HELP!! 10 POINTS
uhm yeah thats all I've got to say

The solution to the IVP given by y''+y=t, y(0)=1, y'(0)=-2 is y(t) = cos(t) - (3/2) sin(t) + (1/2) t.

To solve the Initial Value Problem, we can use the method of undetermined coefficients, which involves assuming a particular form for the solution to the non-homogeneous equation y'' + y = t, and then finding the coefficients of the terms in that form by substituting it back into the equation.

First, we find the general solution to the homogeneous equation y'' + y = 0

The characteristic equation is r² + 1 = 0, which has solutions r = ±i. Therefore, the general solution to the homogeneous equation is

y_h(t) = c₁ cos(t) + c₂ sin(t),

where c₁ and c₂ are constants determined by the initial conditions.

Next, we assume a particular form for the non-homogeneous solution, based on the form of the right-hand side t. Since t is a linear function, we assume that the particular solution has the form

y_p(t) = a t + b.

Substituting this into the differential equation, we get

y''_p + y_p = t

2a + (at+b) = t.

Equating coefficients, we get

a = 1/2, b = 0.

Therefore, the particular solution is

y_p(t) = (1/2) t.

The general solution to the non-homogeneous equation is then the sum of the homogeneous and particular solutions

y(t) = y_h(t) + y_p(t)

= c₁ cos(t) + c₂ sin(t) + (1/2) t.

To determine the constants c₁ and c₂, we use the initial conditions:

y(0) = c₁ cos(0) + c₂ sin(0) + (1/2) (0) = c₁ = 1,

y'(0) = -c₁ sin(0) + c₂ cos(0) + (1/2) (1) = c₂ - (1/2) = -2,

so c₂ = -3/2.

Therefore, the solution to the IVP is

y(t) = cos(t) - (3/2) sin(t) + (1/2) t.

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The probability that the man will hit his target at least once in 4 shots is calculated using the complementary probability of him missing all 4 shots. Since he hits his target 25% of the time, he misses it 75% of the time.

The probability of missing all 4 shots is (0.75)^4 = 0.3164.

Now, to find the probability of hitting the target at least once, subtract the probability of missing all shots from 1:

1 - 0.3164 = 0.6836 or 68.36%.

So, the probability that the man will hit his target at least once in 4 shots is approximately 68.36%.

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We need at least 3.465 gallons of paint to paint the walls of this room.

The area of the two rectangular faces on either end of the prism is:

length x height = 17 x 12 = 204 square feet

The area of the two rectangular faces on the sides of the prism is:

width x height = 15 x 12 = 180 square feet

The area of the top and bottom faces of the prism is:

length x width = 17 x 15 = 255 square feet

The total surface area of the prism is:

2(204) + 2(180) + 2(255) = 1386 square feet

Now, we divide surface area by coverage of one gallon of paint:

1386 / 400 = 3.465

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Answer:

[tex]\frac{24\sqrt{5} }{5}[/tex]

Step-by-step explanation:

Let's start by assigning one of the unknown legs with the variable x.

We know that the other leg is 2 times the length of x, so we can write:

2x

We also know that the length of the hypotenuse is 12.

From here, we can use the Pythagorean Theorem.

Recall that the Pythagorean Theorem is:

[tex]a^2+b^2=c^2[/tex]

where a is the length of one leg, b is the length of the other leg, and c is the length of the hypotenuse.

Let's substitute the values. We have:

[tex]x^2+(2x^2)=12^2=\\x^2+4x^2=144=\\5x^2=144=\\x^2=\frac{144}{5}=\\x=\frac{12}{\sqrt{5} }[/tex]

Let's rationalize the denominator by multiplying the numerator and denominator by [tex]\sqrt{5}[/tex], like so:

[tex]\frac{12}{\sqrt{5} } =\\\frac{12\sqrt{5} }{5}[/tex]

Therefore, [tex]x=\frac{12\sqrt{5} }{5}[/tex]

Let's solve for 2x:

[tex]2x=\\2(\frac{12\sqrt{5} }{5})=\\ \frac{24\sqrt{5} }{5}[/tex]

So, the length of the longest leg is [tex]\frac{24\sqrt{5} }{5}[/tex]

The theorem is shown in a pythagoras theorem is c² = a² + b²

The theorem shown in the Pythagorean theorem is "a² + b² = c²". This theorem is named after the ancient Greek mathematician Pythagoras, who is credited with discovering it.

