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Prove that 1 + tan^2 x = sec^2 x

We know that tan x = sin x/cos x and so tan 2 x = sin 2 x/cos 2 x. We also know that sin 2 x + cos 2 x = 1 because this is a Pythagorean identity. We can rewrite the left hand side as (cos 2 x + sin 2 x)/cos...
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Answered by Eleanor F. • Maths tutor
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Integrate 2x^2 + 4

When we integrate, we raise the power by one and divide the term by the new power. So let's break the question down term by term. When integrating 2x 2 we raise the power by 1 to get 2x 3 . We then divide 2x...
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Answered by Eleanor F. • Maths tutor
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In a science experiment a substance is decaying exponentially. Its mass, M grams, at time t minutes is given by M=300e^(-0.05t). Find the time taken for the mass to decrease to half of its original value.

Firstly, calculate the initial value of of M, by substituting t = 0 into the equation M=300e -0.05t Initially, M 0 = 300e 0 =300 x 1 = 300When the substance mass has decreased to half its initial value, M = ...
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Answered by Bony R. • Maths tutor
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How do you divide fractions and mixed numbers

If the question is as such: 3/4 divided by 2/3 you simply reverse the second fraction (making it 3/2) and now multiply the two together. For example, it should now read 3/4 x 3/2 = 9/8. This can then by put ...
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Answered by Nicholas W. • Maths tutor
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A cycle race is 3069.25 miles. Juan travels at a speed of 15.12 miles per hour. He cycles for 8 hours a day. Estimate how many days Juan will take to complete the race.

s = d/ t= 3069.25/ 15.12It is an estimated value, so you may use rounded values = 3000/ 15= 200 hours He will be travelling 8 hours every day= 200/ 8= 25 days
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Answered by Harith H. • Maths tutor
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