Find two linearly independent solutions of
y" + 1xy = 0 of the form
y_1 = 1 + a_3x^3 + a_6x^6 + -----)
y_2 = x+ b_4x^4 + b_7 + x^7+-----)

Enter the first few coefficients:

Enter
a_3= _______
a_6= _______

b_4= _____
b_7= _____

Answer:

The number of softballs that would fill the room is 221796 softballs

Step-by-step explanation:

First we will determine the Volume of the room.

The volume of a room is given by

\(Volume = lwh\)

From the question, the given dimension of the room is  10 by 12 by 24 foot

Hence the volume of the room = 10 × 12 × 24

= 2880 cubic feet (ft³)

Convert to cubic inches

To do this, multiply the answer in cubic feet by (12 × 12 × 12)

(NOTE: 1 foot = 12 inches)

Hence, 2880 cubic feet = 2880 × 12 × 12 × 12 cubic inches

= 4976640 cubic inches

This is the volume of the room.

To estimate the number of softballs that would fill the room, we will determine the number of softballs which would give a total volume that is equal to the volume of the room.

First, we will find the volume of one softball

Diameter of softball = 3.5 inches

∴ Radius of softball, r = 3.5/2 inches = 1.75 inches

∴ r = 1.75 inches

Now, for the volume of one softball

From,

V = 4/3 (3.14)r^3

\(V = \frac{4}{3}(3.14)r^{3}\)

\(V = \frac{4}{3}(3.14)\) × \(1.75^{3}\)

\(V = 22.43791667\) cubic inches

This is the volume of one softball

The number of softballs that would fill the room will be

= Volume of the room / Volume of one softball

= 4976640 cubic inches / 22.43791667 cubic inches

=221795.9926

≅221796

Hence, the number of softballs that would fill the room is 221796 softballs

Answer:

Step-by-step explanation:

-2(-3) *2+1

6*2+1

12+1

13

Answer:

- 17

Step-by-step explanation:

Evaluate 1 - 2 x^2 where x = -3:

1 - 2 x^2 = 1 - 2×(-3)^2

Hint: | Evaluate (-3)^2.

(-3)^2 = 9:

1 - 29

Hint: | Multiply -2 and 9 together.

-2×9 = -18:

-18 + 1

Hint: | Subtract 18 from 1.

1 - 18 = -17:

Answer:  -17

We will use order of operations (PEMDAS) to solve this.

1.) 33+4(52-42) This is our equation. So, first we are gonna subtract 42 from 52.

2.) 33+4(10) Now that we did that, we are gonna add 4 to 33.

3.) 37(10) Lastly we are gonna multiply 37 by 10.

The answer is gonna be 370. If this helped, maybe consider giving me brainliest :)

Answer:

Did this so the other dude can get brainlest

Step-by-step explanation:

Answer:

123 degrees

Step-by-step explanation:

180 - 57 = 123

Answer:

33

Step-by-step explanation:

123 is not the answer, on edge

Answer:

21,800

Step-by-step explanation:

Total costs is $16,700 x 4 years = 66,800

He saved 21,000 + receives 24,000 (6,000x4) grants for a total of 45,000 saved.

costs of 66,800 - receipts of 45,000 = 21,800 needed.

Answer:

-123

Step-by-step explanation:

13(-x+4)-6 when .x is 13

we just replace x with 13

13(-13+4)-6

13(-9)-6

applying bodmas we multiply 13 by negative 9 before the subtraction aspect

13*-9=-117

-117-6=-123

Answer:

y=2x+3

Step-by-step explanation:

2 is the slope. 3 is the y intercept

Answer:

33.3333333

Have a nice day!      :)

Answer:

7² = 49 ans

Step-by-step explanation:

7² == 49 ans .....

Answer:

49

Step-by-step explanation:

7² = 7 x 7 = 49

Answer:

D: the total score was between 0 and y

Step-by-step explanation:

correct me if im wrong

To find the area of the region interior to r = 9 + 7sin(θ) below the polar axis, we can integrate the function from the lower bound of θ to the upper bound of θ and take the absolute value of the integral.