The Pythagorean theorem applies to right-angled triangles and states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Mathematically, we can express this as:

c² = a² + b²

Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides (called the legs) of the right-angled triangle.

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Answer:

The center of the circle is at (-6, 14), and the radius is 15, so we have this equation:

[tex] {(x + 6)}^{2} + {(y - 14)}^{2} = 225 [/tex]

Thus, the correct Percent response is B) 79%.

Percentage refers to a portion of every hundred. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, it is frequently shown using the percent sign, "%".

If you have 100 apples and distribute 10 of them, for instance, you have distributed 10% of your total apple supply.

We deduct Ms. Yamato's deductions from her gross income to determine her take-home pay:

$2644 - $548.30 = $2095.702.

By dividing her take-home pay by her gross pay and multiplying the result by 100%, we can determine what proportion of her gross pay is taken home:

($2095.70 / $2644) * 100% = 79%

Thus, the correct response is B) 79%.

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The percentage of the large pizza they ate is 100%

To calculate the percentage of pizza they both ate we have to add and then covert the fractions to percentage.

Given from the question

Frank ate 20% of the large pizza and Joey ate 4/5 portion of the large pizza

Converting 4/5 into percentage

For converting into percentage we have to multiply 100 to the fraction

= 4/5 x 100

= 80%

Now, let us proceed by adding the collected two percentages to find out the total percentage of pizza consumed by Frank and Joey

20% + 80%

= 100%

The percentage of the large pizza they ate is 100%.

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The volume of sand in the rectangular prism is 80 percent of the total volume, which can be written as:

0.8 x V = 0.8(L x W x H) cubic inches

A three-dimensional object with six faces, including two at the top and bottom and four lateral faces, called a rectangular prism. The prism's faces are all rectangular in shape. There are three sets of identical faces as a result.

We need to know the dimensions of the rectangular prism to solve the problem. Let's assume the dimensions are length = L inches, width = W inches, and height = H inches.

The volume of the rectangular prism is given by V = L x W x H cubic inches.

If the rectangular prism is filled 80 percent with sand, then 20 percent of the volume is empty space. So, the volume of sand in the rectangular prism is 80 percent of the total volume, which can be written as:

0.8 x V = 0.8(L x W x H) cubic inches

Therefore, we need to know the dimensions of the rectangular prism to find the volume of sand.

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The complete question is:

James fills the rectangular prism 80 percent with sand. How many cubic inches of sand are in the rectangular prism?

Answer:

D: 27(12x² - 5x - 2).

Step-by-step explanation:

The formula for the surface area of a cylinder is: A = 2πr² + 2πrh

Given that the radius of the cylinder is 3x - 2 cm and the height is x + 3 cm, we can substitute these values in the formula and simplify:

A = 2π(3x - 2)² + 2π(3x - 2)(x + 3)

A = 2π(9x² - 12x + 4) + 2π(3x² + 7x - 6)

A = 18πx² - 24πx + 8π + 6πx² + 14πx - 12π

A = 24πx² - 10πx - 4π

A = 2π(12x² - 5x - 2)

Therefore, the answer is option D: 27(12x² - 5x - 2).

Answer:

D

Step-by-step explanation:

I'm sorry, but I cannot provide a definitive answer to your question as I do not have access to the table you are referring to.

However, in general, to find the price per spool of each kind of thread, you would need to know the total price of the package and the number of spools in the package.

To calculate the price per spool, you would divide the total price of the package by the number of spools in the package. For example, if a package costs $10 and contains 50 spools of thread, the price per spool would be $0.20 ($10 ÷ 50 = $0.20).

You can use this method to find the price per spool for each type of thread in the table you are looking at.

