What is the value of 12÷13
?

Part a) After 30 minutes since the accident, the oil slick has a radius of 15 feet (0.5 * 30 = 15). Therefore, the volume of the oil slick is V(15) = 0.08π * 15 ^ 2 = 705.66 cubic feet. Part b) The function (V∘r)(t) = 0.08π * (0.5t) ^ 2 = 0.02πt ^ 2 is obtained by combining the two functions V(r) and r(t).

Part c) The function (V∘r)(t) = 0.02πt ^ 2 tells us the volume of the oil slick in terms of time t. As time increases, the volume of the oil slick also increases exponentially. Part d) To find out after how many minutes the oil slick will be 705 cubic feet, we can set (V∘r)(t) equal to 705, and solve for t. Therefore, t = (705 / 0.02π) ^ 1/2 ≈ 16.4 minutes. Therefore, after 16 minutes and 24 seconds, the oil slick will be 705 cubic feet.

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Sabrina needs to buy at least 8 pairs of socks to get free shipping, so the inequality will be x ≥ 8.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

Sabrina needs to buy at least 100 dollars worth of items to get free shipping, and she already has a 70 dollar sweatshirt in her cart.

Let x be the number of pairs of socks she needs to buy.

Each pair of socks costs 4 dollars, so the cost of x pairs of socks is 4x dollars.

To get free shipping, the total cost of her items must be at least 100 dollars.

Therefore, we can write the inequality -

70 + 4x ≥ 100

Subtracting 70 from both sides, we get -

4x ≥ 30

Dividing both sides by 4, we get -

x ≥ 7.5

Since Sabrina cannot buy a fraction of a pair of socks, she needs to buy at least 8 pairs of socks to meet the minimum spending requirement for free shipping.

Therefore, the solution to the situation is x ≥ 8.

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Answer:

8x²y + 14xy - 6xy²

Step-by-step explanation:

To expand the bracket, you need to multiply each term inside the bracket by 2xy, then recombine the terms.

2xy * 4x = 8x²y

2xy * 7 = 14xy

2xy * -3y = -6xy²

Final answer: 8x²y + 14xy - 6xy²

Answer:

8x^2y+14xy-6xy^2

Step-by-step explanation:

2xy( 4x+7-3y)

Distribute the 2xy to each term inside the parentheses.

2xy * 4x + 2xy +7 + 2xy * -3y

8x^2y+14xy-6xy^2

Answer:

To find the number of word problems on Mylie's math test, we need to multiply the total number of problems by the percentage that were word problems:

Number of word problems = 0.15 x 40

Number of word problems = 6

Therefore, there were 6 word problems on Mylie's math test.

The equation of the sine function is: y = 4 sin(1/4 x).

What is a sine function?

A sine function is a type of trigonometric function that relates the angle of a right triangle to the ratio of the length of its opposite side to its hypotenuse. It is defined as the ratio of the length of the opposite side of an angle in a right triangle to the length of the hypotenuse.

The general form of a sine function is:

y = A sin(Bx + C) + D

where A is the amplitude, B determines the period (B = 2π/period), C is the phase shift, and D is the vertical shift.

Substituting the given values, we get:

A = 4 (amplitude)

Period = 8π

B = 2π/Period = 2π/(8π) = 1/4

C = 0 (no phase shift)

D = 0 (no vertical shift)

the equation of the sine function is:

y = 4 sin(1/4 x)

Note that the value of B is the reciprocal of the period, since the formula for period is T = 2π/B, which can be rearranged to get B = 2π/T.

Hence, the equation of the sine function is: y = 4 sin(1/4 x).

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Step-by-step explanation:

To prove that the eqn provided passes through those points(coordinates..) we just have to inser the value of x and y. As a result we get the valid ans which stands ftrue for both the coordinates. Hence it's proved.

Answer:

---------------------------

Simplify each expression including the given and compare.

