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Zanzabum
2 years ago
15

Match each value with its formula for ABC.

Mathematics
1 answer:
MariettaO [177]2 years ago
4 0

The solution to the question is:

c is 6 = \sqrt{a^{2} + b^{2}  -2abcosC }

b is 5 = \sqrt{a^{2} + c^{2} -2accosB  }

cosB is 2 = \frac{a^{2} + c^{2} - b^{2}   }{2ac}

a is 4 = \sqrt{b^{2} + c^{2} -2bccosA }

cosA is 3 = \frac{b^{2} + c^{2} -a^{2}   }{2bc}

cosC is 1 = \frac{b^{2}  + a^{2} - c^{2}  }{2ab}

<h3>What is cosine rule?</h3>

it is used to relate the three sides of a triangle with the angle facing one of its sides.

The square of the side facing the included angle is equal to the some of the squares of the other sides and the product of twice the other two sides and the cosine of the included angle.

Analysis:

If c is the side facing the included angle C, then

c^{2} = a^{2} + b^{2} -2ab cos C-----------------1

then c =  \sqrt{a^{2} + b^{2}  -2abcosC }

if b is the side facing the included angle B, then

b^{2} = a^{2} + c^{2} -2accosB-----------------2

b =  \sqrt{a^{2} + c^{2} -2accosB  }

from equation 2, make cosB the subject of equation

2ac cosB =  a^{2} +  c^{2} - b^{2}

cosB =  \frac{a^{2} + c^{2} - b^{2}   }{2ac}

if a is the side facing the included angle A, then

a^{2} = b^{2} + c^{2} -2bccosA--------------------3

a =  \sqrt{b^{2} + c^{2} -2bccosA }

from equation 3, making cosA subject of the equation

2bcosA =  b^{2} +  c^{2}  - a^{2}

cosA =  \frac{b^{2} + c^{2} -a^{2}   }{2bc}

from equation 1, making cos C the subject

2abcosC =  b^{2} + a^{2} -  c^{2}

cos C =  \frac{b^{2}  + a^{2} - c^{2}  }{2ab}

In conclusion,

c is 6 = \sqrt{a^{2} + b^{2}  -2abcosC }

b is 5 = \sqrt{a^{2} + c^{2} -2accosB  }

cosB is 2 = \frac{a^{2} + c^{2} - b^{2}   }{2ac}

a is 4 = \sqrt{b^{2} + c^{2} -2bccosA }

cosA is 3 = \frac{b^{2} + c^{2} -a^{2}   }{2bc}

cosC is 1 = \frac{b^{2}  + a^{2} - c^{2}  }{2ab}

Learn more about cosine rule: brainly.com/question/4372174

$SPJ1

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Two triangular pyramids are similar the volume of the large pyramids is 729cm and the volume of the smaller pyramids is 64 cm .
lilavasa [31]

Answer:

18 cm for larger base

Step-by-step explanation:

For similar figures, there is a formula regarding volume, area, and length

Large: small =  y: x   for length

large: small = (y^3) / (x^3)  for volume

729 cm cube/ 64 cm cube  = large : small

9: 4  = large: small  by length

large/ 8cm = 9/ 4

large = 8*(9/4) = 2*9 = 18 cm

8 0
3 years ago
Find the mean of, -21,-24,-37,-52,-56
Marta_Voda [28]

Answer:

-38

Step-by-step explanation:

(-21 + -24 + -37 + -52 + - 56)/5 = -38

8 0
2 years ago
Question is the attachment
astraxan [27]

If both pipes are opened. Then the number of hours to fill up the tank fully is 100 hours.

The complete question is attached below.

<h3>What are ratio and proportion?</h3>

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

Let t be the filling time.

Then we have

Time is inversely proportional to rate of filling tank.

1/20 – 1/25 = 1/t

0.05 - 0.04 = 1/t

          0.01 = 1/t

                t = 1/0.01

                t = 100 hours

More about the ratio and the proportion link is given below.

brainly.com/question/14335762

#SPJ1

5 0
1 year ago
ARI
dezoksy [38]

Answer:

f(x)= 1/2x + 2

Step-by-step explanation:

3 0
3 years ago
[Caculus HW]
Monica [59]
3p=p(1+(.0557/365))^365t. Where, p is the beginning amound at t is the time it takes. You're right, just solve for t. If you need help with that, just ask! :)

EDIT:
Alrighty. So, you divide by p, to get 3=(1+(.0057/365))^365t. Now, we evaluate the inside to get 1.000015616, rounded to 9 decimal places. We now need to use logarithms to figure out what that t is. Trust me on this, or look up the mathematics behind it. We need that 1.0000... as the base for our log, and we need to have the actual subject of the log be the 3. Now that we have log base 1.000015616 of 3, we divide that atrocity by 365. We now get t to be equal to 192.7459133, rounded to 7 decimal places. While this does seem ungodly long, remember that everything in our problem is done in days. So, in reality, that just over half of a year.
4 0
3 years ago
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