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4 years ago

What is the quadratic equation ?

Mathematics

1 answer:

SCORPION-xisa [38]4 years ago

7 0

Ax^2+bx+c ,or x=-b+√b^2-4ac\2a

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A scientist begins with 250 grams of a radioactive substance. After 250 minutes, the sample has decayed to 32 grams. Rounding to

s2008m [1.1K]

Answer:

Part 1 : $A=250 e^{-0.008223t}$

Part 2 : Half life is 84 minutes ( approx )

Step-by-step explanation:

Part 1 : Suppose the function that shows the amount( in grams ) of the substance after t minutes,

$A=A_0 e^{kt}$

If t = 0 min, A = 250 grams,

$250=A_0 e^{0}$

$\implies A_0 = 250$

If t = 250, A = 32 grams,

$32 = A_0 e^{250k}$

$32 = 250 e^{250k}$

$0.128 = e^{250k}$

Taking ln both sides,

$\ln(0.128) = 250k$

$\implies k =\frac{\ln(0.128)}{250}=-0.008223$

Hence, the equation that shows this situation,

$A=250 e^{-0.008223t}$

Part 2 : If A = 250/2 = 125,

$125 = 250 e^{-0.008223t}$

$0.5 = e^{-0.008223t}$

Taking ln both sides,

$\ln(0.5) = -0.008223t$

$\implies t =\frac{\ln(0.5)}{-0.008223}\approx 84$

Therefore, the half life of the substance would be 84 minutes.

8 0

3 years ago

Which transformation makes triangle 2 the image of triangle 1?

KATRIN_1 [288]

Answer:

translation

Step-by-step explanation:

translation is just the movement of a shape, also stays the same size and way

7 0

3 years ago

Read 2 more answers

Please help meeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!if 14 out of 20 students in a college class are male, what percent of the class is

densk [106]

That’ll be 70 percent.

4 0

3 years ago

Read 2 more answers

Carlos has taken an initial dose of a prescription medication.

Marat540 [252]

Answer:

3.48 hours

Step-by-step explanation:

The equation is:

$M(t)=20 e^{-0.86t}$

Where

M(t) is the amount of medication remaining in mg

t is the time it takes, in hours

The questions asks HOW LONG it will take to make the remaining medication to 1 milligrams (1 mg)??

We have to substitute M(t) with "1" and find the corresponding value of "t". We will use natural log to solve this. Shown below:

$M(t)=20e^{-0.86t}\\1=20e^{-0.86t}\\0.05=e^{-0.86t}\\Ln(0.05)=Ln(e^{-0.86t})\\Ln(0.05)=(-0.86t)Ln(e)\\t=\frac{Ln(0.05)}{-0.86}\\t=3.48$

<u>Note: </u> Ln(e) = 1

This means, the amount of time it will take is about 3.48 hours

8 0

3 years ago

For the following set of 20 numbers:

patriot [66]

Answer:

I cannot answer all of this, so I will only answer what I can:

Q1: 13

Q3: 22.5

IQR: 13.5

IQR(1.5): 20.25

Q3 + IQR(1.5) = 43

Q1 - IQR(1.5) = -7.25

I don't know if my calculations are all right but I hope this helps! :)

4 0

3 years ago