Twice a number increased by five is 11. What is the number?

The volume of water filled in the bath tub is 6 feet × 2 feet × 2.2 feet = 26.4 cubic feet. You need 11.83 minutes in the shower to use as much water as the bath.

The volume of water filled in the bath tub is 6 feet × 2 feet × 2.2 feet = 26.4 cubic feet.

The amount of water used in shower = flow rate × time = 2.23 gallons/minute × 8 minutes = 17.84 gallons

Let's convert gallons to cubic feet: 1 cubic foot = 7.5 gallons

17.84 gallons = 17.84/7.5 cubic feet = 2.378 cubic feet

The volume of water used in the shower is 2.378 cubic feet. The volume of water used for taking a bath is 26.4 cubic feet.

To calculate how many minutes one would need in the shower to use as much water as the bath, divide the volume of water used in taking a bath with the amount of water used per minute in the shower as shown:

26.4/2.23=11.83 min

Therefore, one needs 11.83 minutes in the shower to use as much water as the bath.

To know more about volume, visit:

https://brainly.com/question/1578538

#SPJ11

Answer:

can u show me a picture of this problem.

Step-by-step explanation:

Answer:

165°

..

..

..

..

..

..

.............

Answer:

6.

Step-by-step explanation:

Faces in other words is the number of individual shapes on one shape. In this case, how many rectangles is on this shape. Hope this helps have a good day!

Answer:

rectangle is

Edges=12

Faces=6

Vertices=8

(a) We find that the effective yield rate is approximately 6.91%.

(b) The account will have approximately $70,297.97 in it after 22 years.

a) To find the effective yield rate of the investment, we can use the formula for compound interest:

Effective yield rate = (1 + (annual interest rate / number of compounding periods))^{number of compounding periods - 1}

In this case, the annual interest rate is 6.75% (or 0.0675 as a decimal), and the compounding is done monthly, so the number of compounding periods per year is 12.

Plugging in the values, we get:

Effective yield rate = (1 + (0.0675 / 12))^12 - 1

Calculating this expression, we find that the effective yield rate is approximately 6.91%.

b) To find how much money will be in the account in 22 years, we can use the formula for compound interest:

Future value = Principal * (1 + (annual interest rate / number of compounding periods))^(number of compounding periods * number of years)

In this case, the principal is $17,000, the annual interest rate is 6.75% (or 0.0675 as a decimal), the compounding is done monthly, so the number of compounding periods per year is 12, and the number of years is 22.

Plugging in the values, we get:

Future value = $17,000 * (1 + (0.0675 / 12))^(12 * 22)

Calculating this expression, we find that the future value of the account after 22 years is approximately $70,297.97.

Therefore, the account will have approximately $70,297.97 in it after 22 years.

To learn more about compound interest visit:

brainly.com/question/22621039

#SPJ11

The value of the integral C1 and C2 are below:

∫[C1] (y + x – 4ix³) dz = -1/2 + 4/3 i

∫[C2] (y + x – 4ix³) dz = 0

To evaluate the integral, we need to parameterize the given contour C and express it as a function of a single variable. Then we substitute the parameterization into the integrand and evaluate the integral with respect to the parameter.

Let's evaluate the integral along contour C1: the straight line from Z = 0 to Z = 1 + i.

Parameterizing C1:

Let's denote the parameter t, where 0 ≤ t ≤ 1.

We can express the contour C1 as a function of t using the equation of a line:

Z(t) = (1 - t) ×0 + t× (1 + i)

= t + ti, where 0 ≤ t ≤ 1

Now, we'll calculate the differential dz/dt:

dz/dt = 1 + i

Substituting these into the integral:

∫[C1] (y + x – 4ix³) dz = ∫[0 to 1] (Im(Z) + Re(Z) - 4i(Re(Z))³)(dz/dt) dt

= ∫[0 to 1] (t + 0 - 4i(0)³)(1 + i) dt

= ∫[0 to 1] (t + 0)(1 + i) dt

= ∫[0 to 1] (t + ti)(1 + i) dt

= ∫[0 to 1] (t + ti - t + ti²) dt

= ∫[0 to 1] (2ti - t + ti²) dt

= ∫[0 to 1] (-t + 2ti + ti²) dt

Now, let's integrate each term:

∫[0 to 1] -t dt = [-t²/2] [0 to 1] = -1/2

∫[0 to 1] 2ti dt = \(t^{2i}\)[0 to 1] = i

∫[0 to 1] ti² dt = (1/3)\(t^{3i}\) [0 to 1] = (1/3)i

Adding the results together:

∫[C1] (y + x – 4ix³) dz = -1/2 + i + (1/3)i = -1/2 + 4/3 i

Therefore, the value of the integral along contour C1 is -1/2 + 4/3 i.

Let's now evaluate the integral along contour C2: along the imaginary axis from Z = 0 to Z = i.

Parameterizing C2:

Let's denote the parameter t, where 0 ≤ t ≤ 1.

We can express the contour C2 as a function of t using the equation of a line:

Z(t) = (1 - t)× 0 + t × i

= ti, where 0 ≤ t ≤ 1

Now, we'll calculate the differential dz/dt:

dz/dt = i

Substituting these into the integral:

∫[C2] (y + x – 4ix³) dz = ∫[0 to 1] (Im(Z) + Re(Z) - 4i(Re(Z))³)(dz/dt) dt

= ∫[0 to 1] (0 + 0 - 4i(0)³)(i) dt

= ∫[0 to 1] (0)(i) dt

= ∫[0 to 1] 0 dt

= 0

Therefore, the value of the integral along contour C2 is 0.

