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3 years ago

Solve the triangle A=21 C=105 c=5

Mathematics

1 answer:

gregori [183]3 years ago

3 0

Answer:

Granted that uppercase letters are the angles measurements and lowercase letters are the side lengths. I also was unable to round as I don't know to what decimal you need to round to.

First to find the measure of angle B, we must subtract A and C from 180

$180-21-105=54$

B=54

Next, we can use the law of sines in order to find the measures of a and b

As a reminder, The law of sines is

$\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}$

First, lets solve for b

$\frac{b}{sin54}=\frac{5}{sin105} \\\\b=\frac{(5)sin54}{sin105}\\\\b=4.187780119$

Next lets solve for a

$\frac{a}{sin21}=\frac{5}{sin105} \\\\a=\frac{(5)sin21}{sin105}\\\\a=1.85504901$

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A car is travelling at exactly 6 miles per hour and accelerates at a constant rate to exactly 65 miles per hour.

vichka [17]

Answer:

$14878.04878miles/hours^2$

Step-by-step explanation:

Let's find a solution by understanding the following:

The acceleration rate is defined as the change of velocity within a time interval, which can be written as:

$A=(Vf-Vi)/T$ where:

A=acceleration rate

Vf=final velocity

Vi=initial velocity

T=time required for passing from Vi to Vf.

Using the problem's data we have:

Vf=65miles/hour

Vi=6miles/hour

T=14.8seconds

Using the acceleration rate equation we have:

$A=(65miles/hour - 6miles/hour)/14.8seconds$ , but look that velocities use 'hours' unit while 'T' uses 'seconds'.

So we need to transform 14.8seconds into Xhours, as follows:

$X=(14.8seconds)*(1hours/60minutes)*(1minute/60seconds)$

$X=0.0041hours$

Using X=0.0041hours in the previous equation instead of 14.8seconds we have:

$A=(65miles/hour - 6miles/hour)/0.0041hours$

$A=(61miles/hour)/0.0041hours$

$A=(61miles)/(hour*0.0041hours)$

$A=61miles/0.0041hours^2$

$A=14878.04878miles/hours^2$

In conclusion, the acceleration rate is $14878.04878miles/hours^2$

7 0

3 years ago

Can you guys help me out on this? I'm still learning sign, cosign, and tangent :)

lara [203]

Answer:

1. 12/13 and 5/13

2. 5/13 and 12/13

3. The sin of <A and cos of <B are congruent.

Since "Sine" is Opposite/Hypotenuse and Cosine is adjacent hypotenuse...

The opposite of angle A is 12, and the hypotenuse is 12, therefore making 12/13.

The adjacent of angle B is 12, (The adjacent side is the side next to the opposite that is not the hypotenuse) and the hypotenuse is 13, therefore making 12/13. (The hypotenuse never changes no matter how you look at the triangle.)

Sin <A = 12/13

Cos <B= 12/13

7 0

3 years ago

Eights rooks are placed randomly on a chess board. What is the probability that none of the rooks can capture any of the other r

erastova [34]

Answer:

The probability is $\frac{56!}{64!}$

Step-by-step explanation:

We can divide the amount of favourable cases by the total amount of cases.

The total amount of cases is the total amount of ways to put 8 rooks on a chessboard. Since a chessboard has 64 squares, this number is the combinatorial number of 64 with 8, $64 \choose 8 .$

For a favourable case, you need one rook on each column, and for each column the correspondent rook should be in a diferent row than the rest of the rooks. A favourable case can be represented by a bijective function $f : A \rightarrow A ,$ with A = {1,2,3,4,5,6,7,8}. f(i) = j represents that the rook located in the column i is located in the row j.

Thus, the total of favourable cases is equal to the total amount of bijective functions between a set of 8 elements. This amount is 8!, because we have 8 possibilities for the first column, 7 for the second one, 6 on the third one, and so on.

We can conclude that the probability for 8 rooks not being able to capture themselves is

$\frac{8!}{64 \choose 8} = \frac{8!}{\frac{64!}{8!56!}} = \frac{56!}{64!}$

7 0

3 years ago

Tonya plans to join a fitness club. She researched the costs to join different clubs in her area and found that there is a linea

Ne4ueva [31]

Answer: 1 club - Club 2

Step-by-step explanation:

You can find the monthly rates by deducting the cost at 12 months from the cost at 24 months and dividing it by 12.

Club 1 Club 2 Club 3

= (432 - 216) / 12 = (390 - 210) / 12 = (504 - 252) / 12

= $18 = $15 = $21

Multiply these rates by 6 months and any club total cost at 6 month that differs from your answer has a joining fee.

Club 1; Club 2; Club 3

= 18 * 6 = 15 * 6 = 21 * 6

= $108 = $90 = $126

Same as total cost at Joining fee of $30; No joining fee as

6 months so no joining 120 - 90 = $30 this is the same

fee. as total cost at 6

months.

5 0

3 years ago

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Anybody want to role play ???

Afina-wow [57]

Answer:

Thats smarttt

Step-by-step explanation:

You phrased it so it would get pass the brainly bots system, kudos to you!

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3 years ago