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3 years ago

13

There are 16 bacteria in a beaker.Four hours later there are 228 bactriea in the beaker.What is the rate of change per hour in t

he number of bacteria.

1 answer:

saul85 [17]3 years ago

6 0

Answer:

Rate of change per hour in the number of bacteria is r=0.28

Step-by-step explanation:

Given : There are 16 bacteria in a beaker and four hours later there are 228 bacteria in the beaker.

To find : What is the rate of change per hour in the number of bacteria.

Solution :

At initial number of bacteria is 16

After 4 hours number of bacteria is 228

Rate of change per hour is given by

$A=Pe^{rt}$

where A = total number of bacteria, P = initial number of bacteria, r= rate of change , t= time

$228=16(e^{4r})$

$14.25=(e^{4r})$

Taking log both side,

$log(14.25)=4r$

$1.15=4r$

$0.28=r$

Therefore, Rate of change per hour in the number of bacteria is r=0.28

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The hypotenuse of an isosceles right triangle is centimeters longer than either of its legs. Find the exact length of each side.

Varvara68 [4.7K]

Question

The hypotenuse of an isosceles right triangle is 11 centimeters longer than either of its legs. find the exact length of each side.

Answer:

$Hypotenuse:37.56$

$Other\ Legs: 26.56$

Step-by-step explanation:

Let the hypotenuse be y and the other legs be x.

So:

$y = 11 + x$

Required

Determine the exact dimension of the triangle

Using Pythagoras theorem;

$y^2 = x^2 + x^2$

$y^2 = 2x^2$

This gives:

$(11+x)^2 = 2x^2$

Open bracket

$121 + 22x + x^2= 2x^2$

Collect like terms

$2x^2 - x^2 -22x - 121 = 0$

$x^2 -22x - 121 = 0$

Using quadratic formula:

$x = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}$

$x = \frac{-(-22)\±\sqrt{(-22)^2 - 4*1*-121}}{2*1}$

$x = \frac{-(-22)\±\sqrt{968}}{2*1}$

$x = \frac{22\±31.11}{2}$

Split

$x = \frac{22+31.11}{2}\ or\ x = \frac{22-31.11}{2}\\$

$x = \frac{53.11}{2}\ or\ x = \frac{-9.11}{2}$

x can not be negative.

So:

$x = \frac{53.11}{2}$

$x = 26.56$

Recall that:

$y = 11 + x$

$y = 11 + 26.56$

$y = 37.56$

Hence, the dimensions are:

$Hypotenuse:37.56$

$Other\ Legs: 26.56$

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2 years ago

keisha got a fish tank. It fits on table that is exactly 10 inches wide and 12 inches long. When the tank is filled, it can hold

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1800 divided by 120 is 15.

So, 15 inches is the height of the fish tank.

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2 years ago

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We might choose to write a recursive formula rather than an explicit formula to define a sequence because (D) the sequence is strictly geometric.

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2 years ago

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ArbitrLikvidat [17]

Answer:

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2 years ago

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