Joey is running an experiment with a mass on a spring. Joey models the height of the mass above the table he is working on using the equation h(t)=6.85cos(3.42t)+9, where the height is in inches and the time, t, is in seconds since he let the mass free. How many seconds, to the nearest tenth, will it take for the mass to return to its original position?

Answer:

34.2 ; 105.8 ; 12.0

Step-by-step explanation:

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]

c² = a² + b² - 2abcosC

~~~~~~~~~~~~

sinB = [tex]\frac{bsinA}{a}[/tex]

sinB = 7sin40° ÷ 8 ≈  0.562439

m∠B ≈ 34.2°

m∠C = 180° - ( 40° + 34.2° ) = 105.8°

c² = 8² + 7² - 2(8)(7)cos106° ≈ 143.87

c ≈ 12.0 units

Answer:

Below

Step-by-step explanation:

First way:

Find the area of the big triangle and subtract the area of the rectangle.

Area of shaded part = 1/2 * 25 * 34 -  10*24 =  185 m^2

Second way:

Add the area of the 3 shaded triangles:

= 1/2 * 15 * 24 + 1/2 * 5 * 10 + 1/2 * 5 * 10

= 180 + 25 + 25 = 230 m^2

The areas are different. The reason must be that given lengths are not possible for this diagram.

Check The length of the hypotenuse of the large triangle by 2 different methods:

The hypotenuse = √(25^2 + 17^2)

= 30.23.

Now let's work out the hypotenuse of the shaded triangles:

Top one = √(15^2 ^ 12^2) = 19.21

Bottom one = √((5^2 + 10^2) = 11.18

Adding these we get 30.39  which is different than previously calculated but it should be the same.

So what we have here is impossible geometry. This accounts for the different areas.

Answer:

B) 5 units

Step-by-step explanation:

The distance between these points (0, 2) and (5, 2) will be 5 units. Then the correct option is B.

It is the measure of distance between the two points and is known as length. The length is measured in meters generally.

Let one point be (x, y) and another point be (h, k).

Then the distance between the points will be

D² = (x - h)² + (y - k)²

The two pints are given below.

(0, 2) and (5, 2)

Then the distance between these points (0, 2) and (5, 2) will be given as,

D² = (5 - 0)² + (2 - 2)²

D² = 5²

D = 5 units

The distance between these points (0, 2) and (5, 2) will be 5 units. Then the correct option is B.

Learn more about the distance between two points here:

https://brainly.com/question/18296211

#SPJ2

Answer:

96

Step-by-step explanation:

3 floors:

3x16= 48windows per building

2 buildings

2x48=96 windows

Answer:

m = 1     c = -8

Step-by-step explanation:

Answer:

Number of additional inches= x

Number of additional topping= y

Total cost= 8+1.5(x)+0.75(y)

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hope it helps...

have a great day!!

=====================================================

Explanation:

Notice the tickmarks on the segments in the diagram. This tells us that chords DC and CB are the same distance from the center. It furthermore means that DC and CB are the same length, and arcs DC and CB are the same measure

arc DC = arc CB

12x+7 = 18x-23

12x-18x = -23-7

-6x = -30

x = -30/(-6)

x = 5

---------------------

Use this x value to find the measure of arcs DC and CB

We get the same measure for each, which helps confirm we have the correct x value.

The two arcs in question add to 67+67 = 134 degrees. This is the measure of arc DCB. Subtract this from 360 to get the answer

arc DAB = 360-(arc DCB) = 360-134 = 226 degrees

I'm using the idea that (arc DCB) + (arc DAB) = 360 since the two arcs form a full circle.

Answer:

20 students

Step-by-step explanation:

Given that

There are 200 students surveyed

And, the percentage of each games is as follows;

For tennis it is 10%

For basketball it is 30%

For football it is 35%

for baseball it is 25%

We need to find the number of students choose tennis

So, it should be

= 10% of 200

= 20 students

Answer:

Step-by-step explanation:

Five rational number from 68 to 72

69, 70 , 71, 71.1 , 71.2

Answer: 500 cables

Step-by-step explanation:

The population refers to the individuals or the items which are of interest fltonthe researcher during an experiment.

Since the computer department received 10 boxes containing 50 cables each, then the population will be gotten as:

= 10 × 50

= 500 cables

Answer:

440cm³

Step-by-step explanation:

Area of trapezium base=

[tex] \frac{1}{2} \times (a + b) \times h[/tex]

[tex] \frac{1}{2} \times (8 + 14) \times 4[/tex]

[tex] \frac{1}{2} \times 22 \times 4 \\ = \frac{88}{2} \\ = 44 {cm}^{3} [/tex]

Volume=Area or trapezium x Height between trapezium ends

