7. The revenue for the school play is given by: R= -50t^2 + 300t , where “t” is the ticket price in dollars. The cost to produce the play is given by: C = 600-50t. Determine the ticket price that will allow the school play to break even. (Note: breaking even means that revenue = cost.) Sketch the graphs of both equations as seen on your calculator (indicate the window you used
in the space provided).

Answer:

[tex]\mathbf{6xe^xy+y^2e^x = C}[/tex] which implies that C is the integrating factor

Step-by-step explanation:

The correct format for the equation given is:

[tex]y(6x+y +6)dx +(6x +2y)dy=0[/tex]

By the application of the general differential equation:

⇒ Mdx + Ndy = 0

where:

M = 6xy+y²+6y

[tex]\dfrac{\partial M}{\partial y}= 6x+2y+6[/tex]

and

N = 6x +2y

[tex]\dfrac{\partial N}{\partial x}= 6[/tex]

∴

[tex]f(x) = \dfrac{1}{N}\Big(\dfrac{\partial M}{\partial y}- \dfrac{\partial N}{\partial x} \Big)[/tex]

[tex]f(x) = \dfrac{1}{6x+2y}(6x+2y+6-6)[/tex]

[tex]f(x) = \dfrac{1}{6x+2y}(6x+2y)[/tex]

f(x) = 1

Now, the integrating factor can be computed as:

[tex]\implies e^{\int fxdx}[/tex]

[tex]\implies e^{\int (1)dx}[/tex]

the integrating factor = [tex]e^x[/tex]

From the given equation:

[tex]y(6x+y +6)dx +(6x +2y)dy=0[/tex]

Let us multiply the above given equation by the integrating factor:

i.e.

[tex](6xy+y^2 +6y)dx +(6x +2y)dy=0[/tex]

[tex](6xe^xy+y^2 +6e^xy)dx +(6xe^x +2e^xy)dy=0[/tex]

[tex]6xe^xydx+6e^xydx+y^2e^xdx +6xe^xdy +2ye^xdy=0[/tex]

By rearrangement:

[tex]6xe^xydx+6e^xydx+6xe^xdy +y^2e^xdx +2ye^xdy=0[/tex]

Let assume that:

[tex]6xe^xydx+6e^xydx+6xe^xdy = d(6xe^xy)[/tex]

and:

[tex]y^2e^xdx +e^x2ydy=d(y^2e^x)[/tex]

Then:

[tex]d(6xe^xy)+d(y^2e^x) = 0[/tex]

[tex]6d (xe^xy) + d(y^2e^x) = 0[/tex]

By integration:

[tex]\mathbf{6xe^xy+y^2e^x = C}[/tex] which implies that C is the integrating factor

Answer:

[tex]180ft^{3}[/tex]

Step-by-step explanation:

Volume of a cone:

[tex]V=\pi r^{2} \frac{h}{3}[/tex]

Take [tex]\pi[/tex] as 3, as mentioned in the question

'r' is 'radius' ⇒ {diameter is given so divide by 2: 12/2 = 6}

'h' is 'height'

[tex]V=(3)(6)^{2} (\frac{5}{3} )[/tex]

[tex]V=(3)(36)(\frac{5}{3} )[/tex]

[tex]V=108(\frac{5}{3} )[/tex]

{multiply 108 with 5 and then divide the answer by 3}

[tex]V=108[/tex] × [tex]5[/tex]

[tex]V=540[/tex]

[tex]V=540/3[/tex]

[tex]V=180ft^{3}[/tex]

Answer:

Step-by-step explanation:

Binomial Expansion:

[tex](2x-3y)^4 \\\\= 4C_0(2x)^4 (-3y)^0 + 4C_1(2x)^3 (-3y)^1 + 4C_2(2x)^2(-3y)^2 \\\\+ 4C_3(2x)^1 (-3y)^3 + 4C_4(2x)^0 (-3y)^4\\\\=16x^4 + 4(8x^3)(-3y) + 6(4x^2)(9y^2) + 4(2x)(-27y^3) + 81y^4\\\\=16x^4 - 96x^3y + 216x^2y^2-216xy^3 +81y^4[/tex]