Given expression:

Options simplify as:

A)

B)

C)

D)

Yes, an A is received on the test.

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

As per the given data:

x = number of multiple choice questions.

x = 20

y = correctly answered questions.

y = 18

Inequality for receiving A:

3x + 2y ≥ 93

For receiving A, x and y must satisfy the inequality:

3x + 2y ≥ 93

3(20) + 2(18) ≥ 93

96 ≥ 93

Hence, Yes, an A is received on the test.

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The solution to the system of equations, 10x-11=-3y 5y-5=-10x, is x = 2 and y = -3.

To solve the system of linear equations by elimination, we need to eliminate one of the variables to find the value of the other variable. We can do this by multiplying one equation by a constant and adding it to the other equation.

10x - 11 = -3y  (Equation 1)

5y - 5 = -10x  (Equation 2)

We subtract the equations to eliminate the x variable:

10x - 11 - 5y + 5 = -3y + 10x

-5y + 3y = 10x - 10x + 6

-2y = 6

y = -3

Now we find the value of x:

5(-3) - 5 = -10x

-10x = -15 - 5

10x = 20

x = 20/10

x = 2

So, the solution to the system of equations is x = 2 and y = -3.

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Answer:

4v - 9

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

multiply inside to the parentheses and add all commmon numbers getting you to, 5v -18 = 2 then add 18 5v=20 divided to v=4

a)not linear

b)linear

c)not linear

d)linear

(i) T:R2→R2 defined by T(x,y)=(x,∣x+y∣): This transformation is not linear because it is not closed under addition and scalar multiplication.

(ii) T:Rn→R defined by T(x)=a⋅x, where a is a fixed vector of Rn: This transformation is linear because it is closed under addition and scalar multiplication.

(iii) T:P2(R)→P2(R) where (T(f))(x)=f(x)+x: This transformation is not linear because it is not closed under addition and scalar multiplication.

(iv) T:Rn→R defined by T(x)=xTa, where a is a fixed vector of Rn: This transformation is linear because it is closed under addition and scalar multiplication.

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The T(αu + v) = αT(u) + T(v), and so T is linear.

(i) Transformation T: R2 → R2 defined by T(x,y) = (x,|x + y|) is not linear, as the following counterexample proves: let u = (1,1) and v = (−1,2) be vectors in R2. Then:
T(u) = T(1,1) = (1,|1 + 1|) = (1,2)
T(v) = T(−1,2) = (−1,|−1 + 2|) = (−1,1)
However,
T(u + v) = T(1 − 1, 1 + 2) = T(0,3) = (0,|0 + 3|) = (0,3)
T(u) + T(v) = (1,2) + (−1,1) = (0,3)
Thus, T(u + v) ≠ T(u) + T(v), and so T is not linear.

(ii) Transformation T: Rn → R defined by T(x) = a · x, where a is a fixed vector of Rn, is linear. This can be easily checked by verifying that for any vectors x and y in Rn and scalars α and β in R, we have:
T(αx + βy) = a · (αx + βy) = α(a · x) + β(a · y) = αT(x) + βT(y)

(iii) Transformation T: P2(R) → P2(R) where (T(f))(x) = f(x) + x is linear. We can prove this as follows. Let f and g be any polynomials in P2(R) and let α be any scalar in R. Then:
(T(αf + g))(x) = (αf + g)(x) + x = αf(x) + g(x) + x = α(T(f))(x) + (T(g))(x)
Thus, T(αf + g) = αT(f) + T(g), and so T is linear.

(iv) Transformation T: Rn → R defined by T(x) = xT a, where a is a fixed vector of Rn, is linear. We can prove this as follows. Let u and v be any vectors in Rn and let α be any scalar in R. Then:
T(αu + v) = (αu + v)T a = α(uT a) + vT a = αT(u) + T(v)
Thus, T(αu + v) = αT(u) + T(v), and so T is linear.

