Find the value of T……

The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equatio

AnnZ [28]

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

The equation that can be used to models the height as a function of time, based on the given options, is presented as follows; $\displaystyle \underline{ H = 0.5 \cdot cos \left(\frac{\pi}{6} \cdot t \right) + 9.5}$

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

$\displaystyle a = \mathbf{ \frac{Maximum \ value -Minimum \ value}{2}}$

Therefore;

$\displaystyle a = \frac{10 -9}{2} = 0.5$

b = The cycle speed

The period, T, is given as follows;

$\displaystyle T = \mathbf{ \frac{2 \cdot \pi}{b}}$

The period of a block, T = 12 hours

Therefore;

$\displaystyle b = \frac{2 \cdot \pi}{T}$

$\displaystyle b = \frac{2 \cdot \pi}{12} = \mathbf{ \frac{ \pi}{6}}$

$\displaystyle d = \mathbf{ \frac{Maximum \ value +Minimum \ value}{2} = \frac{10 + 9 }{2}} = 9.5$

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

Which gives;

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

$\displaystyle cos \left( -c\right) = \frac{0.5}{0.5} = 1$

-c = arcos(1) = 0

-c = 0

c = 0

The equation is therefore;

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

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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4 0

3 years ago

Read 2 more answers

How to multiply workout

DENIUS [597]

Answer:

Steps to multiply using Long Multiplication

Multiplying 2-Digit by 2-Digit Numbers

Let us multiply 47 by 63 using the long multiplication method.

1. Write the two numbers one below the other as per the places of their digits. Write the bigger number on top and a multiplication sign on the left. Draw a line below the numbers.

2. Multiply ones digit of the top number by the ones digit of the bottom number.

Write the product as shown.

3. Multiply the tens digit of the top number by the ones digit of the bottom number.

This is our first partial product which we got on multiplying the top number by the ones digit of the bottom number.

4. Write a 0 below the ones digit as shown. This is because we will now be multiplying the digits of the top number by the tens digit of the bottom number. Hence, we write a 0 in the ones place.

5. Multiply the ones digit of the top number by the tens digit of the bottom number.

6. Multiply the tens digit of the top number by the tens digit of the bottom number.

This is the second partial product obtained on multiplying the top number by the tens digit of the bottom number.

7. Add the two partial products.

In long multiplication method, the number on the top is called the multiplicand. The number by which it is multiplied, that is, the bottom number is called the multiplier.

So, a long division problem will have:

We follow the same method for multiplying numbers greater than 2-Digits.

The figure below shows the long division method to multiply 357 by 23

4 0

3 years ago

Two thirds of a number, decreased by thirty six, is at most twenty two. Find the number.

Naily [24]

2/3x - 36 ≤ 22
+36 +36
----------------------
2/3x ≤ 58
2x ≤ 174
x ≤ 87

Hope this helps!

4 0

3 years ago

10. A home improvement store advertises 60

Dima020 [189]

Answer:

cost for (not per) 1 sq ft. floor: $84.79

y = total costs

x = sq ft of flooring

y = x4.79 + 80.00

Step-by-step explanation:

i this equation, y = the total cost wile x = square ft. of flooring

to find out the price when we know that 60 sq ft is $287.00 without the instalation fee, all we have to do is divide 287.00 by 60

287 / 60 = 4.79

so we now know how much 1 sq ft. costs, but to implament it into an equation we need to multiply it by the amount of flooring, so we let x be the number of sq ft used

now all we have to do is add the instalation fee, no, we literally add it in the equation at the end, so that it is added after we multiply by sq ft (not before) then after we calculate that, we get the total cost for x sq ft of flooring, or y

hope this answers your question

4 0

3 years ago

Which expression is equal to p + (q + r)

lana66690 [7]

Answer:

the answer for me would be (p+q)+r

here is why I think so

q +pr ( the pr close-by together in maths means multiple so that's out) same goes for C and A it has a negative so that's not equal.

8 0

3 years ago