3. For each differential equation, find the Laplace transform of the solution y:

3y' + 5y = x^2 , y(0) = 2.

y'' − y = 5e^−4x + 2x, y(0) = y'(0) = 0.

y'' + 3y' + 2y = 5 sin(πx), y(0) = y'(0) = 0.​

In accordance with the exponential model, the current forest area is equal to 2801.149 square kilometers after six years.  

According with statement, the forest area decreases exponentially in time. Then, the exponential model is defined by following model:

n(x) = n' · (1 - r)ˣ

Where:

If we know that n' = 4400 km², r = 0.0725 and x = 6 yr, then the current forest area is:

n(6) = 4400 · (1 - 0.0725)⁶

n(6) = 2801.149

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Answer:

Step-by-step explanation:

The equations are not independent. They represent the same graph.

There are an infinite number of solutions.

Answer:

A.  4

Step-by-step explanation:

Given inequality:

\(x+9 < 4x\)

Rearrange the inequality to isolate x.

Subtract x from both sides of the inequality:

\(\begin{aligned}x+9-x & < 4x-x\\9& < 3x\end{aligned}\)

Divide both sides of the inequality by 3:

\(\begin{aligned}\dfrac{9}{3}& < \dfrac{3x}{3}\\\\3& < x\\\\x& > 3\end{aligned}\)

So the values of x that make the inequality true are:

Therefore, from the given answer options, the value of x that makes the inequality true is x = 4.

To check this, substitute x = 4 into the inequality:

\(\begin{aligned}x+9& < 4x\\x=4\implies 4+9& < 4(4)\\13& < 16\end{aligned}\)

As 13 is less than 16, the inequality is true when x = 4.

Answer: 9

Step-by-step explanation: To divide we need to flip the second fraction we are dividing by. For example:

10/1 divided by 1/4 = 10/1 times 4/1. So in this case, the answer is 40.

Now lets try it with 1/9.

X divided by 1/9 = X times 9/1.

So dividing by 1/9 is equal to multiplying by 9.

Answer:

B. Reflexive Property

Step-by-step explanation:

The statement is that BC ~= BC. That is, that BC is congruent to itself. The reason is that all numbers are equal to themself. Angle measures are equal to themself. Segments are equal to themself.

Like looking at a reflection in a mirror. The word "reflection" can help you memorize the reason why something is equal to itself:

Reflexive Property

Problem 1

Reason: We start at 0 and move 4 units left. This is represented by 0+(-4) or 0-4. That simplifies to -4. Then add on 7 to move 7 units to the right to arrive at 3 as the final destination.

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

Problem 2

Reason: We start at 0 and move 8 units to the right. That is represented by +8 or simply 8. Then the +3 will move us 3 more units to the right to get to 11 on the number line. This is one visual way to see why 8+3 = 11.

Answer:

cos P = 71.09

Step-by-step explanation:

cos = \(\frac{adajcent}{hypotenuse}\)

cos P = \(\frac{24}{74}\)

cos P = 0.324

cos-1 of 0.324 is 71.09

cos P = 71.09

Answer:

-25

Step-by-step explanation:

First he bought 3 tires which total costed 105, then returned 2, so he got $70 back, meaning he had $35. Then he found 2 $20 bills, which raised his total to $75. Then, he bought a phone for $90, so he has -25 dollars left

Answer:

0.5 = 0.500

Step-by-step explanation:

Both numbers are five-tenths. The zeros to the right of the 5 are not place holders and do not change the value of the number.

0.5 = 0.500

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

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

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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The expected number of pizzas to be stuffed crust is given as follows:

500.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The sample size is given as follows:

408 + 224 + 208 + 200 = 1040.

Out of these, 208 are stuffed crust, hence the probability is given as follows:

p = 208/1040.

Out of 2500 pizzas, the expected number is then given as follows:

E(X) = 2500 x 208/1040

E(X) = 500.

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Answer:

what u r answering but ya

Step-by-step explanation:

Mai travels abοut 4.2 feet per secοnd faster than Kiran.

Circumference is the distance arοund the οutside οf a circle. It is the length οf the bοundary that enclοses a circle. Tο find the circumference οf a circle, yοu can use the fοrmula C=2πr, where "C" represents the circumference, "π" is a mathematical cοnstant (apprοximately equal tο 3.14159), and "r" is the radius οf the circle (the distance frοm the center οf the circle tο its edge). Sο, the circumference οf a circle is directly prοpοrtiοnal tο its radius. This means that if yοu dοuble the radius οf a circle, its circumference will alsο dοuble.

