Find the slope of the line that passes through (19, 72) and (20, -1).

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:

70%

Step-by-step explanation:

the ratio is 14 to 6 so if you have 14 small milkshakes you would also have 6 regular milkshakes

to find a percentage we can buff up the ratio to add up to 100

14 + 6 = 20

100 / 20 = 5

that means we must multiply each side by 5

14 * 5 = 70

6 * 5 = 30

the ratio is now 70 to 30

you would have 70% of milkshakes that are small

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).

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Answer:

40min

Step-by-step explanation:

Since the ratio is 2:16, we want simplify. both 2 and 16 are dividable by 2.

2 / 2 = 1

16 / 2 = 8.

Now we can use the ratio 1 mile per 8 min. We want the rate of how many min to miles, so we'd multiply 5 by 8 which equals 40.

Therefore it takes him 40min to run 5 miles.

Hope this helps!

Answer:

Bottom right

Explanation:

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

Answer:

120

Step-by-step explanation:

24 + 96 = 120

Hope this helps!

Answer:

x=0 or x=6

Step-by-step explanation:

-4|-2x+6| = -24

|-2x+6| = 6

-2x+6 = 6

-2x = 0

x = 0

-2x+6 = -6

-2x = -12

x = 6

Therefore, x=0 or x=6

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)

Step-by-step explanation:

30/6+3 = 5+3 = 8

hope this helps you.

Answer:

First Graph: the function is symmetrical around y axis -> Even

Second Graph: the function is neither

Answer:

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

9n-4=7n+2

9n-7n=2+4

2n=6

n=6÷2

n=3

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: the answer is 3 3/4

Answer:

Angle 8

Step-by-step explanation:

Refer to the attached picture

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

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Answer:

160

Step-by-step explanation:

32×5 is 60 hope that helps

5x - 8 = 3x + 12

- 3x -3x

You have to subtract them both.

2x - 8 = 12

Answer:

9 1/2n + 11

Step-by-step explanation:

9n + 1/2n + 4 + 7

9 1/2n + 11  or 19/2n + 11

Answer:

9

Step-by-step explanation:

To find the area of a triangle where you know the x and y coordinates of the three vertices, you'll need to use the coordinate geometry formula: area = the absolute value of Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By) divided by 2. Ax and Ay are the x and y coordinates for the vertex of A. The same applies for the x and y notations of the B and C vertices.

Fill in the numbers for each corresponding letter combination within the formula.

Fill in your formula like this: 0(8-10) + 3(0-0) + 9(0-8).

Subtract the numbers within the parentheses.

0 from 8 = 8, 0 from 0 = 0 and 8 from 10 = 2.

Multiply that result by the number to the left of the parentheses.

0 by 8 = 0, 3 by 0 = 0 and 9 by 2 = 18.

Add the three products together.

0 + 0 + 18 = 18

Divide the sum of the three products by 2.

18 ÷ 2 = 9

Answer:36

Step-by-step explanation:

Answer:

8 smoothies: 4:6

2 smoothies: 1:1.5, etc.

Answer:

16

Step-by-step explanation:

[tex]x = 4 \\ 4 + 5(4) - 8 = 16[/tex]

Answer:

R = [tex]\frac{V}{I}[/tex]

Step-by-step explanation:

IR = V ( isolate R by dividing both sides by I )

R = [tex]\frac{V}{I}[/tex]

Answer:

7.8

Step-by-step explanation:

subtract 85 - 77.2

Answer:

steps below

Step-by-step explanation:

f(x) = x³

1. shifted four units to the left: f'(x) = (x+4)³

2. eight units down: f''(x) = (x+4)³ - 8

3. reflected in the y-axis: f'''(x) = (-x+4)³ - 8

The final shape after the transformation is f(x) = -(x + 4)³ - 8.

Original function: f(x) = x³

Shifted four units to the left: f(x) = (x + 4)³

Shifted eight units down: f(x) = (x + 4)³ - 8

Reflected in the y-axis: f(x) = -(x + 4)³ - 8

Hence, the final shape of the function after these transformations is f(x) = -(x + 4)³ - 8.

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Answer:

  f(x) has three real roots and two imaginary roots.

Step-by-step explanation:

The function is degree 5, so will have 5 roots in total. 2 real roots and one complex root are shown. Complex roots come in pairs, so there will be one more, but cannot be two more.

  f(x) has three real roots and two imaginary roots.

__

All five roots must be accounted for. This leaves out the first two choices. The given complex root eliminates the third choice.

Answer:

D

Step-by-step explanation:

did the test

Answer:

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

Step-by-step explanation:

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Answer:

This is the answer, hope it helps you!!

Answer:

56

Step-by-step explanation:

Answer:

7/8x ≥ 14

Step-by-step explanation:

(sum means addition in case you forgot)

You would start by writing 7/8x + 20 ≥ 34

You would then subtract 20 from both sides to isolate the variable x.

You would then have 7/8x ≥  14