Q2 Solve the following initial value problem 1 y" + 4y = ? - sin 3.c y(0)=1, 7(0) by using method of undetermined coefficients. (10 marks)

Answer:

a) 390

b)108

I hope this answer was helpfull for you

Answer:

10

Step-by-step explanation:

Answer:

Isosceles

Step-by-step explanation:

Answer:

1.27

Step-by-step explanation:

When completing word problems, it's always important to first turn everything into an equation.

The volume of a rectangular box is:

\(V=lhw\)

Where l is the length, h is the height, and w is the width.

Which we can write down the equation:

\(47 ft^3=(4w)(6+w)(w)\)

Next up, distribute:

\(47=4w^2(6+w)\\47=24w^2+4w^3\\4w^3+24w^2-47=0\)

We have a cubic equation, you can solve it using a calculator.

We have three solutions, and they are:

\(w=-5.62919529..., -1.64201009..., 1.27120539...\)

Since lengths cannot be negative, there is just one solution: \(w=1.27120539...\)

And rounding it gives:

\(w=1.27\)

And don't forget to put ft at the end!

In conclusion, to compute the chi-square value, we need to know the number of categories and use the appropriate formula or table to find the critical value. The degrees of freedom (df) will be equal to the number of categories minus one (df = k-1).

In the given question, we need to compute the chi-square value to determine the upper bound of the interval. The chi-square value depends on the degrees of freedom (df). To calculate it, we need to know the significance level (α) and the number of categories (k).

Since the question does not provide information about the number of categories, we cannot determine the exact degrees of freedom. However, we can assume that the number of categories is given, and proceed accordingly.

Assuming k is the number of categories, the degrees of freedom (df) will be (k-1).

For example, if there are 5 categories, the degrees of freedom will be (5-1) = 4.

The chi-square value is computed using a chi-square distribution table or a calculator. By using the significance level (α) and the degrees of freedom (df), we can determine the critical value.

In conclusion, to compute the chi-square value, we need to know the number of categories and use the appropriate formula or table to find the critical value. The degrees of freedom (df) will be equal to the number of categories minus one (df = k-1).

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Vertical lines have no slopes.

They have an undefined slope. So, no slope means that the line is vertical.

Answer: 9/4

Step-by-step explanation:

Reciprocal is when the numerator and denominator flips their position

So here, reciprocal of 4/9 = 9/4

Step-by-step explanation:

u need to give the full question

Step-by-step explanation:

they are both linear functions. A function is linear when the degree on X is equal to 1

For the standard normal distribution , the probability will be 0.0401 which means option a is the correct choice.

A standard deviation (or σ) is a degree of ways dispersed the records is when it comes to the mean. Low general deviation approach records are clustered across the mean, and excessive general deviation suggests records are extra unfold out.

Using a standard normal table the area to the right of z = 1.75 is given by

P(z > 1.75) = .0401

Therefore, the correct option is a.

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Answer:

down the middle of an object with vertical symmetry, the two sides  

will be mirror images of each other.

  Examples of capital letters that have vertical symmetry are:

    A H I M O T U V W X Y

Step-by-step explanation:

I believe the answers is it has a 30% chance to land on a letter with a vertical line of symmetry

Correct me if I'm wrong hope this helps plz mark brainliest

Answer:

107.2

Step-by-step explanation:

to get mean it is total sum of values divided by the amount of the value

88+124+234+90=536/5=107.2

Answer:

134

Step-by-step explanation:

To find mean, you add all of the values together and divide by thr total number of values.

88+124+234+90=536.

536/4=134.

Answer:

\(\huge\boxed{\sf -\frac{2}{9} }\)

Step-by-step explanation:

\(\sf \frac{\frac{2}{3}-\frac{5}{6} }{\frac{3}{4} } \\\\= \frac{\frac{2(2)-5}{6} }{\frac{3}{4} } \\\\= \frac{\frac{4-5}{6} }{\frac{3}{4} } \\\\= \frac{-1}{6} / \frac{3}{4} \\\\= \frac{-1}{6} * \frac{4}{3} \\\\= -\frac{1*4}{6*3} \\\\= -\frac{1*2}{3*3} \\\\= -\frac{2}{9} \\\\\rule[225]{225}{2}\)

Hope this helped!