The circumference οf Kiran's ring is:

C1 = 2πr1 = 2π(9 ft) ≈ 56.55 ft

The circumference οf Mai's ring is:

C2 = 2πr2 = 2π(r1 + 8 ft) = 2π(17 ft) ≈ 106.81 ft

Therefοre, Mai travels a distance οf 106.81 - 56.55 = 50.26 feet mοre than Kiran in οne rοtatiοn.

The time it takes fοr οne rοtatiοn is given as 12 secοnds. Therefοre, the speed οf Kiran in feet per secοnd is:

V1 = C1 / t = 56.55 ft / 12 s ≈ 4.71 ft/s

And the speed οf Mai in feet per secοnd is:

V2 = C2 / t = 106.81 ft / 12 s ≈ 8.90 ft/s

The difference in their speeds is:

V2 - V1 = 8.90 ft/s - 4.71 ft/s ≈ 4.2 ft/s

Therefοre, Mai travels abοut 4.2 feet per secοnd faster than Kiran.

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Carrie has 4 more pints of paint than Bryan.

Carrie has 3 gallons of paint, which is equivalent to 12 quarts (1 gallon = 4 quarts). On the other hand, Bryan has 10 quarts of paint.

To compare the quantities in the same unit, we note that 1 quart is equal to 2 pints.

Carrie's 12 quarts of paint is equivalent to 12 × 2 = 24 pints.

Bryan's 10 quarts is equivalent to 10 × 2 = 20 pints.

To find the difference, we subtract Bryan's pint quantity from Carrie's:

24 - 20 = 4 pints.

Therefore, Carrie has 4 more pints of paint than Bryan.

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Check the picture below.

\(\textit{volume of a pyramid}\\\\ V=\cfrac{Bh}{3} ~~ \begin{cases} B=\stackrel{base's}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=\stackrel{7\times 7}{49}\\ V=82 \end{cases}\implies \begin{array}{llll} 82=\cfrac{49h}{3}\implies 246=49h\implies \cfrac{246}{49}=h \\\\\\ 5.02\approx h \end{array}\)

Answer:

1.429 lbs per dollar of sugar

Step-by-step explanation:

multiply by 5 get 10 lbs of sugar for 7 dollars divide by 7 get 1.4285 round up

Based on the cost of two pounds of sugar, we can calculate the quantity of sugar to a dollar to be 0.7 pounds.

You can find out the quantity of sugar you get per dollar using the formula:

= Price of sugar / Number of pounds

Solving gives

= 1.40 / 2

= 0.7 pounds

In conclusion, you get 0.7 pounds.

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The ratios for the rectangles and the ovals is 4 : 3

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

Rectangle = 4

Oval = 3

The ratio can be represented as

Ratio = Rectangle : Oval

When the given values are substituted in the above equation, we have the following equation

Rectangle : Oval = 4 : 3

The above ratio cannot be further simplified

This means that the ratio expression would remain as 4 : 3

Hence, the solution is 4 : 3

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The average distance from the mean is 0.09.

The mean is also known as the average and is calculated by adding up all the values in the set and then dividing the sum by the total number of values.

So, for the given set of data: 24.49, 24.68, 24.77, 24.83, 24.73, the mean would be calculated as follows:

Mean = (24.49 + 24.68 + 24.77 + 24.83 + 24.73) / 5

= 24.70

It tells us what the typical value is within the data set. In this case, the mean value of the data set is 24.70.

Next, let's find the median of the set of data. The median is the middle value of a data set when it is arranged in numerical order. In this case, the data set is already arranged in numerical order, so we can easily find the median.

The median value of the data set is the middle value, which is 24.77.

Now, we will calculate the deviation from the mean for each data point within the set. The deviation from the mean tells us how far each value is from the mean value. This is calculated by subtracting the mean from each value in the set.

Deviation from the mean for each data point:

-0.21, -0.02, 0.07, 0.13, 0.03

As you can see, some values are above the mean, and some are below the mean. The deviation from the mean can be used to determine how spread out the data is from the mean value.

Finally, we will calculate the mean deviation for the set. The mean deviation is the average of the absolute values of the deviation from the mean.

Mean deviation = (|(-0.21)| + |(-0.02)| + |0.07| + |0.13| + |0.03|) / 5

= 0.09

The mean deviation tells us the average distance from the mean value.

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Answer: 81.25

Step-by-step explanation:

Answer:

Armando lost 65 coins each level.

Step-by-step explanation:

Given information,

→ Armando lost 975 coins playing his favorite video game.

→ He lost the same number of coins in each of the 15 levels he played.

Forming the equation,

→ 15x = 975

Now required value of x will be,

→ 15x = 975

→ x = 975/15

→ [ x = 65 ]

Hence, he lost 65 coins each level.

