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loris [4]
3 years ago
13

10 the sides of a triangle are 17ft., 19ft., and 15 ft. find the measure of the angle opposite the longest side. round your answ

er to the nearest degree
Mathematics
1 answer:
nalin [4]3 years ago
4 0
The law of cosines is used for this purpose. It tells you
  c² = a² + b² - 2ab×cos(C)
Solving for the angle C gives
  C = arccos((a² + b² - c²)/(2ab))
  C = arccos(( 17² + 15² - 19²)/(2×17×15))
  C = arccos(153/510)
  C ≈ 72.5424°

The measure of the angle opposite the longest side is about 73°.
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6 0
3 years ago
If 2k, 5k-1 and 6k+2 are the first 3 terms of an arithmetic sequence, find k and the 8th term​
Klio2033 [76]

Answer:

see explanation

Step-by-step explanation:

The common difference d of an arithmetic sequence is

d = a_{2} - a_{1} = a_{3} - a_{2}

Substitute in values and solve for k, that is

5k - 1 - 2k = 6k + 2 - (5k - 1)

3k - 1 = 6k + 2 - 5k + 1

3k - 1 = k + 3 ( subtract k from both sides )

2k - 1 = 3 ( add 1 to both sides )

2k = 4 ⇒ k = 2

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

The n th term of an arithmetic sequence is

a_{n} = a_{1} + (n - 1)d

a_{1} = 2k = 2 × 2 = 4 and

d = 5k - 1 - 2k = 3k - 1 = (3 × 2) - 1 = 5

Hence

a_{8} = 4 + (7 × 5) = 4 + 35 = 39

4 0
3 years ago
The circumference of Circle F is 72 cm. What is the length of Arc DE (the minor arc)?
Tom [10]

You need to first set up the equation:

It would look like 90 divided by 360 multiplied by the given circumference which is 72 cm.

So 90 / 360 x 72

Simply the fraction above, it will give us:

¼ x 72

So the answer would be 18 cm that is the length of DE (minor arc)

4 0
4 years ago
Read 2 more answers
Integrate the following. ∫<img src="https://tex.z-dn.net/?f=5x%5E%7B4%7D%20dx" id="TexFormula1" title="5x^{4} dx" alt="5x^{4} dx
Vadim26 [7]

Answer:

\displaystyle D)  {x}^{5}  +  \rm C

Step-by-step explanation:

we would like to integrate the following Integral:

\displaystyle \int 5 {x}^{4} \, dx

well, to get the constant we can consider the following Integration rule:

\displaystyle \int c{x} ^{n}  \, dx  =  c\int  {x}^{n}  \, dx

therefore,

\displaystyle 5\int  {x}^{4} \, dx

recall exponent integration rule:

\displaystyle \int {x} ^{n}  \, dx  =  \frac{ {x}^{n + 1} }{n + 1}

so let,

  • n = 4

Thus integrate:

\displaystyle  =  5\left( \frac{ {x}^{4+ 1} }{4 +  1}  \right)

simplify addition:

\displaystyle  =  5\left( \frac{ {x}^{5} }{5}  \right)

reduce fraction:

\displaystyle  =  {x}^{5}

finally we of course have to add the constant of integration:

\displaystyle  \boxed{ {x}^{5}  +  \rm C}

hence,

our answer is D)

7 0
3 years ago
Read 2 more answers
Solve a,b,c,d and e.​
Westkost [7]

Answer:

Step-by-step explanation:

a)

 428721

Place of 2's 10s and 10,000s

Therefore its value is 20 and 20,000

Product of the place value = 20 x 20,000 = 4,00,000

b)

37,20,861

Place of 7 is 1,00,000

Therefore the place value is 7,00,000

c)

Greatest 7 digit number is 99,99,999

Adding 1 to it = 99,99,999 + 1 = 1,00,00,000

d)

85642 = 80000 + 5000 + 600 + 40 +2

e)

round off 85642  to nearest thousand = 86,000

7 0
3 years ago
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