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kozerog [31]
3 years ago
15

983.53 in a fraction and word form

Mathematics
1 answer:
trasher [3.6K]3 years ago
4 0
Nine hundred eighty-three and fifty-three hundredths in word form
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Use triangle ABC drawn below & only the sides labeled. Find the side of length AB in terms of side a, side b & angle C o
Brrunno [24]

Answer:

AB = \sqrt{a^2 + b^2-2abCos\ C}

Step-by-step explanation:

Given:

The above triangle

Required

Solve for AB in terms of a, b and angle C

Considering right angled triangle BOC where O is the point between b-x and x

From BOC, we have that:

Sin\ C = \frac{h}{a}

Make h the subject:

h = aSin\ C

Also, in BOC (Using Pythagoras)

a^2 = h^2 + x^2

Make x^2 the subject

x^2 = a^2 - h^2

Substitute aSin\ C for h

x^2 = a^2 - h^2 becomes

x^2 = a^2 - (aSin\ C)^2

x^2 = a^2 - a^2Sin^2\ C

Factorize

x^2 = a^2 (1 - Sin^2\ C)

In trigonometry:

Cos^2C = 1-Sin^2C

So, we have that:

x^2 = a^2 Cos^2\ C

Take square roots of both sides

x= aCos\ C

In triangle BOA, applying Pythagoras theorem, we have that:

AB^2 = h^2 + (b-x)^2

Open bracket

AB^2 = h^2 + b^2-2bx+x^2

Substitute x= aCos\ C and h = aSin\ C in AB^2 = h^2 + b^2-2bx+x^2

AB^2 = h^2 + b^2-2bx+x^2

AB^2 = (aSin\ C)^2 + b^2-2b(aCos\ C)+(aCos\ C)^2

Open Bracket

AB^2 = a^2Sin^2\ C + b^2-2abCos\ C+a^2Cos^2\ C

Reorder

AB^2 = a^2Sin^2\ C +a^2Cos^2\ C + b^2-2abCos\ C

Factorize:

AB^2 = a^2(Sin^2\ C +Cos^2\ C) + b^2-2abCos\ C

In trigonometry:

Sin^2C + Cos^2 = 1

So, we have that:

AB^2 = a^2 * 1 + b^2-2abCos\ C

AB^2 = a^2 + b^2-2abCos\ C

Take square roots of both sides

AB = \sqrt{a^2 + b^2-2abCos\ C}

6 0
3 years ago
The number of laps Katie ran was 2:3.If Louis ran 4 miles, how far did katie run?
agasfer [191]

Answer ran 2 3/4 miles in 1/3 of an hour

2 3/4 miles =11/4 miles in 1/3 of hour

11/4 miles divided by 1/3 hr

11/4 ÷ 1/3

11/4 * 3/1 =33/4 =8 1/4 miles in 1 hr

5 0
3 years ago
Very confusing, please help
Ksivusya [100]

Answer:

A -2*-2 ≠- 4

Step-by-step explanation:

sqrt(-4)

The answer is an imaginary number

-2*-2 = 4 not -4

7 0
3 years ago
Read 2 more answers
in a marathon race (42.195 km), the winner’s time is 2 hours, 13 minutes, and 9 seconds, while the second-place time is 2 hours,
algol [13]

in a marathon race (42.195 km), the winner’s time is 2 hours, 13 minutes, and 9 seconds, while the second-place time is 2 hours, 26 minutes, and 6 seconds . The distance is 2.664 km.

D = distance of marathon = 42.195 km = 42195 m

tw = time taken by winner = 2 h 17 min = 2 (60) + 17 = 137 min = 137 (60) = 8220 sec

Vw = speed of winner

speed of winner is given as

Vw = D /tw = 42195/8220

ts = time taken by second place = 2 h 26 min 14 sec = 2 (60)(60) + (26)(60) + 14 = 8774 s

Vs = speed of second place

speed of second place is given as

Vs = D /ts = 42195/8774

distance of the second place holder from the finish line is given as

D' = Vs (ts - tw)

D' = (42195/8774 )(8774 - 8220)

D' = 2664.24 m

D'= 2.664 km

To learn more about distance  visit:brainly.com/question/15172156

#SPJ4

7 0
1 year ago
What is the explicit rule for the sequence? −3, 0,3,6,9,... Enter your answer in the box.
PtichkaEL [24]

Answer:

  • aₙ = 3n - 6

Step-by-step explanation:

<u>Given sequence:</u>

  • −3, 0,3,6,9,...

<u>This is AP with:</u>

  • The first tern a₁ = - 3
  • Common difference d = 3

<u>The rule for the nth term of the sequence is:</u>

  • aₙ = a₁ + (n - 1)d

<u>Substitute values:</u>

  • aₙ = -3 + (n - 1)(3) =
  •       -3 + 3n - 3 =
  •        3n - 6

3 0
3 years ago
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