What is an equation of the line that passes through the points (-6, -3) and
(-3, -5)?

Answer:

The terms of the polynomial are relatively prime because the highest integer that divides them both is 1.

Step-by-step explanation:

Two numbers are said to be relatively prime if their greatest common factor ( GCF ) is 1 .

Now, the expression we are given in the question is a polynomial;

y² + 7.

The terms of the polynomial y² + 7 are y² and 7 and have no common factor and in fact cannot be factorized further. Thus, these terms are said to be relatively prime because the highest integer that divides them both is 1.

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Answer:

√-2 ≈ 1.41i

Step-by-step explanation:

√-2 = i√2 = i × 1.414.. ≈ 1.41i

Since it had the lowest mean absolute deviation, his scores were closest together in Math.

Hence, lower values of the mean absolute deviation means that the scores are closer, and thus his scores were closest together in Math.

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9 gallons + 7 gallons = 16 gallons

1 qt + 2qt = 3 qts

Total = 16 gallons and 3 qts.

Answer:

4188.8 cm^3

Step-by-step explanation:

We can calculate the volume of a sphere by using the following equation:

\(\frac{4}{3}\pi r^{3}\)

(r=radius)

so let's just plug in what we know

4/3(pi)(10)^3

we can calculate this with a calculator to get 4188.8 cm^3.

Answer:

523.6

Step-by-step explanation:

Delta math

Given the word problem, we can deduce the following information:

1. The game uses two fair number cubes.

2. If the total on the number cubes is either 11 or 2 on your next turn, you win the game.

To determine the probability of winning the next turn, we note that the two cubes have 36 possible outcomes since each dice has six combinations which are independent.

Rolling a 2 would have one possible outcome: (1,1)

Rolling an 11 would have two possible outcomes: (5,6) and (6,5)

So there would be three possible outcomes out of 36:

The combined probability,P, is 1/12. We express this into percent by:

Therefore, the answer is 8.3%.

Answer:

-1/3

Step-by-step explanation:

You multiply the -5 by 2

Then divide the result by 30.

9514 1404 393

Answer:

Step-by-step explanation:

The derivative of P with respect to t is ...

  P' = (x', y') = (4t, 4)

so the slope of the curve for some value of t is ...

  dy/dx = y'/x' = 4/(4t) = 1/t

The line we want to be a tangent is y = x +2, which has a slope of 1. The curve will have a slope of 1 where ...

  1/t = 1   ⇒   t = 1

At t=1, the point P is (2·1², 4·1) = (2, 4). For x=2, the point on the desired tangent is y = x +2 = 2 +2 = 4, or (x, y) = (2, 4).

The curve and the given line both have a slope of 1 at the point (2, 4), so that is the tangent point.

__

The normal to the curve at (2, 4) will have a slope that is the opposite reciprocal of the slope of the tangent: -1/1 = -1. Then point-slope form of the equation of the normal line is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y -4 = -1(x -2) . . . . . . line with slope -1 through point (2, 4)

  y = -x +6 . . . . . . . . equation of the normal line in slope-intercept form

we get that 6.255 × 10¹⁰  larger than 1.5 × 10⁸ by 417 times.

We are given two expressions:

6.255 × 10¹⁰ and 1.5 × 10⁸

We need to tell that how much times is 6.255 × 10¹⁰  larger than 1.5 × 10⁸.

We will do this with the help of division.

So, we get that:

= 6.255 × 10¹⁰  ÷ 1.5 × 10⁸

= 6.255 × 10¹⁰⁻⁸  ÷ 1.5

= 6.255 × 10²  ÷ 1.5

= 625.5 ÷ 1.5

= 417

Therefore, we get that 6.255 × 10¹⁰  larger than 1.5 × 10⁸ by 417 times.

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............ . . . m m. .

Answer:

standard form is Ax + by + c = 0

Step-by-step explanation:

add 5x to each side to get 5x + y - 2 = 0

Answer:

were is the circle to be to be equated

Hello!

