3. (8 points) Find a power series solution (about the ordinary point r =0) for the differential equation y 4x² = 0. (I realize that this equation could be solved other ways - I want you to solve it using power series methods (Chapter 6 stuff). Please include at least three nonzero terms of the series.)

Answer:

x² + 18xi - 81

Step-by-step explanation:

FOIL - First, Outside, Inside, Last

Step 1: Write out expression

(x + 9i)²

Step 2: Expand

(x + 9i)(x + 9i)

Step 3: FOIL

F - x²

O - 9xi

I - 9xi

L - 81i²

Step 4: Combine

x² + 18xi + 81i²

Step 5: Simplify

i² = -1

x² + 18xi + 81(-1)

x² + 18xi - 81

Answer: 9/1

Step-by-step explanation: We can write a ratio using the word "to", using a colon, or using a fraction bar.

The problem asks us to compare the number of

adult tickets to the number of child tickets.

We know that there are 45 adult tickets

and 5 child tickets so we have 45/5.

However, 45/5 is not in lowest terms so we divide

the numerator and denominator by 5 to get 9/1.

So the ratio of adult tickets to child tickets is 9/1.

Answer:

Around 25.8 square units

Step-by-step explanation:

\(A=\dfrac{1}{2}(5)(18)(\sin 35)=\\\\45\cdot \sin 35\approx 25.8\)

Hope this helps!

The amount of each quarterly payment, rounded, for a $30,000 loan with a 6% annual interest rate to be paid off in 10 equal quarterly payments is $2,803 (option B).


To calculate the amount of each quarterly payment, we need to use the formula for calculating the equal payments on an installment loan. In this case, the loan amount is $30,000, the annual interest rate is 6%, and the loan term is 10 quarters.

Using the formula, we can determine that the amount of each quarterly payment is approximately $2,803. This amount is rounded to the nearest whole number, as specified in the question. Therefore, option B, $2,803, is the correct answer. The other options (A, C, and D) are not applicable to the calculation based on the given information.

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well, the volume of that triangular prism will just be the area of the triangle times the length.

now, what's the area of that triangular face?  well, let's say it has a base of "b" and a height of 3, whilst the prism has a length of 6, Check the picture below.

\(\stackrel{\textit{triangle's area}}{\cfrac{1}{2}(b)(3)}\stackrel{\textit{prism's length}}{(6)}~~ = ~~4\frac{1}{2}\implies 9b=\cfrac{9}{2}\implies b=\cfrac{9}{18}\implies b=\cfrac{1}{2}\)

Answer:

17, 15, and  30

Step-by-step explanation:

sorry if I'm wrong

The surds are √17, √15 and √30.

The square roots of numbers that cannot be divided into a whole or rational number are known as surds ().

It is not capable of being correctly expressed in a fraction. A surd, then, is the root of a whole integer with an irrational value.

Take the example of 2 1.414213. If we leave it as a surd 2, it will be more correct.

As, surds those roots that cannot have square root of a number.

So, from the given number √17, √15 and √30 which do not have square roots.

Hence, the surds are √17, √15 and √30.

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Answer:

19,188

Step-by-step explanation:

hope this helps ;)

Answer:

False, 82 inches is not greater than 5 feet and 10 inches

Step-by-step explanation:

1 feet = 12 inches

5x12=60+10=70

82 is greater than 70.

Answer:

input = 6 leads to output = 15

input = 9 leads to output = 21

==================================================

Explanation:

If the input is x = 6, then,

y = 2x+3

y = 2(6)+3

y = 12+3

y = 15 is the output

Repeat those steps for x = 9

y = 2x+3

y = 2(9)+3

y = 18+3

y = 21 is the output

Answer:

12

Step-by-step explanation:

2/4 of 24

24÷4=6

6×2

=12

The expected frequency for each category would be 25. So, option c. 25 is the correct answer.

If you have 100 respondents identifying their region of residence (i.e., north, south, midwest, or west), the expected frequency for each category would be:d. 50

The expected frequency for each category can be calculated by assuming that each category is equally likely to be chosen. Since there are four regions (north, south, midwest, and west) and 100 respondents in total, we can divide the total number of respondents by the number of categories to obtain the expected frequency for each category.

Expected frequency = Total number of respondents / Number of categories

Expected frequency = 100 / 4

Expected frequency = 25

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Answer:

0.3846 is a decimal and 38.46/100 or 38.46%is the percentage for 50/130

Step-by-step explanation:

Pls mark me in brain list

Answer:

0.3846 is a decimal and 38.46/100 or 38.46%is the percentage for 50/130

Step-by-step explanation:

The function that can be used to find total Blake would charge if he delivered the food will be 3 + 0.25m.

