Parallel lines : mastery test

The motion of the hour hand of a clock is a periodic motion that repeats every 12 hours.

Reasons:

The given parameters are;

The variation of the height of the tip of the hour hand = 9 feet to 10 feet

At t = 0, the time = 12.00 a.m.

Required: The equation that can be used to model the height as a function of time.

Solution:

The general form of the cosine function is presented as follows;

y = a·cos(b·x - c) + d

The amplitude = a

[tex]\displaystyle a = \mathbf{ \frac{Maximum \ value -Minimum \ value}{2}}[/tex]

Therefore;

[tex]\displaystyle a = \frac{10 -9}{2} = 0.5[/tex]

b = The cycle speed

The period, T, is given as follows;

[tex]\displaystyle T = \mathbf{ \frac{2 \cdot \pi}{b}}[/tex]

The period of a block, T = 12 hours

Therefore;

[tex]\displaystyle b = \frac{2 \cdot \pi}{T}[/tex]

[tex]\displaystyle b = \frac{2 \cdot \pi}{12} = \mathbf{ \frac{ \pi}{6}}[/tex]

[tex]\displaystyle d = \mathbf{ \frac{Maximum \ value +Minimum \ value}{2} = \frac{10 + 9 }{2}} = 9.5[/tex]

At t = 0, H = The highest point = 10 ft.

Which gives;

[tex]\displaystyle H = \mathbf{0.5 \cdot cos \left(\frac{\pi}{6} \times 0 -c\right) + 9.5} = 10[/tex]

[tex]\displaystyle cos \left( -c\right) = \frac{0.5}{0.5} = 1[/tex]

-c = arcos(1) = 0

-c = 0

c = 0

The equation is therefore;

[tex]\displaystyle H = \mathbf{0.5 \cdot cos \left(\frac{\pi}{6} \cdot t \right) + 9.5}[/tex]

The above equation is the same as; H = 0.5cosine (StartFraction pi Over 6 EndFraction t) + 9.5

Learn more about the cosine function here:

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Answer:

Step-by-step explanation:

The arrows on the ends of the graph mean the graph extends indefinitely left and right. The domain is the horizontal extent of the graph, so it extends from -∞ to +∞, all real numbers.

__

The upward slant of the graph at the ends is ambiguous regarding the vertical extent of the graph. It could mean either of ...

We expect the latter case would be drawn with the ends of the arrows above the peak value shown. However, oscillation tends to involve a certain symmetry, and the graph has no symmetry about the local minimum points. In short the usual clues to the vertical extent are missing. Your guess is as good as mine.

The range could be [-1, 5], or it could be [-1, ∞). We cannot tell from this graph.

_____

Additional comment

The shape of the graph does not seem to match that of a 4th-degree polynomial, so we're not at all certain what sort of function is being plotted here. (A 4th-degree polynomial gets steeper beyond the outside zeros, rather than flatter, as shown here.) A couple of different functions with the approximate characteristics shown are graphed in the attachment.

Answer:

32.5 and 30

Step-by-step explanation:

I counted the unit squares one by one.

Hope this helped! :)

Answer:

but what if it is a virus?

Step-by-step explanation:

Answer:

isnt oit iron pick

Step-by-step explanation:

Answer: ~9.51 kilograms each.

Step-by-step explanation: 723/76=9.5131

Answer:

0.5160

Step-by-step explanation:

Let us assume that the length of fishes in the tank is normally distributed. Thus, x is the random variable representing the length of fishes in the tank. Since the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = standard deviation

number of samples

From the information given,

µ = 15

σ = 4

n = 31

We want to find the probability that x is between (15 - 0.5) inches and (15 + 0.5) inches. The probability is expressed as

P(14.5 ≤ x ≤ 15.5)

For x = 14.5

z = (14.5 - 15)/(4/√31) = - 0.7

Looking at the normal distribution table, the probability corresponding to the z score is 0.2420

For x = 15.5

z = (15.5 - 15)/(4/√31) = 0.7

Looking at the normal distribution table, the probability corresponding to the z score is 0.7580

Therefore,

P(14.5 ≤ x ≤ 15.5) = 0.7580 - 0.2420 = 0.5160

Answer:

5n-2

Step-by-step explanation:

collect like terms

-> (7n-2n)+(-3+1)

simplify

=> 5n-2

Answer:

I can answer this but all you have to do is get the length, weight, and height and multiply it. I was going to do it but I could it find the height, and width.

Proof:-

In ∆TOP and ∆ZAP

[tex]\because\sf\begin{cases}\sf <O\cong <A(Given)\\ \sf TO\cong AZ(Given)\\ \sf <TPO\cong <ZPA(Opposite angles)\end{cases}[/tex]

Hence

∆TOP[tex]\cong[/tex]∆ZPA(Side-Angle-Side)

Step-by-step explanation:

Statement                                                  Reason

∠O ≅ ∠A                                                    Given

TO ≅ AZ                                                    Given

∠OPT and ∠ZPA are vertical angles       Vertical angles theorem

∠OPT ≅ ∠ZPA                                           Definition of vertical angles

ΔTOP ≅ ΔZAP                                           Angle - angle -side AAS postulate

Answer:

6 days

Step-by-step explanation:

2 boys that each work half as fast as the men is equivalent to having one extra man. So instead of 3 men we have 4. 4/3 the manpower means 3/4 the time. 3/4 of 8 is 6.

