 = A*e^0 + 100\\\\\125 - 100 = A\\\\25 = A$

In this case, the function is:

$y = 25*e^{-t} + 100$

Now we want to see which one of the two can represent how a person learns. Just look at the graph below:

The green line is the one for y(0) = 35, and the blue one is for y(0) = 125.

Notice that for small values of t, the blue function is really large, thus it can't really model how a person learns (is larger for smaller values of t than for larger values).

So y(0) = 35 represents better how a <em>person can learn</em> (but not exactly, because you can see that it eventually becomes almost constant, which is something that really does not happen) so the correct option is <u>D: none of the above.</u>

If you want to learn more, you can read:

brainly.com/question/353770