Which function matches the<br> graph?

Name a number that is an integer, but not whole number.

tekilochka [14]

Answer:

-1

Step-by-step explanation:

All negative integers are not whole numbers

4 0

3 years ago

Find a linear second-order differential equation f(x, y, y', y'') = 0 for which y = c1x + c2x3 is a two-parameter family of solu

Alisiya [41]

Let $y=C_1x+C_2x^3=C_1y_1+C_2y_2$ . Then $y_1$ and $y_2$ are two fundamental, linearly independent solution that satisfy

$f(x,y_1,{y_1}',{y_1}'')=0$
$f(x,y_2,{y_2}',{y_2}'')=0$

Note that ${y_1}'=1$ , so that $x{y_1}'-y_1=0$ . Adding $y''$ doesn't change this, since ${y_1}''=0$ .

So if we suppose

$f(x,y,y',y'')=y''+xy'-y=0$

then substituting $y=y_2$ would give

$6x+x(3x^2)-x^3=6x+2x^3\neq0$

To make sure everything cancels out, multiply the second degree term by $-\dfrac{x^2}3$ , so that

$f(x,y,y',y'')=-\dfrac{x^2}3y''+xy'-y$

Then if $y=y_1+y_2$ , we get

$-\dfrac{x^2}3(0+6x)+x(1+3x^2)-(x+x^3)=-2x^3+x+3x^3-x-x^3=0$

as desired. So one possible ODE would be

$-\dfrac{x^2}3y''+xy'-y=0\iff x^2y''-3xy'+3y=0$

(See "Euler-Cauchy equation" for more info)

6 0

3 years ago

PLZ HELP! Need this ASAP! Thx so much!<br><br> Find m∠PMK<br><br> Plz show ur work!

max2010maxim [7]

In ∆MKP and ∆MNP

MK = MN

PK = NP

MP = MP

SO ∆MKP AND ∆MNP ARE CONGRUENT.

SO m<PMN = m<PMK

m<NMK = 50

=> m<PMN + m<PMK = 50

=> 2 m<PMK = 50

=> m<PMK = 50/2 = 25°

3 0

3 years ago

See attachment for the full question

alexandr402 [8]

The inverse of the demand function is; P = 9 - 0.25Q

The profit-maximizing price and quantity are; $8.5 and 2 units.

The maximum profit is; $1

<h3>How to find the inverse of a function?</h3>

A) The demand function we are given is;

Q = 36 - 4P

Making P the subject gives the inverse demand function;

P = (36 - Q)/4

P = 9 - Q/4

P = 9 - 0.25Q

B) The profit-maximization point is the point at which MR = MC.

MR refers to the marginal revenue and MC is the marginal cost.

MC can be calculated as the first derivative of the cost function:

C(Q) = 4 + 4Q + Q²

MC = C'(Q) = 2Q + 4

Total Revenue = Price * Quantity

Total Revenue = (9 - 0.25Q) * Q

Total Revenue = 9Q - 0.25Q²

MR is gotten by differentiating Total Revenue to get;

MR = 9 - 0.5Q

Applying the condition MR = MC, we have;

9 - 0.5Q = 4 - 2Q

Solving for Q gives Q = 2

Thus, profit maximizing quantity is 2.

Thus, profit maximizing price will be;

P(2) = 9 - 0.25(2)

P(2) = $8.5

C) Formula for Maximum Profit is;

Profit = Total Revenue - Total Cost

Total Revenue = 8.5 * 2

Total revenue = $17

Total Cost is;

C(2) = 4 + 4(2) + 2²

C(2) = $16

Thus;

Maximum Profit = 17 - 16 = $1

Read more about Inverse of a function at; brainly.com/question/13948067

#SPJ1

3 0

2 years ago

The total cost of a jacket and a pair of pants was $66.12. If the price of the jacket was $3.26 less than the pair of pants, wha

drek231 [11]

Answer:

The price of the jacket was $31.43

Step-by-step explanation:

Let the cost of a jacket = x

Let the cost of a pair of pants = y

Such that,

x + y = $66.12.........Equation 1.

From the conditional statement,

x = y - $3.26..........Equation 2.

Solve both equations simultaneously, using the substitution method

From Equation 2;

x = y - 3.26

Substitute y - 3.26 for x in Equation 1.

x + y = 66.12, now becomes,

y - 3.26 + y = 66.12

collect like terms

y + y = 66.12 + 3.26

2y = 69.36

y= 69.36/2 = $34.69.

Put y = $34.69 in Equation 2. to obtain x

x = 34.69 - 3.26

x = $31.43

4 0

3 years ago

Which function matches the graph?