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Answer:

-34x+29

Step-by-step explanation:

[tex]7(5-x)-3(9x+2)=7.5-7x-3.9x-3.2=35-7x-27x-6\\=-34x+29[/tex]

The sample space are:

{AR, AS, AT, AE, RA, RS, RT, RE, SA, SR, ST, SE, TA, TR, TS, TE, EA, ER, ES, ET}

The favorable outcomes care:

{RS, RT, SR, ST, TR, TS}

The probability is  0.3 or 30%

Part A:

The sample space represents all possible outcomes that can occur when two cards are randomly selected without replacement from the given pile of cards.

The sample space can be represented as follows:

{AR, AS, AT, AE, RA, RS, RT, RE, SA, SR, ST, SE, TA, TR, TS, TE, EA, ER, ES, ET}

Part B:

The favorable outcomes are those outcomes in which both cards are consonants. In this case, the consonants are R, S, and T.

The favorable outcomes can be represented as follows:

{RS, RT, SR, ST, TR, TS}

Part C:

To calculate the probability of selecting 2 cards that are consonants, we need to find the ratio of favorable outcomes to the sample space.

The number of favorable outcomes is 6, and the size of the sample space is 20.

Therefore, the probability of selecting 2 cards that are consonants is:

P(consonants) = favorable outcomes / sample space

P(consonants) = 6 / 20

P(consonants) = 0.3 or 30%

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Answer: Circumference = 18 π cm

Step-by-step explanation:

We can use this formula to find the circumference of a circle:

➜ r is equal to the radius, also known as half the width of a circle.

      C = 2πr

We will substitute our known values and solve for C by multiplying. Since the answer option includes π in our units, we do not multiply this into the 18.

      C = 2πr

      C = 2π(9)

      C = 18 π cm

Answer: 18π

Step-by-step explanation:

The circumference of a circle is equal to 2πr, with r being equal to the radius. The radius of a circle is defined as the length from any point on the circle to its middlemost point. In this case, we are given the value of the radius as defined by the line. The radius equals 9, which we can plug into the equation.

C= 2πr

C = 2π(9)

C = 18π = 56.55

Hope this helps!

Answer:

Yo wassup bro, at this computer factory, they be making two types of computers, laptops and desktops. They churn out 70 laptops a day and 55 desktops a day. They got a total of 14 machines to make these computers. And they make a total of 905 computers a day. We gotta figure out how many machines are making laptops and how many are making desktops, ya know?

Alright, let's set up a system of equations to solve this. Let's call the number of machines making laptops "x" and the number of machines making desktops "y".

So, we got two equations here:

The total number of computers they make in a day is 905, so we can write: x laptops + y desktops = 905.

They got a total of 14 machines, so we can write: x + y = 14.

Now, let's solve this system of equations to find the values of x and y, man. Once we got those, we'll know how many machines are making laptops and how many are making desktops at this computer factory, yo!

The equation of the line 2x + 3y + 1 = 0 after it has been reflected across y = -1 and rotated about O(2,3) by 180 degrees is -2x + y = 15.

To reflect the line 2x + 3y + 1 = 0 across the line y = -1, we need to subtract twice the y-coordinate of each point on the line from the equation of the line.

This is because the reflection of a point across a line is obtained by reflecting it across the line's perpendicular bisector, which is also the line with the same x-coordinates and twice the distance from the point to the line.

Subtracting twice the y-coordinate, we get:

2x + 3(-2y - 1) + 1 = 0

Simplifying the equation, we get:

2x - 6y - 5 = 0

Now, to rotate the line about the point O(2,3) by 180 degrees, we can use the rotation formula:

x' = 2a - x

y' = 2b - y

where (x,y) are the coordinates of a point on the original line, and (x',y') are the coordinates of the same point after rotation about the point (a,b).

