find the value of each variable using sine and cosine. round your answers to the nearest tenth​

The given differential equation has the answer C₁ +C₂ 1/81 -x⁹ +1/9 x⁹ln(x). It has been solved using the variation of parameters method below.

We have the differential equation xy'' − 8y' = x^8.  In order to solve any differential equation using the variation of parameters method, we first write the equation as and solve -

= xy'' − 8y' = 0

After solving this, we get the Auxiliary equation-

so CF is y = 1/9 x⁹ +  C₁ +C₂

Now, we write -

y1 (x) =  1/9 x⁹

y2 (x) = 1

y1'(x) = x^8

y2'(x) = 0

now, using wronskian formula

= W = -x^8

Now, applying the formulas -

= u =  [tex]- \int{\frac{f(x)y2(x)}{W(x)} } \, dx[/tex] and v = [tex]\int{\frac{f(x)y1(x)}{W(x)} } \, dx[/tex]

= u = log(x) and v = -x⁹/81

now particular integrals are

PI = 1/81 -x⁹ +1/9 x⁹ln(x)

total solution

y = C.F+P.I

y = C₁ +C₂ 1/81 -x⁹ +1/9 x⁹ln(x)

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Answer:

2125 lbs

Step-by-step explanation:

1 gallon = 8.5 lbs

we know 1 gallon * 250 = 250 gallons

multiply both sides by 250 to get 250 gallons on one side

250 gallons = 8.5* 250 lbs = 2125 lbs

Answer:

BC = 18 cm

Step-by-step explanation:

As we can see from the diagram:

AB + BC + CD = AD

⇒ 10 cm + BC + 11 cm = 39 cm

⇒ BC + 21 cm = 39 cm

⇒ BC = 39 cm - 21 cm

⇒ BC = 18 cm

The amount of tin used to make the can is about 478 cm².

To find the amount of tin used to make the can, we need to calculate the total surface area of the can. A can is a cylinder, so we can use the formula for the total surface area of a cylinder to calculate it:

Surface area = 2πr² + 2πrh

Where r is the radius of the can and h is the height of the can.

Given that the height of the can is 12.4 cm, we can use the information that the dashed line across the top of the can is labeled 9 cm to calculate the radius of the can.

r = dashed line / 2 = 9cm / 2 = 4.5 cm

Now we can substitute the values of r and h in the formula:

Surface area = 2π (4.5 cm)² + 2π (4.5 cm) (12.4 cm) = 477.594 cm²

Rounding to nearest square centimeter: 478 cm²

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When the angle of depression from a boat to a fish swimming inside the lake is 60, then 17 meters separate the fish from the boat.

The angle at which a line drawn from one point on a horizontal line to cross another point below the line would intersect is referred to as the angle of depression, as opposed to the angle of elevation. The angle at which the object can be observed from the horizontal line and the horizontal line is called the angle of depression. It is primarily used to determine the distance between two points where we know the angles and an object's distance from the ground.

Let's take the point on the water where the boat touches as A;

let's take the point below the water where the fish's axis and the boat's axis meet as B;

let's take the point where the fish is C.

Since angle C is an alternative angle, we can solve the equation by using tan.

                         The depth of fish in the water = 17√3m

                                  Angle C = 60° (alternative angle)

So , by using tan we get the equation,          

                         17√3/x

                           = tan 60°

                           = 17√3/x

                           = √3

X = 17 m

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The graph is shown in the attached image.

Answer: 140

Step-by-step explanation:

20+10+10+50+35+15

50+20+35+10+15=130

           -

There are $2224.12 need to deposit in an account in order to have $3000 in five years.

What is future value?

Future value is the worth of a financial asset or investment on a specific future date. In other words, future value is the amount of money an investment will be worth, assuming a specific rate of return, after a specific amount of time (interest rate).

Given:

Future value = FV = $3000

Number of years = t = 5

Interest rate = r = 6% = 0.06

Compounding period = n = 12

We have to find the present value form given problem.

Consider, the Future value formula,

[tex]FV = PV(1 + \frac{r}{n})^n^*^t[/tex]

Plug the values in the above formula.

