Help help help math math math

If y = cos(kt), then its first two derivatives are

y' = -k sin(kt)

y'' = -k² cos(kt)

Substituting y and y'' into 49y'' = -16y gives

-49k² cos(kt) = -15 cos(kt)

⇒   49k² = 15

⇒   k² = 15/49

⇒   k = ±√15/7

Note that both values of k give the same solution y = cos(√15/7 t) since cosine is even.

Answer:

  f(x) = 4(x -1)^3·(x +2)

Step-by-step explanation:

Each root x=p indicates the function has a factor (x -p). The factor will be repeated according to the multiplicity of the root.

  f(x) = a(x -1)^3·(x +2)

  f(0) = a(-1)^3·2 = -2a = -8   ⇒   a = 4

The factored form of the equation is ...

  f(x) = 4(x -1)^3·(x +2)

Using the Fundamental Counting Theorem, it is found that the buyer has 180 choices.

Fundamental counting theorem:

States that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

In this question:

Then:

[tex]N = 5 \times 3 \times 2 \times 3 \times 2 = 180[/tex]

The buyer has 180 choices.

To learn more about the Fundamental Counting Theorem, you can take a look at https://brainly.com/question/25799621

Answer:

1) Isolate the radical symbol on one side of the equation

2) Square both sides of the equation to eliminate the radical symbol

3) Solve the equation that comes out after the squaring process

4) Check your answers with the original equation to avoid extraneous values

Step-by-step explanation:

Use midpoint theorem :- The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also 'half of the length of the third side'.

So,

2x = ½ (x + 9)

2x = ½(x) + ½(9)

2x - ½x = 9/2

3/2x = 9/2

x = 9/3

x = 3

____

Hope it helps ⚜

Answer:

Step-by-step explanation:

Find the perimeter of the rectangle

add the lengths of the rectangle's four sides

24 + 11 + 24 + 11 = 70

Answer:

y=4x+2

Step-by-step explanation:

So we start with the slope, which is bad.

But I have an idea

lets write it as

y=4x+? and since x=1 and y=6

6=4+?

Therefore, the y, intercept must be two

Answer:

y=4x+2

Step-by-step explanation:

y-y1=m(x-x1)

y-6=4(x-1)

y=4x-4+6

y=4x+2

Answer: the answer is 3 3/4

Answer:

x >= -2

-2 < x < 1

Answer:

y=1x-8

Step-by-step explanation:

Lets do the same thing we did last time

-3=1(5)+?

-3=5+?

The y intercept is -8

CHECK:

-3=1(5)+-8

-3=5+-8

-3=-3

Answer:

y=x-8

Step-by-step explanation:

y-y1=m(x-x1)

y-(-3)=1(x-5)

y+3=x-5

y=x-5-3

y=x-8

Answer:

8 smoothies: 4:6

2 smoothies: 1:1.5, etc.

Answer:

[tex]\huge\boxed{t=\sqrt{\dfrac{2d}{a}}}[/tex]

Step-by-step explanation:

[tex]d=\dfrac{1}{2}at^2\\\\\dfrac{1}{2}at^2=d\qquad|\text{multiply both sides by 2}\\\\2\!\!\!\!\diagup\cdot\dfrac{1}{2\!\!\!\!\diagup}at^2=2\cdot d\\\\at^2=2d\qquad|\text{divide both sides by}\ a\neq0\\\\\dfrac{a\!\!\!\!\diagup t^2}{a\!\!\!\!\diagup}=\dfrac{2d}{a}\\\\t^2=\dfrac{2d}{a}\to t=\sqrt{\dfrac{2d}{a}}[/tex]

Answer:

B. line

Step-by-step explanation:

A line would fit this description best. A ray wouldnt work because it goes on infinitely in one direction. A point wouldnt work because it is a dot that marks a location, and a segment is bound by 2 points, and cannot go on forever.

The given description would be best fitting to a "line", which is the correct answer would be an option (B).

A Line is formed by a set of points traveling in a straight line but in opposite directions. It has no breadth, no depth (curvature), and no termination, which implies 'it will not finish,' hence it moves in a straight line in opposing directions indefinitely.

This object goes forever in opposite directions. It is infinitely skinny, as it is a set of points that are all lined up.

This description would be best suited to a line.

A ray would not operate since it extends in one direction indefinitely. A point would not work since it is a dot that indicates a position, but a segment is constrained by two points and cannot continue indefinitely.

Hence, the correct answer would be an option (B).

Learn more about the Slope of the Line here:

brainly.com/question/14511992

#SPJ2

He would have 4 pieces of rope

Answer:

7.8

Step-by-step explanation:

subtract 85 - 77.2

Answer:

Bottom right

Explanation:

visualize both triangle connected to the middle rectangle, and that's a triangular prism

Answer:

y=1                 x=1

y = 2x – 1

replace y with x

x=2x-1

x-2x =  - 1

-x = -1

x= 1

y=x =1

Answer:

Step-by-step explanation:

We assume the figure is a parallelogram, so the sum of the marked angles is 180°.

  2y +(7y +9) = 180

  9y +9 = 180 . . . . . . . simplify

  y +1 = 20 . . . . . . . . . divide by 9

  y = 19

m∠BCD = 2y° = 38°

m∠ABC = (7y+9)° = (7·19 +9)° = 142°

1. Add 2.7 and 1.7 together to discover the total amount

2.7 + 1.7 = 4.4

You would walk 4.4 miles if you walked both trials.  

2. Add the amounts of both trail mixes together

1.7 + 1.4 = 3.1

There were 3.1 pounds of trail mix brought on the hiking trip

3. Subtract answer from 2 by 2 and recieve the answer for this question

3.1 - 2 = 1.1

There were 1.1 pounds of trail mix eaten on this hiking trip

4. Answers:

12.7

6.40

1.2

1.32

Answer:

As we use prime factorization for 200, we get 2 × 2 × 2 × 5 × 5 = 200.

Answer:

[tex] = 825 - 657 \\ = 168answer.[/tex]

Step-by-step explanation:

MARK ME AS A BRAINLIST PLZ

Answer:

This is the answer, hope it helps you!!

Answer:

Frequently Asked Questions on LCM of 8 and 9

Find the prime factorization of 8 8 = 2 x 2 x 2

Find the prime factorization of 9 9 = 3 x 3

Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm: LCM = 72 = 2 x 2 x ...

Therefore, the least common multiple of 8 and 9 is 72.

Step-by-step explanation:

The cart slows that at the rate of 20cm/s between 5 and 15secs

Given the rate function expressed as:

r(t) = 2t + 60

If the time is t = 5

r(5) = 2(5) + 60

r(5) = 70cm/s

If the time is t = 15

r(15) = 2(15) + 60

r(15) = 90cm/s

Taking the difference in rate;

Difference = 90cm.s - 70cm/s

Difference = 20cm/s

Hence the cart slows that at the rate of 20cm/s between 5 and 15secs

Learn more on rate of functions here:

https://brainly.com/question/13516577

Answer:

Angle 8

Step-by-step explanation:

Refer to the attached picture

Answer:

Betty had 45 minutes to take her test in mixed number form it is

Step-by-step explanation:

1 hour

1/4 an hour = 15 minutes

1/2 an hour is 30 minutes

1 hr 15- 30= 45

45= 3/4 of and hour remaining to test

Answer:

3n +6n-4=2n+2+5n

9n-4=7n+2

9n-7n=2+4

2n=6

n=6÷2

n=3