Ask question

Ask question

All categories

3 years ago

15

Find the value of y.

1 answer:

Phoenix [80]3 years ago

4 0

$\boxed{y=6\sqrt{3}}$

<h2>Explanation:</h2>

For a better understanding of the problem I've built up two triangles from the given triangular shape. So these two triangles are similar. Therefore, we can solve this problem by using ratios and corresponding sides in this way:

$\frac{x}{3}=\frac{12}{x} \\ \\ x^2=36 \\ \\ x=\sqrt{36} \\ \\ x=6$

But our goal is to find y. Let's call w the height of the small triangle, then:

$w=\sqrt{6^2-3^2}=3\sqrt{3}$

Applying the concept of ratios again:

$\frac{y}{w}=\frac{x}{3} \\ \\ y=w \left(\frac{x}{3}\right) \\ \\ y=3\sqrt{3}\left(\frac{6}{3}\right) \\ \\ \boxed{y=6\sqrt{3}}$

<h2>Learn more:</h2>

Right triangle: brainly.com/question/10684799

#LearnWithBrainly

You might be interested in

Pls help me almost due

iVinArrow [24]

Answer: disagree its backwards

Step-by-step explanation: the x intercept always comes first so its actually (-4,2)

6 0

3 years ago

Read 2 more answers

Shelley wants to purchase a cell phone package, which includes a free phone. The cost of the package is $0.10 per minute, for th

GarryVolchara [31]

Answer:

The function would be linear because the rate of change is constant.

Step-by-step explanation:

Given

$Base= \$89.00$

$Rate = \$0.10$ per minute

See attachment for complete question and options

First, we write the function that calculates the cost (C(t)) for t minutes.

This is calculated as:

$Cost = Base + Rate * t$

$C(t) = 89.00 + 0.10 * t$

$C(t) = 89.00 + 0.10t$

Rewrite as:

$C(t) = 0.10t + 89.00$

A function that has the above format is referred to as a linear function which has the general format

$f(x) = mx + b$

Where

m represents the slope/rate and it is constant

From the list of given options, (a) is correct.

6 0

3 years ago

I need help solving unit rates

guapka [62]

It takes Selma 1/6 of a hour to run 3/4 miles.
Just multiply 3/4 by 6 to get 18/4 which is 4.5 miles or 4 1/2 mile

7 0

3 years ago

1. Express <img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%282x%2B3%29%20%7D" id="TexFormula1" title="\frac{1}{x(2x+3) }" a

katovenus [111]

1. Let a and b be coefficients such that

$\dfrac1{x(2x+3)} = \dfrac ax + \dfrac b{2x+3}$

Combining the fractions on the right gives

$\dfrac1{x(2x+3)} = \dfrac{a(2x+3) + bx}{x(2x+3)}$

$\implies 1 = (2a+b)x + 3a$

$\implies \begin{cases}3a=1 \\ 2a+b=0\end{cases} \implies a=\dfrac13, b = -\dfrac23$

so that

$\dfrac1{x(2x+3)} = \boxed{\dfrac13 \left(\dfrac1x - \dfrac2{2x+3}\right)}$

2. a. The given ODE is separable as

$x(2x+3) \dfrac{dy}dx} = y \implies \dfrac{dy}y = \dfrac{dx}{x(2x+3)}$

Using the result of part (1), integrating both sides gives

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3|\right) + C$

Given that y = 1 when x = 1, we find

$\ln|1| = \dfrac13 \left(\ln|1| - \ln|5|\right) + C \implies C = \dfrac13\ln(5)$

so the particular solution to the ODE is

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3|\right) + \dfrac13\ln(5)$

We can solve this explicitly for y :

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3| + \ln(5)\right)$

$\ln|y| = \dfrac13 \ln\left|\dfrac{5x}{2x+3}\right|$

$\ln|y| = \ln\left|\sqrt[3]{\dfrac{5x}{2x+3}}\right|$

$\boxed{y = \sqrt[3]{\dfrac{5x}{2x+3}}}$

2. b. When x = 9, we get

$y = \sqrt[3]{\dfrac{45}{21}} = \sqrt[3]{\dfrac{15}7} \approx \boxed{1.29}$

8 0

2 years ago

Charmaine is fertilizing her garden. The garden is in the shape of a rectangle. Its length is 12 feet and its width is 10 feet.

Nana76 [90]

Answer:

4 bags

Step-by-step explanation:

lxw

12x10=120

30x4=120

l=length

w=width

6 0

3 years ago