The sum of two consecutive Integers is 123. What is the smallest of the two integers?

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

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How many groups of 2/3 are in 3/5 a. 9/15 b. 9/10 c. 1-1/3 d. 1-1/9

-Dominant- [34]

I believe the answer is B. 9/10

4 0

3 years ago

A ball is dropped to the ground from a height of 100 meters. It rebounds to a height of 50 meters after that first bounce and 25

Lyrx [107]

Answer:

0.78125 m

Step-by-step explanation:

First term of this geometric series is 50 m, and the common ratio is 1/2.

Thus, a(n) = (50 m)(1/2)^(n-1)

After the 7th bounce, the ball will reach a height of a(7) = (50 m)(1/2)^(7 - 1), or

a(7) = 50 / (2^6) m = 0.78125 m

3 0

3 years ago

The ratio of the heights of two similar cylinders is 1:3. If the volume of the smaller cylinder is 67cm3, find the volume of the

Inessa [10]

Answer:

solution given:

similar cylinders ratio 1:3

let the ratio be 1x and 3x respectively:

according to the question:

x/3x=volume of (smaller cylinder/big cylinder)

Volume of big Cylinder=67cm³×3=201cm3

201cm³ is your answer

4 0

3 years ago

-5x-4y=10

strojnjashka [21]

Answer:

y intercept = $(0, ~-\frac{5}{2} )$

x intercept = $(-2, ~0)$

.

Step-by-step explanation:

$-5x - 5y = 10$

.

y intercept

$\to x = 0$

$-5(0) - 4y = 10$

$-4y = 10$

$y = \frac{10}{-4}$

$y = -\frac{5}{2}$

so, the answer is $(0, ~-\frac{5}{2} )$

.

x intercept

$\to y = 0$

$-5x - 4(0) = 10$

$-5x = 10$

$x = \frac{10}{-5}$

$x = -2$

so, the answer is $(-2, ~0)$

.

Happy to help :)

8 0

3 years ago

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