All categories

1 year ago

Sin70° sin130° sin170°=1/8

1 answer:

7 0

Sin 10° Sin 50° sin 70° = 1/8
Now we multiply upper & bottom both side 2/2

then

➡ 1/2 (2sin 10° sin50° 70°)

➡ 1/2 sin10°( 2sin70° sin50°)

we know that
2 sinA sinB = cos (A-B) - cos (A+B)

Then

➡ 1/2 sin 10° ( cos 20° - cos 120°)

➡ 1/2 sin 10° ( cos 20° - cos (90°+30°))

➡ 1/2 sin 10° ( cos 20° +1/2)

➡ 1/2 sin 10° cos 20° +1/4 sin 10°

again we multiply both upper & bottom side 2/2 so

➡ 1/4 ( 2 sin 10° cos 20°). + 1/4 sin 10°

we know that
2 sinA cos B = sin (A+B) - sin (A- B)

➡ 1/4 (sin 30° - sin 10°) + 1/4 sin 10°

➡ 1/4 sin 30° - 1/4 sin 10° + 1/4 sin 10°

we know sin 30° = 1/2

➡ 1/4 × 1/2

➡ = 1/8 hence proved

You might be interested in

The yard behind the Cindy's house is rectangular in shape and has a perimeter of 72 feet. If the length l of the yard is 18 feet

QveST [7]

Let the width of the yard be w.
Since the length is 18feet longer, l = w + 18

Perimeter for rectangle = 2(l + w)

2(l + w) = 72

2(w+18 + w) = 72    Divide 2 on both sides

   (w + 18 + w) = 36

   2w + 18 = 36

   2w = 36 - 18

2w = 18 Divide 2 on both sides

w = 18/2

   w = 9

Recall, length l = w + 18, l = 9 + 18 = 27

Hence width, w = 9, length,l = 27

Area of rectangle = l × w = 27 × 9 = 243

Area of rectangular yard = 243 square feet.

8 0

2 years ago

Taxes on the property buyer Tamara is purchasing are $8,200, due on December 31. If the closing is set for June 29th, using the

rosijanka [135]

The buyer will be paying taxes for 185 days, so will pay

... (185/365)·$8200 = $4156

Your most appropriate choice seems to be $4178, which corresponds to 186 days' taxes.

_____

There are 30 days in each month in the last half of the year, plus 1 additional day in each of July, August, October, and December. The 30th of June also belongs to the buyer (but the 29th, closing day, does not), so there are 180+5 = 185 days for which the buyer must pay taxes. The answer choices don't include that value.

3 0

1 year ago

At a display booth at an amusement park, every visitor gets a gift bag. Some

kotegsom [21]

The bag will often contain all three items every 70 bags ⇒ answer C

Step-by-step explanation:

At a display booth at an amusement park, every visitor gets a gift bag

according to these information:

1. Hat Every 2nd visitor

2. T-shirt Every 7th visitor

3. Backpack Every 10th visitor

We need to know how often a bag will contain all three items

To solve this problem you must find a number divisible by 2, 7, and 10

To find that number start with the multiples of the largest one and

check them with the other two numbers

∵ The largest number is 10

∵ The multiples of 10 are 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , .......

- Look for the first multiple of 10 is divisible by 7

∵ 70 is the first multiple of 10 divisible by 7

∵ 70 is divisible by 2 because its even number

∴ 70 is the smallest number divisible by 2, 7 and 10

The bag will often contain all three items every 70 bags

Learn more:

You can learn more about numbers in brainly.com/question/537998

#LearnwithBrainly

4 0

1 year ago

One of the sides of a parallelogram is 4.2 cm and the altitude to that side is 3.6 cm. Find the perimeter of the parallelogram i

dexar [7]

Area of parallelogram = base * height
base 1 = 4.2 cm
height 1 = 3.6 cm
∴ Area = 4.2 * 3.6 = 15.12

let the other base 2 = x
∴ the altitude of this base = height 2 = 2.4
∴Area = 2.4 x = 15.12
Solve for x
∴ x = 6.3 cm

∴ The perimeter of parallelogram = 2( base 1 + base 2)
= 2 ( 4.2 + 6.3 ) = 21 cm

7 0

2 years ago

Select the correct augmented matrices. Liam wants to buy a car and pay for it in three installments. The total cost of the car i

Alexxandr [17]

Answer:

Step-by-step explanation:

Given:

The total cost of the car is 29,000 dollars. Which is paid in three installments . x , y and z are the installments.

To Find:

The value of x, y and z.

Solving:

It is said that 2 times the 1 installment is $1,000 ore than the sum of the 3 rd installment and 3 times the second installment.

= 2x = 1000 + z + 3y

Transposing:

= z = 2x - 3y - 1000

x + y + z = 29000 + 2100

= x + y + z = 31100

= x + y + 2x - 3y - 1000 = 31100

= 3x - 2y = 32100

First installment at start paid = x (We have assumed)

Remaining Installment which is left to pay = 29,000 - x

(29,000 - x) * 15 /100 = Interest for First

= (29000 - x) * 3/20

=> 4350 - 0.15x

Installment Paid Second = y

(29000 - x) + 4350 - 0.15x - y ) * 15/100 = Interest Second

(29000 - x) + 4350 - 0.15x - y ) * 3/20

= 5002.5 - 0.1725x - 0.15y

Interest of 1st installment + Interest of 2nd installment = 2100

Using this principle solving:

= 4,350 - 0.15x + 5,002.5 - 0.1725x - 0.15y = 2,100

= 0.3225x + 0.15y = 7,252.5

= 6.45x + 3y = 1,45,050

= 12.9x + 6y = 2,90,100

= 4.3x + 2y = 96,700

= 4.3x + 2y = 96700

= 3x - 2y = 32,100

= 7.3x = 1,28,800

= x ≈ 17644 ( 17,643.8356)

3x - 2y = 32,100

= y ≈ 10416 (10,415.7534 )

x + y + z = 31100

= z ≈ 3040 ( 3,040.4110 )

7 0

2 years ago

Sin70° sin130° sin170°=1/8​

Sin70° sin130° sin170°=1/8