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Akimi4
11 days ago
7

Does anyone know thsi

Mathematics
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(a) For what values of k does the function y = cos(kt) satisfy the differential equation 81y'' = −4y? (Enter your answers as a c
tester [12383]

Answer:

k = \frac{2}{9}, k=\frac{-2}{9}

Step-by-step explanation:

The initial scenario is a specific case of the subsequent one, so we will address the second case first.

Consider y = A\sin(kt) + B\cos(kt). Through the utilization of derivatives and trigonometric function properties, it is determined that

y' = A\cdot k \cos(kt)- B \cdot k \sin(kt) = k (A\cos(kt)-B\sin(kt))

y'' = k(-A\cdot k \sin(kt)-B\cdot k \cos(kt)) = -k^2(y)

The equation is represented as 81y''=-4y. It's important to note that since y'' = -k^2y it leads to the equation

-k^2 81y=-4y,

which signifies that k^2 = \frac{4}{81}. Consequently, k=\pm\frac{2}{9}

It's notable that in this instance, the value of k is independent of A and B. Thus, it applies universally to any values of A and B. The first scenario is included since it corresponds to A=0 and B=1.

5 0
3 months ago
You need 20 pounds of grass seed to plant grass inside the baseball diamond below. About how many pounds of grass seed
Leona [12618]
You will require approximately 13 pounds of grass.
6 0
3 months ago
The graph shows the altitude of a helicopter over time. A graph measuring altitude and time. A line runs through coordinates (0,
Zina [12379]
To determine the slope, subtract the y coordinates from each other and the x coordinates as well. That gives us: 10000 - 4000 over 0 - 15, which simplifies to 6000 over -15. When divided, it results in -400. So, the slope amounts to -400. I hope this aids you!:D
6 0
2 months ago
Read 2 more answers
1 kilogram is equivalent to about 2.2 pounds. An orangutan weighs 142 pounds. What is its mass in kilograms? Round your answer t
AnnZ [12381]

The weight of an orangutan is 64.5 kilograms

Solution:

It is stated that the orangutan's weight is 142 pounds

Additionally,

1 kilogram is approximately 2.2 pounds

We will now convert 142 pounds into kilograms

1 kilogram = 2.2 pounds

\text{1 pound } = \frac{1}{2.2} \text{ kilograms }

As a result, 142 pounds translates to

142 \text{ pound } = \frac{1}{2.2} \times 142 \text{ kilogrmas }

\rightarrow \frac{1}{2.2} \times 142 = 64.545 \text{ kilograms }

When rounding to the nearest tenth, we obtain 64.5 kilograms

Therefore the mass of the orangutan is 64.5 kilograms

3 0
3 months ago
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