Brayden just lit a new candle and then let it burn all the way down to nothing. The
candle burned at a rate of 0.75 inches per hour and its initial length was 6 inches.
Write an equation for L, in terms of t, representing the length of the candle
remaining unburned, in inches, t hours after the candle was lit.

The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.

To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:

We have:

Point: (0, 1)

Slope: 5xy

We can start by integrating the slope function to find the equation of the curve:

∫(dy/dx) dx = ∫(5xy) dx

Integrating both sides:

∫dy = ∫(5xy) dx

Integrating with respect to y on the left side gives us:

y = ∫(5xy) dx

To solve this integral, we treat y as a constant and integrate with respect to x:

y = 5∫(xy) dx

Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:

y = 5 * (1/2) * x^2y + C

Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:

1 = 5 * (1/2) * (0)^2 * 1 + C

1 = C

Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:

y = 5 * (1/2) * x^2y + 1

Simplifying further, we have:

y = (5/2) * x^2y + 1

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Answer:

If n is an integer, the function that generate the sequence 10, 12, 14, 16, ...  is \(\mathbf{d(n)=8+2n\:for\:n>1}\)

Option D is correct option

Step-by-step explanation:

We are given the arithmetic sequence:

10, 12, 14, 16, ...

If n is an integer, which of these functions generate the sequence?

We need to find the nth term for the given sequence

The nth term for arithmetic sequence will be: \(a_n=a_1+(n-1)d\)

where aₙ is nth term, a₁ is first term and d is common difference

Looking at the sequence a₁ = 10 and d = 2

So, nth term will be:

\(a_n=a_1+(n-1)d\\a_n=10+(n-1)2\\a_n=10+2n-2\\a_n=8+2n\)

So, nth term is: \(a_n=8+2n\)

In the options below, the only correct answer is option D. so, we can write nth term as: \(d(n) = 8 + 2n\: for\: n > 1\)

So, If n is an integer, the function that generate the sequence 10, 12, 14, 16, ...  is \(\mathbf{d(n)=8+2n\:for\:n>1}\)

Option D is correct option

Answer:

D) 8 + 2n for n > 1

Step-by-step explanation:

P-value = 0.0384

As P-value < 0.05, reject the null hypothesis.

A statistic (a number obtained from the sample) used in statistical hypothesis testing is known as a test statistic. Usually, a hypothesis test is described in words.

A test statistic is a figure obtained from a statistical analysis. It explains how distant your observed data is from the null hypothesis, which states that there is no correlation between the variables or distinction between the sample groups.

The alternative and null hypotheses are listed below.

Lack of hypothesis H0: μ = 13

Ha: 13 Alternative Hypothesis

Statistical test, z = (xbar - mu)/(sigma/sqrt(n))

z = (11 - 13)/(8/sqrt(50))

z = -1.77

Region of Rejection

For α= 0.05, this is a left-tailed test.

Z has a critical value of -1.645.

Therefore, if z -1.645, reject H0 and accept the null hypothesis.

P-value Approach

P-value = 0.0384

As P-value < 0.05, reject the null hypothesis

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To identify the vertical asymptotes, we have to factor the denominator. For horizontal asymptotes, we compare the degrees of the numerator and denominator.

For rational functions, there are vertical and horizontal asymptotes. To identify the vertical asymptotes, we first have to factor the denominator. After that, we should look for values that make the denominator zero. These values can be found by setting the denominator equal to zero and solving for x. The resulting x values would be the vertical asymptotes of the function.

The horizontal asymptote is the line that the function approaches as x goes towards infinity or negative infinity. For rational functions, the horizontal asymptote is found by comparing the degrees of the numerator and the denominator.

If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is y = the ratio of the leading coefficients. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

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Answer:

-a^3 + a^2

Step-by-step explanation:

Combine like terms

(-6a^3 + 5a^3 = -a^3) + (2a^2 - a^2 = a^2)

-a^3 + a^2

Answer:

3/1

Step-by-step explanation:

use slope formula (view picture for steps)

Answer:

sorry if this is really confusing, i can elaborate on anything if you want

Step-by-step explanation:

number 1 the angle in the triangle not described+angle1=180 since it's a line

180-125=55=angle 1

angle 2 should be 55 by vertical angles?

and angle 3 is 180-55-30 (same thing the other angle in the triangle is 180-150

angle 3=95

Answer:

V≈1809.56

Step-by-step explanation:

Answer:

Step-by-step explanation:

One that has the next least in common with the rest.

Answer:

B

Step-by-step explanation:

The end behavior of a function is how the graph behaves as it approaches negative and positive infinity.

