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Talja [164]
2 years ago
12

A central angle θ in a circle of radius 4 m is subtended by an arc of length 5 m. find the measure of θ in degrees. (round your

answer to one decimal place.)
Mathematics
1 answer:
koban [17]2 years ago
5 0

Answer:

\theta=71.6\°

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference is equal to

C=2\pi r

we have

r=4\ m

substitute the values

C=2\pi (4)=8 \pi\ m

step 2

Remember that

360 degrees subtends the arc of length  8 \pi\ m (circumference)

so

by proportion

Find the measure of θ by an arc of length 5 m

assume \pi=3.1416

\frac{360}{8\pi}=\frac{\theta}{5}\\ \\ \theta=360*5/8\pi \\ \\ \theta=71.6\°

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9 hours because 8 x 3 = 24 and 3 x 3 = 9
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Find 2 numbers a and b whose sum is 4 and whose difference is -2​
umka21 [38]

Answer:

a = 1, b = 3.

Step-by-step explanation:

a + b = 4

a - b = -2     Adding to eliminate b:

2a = 2

a = 1

So 1 + b = 4

giving b = 3.

7 0
3 years ago
1. Five gallons of lemonade cost $8.00, which is<br> a rate of _____per____.
Hitman42 [59]

Answer:

1. $1.60

2. gallon

Step-by-step explanation:

Each gallon of lemonade would cost $1.60.

The rate is $1.60 per gallon.

Hope it helps!

3 0
3 years ago
Read 2 more answers
Every year, a car loses 15% of the value it had the year before. If the car's initial value is $ 24,000, then how long will it t
ella [17]

Answer:

4.62 years

Step-by-step explanation:

Half the car's value =>$24,000/2 = $12,000

The formula for exponential decrease =

y = a(1 - r)^t

y = Initial value = $24,000

a = Value after time t = $12,000

r = Decrease rate = 15% = 0.15

t = time in years =??

Hence,

24,000 = 12000 ( 1 - 0.15)^t

Divide both sides by 12000

24000/12000 = 12000 ( 0.85)^t/ 12000

2 = 0.85^t

We take the logarithm of both sides

log 2 = log (0.85)^t

log 2 = t log 0.85

Divide both sides by log 0.85

t = log 2/log 0.85

t = 4.62098120373 years

Approximately = 4.62 years

It would take 4.62 years to be worth half the initial price

8 0
3 years ago
Please help solve 1, and 2
Vadim26 [7]

Answer:

Step-by-step explanation:

1). WXYZ is a rectangle,

  Properties of a rectangle,

  i). Opposite sides are equal and parallel.

  ii). All interior angles measure 90°.

  iii). Diagonals are equal in measure.

a). WY = ZX = 30

 Therefore, ZT = \frac{1}{2}(ZX)

                    ZT=15

b). WY = ZX = 45

c). Since, WY = ZX,

    (4b - 16) = (3b + 5)

    4b - 3b = 16 + 5

     b = 21

2). GOAT is a rhombus and m∠OGA = 35°,

    a). m∠TGA = m∠OGA = 35°

    b). m∠GXO = 90°

    c). m∠GXT = 90°

    d). Since adjacent angles of a rhombus are supplementary,

         m∠OGT + m∠GTA = 180°

         70° + m∠GTA = 180°

         m∠GTA = 110°

         m∠GTO = \frac{1}{2}(m\angle GTA)

                        = \frac{1}{2}(110^{\circ})

                        = 55°

     e). Since, opposite angles of a rhombus are equal,

          m∠OGT = m∠OAT = 70°

     f). m∠GOA = m∠GTA = 110°

7 0
2 years ago
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