To find the area of the region formed by two petals of r = 8sin(3θ), we can integrate the function over the appropriate range of θ and take the absolute value of the integral. To find dy/dx for the given parametric equations x = t^(1/3) and y = 3 - t, we differentiate y with respect to t and x with respect to t and then divide dy/dt by dx/dt.

To find the area of the region interior to r = 9 + 7sin(θ) below the polar axis, we need to evaluate the integral ∫[lower bound to upper bound] |1/2 * r^2 * dθ|. In this case, the lower bound and upper bound of θ will depend on the range of values where the function is below the polar axis. By integrating the expression, we can find the area of the region. To find the area of the region formed by two petals of r = 8sin(3θ), we need to evaluate the integral ∫[lower bound to upper bound] |1/2 * r^2 * dθ|.

The lower bound and upper bound of θ will depend on the range of values where the function forms the desired shape. By integrating the expression, we can calculate the area of the region. To find dy/dx for the parametric equations x = t^(1/3) and y = 3 - t, we differentiate both equations with respect to t. Taking the derivative of y with respect to t gives dy/dt = -1, and differentiating x with respect to t gives dx/dt = (1/3) * t^(-2/3). Finally, we can find dy/dx by dividing dy/dt by dx/dt, resulting in dy/dx = -3 * t^(2/3).

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Answer:

48 and 32

Step-by-step explanation:

both numbers get rounded by 8 going up and down rounding it to 40

In order to make the Alannah's money 3 times the Pamala's money, Pamala need to give Alannah $ 60.

Money with Pamala = $ 84

Money with Alannah = $ 12

Now let the money given by Pamala to Alannah be x

So, for money with  Alannah to become 3 times of the money with Pamala, we get the equation as:

3 ( 84 - x) = ( 12 + x )

252 - 3 x = 12 + x

3 x + x = 252 - 12

4 x = 240

x = 240 / 4

x = $ 60

Pamala gave Alannah $ 60.

Therefore, we get that, in order to make the Alannah's money 3 times the Pamala's money, Pamala need to give Alannah $ 60.

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Answer:

\(x=-1\pm \sqrt{6}i\)

Step-by-step explanation:

\(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)

\(x=\frac{-(2)\pm\sqrt{2^2-4(1)(7)}}{2(1)}\)

\(x=\frac{-2\pm\sqrt{4-28}}{2}\)

\(x=\frac{-2\pm\sqrt{-24}}{2}\)

\(x=\frac{-2\pm\sqrt{-1*24}}{2}\)

\(x=\frac{-2\pm\sqrt{-1}\sqrt{24}}{2}\)

\(x=\frac{-2\pm i\sqrt{4*6}}{2}\)

\(x=\frac{-2\pm i\sqrt{4}\sqrt{6}}{2}\)

\(x=\frac{-2\pm2i\sqrt{6}}{2}\)

\(x=-1\pm \sqrt{6}i\)

The corresponding differential element, rewrite the integral in terms of the new variable, integrate with respect to the new variable, replace the new variable with the original variable, and simplify the expression to find the solution.

To perform u-substitution with indefinite integrals, follow these steps:

Identify a suitable substitution: Look for a part of the integrand that resembles the derivative of a function. Choose a variable u to substitute for that part.

Calculate du: Take the derivative of u with respect to the original variable. This will help us express du in terms of the original variable.

Rewrite the integral: Substitute the chosen variable and du in the original integral, replacing the part to be substituted with u and the corresponding differential element du.

Integrate with respect to u: Treat the integral as a new integral with respect to u. Evaluate the integral using the rules of integration.

Replace u with the original variable: Rewrite the result of the integration in terms of the original variable.

Simplify and solve: If necessary, simplify the expression further or perform additional algebraic manipulations to obtain the final result.

Let's illustrate these steps with an example:

Consider the integral ∫(2x + 3)² dx.

Identify a suitable substitution: Let u = 2x + 3.

