Ask question

Ask question

All categories

3 years ago

12

Russell's uncle buys a 7.5-pound bag of candy for Russell's birthday party. He puts 1 2 of the candy into a piñata. If Russell g

ets 1 5 of the candy from the piñata when it breaks open, how many pounds of candy does he get?

1 answer:

Amanda [17]3 years ago

4 0

Answer:

7.5/2 = 3.75

3.75/5 = .75

he gets .75 pounds of candy

You might be interested in

Anyone up for a discord gc? fredwglss#9486

lyudmila [28]

Answer:

yuhhhh

Step-by-step explanation:

except im grounded... but will def save this for 2 mounths

3 0

3 years ago

Read 2 more answers

Find a second solution y2(x) of<br> x^2y"-3xy'+5y=0; y1=x^2cos(lnx)

rosijanka [135]

We can try reduction order and look for a solution $y_2(x)=y_1(x)v(x)$ . Then

$y_2=y_1v\implies{y_2}'=y_1v'+{y_1}'v\implies{y_2}''=y_1v''+2{y_1}'v+{y_1}''v$

Substituting these into the ODE gives

$x^2(y_1v''+2{y_1}'v+{y_1}''v)-3x(y_1v'+{y_1}'v)+5y_1v=0$

$x^2y_1v''+(2x^2{y_1}'-3xy_1)v'+(x^2{y_1}''-3x{y_1}'+5y_1)v=0$

$x^4\cos(\ln x)v''+x^3(\cos(\ln x)-2\sin(\ln x))v'=0$

which leaves us with an ODE linear in $w(x)=v'(x)$ :

$x^4\cos(\ln x)w'+x^3(\cos(\ln x)-2\sin(\ln x))w=0$

This ODE is separable; divide both sides by the coefficient of $w'(x)$ and separate the variables to get

$w'+\dfrac{\cos(\ln x)-2\sin(\ln x)}{x\cos(\ln x)}w=0$

$\dfrac{w'}w=\dfrac{2\sin(\ln x)-\cos(\ln x)}{x\cos(\ln x)}$

$\dfrac{\mathrm dw}w=\dfrac{2\sin(\ln x)-\cos(\ln x)}{x\cos(\ln x)}\,\mathrm dx$

Integrate both sides; on the right, substitute $u=\ln x$ so that $\mathrm du=\dfrac{\mathrm dx}x$ .

$\ln|w|=\displaystyle\int\frac{2\sin u-\cos u}{\cos u}\,\mathrm du=\int(2\tan u-1)\,\mathrm du$

Now solve for $w(u)$ ,

$\ln|w|=-2\ln(\cos u)-u+C$

$w=e^{-2\ln(\cos u)-u+C}$

$w=Ce^{-u}\sec^2u$

then for $w(x)$ ,

$w=Ce^{-\ln x}\sec^2(-\ln x)$

$w=C\dfrac{\sec^2(\ln x)}x$

Solve for $v(x)$ by integrating both sides.

$v=\displaystyle C_1\int\frac{\sec^2(\ln x)}x\,\mathrm dx$

Substitute $u=\ln x$ again and solve for $v(u)$ :

$v=\displaystyle C_1\int\sec^2u\,\mathrm du$

$v=C_1\tan u+C_2$

then for $v(x)$ ,

$v=C_1\tan(\ln x)+C_2$

So the second solution would be

$y_2=x^2\cos(\ln x)(C_1\tan(\ln x)+C_2)$

$y_2=C_1x^2\sin(\ln x)+C_2x^2\cos(\ln x)$

$y_1(x)$ already accounts for the second term of the solution above, so we end up with

$\boxed{y_2=x^2\sin(\ln x)}$

as the second independent solution.

6 0

4 years ago

Please i need help on this i’m stuck

gtnhenbr [62]

Perimeter would be 6pi+21.4

4 0

3 years ago

Please show me step by step how to do this

riadik2000 [5.3K]

Answer:

You know that the beginning salary is $32,000, and it is raised by $1,000 per year.

a) We want to find a recursive relation, let's try to find a pattern:

S₁ = salary on the first year = $32,000

S₂ = salary on the second year = $32,000 + $1,000 = $33,000

S₃ = salary on the third year = $33,000 + $1,000 = $34,000

and so on.

We already can see that the recursive relation is: "the salary of the previous year plus $1,000", this can be written as:

Sₙ = Sₙ₋₁ + $1,000

Such that S₁ = $32,000

b) Your salary in the fifth year is S₅

Let's construct it:

S₃ = $34,000

S₄ = $34,000 + $1,000 = $35,000

S₅ = $35,000 + $1,000 = $36,000

Your salary on the fifth year is $36,000

c) When we have a recursive relation like:

Aₙ = Aₙ₋₁ + d

The sum of the first N elements is given by:

Sum(N) = N*(2*A₁ + (N - 1)*d)/2

Then the sum of your salary for the first 20 years is:

S(20) = 20*(2*$32,000 + (20 - 1)*$1,000)/2

S(20) = $830,000

6 0

3 years ago

1. A company produces two types of nutritional supplements; Energize and Excel. Energize contains 26 mg of vitamin A, 42 mg of v

geniusboy [140]

Answer:

1)A) Minimize C = 40x + 100y.

2) d) 7x + 8y ≤ 190, 5x + 4y ≤ 22, x ≥ 0, y ≥ 0.

3) B) Min C = 295x + 416y; s.t 23x + 15y ≥ 154, 17x + 25y ≥ 140, x ≥ 0, y ≥ 0.

Step-by-step explanation:

1) Energize pills cost 40 cents each, while Excel pills cost 100 cents each. If x represent the energize pills and y represent the excel pills, the objective function would be:

minimize cost = cost of energize pill + cost of excel pill

Minimize cost = 40x + 100y

2) Let x = the number of mountain bikes they produce, and let y = the number of racing bikes they produce.

7 hours of assemble time to produce a mountain bike and 8 hours of assemble time to produce a racing bike. Since the company has at most 190 hours for assemble time, it can be represented as:

7x + 8y≤ 190

5 hours of mechanical tuning to produce a mountain bike and 4 hours of mechanical tuning to produce a racing bike. Since the company has at most 22 hours for mechanical tuning, it can be represented as:

5x + 4y ≤ 22

Also assemble time and mechanical time must be greater than 0, hence:

x ≥ 0, y ≥ 0

3) The fieldwork constraint can be represented as:

23x + 15y ≥ 154

The time to be spent at university research center can be represented as:

17x + 25y ≥ 140

Both fieldwork time and time spent at university research center mut be greater than 0, hence:

x ≥ 0, y≥ 0

The cost equation is:

Minimize cost = 295x + 416y

5 0

3 years ago