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3 years ago

What is the quadratic formula? Can you help me with an example please?

1 answer:

3 0

Ax^2 + bx +c
Divide both sides of the equation by a, so that the coefficient of x2 is 1. Rewrite so the left side is in form x2 + bx (although in this case bx is actually ). Since the coefficient on x is , the value to add to both sides is.

Source
https://www.montereyinstitute.org/courses/DevelopmentalMath/COURSE_TEXT2_RESOURCE/U16_L5_T2_text_final.html

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Given f(x)= 3x+2, what is the Inverse Function?

Grace [21]

Answer:

Step-by-step explanation:

For this case we must determine the inverse of the following function:

$f(x)=3x-2$

Step 1:

We would write

$y=f(x)$ or $y=3x-2$

Step 2:

We clear x:

$y+2=3x$

$\frac{y+2}{3}=x$

Step 3:

"x" and "y" are exchanged:

$y=\frac{x+2}{3}$

The inverse is:

$f^{-1}(x)=\frac{x+2}{3}$

8 0

3 years ago

Maggie's brother is 5 years younger than three times her age. The sum of their ages is 43.

serious [3.7K]

Wouldn't she be 8 since 8x3 is 24 and 24-5 is 19 which equals to 43 if 24 and 19 are added together.

7 0

4 years ago

A quilt pattern uses a square with 7 1/2 inch sides. Patty wants to make each side 2/3 of the patterns length. Find the new dime

viktelen [127]

The new squares would be 5 inches long on each side. Because 7 1/2 / 3 * 2 = 5

5 0

3 years ago

4 to the 3rd power X blank =1 what is the blank?

BaLLatris [955]

If you mean this: $4^{3x} = 1$ then x = 0. The property in play here is the following: Any number raised to the "0" power is equal to "1". In this case, we would need to set the exponent of 3x = 0 and solve for x...

If you mean the equation: $4^{3} x = 1$ then to solve for x(your blank), simply divide both sides of the equation by $4^{3}$ :

You would have x = $\frac{1}{4^3}$ this can also be written as $4^{-3}$

6 0

4 years ago

Suppose that the population P(t) of a country satisfies the differential equation dP/dt = kP (600 - P) with k constant. Its pop

jeka94

Answer:

The country's population for the year 2030 is 368.8 million.

Step-by-step explanation:

The differential equation is:

$\frac{dP}{dt}=kP(600 - P)\\\frac{dP}{P(600 - P)} =kdt$

Integrate the differential equation to determine the equation of P in terms of t as follows:

$\int\limits {\frac{1}{P(600-P)} } \, dP =k\int\limits {1} \, dt \\(\frac{1}{600} )[(\int\limits {\frac{1}{P} } \, dP) - (\int\limits {\frac{}{600-P} } \, dP)]=k\int\limits {1} \, dt\\\ln P-\ln (600-P)=600kt+C\\\ln (\frac{P}{600-P} )=600kt+C\\\frac{P}{600-P} = Ce^{600kt}$

At t = 0 the value of P is 300 million.

Determine the value of constant C as follows:

$\frac{P}{600-P} = Ce^{600kt}\\\frac{300}{600-300}=Ce^{600\times0\times k}\\\frac{1}{300} =C\times1\\C=\frac{1}{300}$

It is provided that the population growth rate is 1 million per year.

Then for the year 1961, the population is: P (1) = 301

Then $\frac{dP}{dt}=1$ .

Determine k as follows:

$\frac{dP}{dt}=kP(600 - P)\\1=k\times300(600-300)\\k=\frac{1}{90000}$

For the year 2030, P (2030) = P (70).

Determine the value of P (70) as follows:

$\frac{P(70)}{600-P(70)} = \frac{1}{300} e^{\frac{600\times 70}{90000}}\\\frac{P(70)}{600-P(70)} =1.595\\P(70)=957-1.595P(70)\\2.595P(70)=957\\P(70)=368.786$

Thus, the country's population for the year 2030 is 368.8 million.

3 0

3 years ago