[tex]3000 = PV(1+\frac{0.06}{12})^1^2^*^5\\ 3000 = PV(1+0.005)^6^0\\3000 = PV(1.005)^6^0\\PV = 2224.11658[/tex]

PV = $2224.12

Hence, there are $2224.12 need to deposit in an account in order to have $3000 in five years.

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The equation of the ellipse is [tex]\frac{x^2}{49} + \frac{y^2}{65} = 1[/tex]

The given parameters are:

The above means that:

c = 4 and

The semi-major axis, a = 7 i.e 14/2

Calculate b using

[tex]b = \sqrt{c^2 + a^2[/tex]

So, we have:

[tex]b = \sqrt{4^2 + 7^2[/tex]

[tex]b = \sqrt{65[/tex]

Square both sides

[tex]b^2 = 65[/tex]

The standard form of the ellipse is represented as:

[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]

This gives

[tex]\frac{x^2}{7^2} + \frac{y^2}{65} = 1[/tex]

Evaluate

[tex]\frac{x^2}{49} + \frac{y^2}{65} = 1[/tex]

Hence, the equation of the ellipse is [tex]\frac{x^2}{49} + \frac{y^2}{65} = 1[/tex]

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Answer:

The offers are equal at $7,000, after $7,000 more money will be made with a straight commission.

Step-by-step explanation:

.05x = .02x + 210  Subtract .02x from both sides.

.03x  = 210   Divide both sides by .03

x  = $7,000.

The probability of E and F expressed as P(E and F) equals;0.12

We are given;

P(E) = 0.2

P(F|E) = 0.6

Now, P(F/E) is known as conditional probability and it means the probability of event F given the probability of another event E. This can be expressed as; P(F|E) = P(E and F)/P(E)

Thus;

P(E and F) = 0.2 * 0.6

P(E and F) = 0.12

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Using the normal distribution, the z-scores are given as follows:

a) Z = 2.8.

b) Z = 2.8.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Item a:

The parameters are:

[tex]\mu = 15, \sigma = 2.5[/tex]

Hence the z-score is:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{22 - 15}{2.5}[/tex]

Z = 2.8.

Item b:

The parameters are:

[tex]\mu = 38.1, \sigma = 6.35[/tex]

Hence the z-score is:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{55.88 - 38.1}{6.35}[/tex]

Z = 2.8.

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Answer:

100 pi = about 314.16

Step-by-step explanation:

the surface area of a cylinder: SA = 2πrh+2πr^2

we plug in the values of r and h, and get

SA = 50pi + 50pi = 100 pi, which is approximately 314.16

(a) The number of cases on May 1, 2014, was approximately 188.59.

(b) The number of cases on November 24, 2014, was approximately 27107.76.

(c) C(92) = 1715.70.

This means that on the 92nd day from May 1, 2014, the number of Ebola cases in Africa was approximately 1715.70.

Computed using the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex].

We are given that the spread of the Ebola virus in Africa in 2014 could be modeled by the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex], where C represents the number of cases and t represents the number of days since May 1, 2014.

(a) In the question, we are asked for the approximate number of cases on May 1, 2014.

Since, the date is May 1, 2014, t = 0.

Thus, the number of cases, C, can be calculated by putting t = 0, in the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex].

[tex]C(0) = 188.59e^{0.024*0}\\\Rightarrow C(0) = 188.59e^0\\\Rightarrow C(0) = 188.59[/tex]

Thus, the number of cases on May 1, 2014, was approximately 188.59.

(b) In the question, we are asked for the approximate number of cases on November 24, 2014.

Since, the date is November 24, 2014, t = 207.

Thus, the number of cases, C, can be calculated by putting t = 207, in the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex].

[tex]C(207) = 188.59e^{0.024*207}\\\Rightarrow C(207) = 188.59e^{4.968}\\\Rightarrow C(207) = 188.59*143.739121458\\\Rightarrow C(207) = 27107.76[/tex]

Thus, the number of cases on November 24, 2014, was approximately 27107.76.

(c) We are asked to find C(92).

This can be found by putting t = 92, in the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex].