[tex] = 44 \times 10 \\ = 440 {cm}^{3} [/tex]

                 .................................................................................                    

Answer:

1,012

Step-by-step explanation:

72,864 / 72 = 1,012

Answer:

1012 books per bookcase

Step-by-step explanation:

Assuming each bookcase has the same number of books, this is a division task.

Your answer will be given by number of books÷number of bookcases.

In this case, that becomes 72864÷72.

This can be solved to 1012.

**This question involves division and writing integer expressions, which you may wish to revise. I'm always happy to help!

Answer:

You would plote the minutes as your x (1,2,3,4,5) and your height in feet as your y. So some ordered pairs would be (1,35) and (2,60).

Step-by-step explanation:

If it were measured every 15 minutes, the x coordinate, would be multiples of 15.

Hope this helps!

:)

Answer:

B or C

Step-by-step explanation:

if its refering to the answer of 11 × X then the answer is C, but if its not the answer might be B.

Answer:

Table A

Step-by-step explanation:

None of the numbers in the x values are repeating

Answer:

Probability = 16.7

Step-by-step explanation:

Total marbles 9

Choosing 2 red = [tex]4C_2[/tex]

Choosing 2 marbles from 9 marbles = [tex]9C_2[/tex]

Probability percent of choosing 2 red marbles from 9 marbles

                                                          [tex]\frac{4C_2}{9C_2} = \frac{1}{6} \times 100 = 0.1667 \times 100 = 16.7[/tex]

Answer:

16.6

Step-by-step explanation:

4+3+2=9 marbles

4=red

4/9*3/8=1/6

1/6= 16.6

Answer:No

Step-by-step explanation: It is on 3x-3

The point (15, 29) does not satisfy the line y = 2x - 3, and the point (15, 29) is not lying on the line.

It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.

If in the linear equation one variable is present then the equation is known as the linear equation in one variable.

We have a line:

y = 2x - 3

If the point (15, 29) is on the lie then it must satisfy the line.

Therefore putting this point in the equation of the line.

Put x = 15, and y = 29, we get:

29 = 2×15 - 3

     = 30 - 3

29 ≠ 27

29 cannot be equal to 27 it means the point (15, 29) does not satisfy the line and the point is not lying on the line.

Thus, the point (15, 29) does not satisfy the line y = 2x - 3, and the point (15, 29) is not lying on the line.

Learn more about the linear equation here:

brainly.com/question/11897796

Answer:

$13.4

Step-by-step explanation:

Given that :

Tip percentage = 20%

Amount of bill = $67.13

Rounding the bill Amount to then nearest dollar :

$67.13 = $67

Tip amount = 20% of $67

Tip amount = 0.2 * $67

Tip amount = $13.4

Answer:

m = -4

Step-by-step explanation:

The given y= -4x + 5 exactly matches the format of the slope-intercept equation   y = mx + b.

Thus, the gradient (slope) of the given line is -4.

Answer:

Length = 6.5 meters

Width = 4.5 meters

Step-by-step explanation:

Given,

Perimeter of a rectangle is twice the sum of it's length and width.

Length is 2 meters more than twice its width, let the length be x meters so the width becomes (x-2) meters

perimeter of the rectangle,

2{x+(x-2)} meters which is 22 meters (given)

so,

2{x+(x-2)}=22

or, 2(x+x-2)=22

or, 2(2x-2)=22

or, 2x-2=11

or, 2x=13

or, x=6.5

so the length is 6.5 meters and the width is 6.5-2 = 4.5 meters.

Answered by GAUTHMATH

Answer:

-6 and -1

Step-by-step explanation:

The excluded values are the values of x that satisfy [tex]2x^{2} + 14x + 12 = 0[/tex]

Let us solve the equation [tex]2x^{2} + 14x + 12 = 0[/tex]

It's a quadratic equation

Thus, let us calculate the discriminant Δ

Δ [tex]= 14^{2} - 4 .2.12 = 100[/tex]

the discriminant is greater than 0, so the equation has two solutions

[tex]x = \frac{-14 - 10}{4} = \frac{-24}{4} = -6[/tex]  or  [tex]x = \frac{-14+10}{4} = \frac{-4}{4} = -1[/tex]

the excluded values are -6 and -1

Answer:

(5/1)(4-0)-(-5)(-4-3)

Step-by-step explanation:

You could also get an undefined number by putting any number divided by 0.

tbh i think it is 6 i did the math too

Answer:

2√41

Step-by-step explanation:

d = √(x2 - x1)² + (y2 - y1)²

√(-8 - 0)² + [0 - (-10)]²

√(-8)² + (10)²

√(64) + (100)

√164

= 2√41

Answer:

yeah me too

Step-by-step explanation:

Answer:

No, the closest to -451 in the sequence is -429

Step-by-step explanation:

Answer:

nope

Step-by-step explanation:

Answer:

the answer is 47

Step-by-step explanation:

133+x=180