a machinist can produce 114 Parts in 6 minutes at this rate how many parts can the machinist is produce in 15 minutes

Express the following the ratio in the simplest term<br> A 45;6 B 54;36 C 12;8;16

spayn [35]

8 0

3 years ago

For positive acute angles A and B, it is known that cos A= 20/29 and tan B= 11/60. Find the value of cos(A + B) in simplest form

jek_recluse [69]

Answer:

$\displaystyle \cos(A + B) =\frac{969}{1769}$

Step-by-step explanation:

We are given that:

$\displaystyle \cos A=\frac{20}{29}\text{ and } \tan B=\frac{11}{60}$

Where A and B are positive acute angles.

And we want to find cos(A + B).

Recall that cosine is the ratio of the adjacent side to the hypotenuse. Using this information, find the opposite side with respect to Angle A:

$o=\sqrt{29^2-20^2}=21$

Tangent is the ratio of the opposite side to the adjacent side. Find the hypotenuse with respect to Angle B:

$h=\sqrt{11^2+60^2}=61$

In summary:

With respect to Angle A, the adjacent side is 20, opposite is 21, and the hypotenuse is 29.

With respect to Angle B, the adjacent side is 60, the opposite is 11, and the hypotenuse is 61.

We can rewrite our expression as:

$\displaystyle \cos(A+B)=\cos A\cos B-\sin A\sin B$

Using the above information, substitute in the appropriate values. Note that since A and B are positive acute angles, all trigonometric values will be positive. Hence:

$\displaystyle \cos(A + B)=\left(\frac{20}{29}\right)\left(\frac{60}{61}\right)-\left(\frac{21}{29}\right)\left(\frac{11}{61}\right)$

Simplify:

$\displaystyle \cos(A + B) =\frac{1200-231}{1769}=\frac{969}{1769}$

3 0

3 years ago

A football stadium splits ticket sales in ratio of 3 : 4 between the away team and the home team. The home team make £36,000. Wh

Naddika [18.5K]

<h3>Answer is 63,000 pounds</h3>

The ratio 3:4 means for every 3 pounds made in away team tickets versus home team tickets. Multiply both sides by 9000 to have that 4 turn into 36000. The ratio 3:4 will then turn into 27000:36000

With this new ratio, we see that the away team pulls in 27000 and the home team pulls in 36000. Add the two amounts to get the final answer

27000+36000 = 63000

------------

We could alternatively add 3 and 4 (from the ratio 3:4) to get 3+4 = 7. Then multiply by that same scale factor 9000 getting 9000*7 = 63000.

5 0

3 years ago

. 8 yards = __________ inches *

katrin [286]

Answer:

28.8

Step-by-step explanation:

0.8 yards = 28.8 inches

6 0

3 years ago

Read 2 more answers

Build the graph of the equation (x+8)(y-10)=0 FIND THE TWO POINTS

alisha [4.7K]

Answer:

Step-by-step explanation:

Theoretically speaking, both equations need to equal 0.

Let's start with (x + 8)

x + 8 = 0

x = 0 - 8

x = -8

Then, let's go to (y - 10)

y - 10 = 0

y = 10 = 0

y = 10

So, x = -8 & y = 10

Hope that helps!

3 0

3 years ago