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3 years ago

Given: F(x) = x + 2 and G(x) = 3x + 5 (F * G) (x) =

Mathematics

1 answer:

RUDIKE [14]3 years ago

8 0

Answer:

3x²+11x+20

Step-by-step explanation:

x(3x+5)+2(3x+5)

3x²+5x+6x+20

3x²+11x+20

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To calculate the hourly revenue from the buffet after x $1 increases, multiply the price paid by each customer and the average n

spin [16.1K]

Answer:

Step-by-step explanation:

its 8 because u divided the 1x12 and that = 8

7 0

3 years ago

Find the general solution to 1/x dy/dx - 2y/x^2 = x cos x, y(pi) = pi^2

Finger [1]

Answer:

$\frac{y}{x^2}=\sin x+\pi$

Step-by-step explanation:

Consider linear differential equation $\frac{\mathrm{d} y}{\mathrm{d} x}+yp(x)=q(x)$

It's solution is of form $y\,I.F=\int I.F\,q(x)\,dx$ where I.F is integrating factor given by $I.F=e^{\int p(x)\,dx}$ .

Given: $\frac{1}{x}\frac{\mathrm{d} y}{\mathrm{d} x}-\frac{2y}{x^2}=x\cos x$

We can write this equation as $\frac{\mathrm{d} y}{\mathrm{d} x}-\frac{2y}{x}=x^2\cos x$

On comparing this equation with $\frac{\mathrm{d} y}{\mathrm{d} x}+yp(x)=q(x)$ , we get $p(x)=\frac{-2}{x}\,\,,\,\,q(x)=x^2\cos x$

I.F = $e^{\int p(x)\,dx}=e^{\int \frac{-2}{x}\,dx}=e^{-2\ln x}=e^{\ln x^{-2}}=\frac{1}{x^2}$ { formula used: $\ln a^b=b\ln a$ }

we get solution as follows:

$\frac{y}{x^2}=\int \frac{1}{x^2}x^2\cos x\,dx\\\frac{y}{x^2}=\int \cos x\,dx\\\\\frac{y}{x^2}=\sin x+C$

{ formula used: $\int \cos x\,dx=\sin x$ }

Applying condition: $y(\pi)=\pi^2$

$\frac{y}{x^2}=\sin x+C\\\frac{\pi^2}{\pi}=\sin\pi+C\\\pi=C$

So, we get solution as :

$\frac{y}{x^2}=\sin x+\pi$

4 0

3 years ago

What is the balance as a result if having a credit of $84 and a debit of $29

cricket20 [7]

This is a basic subtracting problem.

$84.00 minus $29.00
Debit means it's been taken out of the bank account, so subtracted.
After subtracting the balance will be $55.00.
You can double check your work by adding 55 + 29 = 84.

7 0

3 years ago

What is the value of g^-1(9)

mars1129 [50]

Hi there!

• g(x) = 6x - 3

Then,
if g(x) = y :-

y = 6x - 3

⇒6x = y + 3

⇒x = $\dfrac{\text{y} + 3}{6}$

According to th' question :-

g⁻¹(x) = $\dfrac{\text{x} + 3}{6}$

g⁻¹(9) = $\dfrac{9 + 3}{6}$

g⁻¹(9) = $\dfrac{12}{6}$

g⁻¹(9) = 2

Hence,
The required answer is g⁻¹(9) = 2

~ Hope it helps!

3 0

3 years ago

Read 2 more answers

"Gandalf thinks that fighting ability differs between men, hobbits and elves. To test this, he counts the number of orcs kills b

shepuryov [24]

Answer: a one-way ANOVA

Step-by-step explanation:

A One-Way ANOVA Which is also known as the Analysis of Variance is used to compares the means of two or more independent groups in order to determine if there is statistical relationship that is associating both population means are significantly different. A one way Anova test helps determine if the means of two or more groups are different. From the given example the best year to apply would be the one way anova because it would help in determining the difference between the orcs killed by elves, men and hobbits.

5 0

3 years ago