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irina [24]
3 years ago
9

Find all values of k for which the function y=sin(kt) satisfies the differential equation y′′+16y=0. Separate your answers by co

mmas. isn't the answer just ±4?
Mathematics
1 answer:
ziro4ka [17]3 years ago
5 0

Answer:

0, 4, -4 and they may want you to mention formally all the kt multiples of \pi.

Step-by-step explanation:

Let's do the second derivative of the function: y(t)=sin(k\,t)

y'(t) =k\,cos(k\,t)\\y"(t)=-k^2\,sin(kt)

So now we want:

y"+16\,y'=0\\-k^2\,sin(kt)+\,16\,sin(kt)=0\\sin(kt)\,(16-k^2)=0\\

Then we have to include the zeros of the binomial (16-k^2) which as you say are +4 and -4, and also the zeros of sin(kt), which include all those values of

kt=0\,,\,\pi\,\,,\,2\pi\, ,\,etc.

So an extra one that they may want you to include is k = 0

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An airplane is observed to be approaching the air point. It is at a distance of 12 km from the point of observation and makes an
antoniya [11.8K]

Answer:

The height is 14.3 km

Step-by-step explanation:

Given

distance= 12km

\theta= 50 --- angle of elevation

Required

Determine the height above the ground

The question is illustrated using the attached image.

To calculate the required height, we make use of:

tan(\theta) = \frac{AB}{BC}

Where AB represents the height and BC, the distance.

So:

tan(50) = \frac{AB}{12}

Make AB the subject

AB = 12 * tan(50)

AB = 12 * 1.1918

AB = 14.3016

AB = 14.3km --- approximated

4 0
3 years ago
The sum of the first ten terms of a linear sequence is 145. the sum of the next ten term is 445. find the sum of the first four
chubhunter [2.5K]

The sum of the first four terms of the sequence is 22.

In this question,

The formula of sum of linear sequence is

S_n =\frac{n}{2}(2a+(n-1)d)

The sum of the first ten terms of a linear sequence is 145

⇒ S_{10} =\frac{10}{2}(2a+(10-1)d)

⇒ 145 = 5 (2a+9d)

⇒ \frac{145}{5} =2a+9d

⇒ 29 = 2a + 9d  ------- (1)

The sum of the next ten term is 445, so the sum of first twenty terms is

⇒ 145 + 445

⇒ S_{20} =\frac{20}{2}(2a+(20-1)d)

⇒ 590 = 10 (2a + 19d)

⇒ \frac{590}{10}=2a+19d

⇒ 59 = 2a + 19d -------- (2)

Now subtract (2) from (1),

⇒ 30 = 10d

⇒ d = \frac{30}{10}

⇒ d = 3

Substitute d in (1), we get

⇒ 29 = 2a + 9(3)

⇒ 29 = 2a + 27

⇒ 29 - 27 = 2a

⇒ 2 = 2a

⇒ a = \frac{2}{2}

⇒ a = 1

Thus, sum of first four terms is

⇒ S_4 =\frac{4}{2}(2(1)+(4-1)(3))

⇒ S_4 =2(2+(3)(3))

⇒ S₄ = 2(2+9)

⇒ S₄ = 2(11)

⇒ S₄ = 22.

Hence we can conclude that the sum of the first four terms of the sequence is 22.

Learn more about sum of sequence of n terms here

brainly.com/question/20385181

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6 0
2 years ago
A student solves the compound inequality 15 ≤ 2x + 5 ≤ 17 and finds the solutions of the compound inequality to be all real numb
Georgia [21]

Answer:

The solutions of the compound inequality is 5 ≤ x  ≤ 6

Step-by-step explanation:

A compound inequality is two or more inequalities joined. For its resolution, each inequality must be solved separately. In the case of 15 ≤ 2x + 5 ≤ 17, you have:

Inequality (A) 15 ≤ 2x + 5 and Inequality (B) 2x + 5 ≤ 17

The solution of the inequalities consists of finding the value that the unknown x must take for the inequality to be fulfilled, passing all the terms with x to one member (for example to the first member), and all the numbers (terms without x) to the other member through the opposite operation (The opposite operation to addition is subtraction and vice versa, and the opposite operation to multiplication is division and vice versa). In this case, solving the inequalities:

Inequality (A) 15 ≤ 2x + 5

15 - 5 ≤ 2x

10 ≤ 2x

10÷2 ≤ x

5 ≤ x

Inequality (B) 2x + 5 ≤ 17

2x ≤ 17 -5

2x ≤ 12

x ≤ 12÷2

x ≤ 6

The solution of a compound inequality are all the solutions that have in  common the two inequalities. Graphically, it is as if they were two graphs that overlap.

So, in this case <u><em>the solutions of the compound inequality is 5 ≤ x  ≤ 6</em></u>

In the image you can see the solution to the compound inequality.

5 0
3 years ago
The ratio of three numbers is 7 : 3 : 2. These three numbers have a sum of 228. What is the difference between the largest and t
gregori [183]

Answer:

your mom

Step-by-step explanation:

LOL

7 0
3 years ago
A student graphs three of the four vertices of parallelogram ABCD. Which point could be the fourth vertex of the parallelogram?
Paladinen [302]
The point (6, 3) will make this a parallelogram.

In a parallelogram, both pairs of opposite sides are parallel.  From the choices we have for point D, we want to find the coordinates of the point so that the slope from B to D is the same as the slope from A to C, since parallel lines have the same slope.

m = (y₂-y₁)/(x₂-x₁) = (3-0)/(3-0) = 3/3 = 1 (from point A to C)

This means that for every 1 we go up from point B, we want to go 1 right as well.  3 up and 3 right will get us the point (6, 3), which will give BD the same slope as AC.
5 0
3 years ago
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