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mojhsa [17]
1 year ago
9

If cosa=1/2(a+1/a), verify that. cos2a=1/2(a²+1/a²)​

Mathematics
1 answer:
Alborosie1 year ago
3 0

Answer:

see explanation

Step-by-step explanation:

using the identity

cos2a = 2cos²a - 1 , then

cos2a

= 2[ \frac{1}{2}(a  + \frac{1}{a}) ]² - 1

= 2 [ \frac{1}{4} (a² + \frac{1}{a^2} + 2) ] - 1

= \frac{1}{2} (a² + \frac{1}{a^2} ) + 1 - 1

= \frac{1}{2} (a² + \frac{1}{a^2} ) ← thus verified

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Lucy is tiling her bathroom. She buys white and blue tiles in the
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Answer:

£289.20

Step-by-step explanation:

13:2 = x:16 or 13/2 = x/16

cross multiply: 208 = 2x

simplify: x = 104

16 blue tiles x £2.80 each = £44.80

104 white tiles x £2.35 each = £244.40

44.80 + 244.40 = £289.20

7 0
3 years ago
Rewrite -4/15 as an equivalent fraction
timofeeve [1]

(\frac{-4}{5} ) in the form of Equivalent Fraction can be written as \frac{-4x}{15x}, where "x" is any integer.

As per the question statement, we are provided with a fraction, (\frac{-4}{5} ).

We are required to rewrite the above mentioned fraction in the form of a general Equivalent Fraction.

To solve this question, we need to know what an equivalent fraction is.

Equivalent fractions are those fractions that have different numerators and denominators but are equal to the same value, when simplified.

For example, (\frac{1}{2}, \frac{2}{4}, \frac{3}{6}, \frac{4}{8}) all equate to \frac{1}{2} when simplified.

Now, for this case, equivalent fractions of (\frac{-4}{5} ) are (\frac{-8}{30}, \frac{-12}{45}, \frac{-16}{60},...), where

\frac{-8}{30}=\frac{(-4)*2}{15*2}\\\frac{-12}{45}=\frac{(-4)*3}{15*3}\\ \frac{-16}{60}=\frac{(-4)*4}{15*4}

i.e., the equivalent fractions of (\frac{-4}{5} ) are in the form of  \frac{-4x}{15x}, where "x" can be any integer, (...-6, -5, -4, -3, -2, -1, 2, 3, 4, 5, 6...)

  • Fractions: In mathematics, a fraction is a numerical entity that is not a whole number.

To learn more about fractions, click on the link below.

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5 0
1 year ago
Bryan is taking a road trip to Dallas, Texas. His car can travel 315 miles with 18 gallons of gas. Bryan's s car holds 20 gallon
AlekseyPX
The answer is A) 87.5 miles
6 0
3 years ago
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assume that the number of production defects is 28 and that 14 of these are classified as major defects, 8 are classified as des
Arlecino [84]

Answer:  5

Step-by-step explanation:

Let A denotes the number of major defects and B denotes the number of design defect.

By considering the given information, we have

U=28\ ;\ n(A)=14\ ;\ n(B)=8\ \ ;\ n(A^c\cap B^c)=1

Now, the number of major defects or design defects:

n(A\cup B)=U-n(A^c\cap B^c)=28-11=17

Also,

n(A\cap B)=n(A)+n(B)-n(A\cup B)\\\\\Rightarrow\ n(A\cap B)=14+8-17=5

Hence, the number of  design defects were major=5

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3 years ago
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