Answer:

6 days.

Step-by-step explanation:

The 3 men can build 1/8 of a wall in 1 day.

So 1 man can build 1/24 wall in 1 day.

So 1 boy can build  1/48 in 1 day and 2 boys can build 1/24 wall in 1 day.

So we have the equivalent of  4 men working and they can build 4 * 1/24

= 1/6 of a wall per day

So the answer is 6 days.

Answer:

answer is 121.5

Step-by-step explanation:

Answer:

121.5

Step-by-step explanation:

first make 13 1/2 into a mixed fraction which is 27/2 then multiply by 9/1 you should get 243/2 and once you divide, you should have 121.5

Answer:

Negative Correlation

Step-by-step explanation:

The plot looks like it's going downwards. If it was an equation, it'd be something with y = -x +b.

Answer:

z = 2.5

Step-by-step explanation:

4z = 10

----  -----

4      4

z = 2.5

hope this helps! :D

have a miraculous day, and brainliest is immensely appreciated!! <3

Answer:

(3,4)

Step-by-step explanation:

My old teacher taught me a trick for this. Treat the first number like the y and the second like the x. Count Accordingly from there.

Answer: 28 y

Step-by-step explanation: All you really have to do is multiply 7 by 4y. 7(4y) 28y

Answer:

8

Step-by-step explanation:

Answer:

Total = ($3.86)n, but it ids not among the answer options.

Step-by-step explanation:

P would be equal to the price per pen set ($3.86) times the number of pen sets sold, n.

Total, P = ($3.86)n

I translated the paragraph into these options:

n = 3. 86P     No, n = P/3.86

P = 3. 86/n    No, P = 3.86n

n = 3. 86/P    No, n = P/3,86

P = 3. 86n.

Using proportions, it is found that 7% of the population has blue eyes without blonde hair.

10% of the population has blue eyes. These 10% are composed by:

Hence, the relation according to the proportion of 10% is:

[tex]0.75(0.04) + 0.96x = 0.1[/tex]

[tex]x = \frac{0.1 - 0.75(0.04)}{0.96}[/tex]

[tex]x = 0.0729[/tex]

Out of the entire population:

0.0729(0.96) = 0.07

7% of the population has blue eyes without blonde hair.

You can learn more about proportions at https://brainly.com/question/24372153

Answer:

1.27? :v

Step-by-step explanation:

porque la libra cuesta 1.27 y el solo compro 1.8? la verdad no tiene sentido esta pregunta o quizas abra que hacer una ecuacion...en fin suerte.

Answer:

Q20     b.16

Q21      a.6

Step-by-step explanation:

count charcters  Have a nice day!  ==16

Q21    why 6

because index start with 0 and not 1

just count

H ==> 0

e==> 1

l==> 2

.

.

W=>6

Unit rate is the conversion of one unit to another unit with its standard conversion.

The width of the gymnasium in the blueprint is 4.75 inches.

Unit rate is the conversion of one unit to another unit with its standard conversion.

Example:

1 minute = 60 seconds

1 km = 100 m

1 m = 100 cm

1 feet = 12 inches

We have,

Gymnasium:

Length = 88 feet

Width = 76 feet ____(1)

Blueprint:

Gymnasium:

Length = 5.5 inches

This means,

88 feet = 5.5 inches

Divide both sides by 88.

1 feet = 0.0625 inches ____(2

The width of the gymnasium on the blueprint.

From (1) and (2)

76 feet

= 76 x 1 feet

= 76 x 0.0625 inches

= 4.75 inches.

Thus,

The width of the gymnasium in the blueprint is 4.75 inches.

Learn more about unit conversion here:

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Answer:

The value of the investment

Step-by-step explanation:

From the given system of equation x = 2y and 2x + 5y = 9, using the substitution method we get the value of y = 1.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Solutions to an equation are those values of the variables involved in that equation for which the equation is true.

We have given system of equation

x = 2y

2x + 5y = 9

Using the substitution method

2(2y) + 5y = 9

4y + 5y = 9

9y = 9

y = 1

Learn more about solving equations here:

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Answer:

  y = 2/3x + 3/2

Step-by-step explanation:

18 inches is 3/2 feet. 8 inches is 2/3 feet.

The equation will have a slope of 2/3 ft per year, and an initial value of 3/2 ft.

  y = 2/3x + 3/2

Answer:

5

Step-by-step explanation:

3 - ( - 5 )

= 3 + 5

3 + ? = 3 + 5

? = 5

Answer:

Step-by-step explanation:

A number, a variable, or the product of a number and variable(s)

A letter used to represent an unknown number

The number in front of a variable in a term

A single term, multiple terms connected by an addition or subtraction sign

A number, a term containing no variables

Answer:

-4

Step-by-step explanation:

23+1=24

24/-6=-4