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Savatey [412]
3 years ago
11

A. For what values of k does the function y = cos(kt) satisfy the differential equation 25y'' = −16y?

Mathematics
1 answer:
Oduvanchick [21]3 years ago
6 0

Answer:

Step-by-step explanation:

Given y = coskt

y' = -ksinkt

y'' = -k²coskt

Substitute this y'' into the expression 25y'' = −16y

25(-k²coskt) = -16(coskt)

25k²coskt = 16(coskt)

25k² = 16

k² = 16/25

k = ±√16/25

k = ±4/5

b) from the DE 25y'' = −16y

Rearrange

25y''+16y = 0

Expressing using auxiliary equation

25m² + 16 = 0

25m² = -16

m² = -16/25

m = ±4/5 I

m = 0+4/5 I

Since the auxiliary root is complex number

The solution to the DE will be expressed as;

y = Asinmt + Bsinmt

Since k = m

y = Asinkt+Bsinkt where A and B are constants

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X/9 > 9 is the question and the answer is 81 but Iḿ not sure how my teacher got the answer 81
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Answer:

81 < x

Step-by-step explanation:

\frac{x}{9} > 9 → x > 9 \times 9 → x > 81

* The above answer is written in reverse, which is the exact same result.

I am joyous to assist you anytime.

5 0
3 years ago
Quadratic formula<br> x2 + 3x - 5 = 0
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5 0
3 years ago
Two automobiles leave the same city simultaneously and both head towards another city. The speed of one is 10 km/hour greater th
Veronika [31]

Answer:

5091 Km/hr and 505 km/hr

Step-by-step explanation:

Speed = Distance / Time

Let the speed of first automobile be 'x' and that of the second be 'y'

Since speed of one is 10 times greater than the other. therefore;

⇒ x = 10 y

also let time for faster automobile be 'T' and time for slower auto mobile be 't'

Since first arrive one hour earlier than second, therefore;

⇒ t = T + 1

⇒ For first automobile; x X T = 560 ; substituting for 'x' and 'T'. Therefore;

⇒ 10y (t+1) = 560

⇒ For Second automobile; y X t = 560

⇒ y = \frac{560}{t}

⇒ 10(\frac{560}{t})(t + 1) = 560

⇒ 5600 + \frac{5600}{t} = 560

⇒ 5600 - 560 =  -  \frac{5600}{t}

⇒ t = 1.11 hr

also ; T = 1.11 - 1 = 0.11 hr

Speed of 1st auto  = 560/0.11 = 5091 km /hr

Speed of 2nd auto = 560/1.11 = 505 km/hr

8 0
2 years ago
Can someone help me? Please show your work.
Allushta [10]
We know that the perimeter of a rectangle can be represented by the expression 2l +2w, where l represents the length of the rectangle and w represents the width of the rectangle.

If we substitute in the values given in this problem, we get the expression:
2(2x+6) + 2(x)

Another equivalent expression we can use to express the perimeter is w + w + l + l.

If we substitute in the values given in this problem into this expression, we get:

x + x + 2x + 6 + 2x + 6

Overall, we know that these expressions are equivalent and represent the same value (the perimeter of the rectangle), because if you combine like terms, both expressions simplify to 6x + 12.

Hope this helps!
3 0
3 years ago
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