Pascal's Triangle:

  Zero row                        1

 First row                  1                 1

 Second row          1           2             1

 Third  row         1         3              3          1

 Fourth row    1       4            6           4          1

Answer:

Step-by-step explanation:

C-10,20,-40,80,...[tex] u_{n+1}=(-2)*u_{n}[/tex]. is geometric1

Answer:the awnser would b 2

Step-by-step explanation: it’s telling you if you look at the triangle from ABC it’s 54 degrees, but if you look at it from BAC it’s 30 degrees so you can only draw 2 triangles because no other combination is given the only other information we know is the line connecting A and B is 5 in some length which is a line not a triangle it would be a triangle thou if lines BC and AC were given. Long story short it’s B) 2

Answer:

0.410714

Step-by-step explanation:

Dividend ÷ Divisor = Quotient

Answer:

16

Step-by-step explanation:

[tex](-64)^2/3[/tex]

64 = [tex]2^{6}[/tex]

[tex]2^{6} ^{\frac{1}{3} } ^{2}[/tex]

[tex]2^{ 2^{2} }[/tex]

[tex]2^{4}[/tex]

16

Given:

Values of a polynomial P(x).

[tex]P(-5)=-2[/tex]

[tex]P(-3)=6[/tex]

[tex]P(3)=7[/tex]

[tex]P(5)=-1[/tex]

To find:

The remainder when P(x) is divided by (x+5).

The remainder when P(x) is divided by (x-3).

Solution:

If a polynomial P(x) is divided by (x-a), then the remainder is P(a).

If the polynomial P(x) is divided by (x+5), then the remainder is P(-5).

[tex]P(-5)=-2[/tex]

Therefore, the remainder is -2 when P(x) is divided by (x+5).

If the polynomial P(x) is divided by (x-3), then the remainder is P(3).

[tex]P(3)=7[/tex]

Therefore, the remainder is 7 when P(x) is divided by (x-3).

Answer:

I've attached a picture of a unit circle with the quadrant labeled.

Calculate the degree of 5п 8 radians:

[tex]\frac{5\pi }{8} =\frac{5*180}{8} =\frac{900}{8} =112.5[/tex]

Locate the general location of 112.5° on the unit circle:

It's between 120°([tex]\frac{2\pi }{3}[/tex]) and 90°([tex]\frac{\pi }{2}[/tex]).

Find the quadrant it lies in:

Quadrant II

Answer:

38.5

Step-by-step explanation:

b^2= 29^2+20^2-2×20×29× Cos 102

b^2=841+400-1160 (-0.2079)

=1241- 241.164

b^2=1482.164

b= square root of 1482.164

AC = 38.5

Answer:

Step-by-step explanation:

As,

1/4 = (1×2)/(4×2) = 4/8

4/8 = (4×1)/(8×1) = 4/8

In both case,

The denominator 8 is least common multiple

Answer:

V=πr2h /3

V=πr2h /3=π·2.52·8 /3≈52.35988

so the volume is 52.36 inches

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]Region\ A = 81218576[/tex]

Required

The acres owned by the government

The question is incomplete as the proportion (p) owned by the government is not given.

However, the formula to use is as follows:

[tex]Govt = p * Region\ A[/tex]

Assume the proportion is 28%, the equation becomes

[tex]Govt = 28\% * 81218576[/tex]

[tex]Govt = 22741201.28[/tex]

The acres owned by the government will be 22741201.28

Answer:

94.2 square units.

I got 94.09 but that seems to be the closer answer.

