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2 years ago

The expression below represents the number of bacteria in a petri dish after t hours.

Mathematics

2 answers:

ch4aika [34]2 years ago

5 0

Answer:

Step-by-step explanation:

tiny-mole [99]2 years ago

3 0

Solving this problem requires the supplement of the actual expression. However I believe you forgot to include it with the question.

However I believe that the expression is in the form of:

y = A e^(-k t)

where,

y is the number of bacteria after time t

A is a constant and represents the initial number of bacteria

k is the growth rate in decimal form

t is time

<span>So whatever is located in A is the initial number of bacteria, while k times 100% is the growth rate.</span>

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3 years ago

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2 years ago

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Step-by-step explanation:

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3 years ago

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A parabola can be drawn given a focus of

Volgvan

Answer:

$y=-\frac{1}{4}(x-2)^{2}+9$

Step-by-step explanation:

Any point on a given parabola is equidistant from focus and directrix.

Given:

Focus of the parabola is at $(2,8)$ .

Directrix of the parabola is $y=10$ .

Let $(x,y)$ be any point on the parabola. Then, from the definition of a parabola,

Distance of $(x,y)$ from focus = Distance of $(x,y)$ from directrix.

Therefore,

$\sqrt{(x-2)^{2}+(y-8)^{2}}=|y-10|$

Squaring both sides, we get

$(x-2)^{2}+(y-8)^{2}=(y-10)^{2}\\(x-2)^{2}=(y-10)^{2}-(y-8)^{2}\\(x-2)^{2}=(y-10+y-8)(y-10-(y-8))...............[\because a^{2}-b^{2}=(a+b)(a-b)]\\(x-2)^{2}=(2y-18)(y-10-y+8)\\(x-2)^{2}=2(y-9)(-2)\\(x-2)^{2}=-4(y-9)\\y-9=-\frac{1}{4}(x-2)^{2}\\y=-\frac{1}{4}(x-2)^{2}+9$

Hence, the equation of the parabola is $y=-\frac{1}{4}(x-2)^{2}+9$ .

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3 years ago