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3 years ago

Suppose f(x) =x^2 and g (x) = 2x -3 what is the value of g (4)+f(-3)

Mathematics

1 answer:

Alona [7]3 years ago

6 0

Answer:

Step-by-step explanation:

u just have to plug in the numbers

f(-3)= -3^2

f(-3)= 9

g(4)=2(4)-3

g(4)=5

9+5=14

I hope I'm right and hope I helped:)

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Hey go to attachments and help me out- thanks very much! this is my last question for today so it would really help also stay sa

Llana [10]

Answer:

A) 250 / 8 = 31.25

31.25 x 8 = 250 Know you know that one pancake requires 31.25ml of Milk

31.25 x 4 = 125

So 4 pancakes requires 125ml of Milk

B) 5 / 8 = 0.625

0.625 x 8 = 5 So just like last time, you know that 0.625g of butter is required to make 8 pancakes

0.625 x 12 = 7.5g of Butter

So 12 pancakes requires 7.5g of butter.

Hope this makes sense !

7 0

3 years ago

Solve the following differential equation using using characteristic equation using Laplace Transform i. ii y" +y sin 2t, y(0) 2

kifflom [539]

Answer:

The solution of the differential equation is $y(t)= - \frac{1}{3} Sin(2t)+2 Cos(t)+\frac{5}{3} Sin(t)$

Step-by-step explanation:

The differential equation is given by: y" + y = Sin(2t)

<u>i) Using characteristic equation:</u>

The characteristic equation method assumes that y(t)= $e^{rt}$ , where "r" is a constant.

We find the solution of the homogeneus differential equation:

y" + y = 0

$y'=re^{rt}$

$y"=r^{2}e^{rt}$

$r^{2}e^{rt}+e^{rt}=0$

$(r^{2}+1)e^{rt}=0$

As $e^{rt}$ could never be zero, the term (r²+1) must be zero:

(r²+1)=0

r=±i

The solution of the homogeneus differential equation is:

$y(t)_{h}=c_{1}e^{it}+c_{2}e^{-it}$

Using Euler's formula:

$y(t)_{h}=c_{1}[Sin(t)+iCos(t)]+c_{2}[Sin(t)-iCos(t)]$

$y(t)_{h}=(c_{1}+c_{2})Sin(t)+(c_{1}-c_{2})iCos(t)$

$y(t)_{h}=C_{1}Sin(t)+C_{2}Cos(t)$

The particular solution of the differential equation is given by:

$y(t)_{p}=ASin(2t)+BCos(2t)$

$y'(t)_{p}=2ACos(2t)-2BSin(2t)$

$y''(t)_{p}=-4ASin(2t)-4BCos(2t)$

So we use these derivatives in the differential equation:

$-4ASin(2t)-4BCos(2t)+ASin(2t)+BCos(2t)=Sin(2t)$

$-3ASin(2t)-3BCos(2t)=Sin(2t)$

As there is not a term for Cos(2t), B is equal to 0.

So the value A=-1/3

The solution is the sum of the particular function and the homogeneous function:

$y(t)= - \frac{1}{3} Sin(2t) + C_{1} Sin(t) + C_{2} Cos(t)$

Using the initial conditions we can check that C1=5/3 and C2=2

<u>ii) Using Laplace Transform:</u>

To solve the differential equation we use the Laplace transformation in both members:

ℒ[y" + y]=ℒ[Sin(2t)]

ℒ[y"]+ℒ[y]=ℒ[Sin(2t)]

By using the Table of Laplace Transform we get:

ℒ[y"]=s²·ℒ[y]-s·y(0)-y'(0)=s²·Y(s) -2s-1

ℒ[y]=Y(s)

ℒ[Sin(2t)]= $\frac{2}{(s^{2}+4)}$

We replace the previous data in the equation:

s²·Y(s) -2s-1+Y(s) = $\frac{2}{(s^{2}+4)}$

(s²+1)·Y(s)-2s-1= $\frac{2}{(s^{2}+4)}$

(s²+1)·Y(s)= $\frac{2}{(s^{2}+4)}+2s+1=\frac{2+2s(s^{2}+4)+s^{2}+4}{(s^{2}+4)}$

Y(s)= $\frac{2+2s(s^{2}+4)+s^{2}+4}{(s^{2}+4)(s^{2}+1)}$

Y(s)= $\frac{2s^{3}+s^{2}+8s+6}{(s^{2}+4)(s^{2}+1)}$

Using partial franction method:

$\frac{2s^{3}+s^{2}+8s+6}{(s^{2}+4)(s^{2}+1)}=\frac{As+B}{s^{2}+4} +\frac{Cs+D}{s^{2}+1}$

2s^{3}+s^{2}+8s+6=(As+B)(s²+1)+(Cs+D)(s²+4)

2s^{3}+s^{2}+8s+6=s³(A+C)+s²(B+D)+s(A+4C)+(B+4D)

We solve the equation system:

A+C=2

B+D=1

A+4C=8

B+4D=6

The solutions are:

A=0 ; B= -2/3 ; C=2 ; D=5/3

So,

Y(s)= $\frac{-\frac{2}{3} }{s^{2}+4} +\frac{2s+\frac{5}{3} }{s^{2}+1}$

Y(s)= $-\frac{1}{3} \frac{2}{s^{2}+4} +2\frac{s }{s^{2}+1}+\frac{5}{3}\frac{1}{s^{2}+1}$

By using the inverse of the Laplace transform:

ℒ⁻¹[Y(s)]=ℒ⁻¹[ $-\frac{1}{3} \frac{2}{s^{2}+4}$ ]-ℒ⁻¹[ $2\frac{s }{s^{2}+1}$ ]+ℒ⁻¹[ $\frac{5}{3}\frac{1}{s^{2}+1}$ ]

$y(t)= - \frac{1}{3} Sin(2t)+2 Cos(t)+\frac{5}{3} Sin(t)$

3 0

3 years ago

Look at the figure above. The surface area is _____ square cm.

user100 [1]

Answer: 252

Step-by-step explanation:

6 0

3 years ago

Would someone mind explaining this?

Nesterboy [21]

Answer:

Step-by-step explanation:

i think that because it's multiplying by 3.

3*3= 9

5*3= 15

7*3= 21

9*3= 27

This is the only way i could think of helping in some sort of way! I'm sorry if it's wrong! (´。＿。｀)

Have a great day! (´。＿。｀) / (ﾉ◕ヮ◕)ﾉ*:･ﾟ✧

( ﾟдﾟ)つ Bye

8 0

3 years ago

Find an equation of the line passing through the given points. Use function notation to write the equation. (3,8) and (4,13

Olegator [25]

Answer:

$f(x)=5x-7$

Step-by-step explanation:

The given line passes through the points;

$(x_1,y_1)=(3,8)$

and

$(x_2,y_2)=(4,13)$

Let us find the slope using;

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{13-8}{4-3}$

$m=\frac{5}{1}=5$

The equation is given by;

$y-y_1=m(x-x_1)$

We substitute the values into the formula to obtain;

$y-8=5(x-3)$

$y=5x-15+8$

$y=5x-7$

There the equation of the line is

$f(x)=5x-7$

7 0

3 years ago