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1 year ago

Use Special Right Triangles to solve for the value of y. Leave your answer in SIMPLIFIED radical form.

Mathematics

1 answer:

Scorpion4ik [409]1 year ago

7 0

We can use the sine function and tangent function in order to solve for x and y:

$\begin{gathered} sin(\theta)=\frac{opposite}{hypotenuse} \\ sin(60)=\frac{15}{x} \\ x=\frac{15}{sin(60)} \\ x=10\sqrt{3} \end{gathered}$ $\begin{gathered} tan(\theta)=\frac{opposite}{adjacent} \\ tan(60)=\frac{15}{y} \\ y=\frac{15}{tan(60)} \\ y=5\sqrt{3} \end{gathered}$

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A racquetball club membership costs $22.50 per month. What would a year’s membership cost?

dsp73

Answer:

270 dollars for a year, so 22.50 times 12

8 0

3 years ago

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a pizzeria sells a round pizza with the diameter of 24 inches. what is the area and what is the circumferance

Bond [772]

We have that
Area=pi*r²
D=24 in------------ > r=D/2=24/2=12 in

Area =pi*12²=452.16 in²

the circumference=2*pi*r=2*pi*12=75.36 in

the answer is
the area is 452.16 in² and the circumference is 75.36 in

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3 years ago

John works as a tutor for an hour and as a waiter for an hour. This month, he worked a combined total of hours at his two jobs.

liberstina [14]

Correct Question:

John works as a tutor for $12 an hour and as a waiter for $8 an hour. This month, he worked a combined total of 86 hours at his two jobs.

Let be the number of hours John worked as a tutor this month. Write an expression for the combined total dollar amount he earned this month.

Answer:

Total hours = 86

Let t is the hours he spent on tutoring

then (86-t) is hours spent on waiting

Let Y is the total amount in dollars which is required .

Now;

y = (tutoring hours x 12$) + (waiting hours x 8$)

Y = 12t + 8(86-t)

6 0

3 years ago

Raquel and Van live in two different cities. As part of a project, they each record the lowest prices for a gallon of gas at gas

mylen [45]

Based on the information given, the true statement true about their gas-price data is A. Raquel’s data are most likely closer to $3.42 than Van’s data are to $3.78.

<h3>Solution to the gas-price data.</h3>

It should be noted that a standard deviation simply measures how dispersed the data will be in relation to the mean.

From the complete question, the mean of Raquel's data is given as 3.42 while the standard deviation is given as 0.07. On the other hand, the mean of Van's data is given as 3.78 while the standard deviation is given as 0.23.

Therefore, it can be deduced that Raquel’s data are most likely closer to $3.42 than Van’s data are to $3.78.

Learn more about standard deviation on:

brainly.com/question/19243813

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2 years ago

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For the differential equations dydx=sqrt(y^2−36) does the existence/uniqueness theorem guarantee that there is a solution to thi

julsineya [31]

Answer:

1. (-4,6) there is no a solution to the equation through this point

2. (2,−6) there is no a solution to the equation through this point

3. (−5,39) there is a solution to the equation through this point

4. (−1,45) there is a solution to the equation through this point

Step-by-step explanation:

Using the existence and uniqueness theorem:

Let:

$F(x,y)=\sqrt{y^2-36} \\\\and\\\\\frac{\partial F}{\partial y} =\frac{y}{\sqrt{y^2-36} }$

Now, let's find the domain of $F(x,y)$ , due to the square root:

$y^2-36 \geq 0\\\\y^2\geq 36\\\\y \geq 6\hspace{12}or\hspace{12}y\leq-6$

So the domain of the function is:

$y \in R\hspace{12}y\geq6\hspace{12}or\hspace{12}y\leq-6$

Now, due to the fraction $\frac{\partial F}{\partial y}$ the denominator must be also different from 0, so:

$y^2-36\neq0\\\\y \neq \pm6$

So, the theorem tells us that for each $y_0\in R:\hspace{12}y_0>6\hspace{12}or\hspace{12}y_0$ there exists a unique solution defined in an open interval around $x_0$ .

1. (-4,6) there is no a solution to the equation through this point because $y_0=6$

2. (2,−6) there is no a solution to the equation through this point because

$y_0=-6$

3. (−5,39) there is a solution to the equation through this point because

$y_0>6$

4. (−1,45) there is a solution to the equation through this point because

$y_0>6$

6 0

3 years ago