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damaskus [11]
2 years ago
5

Evaluate cos^2 (n/12)

Mathematics
1 answer:
77julia77 [94]2 years ago
5 0

Answer:

[(2 + √3)/4] = 0.9330127

Step-by-step explanation:

We know that

cos (pi/12) ^ 2 =

cos (pi/12)* cos (pi/12)  =

[(√6 + √2)/4]*[(√6 + √2)/4] =

(0.9659)*(0.9659) = 0.9330127

[(2 + √3)/4] = 0.9330127

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The sales tax in Mansfield is 8.25% on anything purchased. What is the percent of the original price you will pay? Write your an
Fynjy0 [20]
If the tax was 10%, then you’d end up paying the original 100% plus the additional 10% tax, so you’d pay 110% of the original price.

In your example, it’s the same, except you have 8.25% tax, so you’d pay 100%+8,25% or 108.25% of the original price.
That’s stated as a percent.

To convert a percent to a decimal, you divide by 100:
108.25 ÷ 100 = 1.0825

To convert a decimal to a fraction, you have to know the place value of the smallest place. In this case, the 5 is in the ten thousandths place.
10825/10000

You can always double check that fraction on a calculator.
7 0
3 years ago
O is the centre of the circle, EF is a tangent, angle BCE = 28°, angle ACD = 31°
andriy [413]

Answer

a. 28˚

b. 76˚

c. 104˚

d. 56˚

Step-by-step explanation

Given,

∠BCE=28°  ∠ACD=31°  &  line AB=AC .

According To the Question,

  • a. the angle between a chord and a tangent through one of the end points of the chord is equal to the angle in the alternate segment.(Alternate Segment Theorem) Thus, ∠BAC=28°

  • b. We Know The Sum Of All Angles in a triangle is 180˚, 180°-∠CAB(28°)=152° and ΔABC is an isosceles triangle, So 152°/2=76˚

        thus , ∠ABC=76° .

  • c. We know the Sum of all angles in a triangle is 180° and opposite angles in a cyclic quadrilateral(ABCD) add up to 180˚,

Thus, ∠ACD + ∠ACB = 31° + 76° ⇔ 107°

Now, ∠DCB + ∠DAB = 180°(Cyclic Quadrilateral opposite angle)

∠DAB = 180° - 107° ⇔ 73°

& We Know, ∠DAC+∠CAB=∠DAB ⇔ ∠DAC = 73° - 28° ⇔ 45°

Now, In Triangle ADC Sum of angles in a triangle is 180°

∠ADC = 180° - (31° + 45°)  ⇔  104˚

   

  • d. ∠COB = 28°×2 ⇔ 56˚ , because With the Same Arc(CB) The Angle at circumference are half of the angle at the centre  

For Diagram, Please Find in Attachment  

4 0
3 years ago
what is the circumference of the circle with an arc length of 11 and an interior angle of 27° Round to nearest tenth plz
igor_vitrenko [27]

Answer:

146⅔ units

Step-by-step explanation:

27° : 11

360° : X

X = (11/27) × 360

X = 146 ⅔

6 0
3 years ago
Read 2 more answers
Here are the dimensions of the oven tray Lucy bakes the cakes on. ←700mm→↑600mm↓.A cake tin is 25cm in diameter. How many cake t
GREYUIT [131]
700*600=420,000
420,000/10=42,000
Diameter = 25
so radius = 12.5
Pi*12.5^2=625/4Pi
42,000/625/4 Pi =86.56169741
=86.6
she can fit 86 tins
8 0
3 years ago
Read 2 more answers
Which statement is true
satela [25.4K]

It would be the first one

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
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