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If a car is going 100 miles per hour, the car goes 100 miles in one hour.

Answer:36 seconds

Step-by-step explanation:

100 miles per hour, it would take me approximately 36 seconds to travel 1 mile.

Answer:

Your answer is x = 7.

Step-by-step explanation:

<HFG + <YFG = 180°

180° - <HFG = <YFG

<H + <G + <HFG = 180°

<H + <G  = 180° - <HFG

<H + <G  = <YFG

(6x + 8) + (65°)  = (3+16x)

6x + 8 + 65 = 16x + 3

Get x on one side and the other numbers on the other side.

8 + 65 - 3 = 16x - 6x

70 = 10x

x = 7

You can plug in x into the angle to solve for their angles.

Answer:

x = 7

Step-by-step explanation:

∠HFG must equal to 180° - ∠YFG. Because there are 180° in a triangle, we can subtract the known value, 65°, and be left with 115°.

From there, an equation can be formed.

115° = 6x + 8 + 180 - (3+16x)

115°= 6x + 188 - 3 - 16x

115°= 185 - 10x

-70° = -10x

x = 7

The mean and variance of the sales of cars from company FF in 8 different months

The mean and variance of the sales of cars from company FF in 8 different months are A. Mean = 10.5, Variance = 13.43. This can be calculated by adding up all the sales and then dividing by the number of months (6 + 7 + 8 + 9 + 11 + 12 + 15 + 16 = 84) and then dividing by 8 to get the mean (84 / 8 = 10.5). To calculate the variance, we first subtract the mean from each data point (6 - 10.5 = -4.5, 7 - 10.5 = -3.5, 8 - 10.5 = -2.5, 9 - 10.5 = -1.5, 11 - 10.5 = 0.5, 12 - 10.5 = 1.5, 15 - 10.5 = 4.5, 16 - 10.5 = 5.5) and then square each difference (-4.52 = 20.25, -3.52 = 12.25, -2.52 = 6.25, -1.52 = 2.25, 0.52 = 0.25, 1.52 = 2.25, 4.52 = 20.25, 5.52 = 30.25). We then add all of these values together and divide by the number of months (20.25 + 12.25 + 6.25 + 2.25 + 0.25 + 2.25 + 20.25 + 30.25 = 93.5) and divide by 8 to get the variance (93.5 / 8 = 11.6875). The variance is 11.6875, which is equivalent to 13.43 when rounded to two decimal places. Therefore, the mean and variance of the sales of cars from company FF in 8 different months are A. Mean = 10.5, Variance = 13.43.

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Therefore , the solution of the given problem of function comes out to be the function that fits the given graph is f(x) = [x] + 1.

In addition to numbers, symbols, but also their constituent expression parts, anatomy, construction, and both real and fictitious geographic places are all covered in the study of mathematics. A function explains the connections between various variables, which all have a related outcome. A function is composed of a number of unique parts that, when combined, result in particular outputs for each input.

Here,

The largest number that is less than or equal to x is returned by the greatest integer function, denoted by [x]. For instance, [3.4] = 3, [-2.8] = 3, and [5] = 5 are all equal.

The curve of the largest integer function is moved up one unit by the function f(x) = [x] + 1.

The graph of the largest integer function is moved up by zero units by the function f(x) = [x].

The largest integer function's graph is reflected and moved down by one unit by the function f(x) = -[x] - 1.

The curve of the largest integer function is moved down by one unit by the function f(x) = [x] - 1.

Therefore, the function that fits the given graph is f(x) = [x] + 1.

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Interest on $600 after 50 days of depositing is $4.53

In finance and economics, interest is the amount paid by a borrower or deposit-taking financial institution to a lender or depositor in excess of the repayment of the principal at a specified rate. It is different from a fee that a borrower can pay to a lender or a third party.