[tex]C(92) = 188.59e^{0.024*92}\\\Rightarrow C(92) = 188.59e^{2.208}\\\Rightarrow C(92) = 188.59*9.09750317953\\\Rightarrow C(92) = 1715.70[/tex]

Thus, C(92) = 1715.70.

This means that on the 92nd day from May 1, 2014, the number of Ebola cases in Africa was approximately 1715.70.

The complete question is:

"The spread of the Ebola virus in Africa in 2014 could be modeled by [tex]C(t) = 188.59e^{0.024t}[/tex] where C represents the number of cases and t represents the number of days since May 1, 2014. (source: http://www.geert.io/exponential-growth-of-ebola.html)

a. [3 pts] Approximately how many cases were there on May 1, 2014?

b. [3 pts] How many cases were projected by November 24, 2014?

c. [4 pts] Find C(92) and explain what it means in the context of the problem.

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Watthours are the units used to measure the amount of electricity used over time.

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Answer:

Step-by-step explanation:

Answer:

B. More than 90

Step-by-step explanation:

Hope this helps!

Answer: 5(5 + 9). This expression can be solved by multiplying 5 by both the addends. So, 5(5) + 5(9) = 25 + 45 = 70.

Step-by-step explanation:

Answer:

I would say A.

Step-by-step explanation:

The chance of getting no fives in 20 spins with 8 equal sectors is 1 in 160. The data is also slightly skewed left. All the other graphs are not skewed and have 1 or more outcome for each box. This indicates an unfair data-generating process for plot A.

I won't go into much depth of this analysis, but it should be enough to make you understand what is going on.

Hope this helps!

Answer:

If you start at (-4,3) and move 8 units to the right and 10 units down, you would end up at the point (4,-7).

The point is located in the 3rd quadrant, where the x-coordinates are negative and the y-coordinates are negative.

It's important to note that moving 8 units to the right means moving to the positive direction on x-axis and moving 10 units down means moving to the negative direction on y-axis.

The value of the expression [tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex] after substituting y = 7 is 108

The given expression is:

[tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex]

Simplifying the expression, we have:

[tex]2+4+y^2+4+y^2\\\\2y^2+10[/tex]

Substitute y = 7 into the simplified expression

[tex]2(7)^2+10\\\\=2(49)+10\\\\=98+10\\\\=108[/tex]

Therefore, after substituting y = 7, into the expression [tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex], the resulting value is 108

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Answer: -1

Step-by-step explanation: khan academy

Answer:

Diameter of sphere = 18 cm

Step-by-step explanation:

     Diameter = 18 cm

                  r = 18÷ 2 = 9 cm

                 h = 12 cm

[tex]\sf \boxed{\bf Volume \ of \ cylinder = \pi r^2h}[/tex]

                                    = π * 9 * 9 * 12 cm³

  [tex]\sf \boxed{\text{\bf Volume of sphere = $\dfrac{4}{3} \pi r^3$}}[/tex]

Solid cylinder is melted and turned into a solid sphere.

Volume of sphere = volume of cylinder

 [tex]\sf \dfrac{4}{3}\pi r^3 = \pi *9*9*12[/tex]

      [tex]\sf r^{3}= \dfrac{\pi *9*9*12*3}{4*\pi }\\\\ r^{3}=9 * 9 *3 *3\\\\\\r = \sqrt[3]{9*9*9}\\\\ r = 9 \ cm\\\\diameter = 9*2\\\\\boxed{diameter \ of \ sphere = 18 \ cm}[/tex]

Answer: It depends on how important you think sweet sixteen is, and how much money you have.

Step-by-step explanation:

First, if there is a lot of guests (I consider 32 a lot, but I don't know what you think), you need a lot of birthday cake, a lot of food and drinks, and entertainment. And that costs a lot of money. So, if you want to cross guests off the list to save money, I feel that that would be the more prudent choice.

The pairs of prime numbers (p,q) such that  p^2-p=37q^2-q is (43, 7)

The expression is given as:

p^2 - p=37q^2 - q

The boundary or range of numbers of p and q is not given.

