) find the solution of y"+2y'=64sin(2t)+64cos(2t) with y(0)=9 and y'(0)=9

Final answer:

The overall mechanical advantage of an apple peeler with component mechanical advantages of 2, 3, and 12 is the product of these numbers, which is 72. This implies that the input force applied to the apple peeler is multiplied by 72 times.

Explanation:

The student is asking about the overall mechanical advantage of an apple peeler, which is a complex machine made up of components with individual mechanical advantages. To find the total mechanical advantage of a complex machine, you would multiply the mechanical advantages of each component together.

Given that the mechanical advantages of the component machines are 2, 3, and 12, we can calculate the overall mechanical advantage as follows:

Mechanical Advantage of Component 1: 2

Mechanical Advantage of Component 2: 3

Mechanical Advantage of Component 3: 12

To find the overall mechanical advantage, just multiply these together:

Overall Mechanical Advantage = 2 × 3 × 12 = 72

So, the overall mechanical advantage of the apple peeler is 72. This means the input force is multiplied 72 times.

The probability that Ignatz rolls his first 5 before he rolls his second (not necessarily distinct) even number is: 13/32

Define Event A: Rolling 5 before an even number.

Define Event B: Rolling an even number before a 5 (complementary event to event A).

Case 1: 5 in the first roll (1 way). Then, any other number (not 2, 4, or 6) in the remaining rolls (5 possibilities each).

Favorable outcomes: [tex]1 * 5 * 5 * 5 * 5.[/tex]

Case 2: 5 in the second roll (similar to case 1).

Favorable outcomes: [tex]5 * 1 * 5 * 5 * 5.[/tex]

We can continue using the same logic for cases where 5 appears in the third, fourth, or fifth roll.

Since there are multiple ways to achieve event A, we add the favorable outcomes from each case.Total Favorable Outcomes (A) = Favorable Outcomes (Case 1) + Favorable Outcomes (Case 2) + ... + Favorable Outcomes (Case 5)

= [tex]1 * 5^4 + 5 * 1 * 5^4 + 5^2 * 1 * 5^3 + 5^3 * 1 * 5^2 + 5^4 * 1 * 5[/tex]

Probability (A) = Favorable Outcomes (A) / Total Outcomes

[tex]= ( 1 * 5^4 + 5 * 1 * 5^4 + 5^2 * 1 * 5^3 + 5^3 * 1 * 5^2 + 5^4 * 1 * 5) / 6^5[/tex]

Event B is the opposite of event A. Since events A and B cover all possibilities, their probabilities sum to 1.

Probability (B) = 1 - Probability (A)

Therefore, the probability of rolling a 5 before an even number (event A) is 1 - Probability (B).

Answer:

Step-by-step explanation:

In spherical coordinates, equations in the form of [tex]4z^2 = 5x^2 + 5y^2[/tex] can be written as [tex]4ρ^2cos^2(θ) = 5ρ^2sin^2(θ)[/tex], and equations in the form of x^2 + 3z^2 = 4 can be written as ρ^2sin^2(θ) + 3ρ^2cos^2(θ) = 4.

(a) In spherical coordinates, the equation [tex]4z2 = 5x2 + 5y2[/tex] can be written as [tex]4ρ2cos2(θ) = 5ρ2sin2(θ)[/tex]. Here, ρ represents the distance from the origin to the point and θ represents the angle measured from the positive x-axis to the point in the xy-plane.

(b) For the equation x2 + 3z2 = 4, we can rewrite it in spherical coordinates as[tex]ρ2sin2(θ) + 3ρ2cos2(θ) = 4.[/tex]

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area of parallogram now = 8*10 = 80 square units

 if the sides are multiplied by 4 the new dimensions would be

8*4 = 32, 10*4 = 40

 area would be 32 *40 = 1280 square units

1280 /80 = 16

 the area multiplied 16 times which is the multiple squared ( 4^2 = 16)

Answer:

13.64 minutes

Step-by-step explanation:

The first machine works at the rate x = 1 bale/ 25 min.

The second machine works at the rate y = 1 bale/30 min.

The combined rate is

x + y = 1/25 + 1/30 bales/min

        = (30 + 25)/(25*30) = 55/750

        = 11/150 bales/min

The time for both machines to pick 1 bale of cotton is

(1 bale)/(11/150 bales/min) = 150/11 min = 13.64 min

So if you take rsm, you have to input 13.64 otherwise it won't work. :)

The question involves linear regression and the sum of squared errors (SSE), which quantify the total deviation of the response values from the fitted line. If y=3 + 2x is the best-fit line, then the SSE for the line y=3 + 2.5x would be greater than 13,712.

The question involves the concept of linear regression and the sum of squared errors (SSE). The SSE of a regression line is quantified by the difference between the observed and predicted values of the dependent variable, each squared and added together. These show how well the regression line fits the data.

In the context of this question, you're given the SSE for the line y = 3 + 2x. However, you're asked about the SSE for the line y = 3 + 2.5x. Since the slope of this new line is steeper, the predicted y-values will be different from those from the original line and generally farther from the actual data points. Therefore, it can be said that if the line y = 3 + 2x is the best-fit line, then the SSE for the line y = 3 + 2.5x would be greater than 13,712.

Error in prediction is generally greater when we move away from the least-squares regression line. Thus the SSE provides a quantifiable way to determine the line that best fits the data.

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The answer is: The triangle is a SCALENE Triangle.

As all the sides of the triangle are unequal. Therefore,it is a scalene triangle.

What are the 3 main types of triangles?

According to the length of sides, triangles can be classified into 3 categories i.e., Scalene, Isosceles, and Equilateral triangles.

A scalene triangle is a triangle in which all three sides are of different lengths, and all three angles are of different measures. However, the sum of all the interior angles is always equal to 180 degrees.

An isosceles triangle is a triangle in which two sides have the same length.

An equilateral triangle is a triangle with all three sides of equal length, corresponding to what could also be known as a "regular" triangle.

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