Given,

Principal amount = $600

Interest rate = 5.5%

Compounded daily for 50 days

By the interest table,

$1 compounded daily at 5.5% rate for 50 days = $1.00755

$600 compounded daily at 5.5% rate for 50 days

= $600 × 1.00755

= $604.53

Interest = Amount with interest - Principal

Interest = $604.53 - $600

Interest = $4.53

Hence, $4.53 is the interest on $600 after 50 days of depositing.

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The chart that cοuId be used tο dispIay the data is D. Bοx pIοt; because the data is categοricaI.

A bοx pIοt, οften knοwn as a bοxpIοt, is a methοd in descriptive statistics fοr graphicaIIy dispIaying the IοcaIizatiοn, spread, and skewness grοups οf numericaI data thrοugh their quartiIes.

Bοx pIοts are used tο depict the distributiοns οf numericaI data vaIues, particuIarIy when cοmparing them acrοss variοus grοups. They are designed tο cοnvey high-IeveI infοrmatiοn at a gIance, prοviding generaI infοrmatiοn abοut the symmetry, skew, variance, and οutIiers οf a grοup οf data.

In this case, since the data set Iists the favοrite chοice οf rοck bands, the bοx pIοt can be used.

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Complete question:

A data set lists the favοrite chοice οf rοck bands. Which οf the fοllοwing charts cοuld be used tο display the data, and why?

Bar chart; because the data is categοrical

Bar chart; because the data is numerical

Bοx plοt; because the data is categοrical

Bοx plοt; because the data is numerical

Step-by-step explanation:

when x=2

y=2(2)-1

y=4-1

Answer:

slope = -2, Y intercept = -1

Step-by-step explanation:

[tex]y = mx + c[/tex]

[tex]where \: m \: is \: the \: slope \: and \: c \: is \: the \: intercept[/tex]

So compare the equation with y= -2x-1

Therefore m = -2, c = -1

Correct statement: Two vectors are perpendicular if and only if the dot product of the two vectors is zero.

Explanation:

Two vectors are perpendicular if and only if the dot product of the two vectors is zero. This is equivalent to saying that the angle between the two vectors is 90 degrees. Therefore, the statement "Two vectors are perpendicular if and only if the angle between them is 90 degrees" is correct.

Every orthonormal set is linearly independent. This statement is also correct. An orthonormal set of vectors is a set of vectors that are pairwise perpendicular and have length 1.

Since the dot product of any two distinct vectors in an orthonormal set is 0, it follows that any linear combination of these vectors will also have a dot product of 0 with any other vector in the set.

Therefore, the only solution to a linear combination of these vectors being equal to the zero vector is for all the coefficients to be 0, which implies linear independence.

Every orthogonal set is linearly independent. This statement is also correct. An orthogonal set of vectors is a set of vectors that are pairwise perpendicular, but not necessarily of length 1.

Similar to the previous argument, the dot product of any two distinct vectors in an orthogonal set is 0, which implies linear independence.

R^n has an orthonormal basis. This statement is also correct. An orthonormal basis for a vector space is a basis consisting of orthonormal vectors. It can be shown that any finite-dimensional inner product space has an orthonormal basis, and R^n is a finite-dimensional inner product space with the standard dot product.

The zero vector is perpendicular to all other vectors. This statement is false. The zero vector is orthogonal to all other vectors, but not necessarily perpendicular, as the concept of perpendicularity requires the vectors to have a nonzero length.

Any orthonormal set in R^n is a basis. This statement is also correct. An orthonormal set of n vectors in R^n must span the entire space, as any vector in the space can be expressed as a linear combination of these vectors.

Furthermore, any set of n linearly independent vectors in R^n is a basis, so the fact that an orthonormal set is linearly independent (as shown in statement 2) implies that it is a basis.

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x = -4 - 4√2/6 and x = -4 + 4√2/6.

