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3 years ago

Of T

Mathematics

1 answer:

Kisachek [45]3 years ago

5 0

Answer:

At 50 km/hr, she travels a distance of 40 km

At 100 km/hr, she travels a distance of 160 km

Step-by-step explanation:

The general formula for distance = d = r*t

distance / rate = time

x/50 + y / 100 = 2.4 Multiply by 100

2x + y = 240

x + y = 200

Subtract the two equations

x = 40 km

y = 200 - 40

y = 160 km

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A freshly inoculated bacterial culture of Streptococcus contains 100 cells. When the culture is checked 60 minutes later, it is

Luba_88 [7]

Answer:

$P(t) = 100e^{0.0251t}$

The doubling time is of 27.65 minutes.

Step-by-step explanation:

Exponential equation of growth:

The exponential equation for population growth is given by:

$P(t) = P(0)e^{kt}$

In which P(0) is the initial value and k is the growth rate.

A freshly inoculated bacterial culture of Streptococcus contains 100 cells.

This means that $P(0) = 100$ . So

$P(t) = 100e^{kt}$

When the culture is checked 60 minutes later, it is determined that there are 450 cells present.

This means that $P(60) = 450$ , and we use this to find k. So

$450 = 100e^{60k}$

$e^{60k} = 4.5$

$\ln{e^{60k}} = \ln{4.5}$

$60k = \ln{4.5}$

$k = \frac{\ln{4.5}}{60}$

$k = 0.0251$

$P(t) = 100e^{0.0251t}$

Doubling time:

This is t for which P(t) = 2P(0) = 200. So

$200 = 100e^{0.0251t}$

$e^{0.0251t} = 2$

$\ln{e^{0.0251t}} = \ln{2}$

$0.0251t = \ln{2}$

$t = \frac{\ln{2}}{0.0251}$

$t = 27.65$

The doubling time is of 27.65 minutes.

7 0

3 years ago

Someone help me with math homework

iVinArrow [24]

I hope this helps you

8/4=8/4=18/9=2

Side - Side - Side

6 0

3 years ago

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The hypotenuse of a right triangle measures 58 cm and one of its legs measures 42 cm. What is the length of the missing leg? 10

Nutka1998 [239]

If the hypotenuse is 58cm, and one of the others legs is 42cm the answer would be 40cm

Explanation:

Here you have to use the formula

${a}^{2} + {b}^{2} = {c}^{2}$
Then you have to pose the formula in terms of one of the legs, so:

${a}^{2} = {c}^{2} - {b}^{2}$
$a = \sqrt{ {c}^{2} - {b}^{2}}$
So when you change the letter for numbers you have that:

$a = \sqrt{ {58}^{2} - {42}^{2} }$

a=40

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3 years ago

Find the 92nd term of the arithmetic sequence 11, 19, 27,

fgiga [73]

Answer:

739

Step-by-step explanation:

a sub 92 = 11 + (92 - 1) * 8

a sub 92 = 11 + 728

a sub 92 = 739

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3 years ago

3 increased by a number

zimovet [89]

Answer:

4 or5or6

Step-by-step explanation:

3+1=4

3+2=5

3+3=6

6 0

1 year ago

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