~AH1807

Answer:

$5.3

Step-by-step explanation:

1) Ask yourself: How much money is left to spend?

- Subtract the cost to rent the park shelter:

3,500 - 250 = 3,250

- Find the total amount of money spent on gifts for students:  

300 * 5.50 = 1,650  

- Subtract the total money spent on gifts for students:

3,250 - 1,650 = 1,600

2) Ask yourself: How much can be spent per student?

- Divide the money left by the number of students:

1,600 / 300 = 5.3

The possible values of x, so that the relation does not form a function, is given as follows:

x = -2 or x = -5.

To verify whether a relation represents a function, we need to observe if each input is mapped to only one output.

The points for the function in this problem are given as follows:

(-2,5),(-5,9),(x,-3)

The meaning of each point is that:

The relation is not a function, meaning that the value of x is either of x = -2 or x = -5, which are already mapped to another value of x.

The problem asks for the values of x so that the relation is not a function, considering the three points that were given on the problem.

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Answer:

Step-by-step explanation:

6 + a

Putting value of a

6 + 3 = 9

5b

Putting value of b

5(2) = 10

C - 1

Putting value of c

12 - 1 = 11

The number of bacteria there would be in the petri dish after 7 hours is 7,324.

As the bacteria placed in a petri dish doubles every 15 hours, it represents a geometric growth model.  Geometric growth refers to the situation where successive changes in a population differ by a constant ratio. Hence, the nth term (after the first term) is given by ar^n where a is the initial amount, r is the constant ratio also called common ratio, and n is the number of periods/terms. Based on the given information. the initial number of bacteria a = 5300 and the constant ratio = 2. The number of period n = x/15. As x = 7 hours,

The number of bacteria = 5300*2^(7/15) = 7324.13 ≈ 7324

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Answer: 4x^2

Step-by-step explanation:

Sorry I don't know how to explain I hope this helps you have a great day

The circumference of Monka's bicycle wheel is times larger than the circumference of Kevin's tricycle wheel.

Monica's bicycle wheel circumference = 2π × 16

= 2 × 3.14 × 16

= 100.48

Kevin's tricycle wheel circumference = 2π × 8

= 2 × 3.14 × 8

= 50.24

Monica's bicycle wheel circumference is 100.48 inches.

Kevin's tricycle wheel circumference is 50.24 inches.

100.48 ÷ 50.24 = 2

Therefore, the circumference of Monka's bicycle wheel is two times larger than the circumference of Kevin's tricycle wheel.

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Hey there!

The answer is D

We solve this by multiplying the exponents, and we get 15:

3 x 5 = 15

So, the answer is 2^15

Hope it helps and have a great day!

The blood platelet count is an illustration of normal distribution Approximately 95% of the data lies within 2 standard deviations of the mean. There are approximately 99.7% of women with platelet count between 65.2 and 431.8

The given parameters are:

μ = 248.5

\(\sigma = 61.1\\\)

(a) The percentage within 2 standard deviation of mean or between 126.3 and 370.7

Start by calculating the z-score, when x = 126.3 and x = 370.7

\(Z = \frac{(x-u)}{\sigma}\)

So, we have:

x = -2

Also,

x = 2

The empirical rule states that:

Approximately 95% of the data lies within 2 standard deviations of the mean.

Hence, there are approximately 95% of women with platelet count within 2 standard deviations of the mean.

(b) The percentage with platelet count between 65.2 and 431.8

Start by calculating the z-score, when x = 65.2 and x = 431.8

So, we have:

Z =-3

Also:

Z = 3

The empirical rule states that:

Approximately 99.7% of the data lies within 3 standard deviations of the mean.