Hi there! The equation 3x5/3 + 96 = 0 can be rewritten as x5 + 32 = 0. In order to solve for the real solutions of this equation, we can use the Quadratic Formula, which states that for the equation ax2 + bx + c = 0, the real solutions are given by x = (-b ± √b2 - 4ac)/2a. Substituting the values for a, b, and c, we get x = (-32 ± √322 - 4*3*0)/6, which simplifies to x = (-32 ± √1024)/6, or x = -4 ± 4√2/6. Therefore, the real solutions for the equation are x = -4 - 4√2/6 and x = -4 + 4√2/6.

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The logarithmic statement [tex]log_(4)(1)/(16)=-2[/tex] can be translated into the equivalent exponential statement [tex]4^(-2)=(1)/(16)[/tex].

The logarithmic statement [tex]log_(4)(1)/(16)=-2[/tex] can be translated into an equivalent exponential statement by using the definition of logarithms. The definition of logarithms states that if [tex]log_(b)(a)=c[/tex], then [tex]b^c=a.[/tex]

Using this definition, we can translate the logarithmic statement[tex]log_(4)(1)/(16)=-2[/tex] into an equivalent exponential statement by rearranging the terms.

The equivalent exponential statement would be[tex]4^(-2)=(1)/(16)[/tex]. This means that 4 raised to the power of -2 is equal to 1/16.

So, the logarithmic statement [tex]log_(4)(1)/(16)=-2[/tex]can be translated into the equivalent exponential statement[tex]4^(-2)=(1)/(16)[/tex].

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Alex is currently 24 years old and Precy is currently 6 years old.

To solve this problem, we can use a system of equations.

Let A be Alex's current age and P be Precy's current age.

The first equation we can create is:

A + 3 = 3(P + 3)

The second equation we can create is:

A - 1 = 7(P - 1)

Now we can solve for one of the variables and substitute it into the other equation. From the first equation, we can isolate A:

A = 3P + 6

Substituting this value of A into the second equation:

3P + 6 - 1 = 7P - 7

Simplifying:

2P = 12 P = 6

Now we can substitute this value of P back into the first equation to find A:

A = 3(6) + 6 A = 24

So Alex is currently 24 years old and Precy is currently 6 years old.

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The number that would have to be added to "complete the square" is 90.25.

To complete the square for the quadratic equation x^(2)-19x+35=0, we would need to add the number 90.25 to both sides of the equation.

Step-by-step explanation:

1. Start with the given equation: x^(2)-19x+35=0
2. Move the constant term to the right side of the equation: x^(2)-19x=-35
3. Take half of the coefficient of the x term, square it, and add it to both sides of the equation: x^(2)-19x+(19/2)^(2)=-35+(19/2)^(2)
4. Simplify the right side of the equation: x^(2)-19x+90.25=-35+90.25
5. Combine like terms on the right side of the equation: x^(2)-19x+90.25=55.25
6. Write the left side of the equation as a perfect square: (x-9.5)^(2)=55.25
7. Take the square root of both sides of the equation: x-9.5=±√55.25
8. Solve for x: x=9.5±√55.25

Therefore, the number that would have to be added to "complete the square" is 90.25.

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Interest rates vary between lenders and can drastically change the monthly payment.

The interest rate is the cost of borrowing money from a lender. It determines how much extra you will pay on top of the principal amount borrowed.

The interest rate is a crucial factor to consider when shopping for loans because it directly affects the total cost of the loan.

Higher interest rates mean that you will pay more over the life of the loan, resulting in a higher monthly payment.

Lower interest rates mean that you will pay less over the life of the loan, resulting in a lower monthly payment.

Thus, choosing a loan with a lower interest rate can save you a significant amount of money in the long run.

Hence, Interest rates vary between lenders and can drastically change the monthly payment.