Answer:     b

Step-by-step explanation:

i took the quiz duhh

Answer:

3/10 + 5/10 = 8/10

8/10 kilometers

Step-by-step explanation:

Answer:

3/10+1/2=3/10+5/10

=8/10km

Answer:

12.5 cups of flour are needed

Step-by-step explanation:

Divide 20 dozen by 8 dozen to find the scale factor:

20 / 8 = 2.5

He needs 2.5 times more flour.

Multiply 5 cups by 2.5:

5 x 2.5 = 12.5 cups of flour are needed.

Hopefully this helps!

Answer:

5 pellets per fish

Step-by-step explanation:

5 p = 1 f

Answer:

Step-by-step explanation:

Additionally that answer is wrong

Answer:

Hello! answer: 10

Step-by-step explanation:

you do a^2+b^2=c^2 meaning

8 × 8 + 6 × 6 will equal a number which then we have to find out the square root of that number meaning what number you can multiply by itself to get that number so...

8 × 8 = 64

6 × 6 = 36

64 + 36 = 100

√100 = 10

10 × 10 = 100 therefore the missing length is 10 hope that helps!

Answer:

\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Step-by-step explanation:

Convert 1/2 + i√3/2 to rectangular form

\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)

Use DeMoivre's Theorem

\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

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\(4 \: min = 4 \times 28 \: copies\)

\(15 \: sec = \frac{1}{4} \: min = \frac{1}{4} \times 28 \: copies \\ \)

\(4 \times 28 + \frac{1}{4} \times 28 = 112 + 7 = 119 \: copies \\ \)

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Answer:

7140 copies

Step-by-step explanation:

28 copies =1 minute

x copies= 4 minutes 15 seconds (255 seconds)

cross multiply

x copies=28 *255

x copies = 7140

Answer:

2*2*2*2*5*7= 560

Step-by-step explanation:

please mark brainiest hope it works out for you

Answer:

2^4*5*7

Step-by-step explanation:

2^4*5*7

-19.99; The line of best fit underpredicts the student's science test score.

So correct option is A.

A prediction is an estimation or forecast about future events or conditions, based on past data and trends, current information, and/or mathematical models. Predictions can be made in various fields, such as finance, weather, sports, social sciences, and natural sciences. The accuracy of predictions depends on many factors, including the quality of the data used, the assumptions made, the complexity of the system being analyzed, and the reliability of the methods used. Predictions are not always accurate and are often subject to revision as new information becomes available.

The predicted science score for the student with IQ 100 can be calculated using the line of best fit:

ŷ = −20.3 + 0.7489 * 100 = 71.59

The residual is the difference between the actual science test score and the predicted science score:

residual = actual score - predicted score = 52.6 - 71.59 = -19.99

So the line of best fit underpredicts the student's science test score by 19.99 points.

Therefore, the residual is:

-19.99; The line of best fit underpredicts the student's science test score.

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The simplified expression is \(-4x^2 + 3x + 1\), which is a quadratic polynomial. Option D.

To simplify the expression \((8x^2 + 3x) - (12x^2 - 1)\), we can distribute the negative sign to each term within the parentheses:

\(8x^2 + 3x - 12x^2 + 1\)

Next, we can combine like terms by adding or subtracting coefficients of similar powers of x:

\((8x^2 - 12x^2) + 3x + 1\)

Simplifying further, we have:

\(-4x^2 + 3x + 1\)

The resulting polynomial \(-4x^2 + 3x + 1\) is a quadratic polynomial since it has a highest power of x^2 (the exponent of x is 2), which is\(-4x^2.\)Quadratic polynomials are polynomials of degree 2 and can be represented by a parabola when graphed.

In summary, the simplified expression \((8x^2 + 3x) - (12x^2 - 1)\) simplifies to \(-4x^2 + 3x + 1\) , which is a quadratic polynomial. So Option D is correct

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Note the complete question is

The given functions are:

A linear function is a polynomial of degree 1 of the form:

y = m*x +b

For example, the first option:

72 = x^3 + y

Depends on x cubed, so this is a polynomial of degree 3, which means that this is non-linear.

The second option is:

y + 1 = 5*(x - 9)

This only depends on x, so this is a linear function.

-y - x^2 = 4.5

Is non-linear, because this is a degree 2.

7y + 2x = 12

This is linear, because the degree is 1.

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Answer:

The given functions are:

72 = x^3 + y  → non-linear.

y + 1 = 5*(x - 9) → linear function.

-y - x^2 = 4.5 → non-linear.

7y + 2x = 12 → linear function.