Hence, there are approximately 99.7% of women with platelet count between 65.2 and 431.8

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Filling the table to show the relationship between the total cost, c, and the number of books ordered is as follows:

Number of Books      Total Cost ($)

            2                     $17 ($6 x 2 + $5)

            6                     $41  ($6 x 6 + $5)

           10                    $65  ($6 x 2 + $5)

The total cost is a function of the number of units and the variable cost per unit plus the fixed costs.

For instance, the total cost of 9 books, in this scenario, is $59 ($6 x 9 + $5).

Cost per book = $6

Shipping fee = $5

Number of Books      Total Cost ($)

            2                   $17 ($6 x 2 + $5)

            6                  $41  ($6 x 6 + $5)

           10                 $65  ($6 x 2 + $5)

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Answer:

irrational numbers

Step-by-step explanation:

8.

sqrt(13) is not a whole number, a natural number, an integer, or a rational number.

Answer: irrational numbers

(a) Percentage of problems take less than 300 seconds or 5 minutes =41.77%

(b) 58.23% percent of the problems take more than 300 seconds or 5 minutes to resolve.

(c)The standard deviation of the random variable is 24.49

(b) Takes the technician between 30 seconds to 600 seconds to resolve the problem.

90 seconds = 90/60 = 1.5 minutes

600 seconds =600/60 =  10 minutes

So,

\(\mathrm{x} \sim \mathrm{U}(1.5,10)\\P(x > 5 \min )=?\)

\($$\begin{aligned}& \mathrm{f}(\mathrm{x})=\frac{1}{\mathrm{~b}-\mathrm{a}} ; \mathrm{a} < \mathrm{x} < \mathrm{b} \\& \mathrm{f}(\mathrm{x})=\frac{1}{10-1.5} ; 1.5 < \mathrm{x} < 10 \\& \mathrm{f}(\mathrm{x})=\frac{1}{8.5} \\& \begin{aligned}& \mathrm{P}(\mathrm{X} > 5)=\left(\frac{1}{8.5}\right)(10-5) \\&=\frac{5}{8.5} \\&=0.58823 \\&= 58.23 \%\end{aligned}\end{aligned}$$\)

So, 58.23% percent of the problems take more than 300 seconds or 5 minutes to resolve.

(a) Percentage of problems take less than 300 seconds or 5 minutes = 100-58.23 =41.77%

c) A spread metric for a random variable distribution that identifies how far the values deviate from the anticipated value. It is common to write or X as the random variable σX standard deviation.

where x is given as 600

σ(x)=\(\sqrt{x}\)

substitute the value in above equation we get.

\(\sigma(x)=\sqrt{600} =24.49\)

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Answer:

D

Step-by-step explanation:

A coefficient is the number before a variable. The D statement isn't true because the coefficient would be 2 instead of 2m. 2m would be the whole term.

Answer:

D

Step-by-step explanation:

The coefficient is the number in front of the variable. the number in front of the second variable is 2, not 2m

Answer:

30

Explanation:

To know the output value of the function, we need to replace x by -5 and calculated f(x). So:

Therefore, if the input x is -5, the output f(x) is 30

So, the answer is 30.

This question is asking for the y-intercept. The y-int is when x = 0.

First, plug in x as 0...

y = 3(0) + 5

y = 0 + 5

y = 5

Lines come in the form y = mx + b

m is slope, b is the y-intercept

Answer:

18x

Step-by-step explanation:

-It is the same as 3x^-2 • 6x^3.

-Multiply the constants (in this case 3 and 6 =18)

-Add the exponents (-2+3=1)

-Your answer is 18x

The area of the enlarged rectangle is 588 square units.

The original rectangle has a length of 8 units and a width of 6 units.

To find the area of the enlarged rectangle, we need to multiply the length and width of the original rectangle by the scale factor of 3.5.

Enlarging the length: 8 * 3.5 = 28 units.

Enlarging the width: 6 * 3.5 = 21 units.

The enlarged rectangle has a length of 28 units and a width of 21 units.

To find the area, we multiply the length and width of the enlarged rectangle: 28 * 21 = 588 square units.

Therefore, the area of the enlarged rectangle is 588 square units.

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