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Answer:

To find cos x, we can use the trigonometric identity:

cos^2 x + sin^2 x = 1

Rearranging this identity, we get:

cos^2 x = 1 - sin^2 x

Substituting the given value of sin x (2/3), we get:

cos^2 x = 1 - (2/3)^2

= 1 - 4/9

= 5/9

Taking the square root of both sides, we get:

cos x = ±√(5/9)

Since cosine is positive in the first quadrant, where sin x is positive, we can take the positive square root:

cos x = √(5/9)

We can simplify this expression by noting that both the numerator and denominator have a common factor of 5. We can simplify by factoring out this common factor:

cos x = √(5/9)

= √(5)/√(9)

= √(5)/3

Therefore, cos x = √(5)/3.

The work performed on the steam in this compression process per kilogram is -50 kPa*V/kg.\

To find the work performed on the steam in this compression process per kilogram, we need to use the following formula:

W = PΔV

Where W is the work, P is the pressure, and ΔV is the change in volume.Since the process is isothermal, the pressure and volume are inversely proportional.

This means that if the pressure is doubled, the volume will be halved. In this case, the pressure is constant at 100 kPa, and the volume is halved because half of the vapour has condensed.

Therefore, the change in volume is:

ΔV = V/2 - V = -V/2

Substituting this into the formula for work, we get:

W = PΔV = (100 kPa)(-V/2) = -50 kPa*V

To find the work per kilogram, we need to divide the work by the mass of the steam. Since the mass is not given in the question, we can assume it is 1 kilogram. Therefore, the work per kilogram is:

-50 kPa*V/1 kg = -50 kPa*V/kg

So the work performed on the steam in this compression process per kilogram is -50 kPa*V/kg.\

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The range of possible side lengths for the third side is 15 yd < x < ∞.

According to the triangle inequality, the lengths of any two sides of any triangle must add up to at least the length of the third side.

We can use the triangle inequality theorem to determine the range of possible side lengths for the third side of each triangle. The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

10.5 km and 11 km:

Let's call the length of the third side x. Applying the triangle inequality theorem, we get:

5 + x > 11

10 + x > 5

Simplifying, we get:

x > 6

x > -5

Therefore, the range of possible side lengths for the third side is 6 km < x < ∞.

12 mi and 12 mi:

Let's call the length of the third side x. Applying the triangle inequality theorem, we get:

12 + x > 12

12 + x > 12

Simplifying, we get:

x > 0

x > 0

Therefore, the range of possible side lengths for the third side is 0 mi < x < ∞.

25 yd and 10 yd:

Let's call the length of the third side x. Applying the triangle inequality theorem, we get:

10 + x > 25

25 + x > 10

Simplifying, we get:

x > 15

x > -15

Therefore, the range of possible side lengths for the third side is 15 yd < x < ∞.

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Answer:

639 visitors in October

Step-by-step explanation:

I'll assume the "23" is meant to be 2/3.  If so:

We learn that attendance for November is 2/3 that of October.  Let's put that into an equation.  Let x be the October attendance and y the November attendance.

    y = (2/3)x  [Nov = (2/3) of Oct]

We are told that y = 426

  y = (2/3)x

  426 = (2/3)x

(426)*(3/2) = x

  x = 639

October's attendance was 639 visitors.

matrix is 0.3 x 4 = 1.10

To determine the determinant of this 3 x 3 matrix, you can use the Laplace Expansion method. First, cross out the third column and calculate the determinant of the 2 x 2 matrix that remains:

0.6 0.8

0.5 0

The determinant of this 2 x 2 matrix is 0.6 x 0 - 0.8 x 0.5 = 0.3.

Next, multiply this result by the last element of the third column, which is 4. So the determinant of the 3 x 3 matrix is 0.3 x 4 = 1.10.

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Answer:

Using the difference of squares formula, we have:

(r³ - 6t¹) (r³ + 6t¹) = r³ × r³ - r³ × 6t¹ - 6t¹ × r³ - 6t¹ × 6t¹

= r^6 - 36t²

Therefore, the expression in simplest form is r^6 - 36t².