Calculate du: Take the derivative of u with respect to x: du/dx = 2. Rearrange the equation to solve for du: du = 2 dx.

Rewrite the integral: In terms of u and du, the integral becomes ∫u² (du/2).

Integrate with respect to u: Treat the integral as a new integral with respect to u: (1/2) ∫u² du = (1/2) * (u³/3) + C, where C is the constant of integration.

Replace u with the original variable: Substitute back u = 2x + 3 in the result: (1/2) * ((2x + 3)³/3) + C.

Simplify and solve: Further simplify the expression if necessary to obtain the final result.

In summary, to perform u-substitution with indefinite integrals, identify a suitable substitution, calculate the corresponding differential element, rewrite the integral in terms of the new variable, integrate with respect to the new variable, replace the new variable with the original variable, and simplify the expression to find the solution.

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The response y(t) graphically, we can first plot the individual functions h(t) and x(t) on a graph, and then determine their convolution to obtain y(t). Let's go step by step:

Plotting h(t):

The function h(t) is defined as h(t) = [u(t-1) - u(t-4)].

The unit step function u(t-a) is 0 for t < a and 1 for t ≥ a. Based on this, we can plot h(t) as follows:

For t < 1, h(t) = [0 - 0] = 0

For 1 ≤ t < 4, h(t) = [1 - 0] = 1

For t ≥ 4, h(t) = [1 - 1] = 0

So, h(t) is 0 for t < 1 and t ≥ 4, and it jumps up to 1 between t = 1 and t = 4. Plotting h(t) on a graph will show a step function with a jump from 0 to 1 at t = 1.

Plotting x(t):

The function x(t) is defined as x(t) = t[u(t) - u(t-2)].

For t < 0, both u(t) and u(t-2) are 0, so x(t) = t(0 - 0) = 0.

For 0 ≤ t < 2, u(t) = 1 and u(t-2) = 0, so x(t) = t(1 - 0) = t.

For t ≥ 2, both u(t) and u(t-2) are 1, so x(t) = t(1 - 1) = 0.

So, x(t) is 0 for t < 0 and t ≥ 2, and it increases linearly from 0 to t for 0 ≤ t < 2. Plotting x(t) on a graph will show a line segment starting from the origin and increasing linearly with a slope of 1 until t = 2, after which it remains at 0.

Obtaining y(t):

To obtain y(t), we need to convolve h(t) and x(t). Convolution is an operation that involves integrating the product of two functions over their overlapping ranges.

In this case, the convolution integral can be simplified because h(t) is only non-zero between t = 1 and t = 4, and x(t) is only non-zero between t = 0 and t = 2.

The convolution y(t) = h(t) * x(t) can be written as:

y(t) = ∫[1,4] h(τ) x(t - τ) dτ

For t < 1 or t > 4, y(t) will be 0 because there is no overlap between h(t) and x(t).

For 1 ≤ t < 2, the convolution integral simplifies to:

y(t) = ∫[1,t+1] 1(0) dτ = 0

For 2 ≤ t < 4, the convolution integral simplifies to:

y(t) = ∫[t-2,2] 1(t - τ) dτ = ∫[t-2,2] (t - τ) dτ

Evaluating this integral, we get:

\(y(t) = 2t - t^2 - (t - 2)^2 / 2,\) for 2 ≤ t < 4

For t ≥ 4, y(t) will be 0 again.

Maximum value of y(t):

To find the value of t at which y(t) reaches its maximum value, we need to examine the expression for y(t) within the valid range 2 ≤ t < 4. We can graphically determine the maximum by plotting y(t) within this range and identifying the peak.

Plotting y(t) within the range 2 ≤ t < 4 will give you a curve that reaches a maximum at a certain value of t. By visually inspecting the graph, you can determine the specific value of t at which y(t) reaches its maximum.

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Answer:

If I'm not mistaking, they want you to find the number in the middle that's between X and Z.

That number would be 3.

Hope this helps a bit! :)

Answer:

y would be at 3

Step-by-step explanation:

I hope this helps!

