How long is line UW?

Mathematics

1 answer:

Neko [114]3 years ago

5 0

Answer: UW= 9√3

Step-by-step explanation:

This right triangle is a 30-60-90 triangle. This is a special triangle. Since this is a special triangle, the hypotenuse is 2x.

The hypotenuse is 18. We can figure out the length of x.

2x=18

x=9

Since we got 9, you would think it is the answer, but it's not. The length across the 60° angle is x√3. Now that we know the length across from 60°, we can plug in x.

9√3

We can check our answer by using Pythagorean Theorem.

9²+(9√3)²=18²

81+243=18²

324=324

Since they are equal, we know we have the right answer.

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murzikaleks [220]

Answer:

0.31 yr

Step-by-step explanation:

The formula for interest compounded continuously is

$FV = PVe^{rt}$

FV = future value, and

PV = present value

If FV is twice the PV, we can calculate the doubling time, t

$\begin{array}{rcl}2 & = & e^{rt}\\\ln 2 & = & rt\\t & = & \dfrac{\ln 2}{r} \\\end{array}$

1. Brianna's doubling time

$\begin{array}{rcl}t & = & \dfrac{\ln 2}{0.065}\\\\& = & \textbf{10.663 yr}\\\end{array}$

2. Adam's doubling time

The formula for interest compounded periodically is

$FV = PV\left (1 + \dfrac{r}{n} \right )^{nt}$

where

n = the number of payments per year

If FV is twice the PV, we can calculate the doubling time.

$\begin{array}{rcl}2 & = & \left (1 + \dfrac{0.0675}{4} \right )^{4t}\\\\&= & (1 + 0.016875 )^{4t}\\& = & 1.016875^{4t}\\\ln 2& = & 4 (\ln 1.01688)\times t \\& = & 0.066937t\\t& = & \dfrac{\ln 2}{0.066937}\\\\& = & \textbf{10.355 yr}\\\end{array}$