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KatRina [158]
3 years ago
15

PLEASE HELP ME

Mathematics
1 answer:
Citrus2011 [14]3 years ago
6 0
The answer is -15 yayaya
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Find constants a and b such that the function y = a sin(x) + b cos(x) satisfies the differential equation y'' + y' − 7y = sin(x)
Elza [17]
The first thing we must do in this case is find the derivatives:
 y = a sin (x) + b cos (x)
 y '= a cos (x) - b sin (x)
 y '' = -a sin (x) - b cos (x)
 Substituting the values:
 (-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
 We rewrite:
 (-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
 sin (x) * (- a-b-7a) + cos (x) * (- b + a-7b) = sin (x)
 sin (x) * (- b-8a) + cos (x) * (a-8b) = sin (x)
 From here we get the system:
 -b-8a = 1
 a-8b = 0
 Whose solution is:
 a = -8 / 65
 b = -1 / 65
 Answer:
 
constants a and b are:
 
a = -8 / 65
 
b = -1 / 65
4 0
2 years ago
Tom Harding is a proofreader. He is paid $0.23 for every page he proofs. What is Tom's total pay for a week in which he proofrea
natka813 [3]
Alrighty, what I was always taught was to start by writing out what you know from the question.

What I know:
-Tom is paid $0.23 for every page of proofs.
-He proofreads 1,992 pages.

In order to figure out how much money Tom has made, we need to multiply 0.23 by 1,992. Multiplying allows us to see the total amount of money made by proofreading x amount of pages - for every page he proofreads, he makes $0.23.
0.23×1992=458.16

Therefore, Tom made $458.16.

Hope this helps!

3 0
3 years ago
Help solving this math problem
daser333 [38]

Diagram of two triangles

The two triangles are similar because they are both right triangles, meaning that one angle is 90° and the other two are acute (less than 90°).

The diagram on the left is missing its hypotenuse - the variable <em>c</em><em>.</em><em> </em>The hypotenuse is opposite of the right angle. The diagram on the right side is missing one of its legs.

Note: The hypotenuse is the <em>longest</em><em> </em>side of a right triangle.

Word Problen

The legs are 21 blocks and 20 blocks because they are by the right angle. Use the Pythagorean theorem to find the diagonal path's length, which is the hypotenuse.

{a}^{2}  +  {b}^{2}  =  {c}^{2}

Standard form of Pythagorean theorem.

{21}^{2}  +  {20}^{2}  =  {c}^{2}

Equation with the legs substituted and the missing hypotenuse value - <em> </em><em>c</em><em>.</em>

841 =  {c}^{2}

Square the legs and add.

\sqrt{841}  = c

29 = c

Take the square root and simplify. The square root of 841 is 29 and -29, but distance is positive.

Thus the diagonal distance is 29 blocks.

Check by substituting.

5 0
3 years ago
Need help ASAP
diamong [38]

Answer:

b. {-9, 3}.

Step-by-step explanation:

x^2 + 6x - 27 = 0

We need 2 numbers whose product is -27 and whose sum is + 6.

These are + 9 and - 3. So the factors are:

(x - 3)(x + 9) = 0

(x - 3) = 0 or (x + 9) = 0

x = 3 or -9.

7 0
3 years ago
Read 2 more answers
Someone help me please, 25 points
ycow [4]
A. (x+8)^ 2 + 1
B. (x-3)^ 2 - 8
C. ( x - 3/2) ^ 2 - 1/4
4 0
2 years ago
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