Answer:

2√10 km

Step-by-step explanation:

By Pythagoras theorem,

x^2 + 9^2 = 11^2

x^2 + 81 = 121

x^2 = 121 - 81

x^2 = 40

= 4 x 10

x^2 = 2^2 x 10

x = 2√10 km

Answer:

[tex]Area = \frac{1}{2} * AC * D[/tex]

Step-by-step explanation:

From the complete question, we have:

Length D to be perpendicular to side AC

So, the area of the triangle is:

[tex]Area = \frac{1}{2} * Base * Height[/tex]

Since:

Length D is perpendicular to side AC

Then:

[tex]Base = AC[/tex]

[tex]Heigjt =D[/tex]

So:

[tex]Area = \frac{1}{2} * AC * D[/tex]

Answer:

there you go

Step-by-step explanation:

angle DOB is 60 degree.

Answer:

see explanation

Step-by-step explanation:

Given ∠ DOC = 90° then

∠ DOB = 90 - p and

Since AOB is a straight angle , then

4p + 90 - p = 180

3p + 90 = 180 ( subtract 90 from both sides )

3p = 90 ( divide both sides by 3 )

p = 30

4p = 4 × 30 = 120

Then

∠ DOB = 180° - 4p = 180° - 120° = 60°

Answer:

sorry I don't know

Step-by-step explanation:

.........

Answer:

Check off both of the boxes

Step-by-step explanation:

In your reponse you included that most ancient societies didn't have symbols for math operations and didn't have symbols for variables/unknown quantities.

Hope it helps (●'◡'●)

Answer:

= 19, 240 $

Step-by-step explanation:

cost of 1 computer = $ 740

cost of 26 computers = 26 × 740

= 19, 240 $

so the school spent 19, 240 $

Answer:

Step-by-step explanation:

slope>0 so graph is increasing.

Answer:

$5

Step-by-step explanation:

Find the markup by finding 25% of 20:

20(0.25)

= 5

So, the markup is $5

Step-by-step explanation:

The reserve ratio is the central bank's mandate for banks to keep a certain reserve requirements, which are excess cash deposits that must be kept on hand and not loaned out.

Raising the ratio is contractionary since less loans can be made, but this also solidifies banks' balance sheets.

If the Federal Reserve instead lowers the reserve ratio through an expansionary monetary policy, commercial banks are required to hold less cash on hand and can make more loans.

The lowering of the interest rate on reserves, considered an expansionary monetary policy, as it encourages banks to lend money instead of keeping it in reserve.

Hence, option 1 is correct.

Lowering the interest rate on reserves is considered an expansionary monetary policy because it incentivizes banks to lend out their excess reserves rather than keeping them idle in reserve accounts. When the central bank reduces the interest rate on reserves, it effectively lowers the opportunity cost for banks to hold reserves.

As a result, banks are more inclined to lend money to consumers and businesses at lower interest rates, which stimulates borrowing and spending in the economy. Increased lending and spending contribute to economic expansion and growth, making it an expansionary monetary policy.

Thus, lowering the interest rate encourages banks to lend money instead of keeping it in reserve.

Learn more about monetary policy here:https://brainly.com/question/28199887

#SPJ4

Answer:

1) 3000 + 125m

2) 3000 + 125m = 5000

3) M= 16

4) It would take 16 months

Step-by-step explanation:

Okay so no since there are no other transaction and you already have a balance of 3000 with a monthly Fee of 125 the equation shpuld be like this.

So every month you add 125,we dont know how much months we have to pay so we can use the variable given to us in this case “M”. So your base expression should look like this,

3000 + 125m (3000 base fee that doesnt change, and 125 every month fee)

Then it asked us to put it as the final balance as 5000, so using the base expression we can do this

3000 + 125m = 5000

Now to solve it you would solve it like any other equation

5000-3000=2000

2000=125m

2000/125= 16

Okay so m = 16

M in this case stands for months so the final answer would be it would take 16 months to reach the final balance of 5000

Answer:

x > 3

Step-by-step explanation:

3x-9-5x > -3x - 6

3x-5x+3x > -6+9

x > 3

Answer:

Step-by-step explanation:

Population size: 17

Median: 30

Minimum: 12

Maximum: 49

First quartile: 21

Third quartile: 35

Interquartile Range: 14

Outliers: none