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3 years ago

A machine make 24 items in 8 minutes how many can it make in 14

1 answer:

6 0

So to solve we need to find out how many items per minute so 24 / 8 = 3 so the machine make 3 items per minute so now we take 3 and multiply it by 14 3 * 14 = 42 so 42 is our answer

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Use the given information to find the exact value of the trigonometric function

eimsori [14]

$\begin{gathered} \csc \theta=-\frac{6}{5} \\ \tan \theta>0 \\ \cos \frac{\theta}{2}=\text{?} \end{gathered}$

Half Angle Formula

$\cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}}$ $\tan \theta>0\text{ and csc}\theta\text{ is negative in the third quadrant}$ $\begin{gathered} \csc \theta=-\frac{6}{5}=\frac{r}{y} \\ x^2+y^2=r^2 \\ x=\pm\sqrt[\square]{r^2-y^2} \\ x=\pm\sqrt[\square]{6^2-(-5)^2} \\ x=\pm\sqrt[\square]{36-25} \\ x=\pm\sqrt[\square]{11} \\ \text{x is negative since the angle is on the 3rd quadrant} \end{gathered}$ $\begin{gathered} \cos \theta=\frac{x}{r}=\frac{-\sqrt[\square]{11}}{6} \\ \cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}} \\ \cos \frac{\theta}{2}is\text{ also negative in the 3rd quadrant} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{1+\frac{-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{\frac{6-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}} \\ \\ \end{gathered}$

Answer:

$\cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}$

Checking:

$\begin{gathered} \frac{\theta}{2}=\cos ^{-1}(-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}) \\ \frac{\theta}{2}=118.22^{\circ} \\ \theta=236.44^{\circ}\text{ (3rd quadrant)} \end{gathered}$

Also,

$\csc \theta=\frac{1}{\sin\theta}=\frac{1}{\sin (236.44)}=-\frac{6}{5}\text{ QED}$

The answer is none of the choices

7 0

1 year ago

Tess created a Pythagorean triple of (24, 32, 40) by multiplying the known Pythagorean triple 3, 4, and 5 by 8. Is Tess correct?

pentagon [3]

Answer:

(24, 32, 40) is a Pythagorean triplet.

Option A) Yes, as long as each number in the Pythagorean triple is multiplied by the same whole number.

Step-by-step explanation:

We are given the following in the question:

Pythagorean triplet: (3,4,5)

New Pythagorean triplet obtained = (24, 32, 40)

Pythagoras theorem:

For a right angles triangle the sum of square of sides of triangle is equal to the square of hypotenuse of triangle.

Verification:

$24^2 + 32^2\\=576 + 1024\\=1600\\=40^2$

Yes, Tessa is correct.

(24, 32, 40) is a Pythagorean triplet.

Pythagorean triple be created using multiplies of a known Pythagorean triple

Option A) Yes, as long as each number in the Pythagorean triple is multiplied by the same whole number.

8 0

3 years ago

Read 2 more answers

What is a unit rate?

Ksivusya [100]

Answer:

<em>A unit rate is something over a unit of something else. </em>

<u>Such as:</u> (50 miles) / hour

If you have (150 miles) / 3 hours

This is not a unit rate, therefore you have to divide the top and bottom by 3 to get the unit rate

(150/3 miles) / (3/3 hours)

(50 miles) / hour

Hope this helps :)

5 0

3 years ago

Are these correct? If not help me please??

Verizon [17]

Answer: no, no, yes, no, yes, yes

Step-by-step explanation:

x + 1, 2x, these are not equivalent

10x, 5(x+5)

5(x+5) distribute the 5 to get 5(x+5) = 5x + 25

5x + 25 is not equal to 10x, so no

1 + 2x = 2x + 1, these are equivalent since the constant and coefficients are the same

yes

2x, 2x - 5, these are not equivalent since once has a constant of -5 while the other does not

15x -1, 3(x+4x) - (3-2)

3(x+4x) - (3-2) combine like terms

3(5x) - (1) multiply through parentheses

= 15x -1

so 15x - 1 = 3(x+4x) - (3-2), these are equivalent

yes

1/2 * (4x-2),2x-1

1/2 * (4x-2) multiply through parentheses to get

2x - 1

so these two are equivalent

yes

3 0

3 years ago

Read 2 more answers

A granite installation company schedules its services based on the installation space. It schedules 3 hours for a standard kitch

dsp73

Answer:

Part A

3 Bathroom and 3 Kitchen

Part B.

$13,500

Step-by-step explanation:

Bathroom per day = 3

Average profit of Bathroom = $1,200 per hour

Kitchen per day = (12 hours - 3 hours)/3 = 3 kitchen

Average Profit from Kitchen = $3,300 / 3 = $11,00 per hour

As the company cannot do more than 3 bathrooms which has higher per hour average profit, the remaining 9 hours will be utilized for Kitchen Installation.

Part A.

Company will do 3 Bathrooms and 3 Kitchens in order to maximize the profit under given condition.

Part B.

Total Earning = ($1,200 x 3 ) + ($1,100 x 9 ) = $3,600 + $9,900 = $13,500

The company will earn Average profit of $13,500.

5 0

3 years ago

Read 2 more answers