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Anuta_ua [19.1K]
2 years ago
9

If y=a sin 3x+ b cos 3x and

la1" title="\frac{d^{2} y }{dx^{2} }" alt="\frac{d^{2} y }{dx^{2} }" align="absmiddle" class="latex-formula"> = ky, then what is the value of k?
Someone pls asnwer, correct answer will be marked as the brainiest. No spam!!
Mathematics
1 answer:
Black_prince [1.1K]2 years ago
3 0

Step-by-step explanation:

You have to do first and second derivatives :

y = a sin 3x + b cos 3x

dy/dx = 3a cos 3x - 3b sin 3x

d²y/dx² = - 9a sin 3x - 9b cos 3x

Next, you have to compare it :

let d²y/dx² = ky,

-9a sin 3x - 9b cos 3x = k(a sin 3x + b cos 3x)

-9(a sin 3x + b cos 3x) = k(a sin 3x + b cos 3x)

Therefore, k is equals to 9.

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Find the volume of the rectangular prism
HACTEHA [7]

Answer:

421.875

Step-by-step explanation:

because the formula of the rectangular prism is l*w*h

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Alicia used 4 gallons of gasoline to travel 90 miles. At the same rate, how far can she travel on a full tank that holds 18 gall
MrRa [10]
90 miles/4 gallons = 22.5 miles/1 gallon.

22.5 miles*18 gallons= 405 miles

the answer is 405 miles
6 0
3 years ago
Rectangular windows are being made into a wall of windows for an office building. Each wall is 14 feet tall and 12 feet wide. Th
Artemon [7]

Answer:

  168/(x² +7x)

Step-by-step explanation:

The height of each window is 14/(x+7), and the width of each window is 12/x. The area of each window is the product of its height ans width:

  area = (14/(x+7))(12/x) = 168/(x(x +7))

  area = 168/(x² +7x)

_____

<em>Comment on the problem</em>

There is not enough information given to determine suitable values for x. If x is 42, each window is a square 3 3/7 inches on a side.

7 0
3 years ago
How can I find a?<br> (Trigonometric Ratios)
earnstyle [38]

Step-by-step explanation:

Hey there!

<u>Use</u><u> </u><u>cos</u><u> </u><u>ratio to</u><u> </u><u>find </u><u>the</u><u> </u><u>value</u><u> </u><u>of</u><u> </u><u>'</u><u>a'</u><u>.</u>

As per given, we can state that it is a Right angled triangle, so taking 38° reference angle.

We get;

p = AC

b = 6

and h= a

Here, <u>Use</u><u> </u><u>the</u><u> </u><u>value</u><u> </u><u>of</u><u> </u><u>b</u><u>,</u><u> </u><u>h</u><u> </u><u>and</u><u> </u><u>3</u><u>8</u><u>°</u><u> </u><u>angle</u><u> </u><u>to</u><u> </u><u>find</u><u> </u><u>the</u><u> </u><u>value</u><u> </u><u>of</u><u> </u><u>a</u><u>.</u>

\cos(38° )  =  \frac{b}{h}

\cos(38°)  =  \frac{6}{a}

0.7881 =  \frac{6}{a} [ cos(38°=0.7881]

0.7881a = 6

a =  \frac{6}{0.7881}

Therefore the measure of a is 7.61 Or 8.

<em><u>Hope</u></em><em><u> </u></em><em><u>it helps</u></em><em><u>.</u></em><em><u>.</u></em>

6 0
3 years ago
Find the length of the shorter diagonal of a rhombus if:
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a) Area of rhombus = ½ * (diagonal1)*(diagonal 2)

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b) Area of rhombus = ½ * (diagonal1)*(diagonal 2)

Let the ratio be x

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Multiply both side by 2

294 = (2x)*(3x)

294 = 6x^2

Divide both side by 6

294/6 = 6x^2/6

49 = x^2

x= 7 unit

8 0
3 years ago
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