Answer:

r^2+3r-4

Step-by-step explanation:

combine like terms:

2r+r

vvvv

3r+r^2-4

rearrange terms:

r^2+3r-4

The mass of the original sample of phosphorus-32 was approximately 717.7 grams.

To solve this problem, we can use the radioactive decay formula:

A = Ao * 2^(-t/h)

Where:

A = resulting amount after time t

Ao = initial amount (at t=0)

t = time

h = half-life of the substance

In this case, we are given that the half-life of phosphorus-32 is 14.28 days. We want to find the initial mass, represented by Ao.

After approximately 57 days, 55 g of phosphorus-32 remain unchanged. Let's plug these values into the equation:

55 = Ao * 2^(-57/14.28)

To solve for Ao, we can isolate it by dividing both sides of the equation by 2^(-57/14.28):

55 / 2^(-57/14.28) = Ao

Using a calculator to evaluate 2^(-57/14.28), we find that it is approximately 0.07666.

Therefore, the initial mass, Ao, is:

Ao = 55 / 0.07666 ≈ 717.7 g

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We could expect $30.00 to gain after 20 tosses.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of sample

The probability of all the events occurring need to be 1.

if the toss of a coin comes down heads, you win a dollar. if it comes down tails, you lose fifty cents.

We need to find out How much would you expect to gain after 20 tosses (in $ dollars).

Because if you think about it, you will see that about half of them are going to be heads and the other half are going to be tails.

Therefore, We could expect $30.00 to gain after 20 tosses.

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First graph is the correct one.

when x= 1

y=f(x) = -√1 = -1

when x= 2

y= -√2

The probability of drawing the ace of diamonds is determined by the number of possible outcomes (52 cards in a standard deck) and the number of favorable outcomes (1 ace of diamonds). Your answer: a. classical method

The method of assigning probabilities used in this scenario is the classical method, where the probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, there is only one favorable outcome (drawing the ace of diamonds) out of 52 possible outcomes (drawing any card from a standard deck of 52 cards).

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The alternative and hull hypotheses is H₀: P=0.03, H₁: P≠0.03.

Given that,

According to a representative of the Ohio Department of Education, 3% of graduating high school seniors in Ohio have dropped out in recent years. Out of the 600 pupils enrolled, 30 students from Podunk High School dropped out of school last year.

We have to find is there enough data to say that this school's dropout rate is higher than the state average. Using symbols and words, state the alternative and hull hypotheses.

We know that,

n is 600,

3% Ohio high school seniors dropout.

30 dropout out of 600 in Podunk high school.

Here,

H₀: μ₁=μ₂  vs   H₁:μ₁≠μ₂

In coordinates,

H₀⇒ dropout number is equal for both schools.

H₁⇒ dropout number not equal for both schools.

H₀: P=0.03, H₁: P≠0.03.

Therefore, The alternative and hull hypotheses is H₀: P=0.03, H₁: P≠0.03.

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Answer:

see below

Step-by-step explanation:

based on Vertical Angles Theorem

look at the vertical line, 128 + ∠3 = 180

so ∠3=52

∠2 = 128

Look at the triangle:

∠4 = 90 - ∠3 = 90- 52 = 38 = ∠6

∠5=180-∠4 =180-38 =142 = ∠7

∠1 = 180-90 = 90

Answer:

If we are solving for 'k,' then k = -9

It should be noted that based on the information given, the values of x and y in the linear pattern will be 12 and 21.

It should be noted that since this is a linear pattern, it should be noted that it illustrates that the values in between them are the same.

It should be noted that the numbers that fits into the scenario are 3, 12, 21 and 30. There's a difference of 9 between them.

Therefore, it should be noted that based on the information given, the values of x and y in the linear pattern will be 12 and 21.

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Answer:

its 100 so it would literally just be 100 - 21

Step-by-step explanation:

Answer:

22%

Step-by-step explanation:

1- 11000/50000 = 0.22

2- 0.22 x 100 = 22%

.. ..