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MrRa [10]
3 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]3 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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kotegsom [21]
Thank you for posting your question here at brainly. Feel free to ask more questions.  

The best and most correct answer among the choices provided by the question is <span>(D) f(n) = 0.9 * f(n - 1) + 10, f(0) = 175, n > 0 .</span> <span>       
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4 0
3 years ago
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Simplify the expression (x^3- 5x^2 + 7x - 12) ÷ (x – 4) using long division​
Kisachek [45]

Answer:

{x}^{2} - x + 3

Step-by-step explanation:

Instead, since the divisor is in the form of x - c, use what is called Synthetic Division. Remember, in this formula, -cgives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:

4| 1 −5 7 −12

↓ 4 −4 12

_______________

1 −1 3 0 → {x}^{2} - x + 3

You start by placing the c in the top left corner, then list all the coefficients of your dividend [x³ - 5x² + 7x - 12]. You bring down the original term closest to c then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient can be an {x}^{2}, the −1 [x] follows right behind it, and bringing up the rear, comes the 3, giving you the quotient of {x}^{2} - x + 3.

I am joyous to assist you anytime.

5 0
3 years ago
(PLEASE HELP!!!)Where does the following graph have clusters of data? Select all that apply.
grigory [225]

Answer:

1-5

Step-by-step explanation:

It has clusters from 1 to 5 because that is where all the dots are that are not seperated.

8 0
3 years ago
Suppose that y varies directly with x<br> and y = 10 when x = 20. What is y<br> when x = 15?
tresset_1 [31]

Answer: y = 7.5

Step-by-step explanation:

Suppose that y varies directly with x

That is, y∝x

Convert y∝x to a full equation by introducing a constant k to the right hand side.

Therefore, y = kx

Given that y = 10 and x = 20

Substitute y and x in the equation above. We have;

10 = k(20)

10 = 20k

20k = 10

k = 10/20

k = 0.5

Since k = 0.5, the equation y = kx becomes y = 0.5x

Now, to find y if x = 15, substitute x in equation y = 0.5x

Therefore, y = 0.5(15)

y = 7.5

5 0
3 years ago
A naval engineer uses the function, P, to analyze the effects of water pressure on submarines. The function P(d) measures the pr
saw5 [17]

The function that the naval engineer uses related P (pressure) and d (depth of ocean).

<em>Is there any restriction on the domain ( d: depth of the ocean)? Yes!</em>

The domain would be from 0 (at sea level or 0 depth) until the depth of the ocean (which is not infinite). Hence, we can write:

0\leq d\leq DepthOfSeaFloor

Choice D is the correct one.


ANSWER: D

5 0
3 years ago
Read 2 more answers
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