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4 years ago

A frame shop owner is working with her apprentice, who takes four times as long as

Mathematics

1 answer:

Lunna [17]4 years ago

6 0

Answer:

1 hour

Step-by-step explanation:

25min=1 poster for the shop owner

25×4=100

100×8=800

800÷25=32 posters in 8hrs for the shop owner

1hr×8=8 posters for the apprentice

thus 40 in total

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Find an equation in standard form for the hyperbola with vertices at (0, ±6) and foci at (0, ±9).

Dvinal [7]

<span>For given hyperbola:
center: (0,0)
a=7 (distance from center to vertices)
a^2=49
c=9 (distance from center to vertices)
c^2=81
c^2=a^2+b^2
b^2=c^2-a^2=81-49=32
Equation of given hyperbola:

..
2: vertices (0,+/-3) foci (0,+/-6)
hyperbola has a vertical transverse axis
Its standard form of equation: , (h,k)=(x,y) coordinates of center
For given hyperbola:
center: (0,0)
a=3 (distance from center to vertices)
a^2=9
c=6 (distance from center to vertices)
c^2=36 a^2+b^2
b^2=c^2-a^2=36-9=25
Equation of given hyperbola:
</span>

4 0

3 years ago

let sin(θ) =3/5 and tan(y) =12/5 both angels comes from 2 different right trianglesa)find the third side of the two tringles b)

statuscvo [17]

In a right triangle, we haev some trigonometric relationships between the sides and angles. Given an angle, the ratio between the opposite side to the angle by the hypotenuse is the sine of this angle, therefore, the following statement

$\sin (\theta)=\frac{3}{5}$

Describes the following triangle

To find the missing length x, we could use the Pythagorean Theorem. The sum of the squares of the legs is equal to the square of the hypotenuse. From this, we have the following equation

$x^2+3^2=5^2$

Solving for x, we have

$\begin{gathered} x^2+3^2=5^2 \\ x^2+9=25 \\ x^2=25-9 \\ x^2=16 \\ x=\sqrt[]{16} \\ x=4 \end{gathered}$

The missing length of the first triangle is equal to 4.

For the other triangle, instead of a sine we have a tangent relation. Given an angle in a right triangle, its tanget is equal to the ratio between the opposite side and adjacent side.The following expression

$\tan (y)=\frac{12}{5}$

Describes the following triangle

Using the Pythagorean Theorem again, we have

$5^2+12^2=h^2$

Solving for h, we have

$\begin{gathered} 5^2+12^2=h^2 \\ 25+144=h^2 \\ 169=h^2 \\ h=\sqrt[]{169} \\ h=13 \end{gathered}$

The missing side measure is equal to 13.

Now that we have all sides of both triangles, we can construct any trigonometric relation for those angles.

The sine is the ratio between the opposite side and the hypotenuse, and the cosine is the ratio between the adjacent side and the hypotenuse, therefore, we have the following relations for our angles

$\begin{gathered} \sin (\theta)=\frac{3}{5} \\ \cos (\theta)=\frac{4}{5} \\ \sin (y)=\frac{12}{13} \\ \cos (y)=\frac{5}{13} \end{gathered}$

To calculate the sine and cosine of the sum

$\begin{gathered} \sin (\theta+y) \\ \cos (\theta+y) \end{gathered}$

We can use the following identities

$\begin{gathered} \sin (A+B)=\sin A\cos B+\cos A\sin B \\ \cos (A+B)=\cos A\cos B-\sin A\sin B \end{gathered}$

Using those identities in our problem, we're going to have

$\begin{gathered} \sin (\theta+y)=\sin \theta\cos y+\cos \theta\sin y=\frac{3}{5}\cdot\frac{5}{13}+\frac{4}{5}\cdot\frac{12}{13}=\frac{63}{65} \\ \cos (\theta+y)=\cos \theta\cos y-\sin \theta\sin y=\frac{4}{5}\cdot\frac{5}{13}-\frac{3}{5}\cdot\frac{12}{13}=-\frac{16}{65} \end{gathered}$

4 0

1 year ago

7.Suppose that water is entering a cylindrical water tank so that the initial height of the water is 3 cm and the

lukranit [14]

Answer:

$H(t) = 3*2^{t/30}$

Step-by-step explanation:

Height doubles at every 30 seconds, so let's call n how many times it happens, and the t the total time:

n = t/30

If the height doubles one time, it is multiplied by 2, if it doubles 2 times, it's multiplied by 2², for n times, it is multiplied by 2ⁿ, so for an initial height equal to 3:

$H(t) = 3*2^{t/30}$

4 0

3 years ago

Kim is reading a book with 380 pages. She read 20 pages each day until she reached Part 2 of the book. Part 2 of the book is 160

Talja [164]

Answer:

11 days

Step-by-step explanation:

first you subtract the 160 from 380 becuase thats a different part than you divide that number by 20 pages a day and end up with 11 days it took

8 0

3 years ago

Read 2 more answers

In an art history class there are two male students for every three female students. What is the ratio of female to male student

mylen [45]

Answer:

3:2

Step-by-step explanation:

3 females every 2 males

7 0

3 years ago