From the information given, we are told that Blake delivers food for Uber eats and charges customers a $3 delivery fee plus $0.25 per mile.

Therefore, in order to deliver the food to m miles away, the amount that'll be charged will be:

= 3 + (0.25 × m)

= 3 + 0.25m

In conclusion, the function is 3 + 0.25m.

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Answer: b

Step-by-step explanation:

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The transformation of a function may involve any change. The correct option is A.

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Vertical shift

Stretching:

Given the function of f(x) as sin(x), Now it can be seen the graph of the two functions is parallel, but the function f(x) has a y-intercept of 0, while h(x) has a y-intercept of 1. Therefore, we can write,

h(x) = f(x) + 1

The function is shifted up by 1 unit.

Hence, the transformation of the function is correctly described in the first option.

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The domain is the region inside the circle and between the two vertical lines. Here's a sketch:

To find the domain of the function \($f(x,y) = \ln(x+y+1)$\), we need to determine the values of \($x$\) and \($y$\) for which the natural logarithm is defined. Since the argument of the logarithm is \($x+y+1$\), we must have \($x+y+1 > 0$\), or equivalently, \($y > -x-1$\). Therefore, the domain of \($f(x,y)$\) is the set of all points \($(x,y)$\) such that \($y > -x-1$\).

To find the domain of the function \($f(x,y) = \sqrt{4-x^2-y^2} + \sqrt{1-x^2}$\), we need to determine the values of \($x$\) and \($y$\) for which both square roots are defined.

The first square root is defined when \($4-x^2-y^2\geq 0$\), or equivalently, \($x^2+y^2\leq 4$\). The second square root is defined when \($1-x^2\geq 0$\), or equivalently, \($-1\leq x\leq 1$\). Therefore, the domain of \($f(x,y)$\) is the set of all points \($(x,y)$\) such that \($x^2+y^2\leq 4$\) and \($-1\leq x\leq 1$\).

To sketch the domain of \($f(x,y) = \ln(x+y+1)$\), we can draw the line \($y=-x-1$\), which separates the domain from the points where the natural logarithm is not defined. The domain is the region above this line. Here's a sketch:

To sketch the domain of \($f(x,y) = \sqrt{4-x^2-y^2} + \sqrt{1-x^2}$\), we can draw the circle \($x^2+y^2=4$\) and the vertical line segments \($x=-1$\) and \($x=1$\), which bound the interval \($-1\leq x\leq 1$\) where the second square root is defined. The domain is the region inside the circle and between the two vertical lines. Here's a sketch:

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The marginal revenue function, locate the demand function is P = 0.02x² -0.025x + 152 when R'(x) = 0.06x² - 0.05x + 152.

Given that,

We have to find for the marginal revenue function, locate the demand function.

Remember that the income is zero if no things are sold:

R'(x) = 0.06x² - 0.05x + 152

p(x) is what.

We know that,

MR = dTR/dx = 0.06x² - 0.05x + 152

Integrating the marginal revenue function , we get total revenue function,

MR = TR

= (0.06x²⁺¹)/(2+1) - (0.05x¹⁺¹)/(1+1) + 152x

= (0.06x³)/3 - (0.05x²)/2 + 152 x

TR  = 0.02 x³ - 0.025 x² + 152 x

TR = (P)(Q) = (P)(x) =  0.02 x³ - 0.025 x² + 152 x

P = ( 0.02 x³ - 0.025 x² + 152 x)/x

P = 0.02x² -0.025x + 152

Therefore, The marginal revenue function, locate the demand function is P = 0.02x² -0.025x + 152 when R'(x) = 0.06x² - 0.05x + 152.

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Examples of random variables are option A: the weight of a bag of a dozen apples, and option C: the number of dots uppermost of rolling a pair of dice.

Because they can only have a finite number of values, discrete random variables include things like the weight of a bag of twelve apples and the number of dots that appear on top of a pair of dice.

Examples of continuous random variables are the length of an airline flight and the quantity of drive-through clients at a bank on a particular day since they might have any value within a specified range.

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Correct question:

Choose the random variables from this set that are discrete. select all that apply. multiple select question.

the weight of a bag of a dozen apples.

the travel time of an airline flight.

the number of dots uppermost of rolling a pair of dice.

number of drive-thru customers to the bank on a given day.

Using Pythagoras theorem to find the diagonals since the length and width makes a right angle triangle to the diagonals, the length of the diagonals of the small rectangle is √1.75 unit

Pythagoras Theorem states that in any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Mathematically, it can be expressed as: a² + b² = c² where a and b are the shorter sides of the triangle and c is the hypotenuse.

In this problem, we need to find the diagonal of the small rectangle.

If the area of the small square was 7 unit²

It's length (l) will be ;

l = √7

l = √7 unit

But the square is divided into four congruent rectangle, using the area of the small square,

A = 7 unit²

new area = 7 / 4 =  1.75 unit²

The area of a rectangle is L * W

Assuming both have the same value, we can simply take the square root as the length of the small rectangle

L = √1.75 unit

The length of a diagonal of a small rectangle is √1.75 unit

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Answer:

x = 0.

Step-by-step explanation:

4x = 3x

4x - 3x = 0

x = 0

Hope this helps!

The best interpretation of the given equation is x = 0

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Given that, Kate begins solving the (6x – 3) = (6x – 4). Her work is correct and is shown below. (6x – 3) = (6x – 4)

4x – 2 = 3x – 2 When she adds 2 to both sides, the equation becomes 4x = 3x

After performing the operations, we get,

4x = 3x

This is only possible when x = 0

Hence, the best interpretation of the given equation is x = 0

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Jennie has 1.5 liters of soda left. if Jennie poured ¼ of a 2 liter bottle of soda into the punch bowl, she poured 2/4 or 1/2 of a liter into the bowl. This means she has 2 - 1/2 = 1.5 liters of soda left.

Sure! To find the amount of soda Jennie has left, we start with a 2 liter bottle. She poured ¼ of it into the punch bowl, which is equivalent to 2/4 or 1/2 liter. To calculate the remaining amount, we subtract the amount poured (1/2 liter) from the original amount (2 liters). So, 2 - 1/2 equals 1.5 liters. Therefore, Jennie has 1.5 liters of soda left after pouring ¼ of the 2 liter bottle into the punch bowl.

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Without additional information, it is impossible to determine the probability that the toy is not cool.

Without additional information, it is impossible to determine the probability that the toy is not cool. This is because the color of the toy does not provide any information about its coolness. For example, a red toy could be a cool action figure or a boring stuffed animal. Therefore, the color of the toy does not provide any insight into its coolness, and thus any probability assigned to the toy being not cool would be purely speculative and not based on any information. In order to determine the probability that the toy is not cool, we would need additional information, such as what the toy is, what its features are, or who makes it.

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Answer:

Our calculator limits your interest deduction to the interest payment that would be paid on a $1,000,000 mortgage. Interest rate: Annual interest rate for this

Step-by-step explanation:

The expected value of these outcomes are  $262.5, $496 and $648 respectively

You should know that the expected value are the proportion of the values when valued with the percentages

The given values are $210, $320 and $540

The given percentages are 25%, 55% and 20%

The expected values are

0.25*210 = $52.5+210=$262.5

0.55*320=176+320=$496

0.20*540=108+540=$648

Therefore the projected values of the project are  $262.5, $496 and $648 respectively

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Answer:

Step-by-step explanation:

You have 2 points given. Take them seriously. They represent actual numbers that don't need to be rounded.

The two points are (2,-2) and (-3,-6)

Now construct a line in point intercept form from these two points.

m = (y2 - y1)/(x2 - x1)

m = (-2 - - 6)/(2 - - 3)

m = 4/5

So far what you know is

y = 0.8 x + b

Use either one of the two points to get b (the y intercept)

x = 2

y = - 2

-2 = 0.8*2 + b

-2 = 1.6 + b             Subtract 1.6 from both sides

-3.6 = b

y = 0.8x - 3.6

3

Answer:

-10

Step-by-step explanation:

f(-4)=-(-4)-5

f(-4)=-1

g(-6)=2(-6)+3

-12+3

g(-6)=-9

add together:

-1+-9

=-10

Answer:

180 meters

Step-by-step explanation:

56*2 + 34*2 = 180 meters

Answer:

  55 meters

Step-by-step explanation:

The length in meters is found by converting the units from feet to meters. The length in feet is found by computing the perimeter of a rectangle with the given dimensions.

__

The formula for the perimeter of a rectangle is ...

  P = 2(L +W)

For a rectangle with length L = 56 ft and width W = 34 ft, the perimeter is ...

  P = 2(56 ft +34 ft) = 2(90 ft) = 180 ft.

__

Each foot is 0.3048 meters. Multiplying that length by the number of feet gives the number of meters.

  180(1 ft) = 180(0.3048 m) = 54.864 m

Mr. Smith will need 55 meters of fencing.