Substituting the coordinates of two points on the line, we get:

(0,-1) → x' = 2(2) - 0 = 4, y' = 2(3) - (-1) = 7

(-1/2,0) → x' = 2(2) - (-1/2) = 4 1/2, y' = 2(3) - 0 = 6

Now, we can use the two points (4,7) and (4 1/2,6) to find the equation of the rotated line using point-slope form:

slope = (6-7) / (4 1/2 - 4) = -2

y - 7 = -2(x - 4)

y = -2x + 15

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Answer:

Step-by-step explanation:

Graph #          Matching equation

1                             |-3x|

2                            |-x|

3                           -|2x|

You can tell which one matches by finding the slope and whether the V points up or down

The value of x for the given triangle through which the perimeter of the given relation is satisfied is 10.

What about perimeter of triangle?

The perimeter of a triangle is the total length of its boundary, which is the sum of the lengths of its three sides. The perimeter can be thought of as the distance around the triangle, and it is measured in units of length such as centimeters, meters, or feet. The perimeter of a triangle is an important geometric property that is used in many practical applications, such as calculating the amount of fencing needed to enclose a triangular-shaped garden or determining the length of wire required to form a triangular circuit.

According to the given information:

The perimeter of triangle is sum of all sides of the triangle

In which,

2x + 4 + 3x - 8 + x - 2 = 54

6x - 6  = 54

6x = 60

x = 10

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Answer: 77

Step-by-step explanation: You could set up a proportion for this question. 1.5 centimeters = 3.5 meters x centimeters = 180 meters 1.5 x 180 / 3.5 Rounded to the nearest whole number, the answer is 77.

The exponential function to represent the number of new participants of the challenge as a function of the day number, is f(x) = 12 × 4ˣ.

Let f(x) be the number of new participants on day x.

On day 0 (today), Aliyah, Kim, and Reese are the only participants. They each send selfies to 4 friends, so there will be 3 x 4 = 12 new participants on day 1.

From day 1 onwards, each new participant will send selfies to 4 friends. Therefore, the number of new participants will quadruple each day. This gives us an exponential growth function:

f(x) = 12 × 4ˣ

where f(x) represents the number of new participants on day x.

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The trigonometry functions when calculated are sin(A) = 18/34 and cos(A) = 30/34

From the question, we have the following parameters that can be used in our computation:

The right triangle

Where we have

Using the above as a guide, we have the following:

sin(A) = 18/34

cos(A) = 30/34

Hence, the values are sin(A) = 18/34 and cos(A) = 30/34

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The volume of water in the tank won't be enough for the fish.

A cuboid is a solid shape or a three-dimensional shape. The volume of a cuboid is expressed as;

V = l×w× h

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

The volume of water needed by the fish is 700,000× 1litre = 700,000 litres.

The volume of water the tank can occupy is

V = l× b× h

V = 80× 1200× 70

V = 6,720,000cm³

in litres ;

V = 6,720,000/1000

V = 6720litres

therefore the volume water in the tank is not enough for the fish

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Answer: 4

Step-by-step explanation:

Given:

   [tex]2log_62+3log_63+log_612[/tex]

Rewrite using the power property:

   [tex]log_62^2+log_63^3+log_612[/tex]

Rewrite by adding the logarithms together (multiplying) since they all have a common base of 6:

   [tex]log_6(2^2*3^3*12)[/tex]

Simplify by multiplying:

   [tex]log_6(4*27*12)[/tex]

   [tex]log_6(1,296)[/tex]

Evaluate the logarithm:

   [tex]log_6(1,296)[/tex]

   4

Answer:

Step-by-step explanation:

the 32 pack because it costs just slightly more

Answer: First choice 480t = 300t + 900

Step-by-step explanation:

A factory has two assembly lines, M and N, that make the same toy. On Monday, only assembly line M was functioning and it made 900 toys.  

On Tuesday, both assembly lines were functioning for the same amount of time. Line M made 300 toys per hour and line N made 480 toys per hour. Line N made as many toys on Tuesday as line M did over both days.

Write an equation that can be used to find the number of hours, t, that the assembly lines were functioning on Tuesday.