Let's take a look at each end.

As x approaches negative infinity:

As x approaches the left towards negative infinity, we can see that the graph is shooting straight upwards.

Therefore, as \(x\rightarrow-\infty\), our function f(x) is increasing and increasing up towards positive infinity.

Therefore, the end behavior at the left will be:

\(\text{As } x\rightarrow-\infty, f(x)\rightarrow\infty\)

As x approaches (positive) infinity:

As x approaches the right towards positive infinity, we can see the that graph is also shooting straight upwards.

Therefore, the end behavior will be exactly the same. As x approaches positive infinity, f(x) also approaches positive infinity.

Therefore, the end behavior at the right will be:

\(\text{As } x\rightarrow \infty, f(x)\rightarrow \infty\)

Therefore, our answer is B.

Answer:

  85.2 m²

Step-by-step explanation:

Perhaps one of the easiest ways to decompose this composite figure is to consider it as a rectangle with a triangle removed from it.

__

The vertical dimension of the missing triangle is 8-4 = 4 m. The horizontal dimension of the missing triangle is 11.4 -8.4 = 3 m. The overall rectangle, including the missing triangle, is 11.4 m wide and 8 m high.

The area of the figure is ...

  area = rectangle area - triangle area

  = (11.4 m)(8 m) -1/2(4 m)(3 m) = 91.2 m² -6 m² = 85.2 m²

The area of the shape is 85.2 square meters.

_____

Additional comment

The area of a rectangle is the product of its length and width:

  A = LW

The area of a triangle is half the product of its base and height:

  A = 1/2bh

Answer:

Step-by-step explanation:

Basically you turn 1/2 into fourths,  1/2 = 2/4

After that you would multiply 4 2/4 x 2 1/4

Then you get 10.125 turned into a fraction is 81/8

Answer: 40

Step-by-step explanation:

because I just had that on my math test and got it wrong

A scientific observation must be reproducible (option a).

A scientific observation must be reproducible, meaning that the results can be consistently obtained by multiple researchers or through repeated experiments. Reproducibility is a fundamental principle of scientific research as it allows for independent verification and validation of observations.

It ensures that the observed phenomenon or data is not a chance occurrence or influenced by individual biases. By reproducing the observation, scientists can establish the reliability and robustness of the findings. The correct option is a.

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Answer:

y = mx + b

Step-by-step explanation:

so you first put the points on the graph and connect them with a slanted line.

Next, for your equation start of with y =

then, your going to find your slope, after you find it put it in front of x (slope x) (Ex; if the slope was 3 then it would look like this 3x)

finally you write + and the y intercept (at which point the line goes through the y axis)

the equation together should look like y = slope x + y intercept

Answer:

uuuu

Step-by-step explanation:

Answer:

1. A heterotroph

2. An autotrophs

3. Genus

4. An habitat

5.The binomial nomenclature system combines two names into one to give all species unique scientific names.

6. Carolus Linnaeus

7. Living organisms residing in a habitat are called biotic components.

8. Photosynthesis

Answer:

I'm probably wrong but I think it's D

Separated Variable Equation: Example: Solve the separated variable equation: dy/dx = x/y To solve this equation, we can separate the variables by moving all the terms involving y to one side.

A mathematical function, whose values are given by a scalar potential or vector potential The electric potential, in the context of electrodynamics, is formally described by both a scalar electrostatic potential and a magnetic vector potential The class of functions known as harmonic functions, which are the topic of study in potential theory.

From this equation, we can see that 1/λ is an eigenvalue of A⁻¹ with the same eigenvector x Therefore, if λ is an eigenvalue of A with eigenvector x, then 1/λ is an eigenvalue of A⁻¹ with the same eigenvector x.

These examples illustrate the process of solving equations with separable variables by separating the variables and then integrating each side with respect to their respective variables.

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An equation that mode the relationship between thee two variable is y=2x+3 .

Let x represent the number of 6-month period worked

Let y represent the total number of paid vacation day

According to the question,

When he started work, he was given three paid day of vacation. For each six-month period he pay at the job, his vacation is increased by two day.

Each year has 2 six-month periods. After 4.4 years Roberto will have worked 8.8 six-month periods. He will have been given vacation days for each of the 8 whole working periods he has completed. x=8 y=2*8+3 y=19

An equation that mode the relationship between thee two variable is y=2x+3 (Total vacation time equals 2 days times x plus the 3 days he was given at the start).