So, we make use of numbers between 2 (because 1 is not a prime number) and a very large number (say 1000000)

i.e. 2 ≤ p ≤ 1000000 and 2 ≤ b ≤ 1000000

Using the above range, we have the following program to determine the pairs of prime numbers (p, q).

for a in range(2,1000000):

  for b in range(2,1000000):

      if ((a* *2) - a) == (37 * (b* *2) - b):

          print(str(a)+","+str(b))

The output of the above program is:

(43, 7)

The above represent all pairs of prime numbers (p,q) such that p^2 - p=37q^2 - q

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Answer: 22/85

Step-by-step explanation:

Answer:

22/85

Step-by-step explanation:

Answer:

Step-by-step explanation:

7/20 + 3/16 = x

x = 7/20 + 3/16

LCM of 20 and 16 = 80

x = 28/80 + 15/80

x =  43 /80

Answer:

x = 0.5375

Step-by-step explanation:

=7/20 + 3/16 = x

=LCM = 80

=80×7/20 + 80×3/16 = x × 80

=4×7 + 5×3 = x × 80

=28 + 15 = 80x

=43 = 80x

=43/80 = 80x/80

=43/80 = x

=0.5375 = x.

Sorry but I don't know how to use the slash mark (/).

Answer:

7

Step-by-step explanation:

Let's look at powers of 3 and if a pattern forms for the ones digit.

3^0 = 1

3^1 = 3

3^2 = 9

3^3 = 27

3^4 = 81

3^5 = 243

3^6 = 729

3^7 = 2187

3^8 = 6561

3^9 = 19683

3^10 = 59049

3^11 = 177147

etc.

Using the table above, we see a repeating pattern for the ones digit:

1, 3, 9, 7, 1, 3, 9, 7, 1, 3, 9, 7, etc.

Now let's look at the exponent of 3 compared to the ones digit.

exponent, ones digit

0, 1

1, 3

2, 9

3, 7

4, 1

5, 3

6, 9

7, 7

etc.

Let's write the exponent of 3 as a multiple of 4 plus an integer followed by the ones digit.

4 × 0 + 0, 1

4 × 0 + 1, 3

4 × 0 + 2, 9

4 × 0 + 3, 7

4 × 1 + 0, 1

4 × 1 + 1, 3

4 × 1 + 2, 9

4 × 1 + 3, 7

etc.

When the exponent is a multiple of 4, the ones digit is 1.

When the exponent is 1 added to a multiple of 4, the ones digit is 3.

When the exponent is 2 added to a multiple of 4, the ones digit is 9.

When the exponent is 3 added to a multiple of 4, the ones digit is 7.

Now let's look at out exponent, 2091.

2091/4 = 522.75

2091 = 4 × 522 + 3

2091 is 3 added to a multiple of 4, so the ones digit is 7.

Solving a system of equations we will see that we need to use 40 liters of the 80% acid solution, and the other 20 liters are of the 35% acid solution.

First, we need to define the variables:

We know that we want to produce 60 liters of 65% acid, then we have the system of equations:

x + y = 60

x*0.35 + y*0.80 = 60*0.65

(in the second equation we wrote the percentages in decimal form).

To solve this we need to isolate one of the variables in one equation and then replace it in other one, isolating x we get:

x = 60 - y

Replacing that in the other equation:

(60 - y)*0.35 + y*0.80 = 60*0.65

y*(0.80 - 0.35) = 60*(0.65 - 0.35)

y*0.45 = 60*0.30

y = 60*0.30/0.45 = 40

So we need to use 40 liters of the 80% acid solution, and the other 20 liters are of the 35% acid solution.

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The coordinates of point C are (-9, 1)

The points are given as:

A = (-21, -7)

B = (-6, 3)

m : n = 4 : 1

The coordinates of point C is calculated as:

[tex]C = \frac{1}{m+n} *(mx_2 + nx_1, my_2+ ny_1)[/tex]

So, we have:

[tex]C = \frac{1}{4+1} *(4 * -6 + 1 * -21, 4 * 3+ 1 * -7)[/tex]

This gives

[tex]C = \frac{1}{5} *(-45, 5)[/tex]

This gives

C = (-9, 1)

Hence, the coordinates of point C are (-9, 1)

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Answer:

270 uits

Step-by-step explanation: