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deff fn [24]
3 years ago
11

Antonio's toy boat is bobbing in the water next to a dock. Antonio starts his stopwatch, and measures the vertical distance from

the dock to the height of the boat's mast, which varies in a periodic way that can be modeled approximately by a trigonometric function. The vertical distance from the dock to the boat's mast reaches its highest value of -27 \text{ cm}−27 cmminus, 27, space, c, m every 333 seconds. The first time it reaches its highest point is after 1.31.31, point, 3 seconds. Its lowest value is -44\text{ cm}−44 cmminus, 44, space, c, m. Find the formula of the trigonometric function that models the vertical height HHH between the dock and the boat's mast ttt seconds after Antonio starts his stopwatch. Define the function using radians.

Mathematics
1 answer:
Firlakuza [10]3 years ago
7 0

Answer:

Step-by-step explanation:

Since we're given a time at which the height is maximum, we can use a cosine function for the model.

The amplitude is half the difference between the maximum and minimum: (-27 -(-44))/2 = 8.5 cm.

The mean value of the height is the average of the maximum and minimum: (-27 -44)/2 = -35.5 cm.

The period is given as 3 seconds, and the right shift is given as 1.31 seconds.

This gives us enough information to write the function as ...

  H(t) = (amplitude)×cos(2π(t -right shift)/period) + (mean height)

  H(t) = 8.5cos(2π(t -1.31)/3) -35.5 . . . . cm

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What's the issue? You gave the possible answers but that's about it.

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3 years ago
Kristen invests $ 5745 in a bank. The bank 6.5% interest compounded monthly. How long must she leave the money in the bank for i
podryga [215]

Answer:

1. 10.7 years

2. 17.0 years

3. 2nd option

Step-by-step explanation:

Use formula for compounded interest

A=P\cdot \left(1+\dfrac{r}{n}\right)^{nt},

where

A is final value, P is initial value, r is interest rate (as decimal), n is number of periods and t is number of years.

In your case,

1. P=$5745, A=2P=$11490, n=12 (compounded monthly), r=0.065 (6.5%) and t is unknown. Then

11490=5745\cdot \left(1+\dfrac{0.065}{12}\right)^{12t},\\ \\2=(1.0054)^{12t},\\ \\12t=\log_{1.0054}2,\\ \\t=\dfrac{1}{12}\log_ {1.0054}2\approx 10.7\ years.

2. P=$5745, A=3P=$17235, n=12 (compounded monthly), r=0.065 (6.5%) and t is unknown. Then


17235=5745\cdot \left(1+\dfrac{0.065}{12}\right)^{12t},

3=(1.0054)^{12t},

12t=\log_{1.0054}3,

t=\dfrac{1}{12}\log_{1.0054}3\approx 17.0\ years.

3. <u>1 choice:</u> P=$5745, n=12 (compounded monthly), r=0.065 (6.5%), t=5 years and A is unknown. Then

A=5745\cdot \left(1+\dfrac{0.065}{12}\right)^{12\cdot 5},\\ \\A=5745\cdot (1.0054)^{60}\approx \$7936.39.

<u>2 choice:</u> P=$5745, n=4 (compounded monthly), r=0.0675 (6.75%), t=5 years and A is unknown. Then

A=5745\cdot \left(1+\dfrac{0.0675}{4}\right)^{4\cdot 5},\\ \\A=5745\cdot (1.0169)^{20}\approx \$8032.58.

The best will be 2nd option, because $8032.58>$7936.39

5 0
2 years ago
Read 2 more answers
BRAINLIEST AND 100 POINTS. Please help by explaining how you got the answer
spayn [35]

Answer:

it may be A log x ........

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3 years ago
How long did it take the airplanes to reach 12,000 ft?​
Svetach [21]

Answer:it didnt

Step-by-step explanation:

7 0
3 years ago
At a hockey game a vender sold a combined total of 105 sodas and hot dogs. The number of sodas sold was 39 more than the number
yKpoI14uk [10]

Answer:

<em>Hot dog sold = 33</em>

<em>Sodas Sold = 72</em>

Step-by-step explanation:

<u><em>Given:</em></u>

<em>At a hockey game a vender sold a combined total of 105 sodas and hot dogs. The number of sodas sold was 39 more than the number of hot dogs sold</em>

<u><em>To Find:</em></u>

<em>Number of soda/hot dog sold</em>

<u><em>Solve:</em></u>

<em>h + ( 39 + h ) = 105</em>

<em>h + 39 + h = 105</em>

<em>2h + 39  = 105</em>

<em>h + 19.5 = 52.5</em>

<em>h = 52.5 - 19.5 </em>

<em>This as a system does not use any inequality. "39 more than" means, +39.</em>

<em>h = 33    meaning    d= 72</em>

<em />

<em>Add to check Answer:</em>

<em>33 + 72 = 105</em>

<em>Thus,</em>

<em>Hot dog sold = 33</em>

<em>Sodas Sold = 72</em>

<em />

<u><em>Kavinsky </em></u>

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