Let's consider what the question asks for:

 ==> equation of tangent line to y = 3sin(x)

    --> at:  x = 5π/4

To find the slope of the line at a specific point on the function

  --> MUST find the derivative of equation

         \(\frac{d}{dx} 3sin(x)=3cos(x)\)

Derivative is function to find slope of function at every specific point

    --> let's find the slope at x = 5π/4

           \(3cos(x)=3*cos(\dfrac{5\pi }{4} )=3*(-\dfrac{\sqrt{2} }{2} )=-\dfrac{3\sqrt{2} }{2}\)

Now that we found the slope, we must also find the point at which the tangent line touches the function

    --> simply plug x = 5π/4' to find y

              \(y=3sin(\dfrac{5\pi }{4} )=-\dfrac{3\sqrt{2} }{2}\)

    --> thus our point which the tangent line and function touch is

                   \((\dfrac{5\pi }{4},-\dfrac{3\sqrt{2} }{2} )\)

Now let's write our tangent line's equation in point-slope form:

        \(y+\dfrac{3\sqrt{2} }{2} =-\dfrac{3\sqrt{2} }{2} (x-\dfrac{5\pi }{4})\)     <== Answer

Answer:

8^5 + 2 = Trisha's Tokens

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

8 x 5 +2

Answer:

A, D and B must be in a straight line.

Step-by-step explanation:

If D is between A and B, than AD+DB=AB

This would mean A, D and B would be in a straight line.

Answer:

It will take Ramona 25 months or 2 years and 1 month to pay back for the car.

Answer: $3,276

Step-by-step explanation:

To find the amount of interest needed to be paid, you needed to multiply the amount of money by your interesate rate.

= 3150 x 0.04

= 126

So, we add this extra amount to be paid to the exisiting total

= 3150 + 126

= $3,276

Answer: -20

Step-by-step explanation:

Consider the number as x,

2(x+30)=20

x+30=20/2

x+30=10

x=10-30

x=-20

Answer:

Step-by-step explanation:

first, rearrange the equation: y= -\(\frac{x}{6}\) +\(\frac{1}{3}\)

slope= -1/6

y intercept: 1/3

Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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Step-by-step explanation:

Hey there!

After looking at the figure we can state that;

X + 53° = 105°. { the exterior angle is equal to the sum of adjacent interior angle}

X = 105° - 53°

Therefore, X = 52°

Hope it helps...

Answer:

The better buy is to buy 10 kilograms of potatoes at $ 3.92, since each kilogram costs $ 0.392.

Step-by-step explanation:

To find the cost per unit in each case and then state which is the better buy, the following calculations must be performed:

6kg of potatoes for $ 2.45:

2.45 / 6 = 0.408

15 kg of potatoes for $ 5.9:

5.90 / 15 = 0.393

10 kg of potatoes for $ 3.92:

3.92 / 10 = 0.392

Thus, the better buy is to buy 10 kilograms of potatoes at $ 3.92, since each kilogram costs $ 0.392.

Answer:

g(x)=9x^3-x^2+2 for g(2)

Step-by-step explanation:

g(2)=9.2^3-2^2+2

=18^3-2^2+2

=18^1^4

=18^4

=104,976

The profit function is P(x) = -500.523x^2 + 600x - 200.

To find the profit function, P(x), we need to subtract the cost function, C(a), from the revenue function, R(x).

Given:

Cost function: C(a) = 500x^2 + 300

Revenue function: R(x) = -0.523x^2 + 600x - 200 + 300

Profit function, P(x), is obtained by subtracting the cost function from the revenue function:

P(x) = R(x) - C(a)

P(x) = (-0.523x^2 + 600x - 200 + 300) - (500x^2 + 300)

Simplifying the expression:

P(x) = -0.523x^2 + 600x - 200 + 300 - 500x^2 - 300

P(x) = -500x^2 - 0.523x^2 + 600x + 300 - 200 - 300

P(x) = -500x^2 - 0.523x^2 + 600x - 200

Combining like terms:

P(x) = (-500 - 0.523)x^2 + 600x - 200

Simplifying further:

P(x) = -500.523x^2 + 600x - 200

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Answer:

We can use the formula for compound interest to find the future value (FV) of Natalie's investment:

FV = P * (1 + r/n)^(n*t)

Where:

P is the principal amount (the initial investment), which is $2,000 in this case

r is the annual interest rate as a decimal, which is 11% or 0.11

n is the number of times the interest is compounded per year, which is 12 since interest is compounded monthly

t is the number of years, which is 20

Substituting the values into the formula, we get:

FV =

2

,

000

∗

(

1

+

0.11

/

12

)

(

12

∗

20

)

�

�

=

2,000 * (1.00917)^240

FV = $18,255.74

Therefore, after 20 years of compounded monthly interest at a rate of 11%, Natalie's investment of 2,000 will be worth approximately 18,256.

Answer:

$17,870

Step-by-step explanation:

You must use the formula for compound interest.

A = P(1 + r/n)^nt

I suggest you look it up at some point so that you can do these more easily in the future!