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MrRa [10]
2 years ago
13

Prove that the max and min values of asinX + bcosX are respectively sqrt.(a^2+b^2) and -sqrt(a^2+b^2) .

Mathematics
1 answer:
strojnjashka [21]2 years ago
6 0
The solution to the problem is as follows:
let y = asinx + bcosx 
<span>
dy/dx = acosx - bsinx </span>
<span>
= 0 for max/min </span>
<span>
bsinx = acosx </span>
<span>
sinx/cosx = a/b </span>
<span>
tanx = a/b </span>
<span>
then the hypotenuse of the corresponding right-angled triangle is √(a^2 + b^2) </span>

<span>the max/min of y occurs when tanx = a/b </span>
<span>
then sinx = a/√(a^2 + b^2) and cosx = b/√(a^2 + b^2) </span>
<span>
y = a( a/√(a^2 + b^2)) + b( b/√(a^2 + b^2)) </span>
<span>
= (a^2 + b^2)/√(a^2 + b^2) </span>
<span>
= √(a^2 + b^2)</span>

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
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You have two parents, four grandparents, eight greatgrandparents, and so forth.
Leviafan [203]
A.
In the first generation we have 2 ancestors.
In the second generation we have 4 ancestors or 2^{2} ancestors.
In the third generation we have 8 ancestors ot 2^{3} ancestors.

We can see that each succesive generation has two times more members. The sum is:
2+4+8+16+...+ 2^{40}

To calculate number of ancestors we can use formula <span>for the sum of a geometric sequence. Geometric sequence is sequence of numbers that differ by a certain factor. This factor is called ratio. Formula is:
</span>S= a_{1} * \frac{1- r^{n} }{1-r}
<span>Where:
S -> sum
a1 -> first member of a sequence
r -> ratio
n -> number of elements

For this question:
a1 = 2
r = 2
n = 40
</span>S= 2* \frac{1- 2^{40} }{1-2} =2 199 023 255 550
<span>
b.
1 generation = 25 years
40 generations = 40 * 25 = 1000 years

c.
Total number of people who have ever lived = </span>10^{10}
Number of ancestors in 40 generations = 2.2*10^{12}

The number of ancestors is greater than total number of people who have ever lived. This means that not all ancestors were distinct and that in each generation both men and women had children with more than one partner.
8 0
3 years ago
Don’t understand again?
Makovka662 [10]

<u><em>10 2/7 ÷ 3/14</em></u>              First Write The Equation

<u><em>72/7 ÷ 3/14</em></u>                Use KCF which is Keep, Change, and Flip

<u><em>1008/21</em></u>                      Use Division Of Equality

<u><em>Answer: 48</em></u>

8 0
3 years ago
You invest an initial $1,000 in an account that has an annual interest rate of 2%, compounded quarterly. How much money will you
stellarik [79]
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3 0
3 years ago
When x = 12<br> , y = 47. What is the value of y when x = 312<br> ?
grandymaker [24]

Answer:

1222

Step-by-step explanation:

312/12 = 26

So, you have to multiply y (47) by 26

This will get you 1222

4 0
3 years ago
Read 2 more answers
Please help another assignment I’m not very good at math !!
juin [17]

Answer:

Prime Factorization of 576

576=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3

Prime Factorization of 64

64=2\times 2\times 2\times 2\times 2\times 2

The Expression in simplest form is

\sqrt{\dfrac{576}{64} }=\dfrac{3}{1}

Step-by-step explanation:

Simplify:

\sqrt{\dfrac{576}{64} }

Now,

Prime Factorization of 576

576=2\times 288\\576=2\times 2\times 144\\576=2\times 2\times 2\times 72\\576=2\times 2\times 2\times 2\times 36\\576=2\times 2\times 2\times 2\times 2\times 18\\576=2\times 2\times 2\times 2\times 2\times 2\times 9\\576=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3

Prime Factorization of 64

64=2\times 32\\64=2\times 2\times 16\\64=2\times 2\times 2\times 8\\64=2\times 2\times 2\times 2\times 4\\64=2\times 2\times 2\times 2\times 2\times 2

Now,

\sqrt{\dfrac{576}{64} }=\sqrt{\dfrac{2\times 2\times 2\times 2\times 2\times 2\times 3\times 3}{2\times 2\times 2\times 2\times 2\times 2} }\\ \sqrt{\dfrac{576}{64} }=\sqrt{\dfrac{3\times 3}{1}}\\\therefore \sqrt{\dfrac{576}{64} }=3

The Expression in simplest form is

\sqrt{\dfrac{576}{64} }=\dfrac{3}{1}

8 0
3 years ago
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