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Answer:

x=9

Step-by-step explanation:

13x-32 and 7x+22 are equal to each other (angles) so

13x-32=7x+22

13x-7x=22+32

6x=54

x=54/6

x=9

Answer:

1.59

Step-by-step explanation:

Divide 2,787 by 1,750

The best answer in English form for the statement ∃x¬P(x) is "There is a person who does not run every weekday."

The statement ∃x¬P(x) states that there exists a person x for whom P(x) is not true. Here, P(x) represents the statement "x runs 1 hour every weekday." Thus, the best answer in English form would be "There is a person who does not run every weekday." This implies that at least one individual does not participate in the activity of running for 1 hour on each weekday. It does not specify the reasons for not running or the alternative activities they may engage in. It simply confirms the existence of at least one person who deviates from the pattern of running every weekday.

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Complete Question:

Let P(x)P(x) = “xx runs 1 hour every weekday.” Select the best answer in English form for the following:

∃x¬P(x)

a. There is a person who does not run every weekday

b. There is no one who runs for 1 hour every weekday

c. There is a person who walks 1 hour every weekday

d. There is no one that doesn't run 1hr for no weekdays

e. There is a person who jogs every weekday

f. There is a person that does not run for 1hr every weekday

Answer:

16. 3

17. 12 / 7

18. 24 / 5 ( or ) 4.8

Step-by-step explanation:

16.

2 / ( x - 1 ) = 1

2 = x - 1

x = 2 + 1

x = 3

17.

( x / 3 ) + ( x / 4 ) = 1

LCM ( 3, 4 ) = 12

x / 3 = 4x / 12

x / 4 = 3x / 12

( x / 3 ) + ( x / 4 ) = 1

( 4x / 12 ) + ( 3x + 12 ) = 1

( 4x + 3x ) / 12 = 1

7x / 12 = 1

7x = 12

x = 12 / 7

18.

( x / 3 ) + ( x / 2 ) = 4

LCM ( 3, 2 ) = 6

x / 3 = 2x / 6

x / 2 = 3x / 6

( x / 3 ) + ( x / 2 ) = 4

( 2x / 6 ) + ( 3x / 6 ) = 4

( 2x + 3x ) / 6 = 4

5x / 6 = 4

5x = 24

x = 24 / 5

( or )

x = 4.8

Answer:d

Step-by-step explanation:

The equation of the tangent line at x = 0 for the function f(x) = -13√(x^2 + 1), x > 0 is y = 1.

To find the equation of the tangent line at x = 0, we need to determine the slope of the tangent line at that point. The slope can be found by taking the derivative of the function f(x).

First, let's find the derivative of f(x):

f'(x) = -13 * (1/2) * (x^2 + 1)^(-1/2) * 2x = -13x / √(x^2 + 1)

Next, substitute x = 0 into the derivative to find the slope at x = 0:

f'(0) = -13(0) / √(0^2 + 1) = 0

Since the derivative is 0 at x = 0, it indicates that the tangent line at that point is horizontal and has a slope of 0.

The equation of a horizontal line passing through the point (0, f(0)) is y = f(0). Substituting x = 0 into the original function, we get:

f(0) = -13√(0^2 + 1) + 1 = -13√1 + 1 = -13 + 1 = -12

Therefore, the equation of the tangent line at x = 0 is y = -12.

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The angle of rotation of a conic section is equal to -36 degrees.

Mathematically, the general form of the equation of a conic section is represented or modeled by this mathematical expression:

Ax² + Bxy + Cy² + Dx + Ey + F = 0

Where:

A, B, and C are not all equal to zero.

In Mathematics, the angle of rotation of a conic section can be calculated by using this formula:

Cot(2θ) = [A - C]/B

Where:

θ represents the angle of rotation of a conic section.

From the information provided, we have the following parameters:

3x² - 2√3xy + y² + 2x + 2√3 = 0

A = 3

B = -2√3

C = 1

Substituting the given parameters into the formula, we have;

Cot(2θ) = [3 - 1]/-2√3

Cot(2θ) = -2/2√3

Cot(2θ) =  -1/√3

1/tan(2θ) =  -1/√3

tan(2θ) = -√3

2θ = tan⁻¹(-√3)

2θ = -71.57

Angle of rotation, θ = -71.57/2

Angle of rotation, θ = -35.79 ≈ -36 degrees.

Note: A negative angle of rotation indicate a counterclockwise rotation.

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Answer:

3 hours :)

Step-by-step explanation:

5 km x 3 = 15km

also i hope you can catch up on ur work :)

Answer:

The value of x to the nearest tenth is 10.5.

Step-by-step explanation: