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Makovka662 [10]
3 years ago
14

On June 1, a fast-growing species of algae is accidentally introduced into a lake in a city park. It starts to grow and

Mathematics
1 answer:
xxTIMURxx [149]3 years ago
4 0

Answer:

June 29

Step-by-step explanation:

Since the question clearly states that the rate of algae growth is such that the area it covers doubles every day then the inverse is also true, i.e. going back a day the area covered is half.

It can be simply assumed that on the previous date from the day the entire lake was covered, half of the area must have been covered. This means that on the day prior to June 30 the lake was half covered, i.e. June 29

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1 year ago
During halftime of a basketball ​game, a sling shot launches​ T-shirts at the crowd. A​ T-shirt is launched from a height of 4 f
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Answer:

(a) The time the T-shirt takes to maximum height is 2 seconds

(b) The maximum height is 68 ft

(c) The range of the function that models the height of the T-shirt over time given above is 4 + 64\cdot t - 16 \cdot  t^{2}

Step-by-step explanation:

Here, we note that the general equation representing the height of the T-shirt as a function of time is

h = h_1 + u\cdot t - \frac{1}{2} \cdot g  \cdot  t^{2}

Where:

h = Height reached by T-shirt

t = Time of flight

u = Initial velocity = 64 ft/s

g = Acceleration due to gravity (negative because upward against gravity) = 32 ft/s²

h₁ = Initial height of T-shirt = 4 ft

(a) The maximum height can be found from the time to maximum height given as

v = u - gt

Where:

u = Initial velocity = 64 ft/s

v = Final upward velocity at maximum height = 0 m/s

g = 32 ft/s²

Therefore,

0 = 64 - 32·t

32·t = 64 and

t = 64/32 = 2 seconds

(b) Therefore, maximum height is then

h = 4 + 64\times 2 - \frac{1}{2} \times 32  \times  2^{2}

∴ h = 68 ft

The T-shirt is then caught 41 ft above the court on its way down

(c) The range of the function that models the height of the T-shirt over time given above is derived as

h = h_1 + u\cdot t - \frac{1}{2} \cdot g  \cdot  t^{2}

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h₁ = 4 ft

The equation becomes

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