ANS

Let say t is time in hrs for Which Both Assembly line worked

M made 300 toys per hr on Tuesday

Toys made on Tuesday at Assembly line M = 300 × t  = 300t  toys

N made 480 toys per hr on Tuesday

Toys made on Tuesday at Assembly line N = 480 × t  = 480t  toys

Toys Made by N on Tuesday  = Toys made by M on Tuesday + Toys made by M on Monday

480t = 300t + 900

=> 180 t = 900

=> t = 900/180

=> t = 5 hr

N capacity on tuesday Per hour * t  = M capacity on tuesday per hour  * t  + Toys made by M on Monday

N = N capacity on tuesday Per hour

M = M capacity on tuesday Per hour

=> t (N - M ) = 900

=> t = 900/(N-M)

Ricardo used w/100 Ccf of water.

Given that, Ricardo household used w cubic feet of water in a month of summers,

we need to express the number of ccf of water they used algebraically,

Ccf = A CCF is a unit of measurement of volume.

The CCF is used to measure gas consumption, used in the billing of natural gas and water delivered to households.

1 CCF = 100 cubic feet

CCF means Centum Cubic Feet.

1 cubic feet = 0.01 Ccf

Therefore,

w cubic feet = 0.01 × w Ccf

= w / 100

Hence, Ricardo used w/100 Ccf of water.

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Using the above information, we can calculate the missing figures in the table and this is shown on the table attached.

For the "Shorts" row: It's given that 42 people were wearing shorts.

Therefore, the "Close-Toed Shoes" column in the "Shorts" row is also 42, and the "Total" column is the sum of open-toed and closed-toed shoes, which is 84.

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See text below

30 people surveyed were wearing open-toed shoes.

1/3 of the people with open-toed shoes were wearing

pants.

• 42 people were wearing shorts.

Twice as many people were wearing closed-toed shoes

than open-toed shoes.

Complete the table using the information given.

                   Open-Toed Shoes              Close-Toed Shoes         Total

Shorts                     -------                           ------                               --------

Pants                         ------                           ----------                            ------

Total                          ------                           ----------                            ---------

The period of a cosine function of the form y = cos bx is equal to T= 2π/b where 'T' is the period of the cosine function and b is the coefficient of x in the function.

This formula tells us that the period of the cosine function is equal to the length of one complete cycle of the function.

it represents  the distance along the x-axis for the cosine function to complete one full oscillation.

The period of a cosine function of the form y = cos bx, first identify the coefficient b.

Use the formula T= 2π/b  to calculate the period 'T'.

For example,

Consider cosine function y = cos 2x,

The coefficient of x is 2.

Using the formula above, the period is equal to

Period = 2π/2

           = π

So the period of the function y = cos 2x is π.

This implies that the cosine function completes one full oscillation every π units along the x-axis.

Therefore, the formula used to calculate the period of the cosine function y = cos bx is given by T= 2π/b.

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Thus, the appropriate measure of variability found for the given data is 10.

The difference here between maximum and smallest values in a data set is known as the range. Utilizing the exact same units as the data, it measures variability. More variability is shown by larger values.

Given length of ribbons:

3, 6, 9, 11, 12, 13

Minimum value = 3

Maximum value = 13

Actually, the range, which is determined by deducting the lowest value from the greatest value in the dataset, would be the proper measure of variability for this data.

Range = Maximum value - Minimum value

Range = 13 - 3

Range = 10

Thus, the appropriate measure of variability found for the given data is 10.

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Terrell hit 0.8 of his home runs during the first half of the baseball season, which is the decimal equivalent of the fraction (4)/(5).

A fraction is a way of representing a part of a whole, where a whole is divided into equal parts and the fraction represents the number of those equal parts that are being considered.

A decimal number is a number expressed in the base-ten positional system, where each digit can take one of ten possible values and the value of each digit is determined by its position relative to the decimal point.

To write a fraction as a decimal, you simply divide the numerator (the top number) by the denominator (the bottom number). In this case, the fraction is (4)/(5), which means Terrell hit 4 out of 5 home runs during the first half of the season

(4)/(5) = 0.8

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The given question is incomplete, the complete question is:

Terrell hit a total of 10 home runs during the baseball season. He hit (4)/(5) of the home runs during the first half of the season. Write the fraction of home runs hit during the first half of the season as a decimal.