In summary:

∫[C1] (y + x – 4ix³) dz = -1/2 + 4/3 i

∫[C2] (y + x – 4ix³) dz = 0

Learn more about integral here:

https://brainly.com/question/31059545

#SPJ11

Considering the expression of a line, the slope of the line that passes through the points (1,-6) and (-2,-8) is 2/3.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:

m= (y₂ - y₁) ÷ (x₂ - x₁)

Being (x₁, y₁)= (1, -6) and (x₂, y₂)= (-2, -8), the slope m can be calculated as:

m= (-8 - (-6)) ÷ (-2 - 1)

m= (-8 +6) ÷ (-2 - 1)

m= (-2) ÷ (-3)

m= 2/3

Finally, the slope in this case is 2/3.

Learn more about the equation of a line having 2 points:

brainly.com/question/12851029

brainly.com/question/19496333

#SPJ1

Answer:

3 1/8 lbs left

Step-by-step explanation:

\(5\frac{3}{4} -\frac{1}{8} -2\frac{1}{2}\)

\(\frac{23}{4} -\frac{1}{8} -\frac{5}{2}\)

\(\frac{46}{8} -\frac{1}{8} -\frac{20}{8}\)

\(\frac{46-1-20}{8}\)

\(\frac{25}{8}\) lbs

After calculation, the average salary is 865.8644 thousands of dollars and average tenure is 7.955 years. Number of CEOs who are in their first year as CEO is equal to 5.

Here are the steps in R Studio to perform the tasks:

(a) Finding the average salary and the average tenure in the sample:

Load the CEOSAL2 data set in R Studio using the read.csv function.

       ceos <- read.csv("CEOSAL2.csv")

Calculate the average salary using the mean function:

       average_salary <- mean(ceos$salary)

Calculate the average tenure using the mean function:

average_tenure <- mean(ceos$ceoten)

(b) Finding the number of CEOs in their first year as CEO and the longest tenure as CEO:

Use the sum function and a logical test to count the number of CEOs in their first year as CEO:

first_year_ceos <- sum(ceos$ceoten == 0)

Use the max function to find the longest tenure as CEO:

longest_tenure <- max(ceos$ceoten)

Read more about Average Calculations:

https://brainly.com/question/14371457

#SPJ4

When the cost of a gallon of milk increases from $2.81 to $3.48 over a period of 10 years the annual inflation rate is 2.15 percent.

What is a annual inflation rate?

A percentage is used to represent the inflation rate. For instance, a yearly inflation rate of 2% indicates that the cost of products and services as a whole has increased by 2%. As an illustration, a product that cost $10 last year will cost $10.20 this year.

Here, we have

Given

The cost of the gallon of milk earlier was $2.81

The cost of a gallon of milk now is $3.48.

The total time period is 10 years.

r = (F/P)ⁿ⁻¹ - 1

r = {(3.48/2.81)^(1/10) - 1}×100

r = {(1.238)^(1/10) - 1}×100

r = 0.0215 ×100

r = 2.15

Hence, when the cost of a gallon of milk increases from $2.81 to $3.48 over a period of 10 years the annual inflation rate is 2.15 percent.

To learn more about the annual inflation rate from the given link

https://brainly.com/question/24723238

#SPJ1

Answer:

u arrange it mathematically and then you'll be able to get the answer

When interpreting the expression as \((tanx)^{(sinx)\), the limit using L'Hospital's Rule is -∞ as x approaches 0+. However, when interpreting the expression as\(tan(x^{sinx})\), the limit is not well-defined due to the indeterminate form of 0^0.

To calculate the limit using L'Hospital's Rule, let's consider both interpretations of the expression and find the limits for each case:

Case 1: lim\((tanx)^{(sinx)\) as x approaches 0+

Taking the natural logarithm of the expression, we have:

\(ln[(tanx)^{(sinx)}] = sinx * ln(tanx)\)

Now, we can rewrite the expression as:

\(lim [sinx * ln(tanx)]\)as x approaches 0+

Applying L'Hospital's Rule, we differentiate the numerator and denominator:

\(lim [(cosx * ln(tanx)) + (sinx * sec^{2}(x))] / (1 / tanx)\) as x approaches 0+

Simplifying the expression:

\(lim [cosx * ln(tanx) + sinx * sec^{2}(x)] * tanx\) as x approaches 0+

\(lim [cosx * ln(tanx) + sinx * sec^{2}(x)] * (sinx / cosx)\) as x approaches 0+

\(lim [(cosx * ln(tanx) + sinx * sec^{2}(x)) / cosx] * sinx\) as x approaches 0+

\(lim [ln(tanx) + (sinx / cosx) * sec^{2}(x)] * sinx\) as x approaches 0+

\(lim [ln(tanx) + tanx * sec^{2}(x)] * sinx\) as x approaches 0+

Since lim ln(tanx) as x approaches 0+ = -∞ and\(lim (tanx * sec^{2}(x))\) as x approaches 0+ = 0, we have:

\(lim [ln(tanx) + tanx * sec^{2}(x)] * sinx\) as x approaches 0+ = -∞

Therefore, the limit of \((tanx)^{(sinx)\) as x approaches 0+ using L'Hospital's Rule is -∞.

Case 2: lim\(tan(x^{sinx})\)as x approaches 0+

We can rewrite the expression as:

lim\(tan(x^{(sinx)})\) as x approaches 0+

This expression does not have an indeterminate form of \(0^0\), so we do not need to use L'Hospital's Rule. Instead, we can substitute x = 0 directly into the expression:

lim \(tan(0^{(sin0)})\) as x approaches 0+

lim\(tan(0^0)\)as x approaches 0+

The value of \(0^0\) is considered an indeterminate form, so we cannot determine its value directly. The limit in this case is not well-defined.

For more question on L'Hospital's Rule visit:

https://brainly.com/question/24116045

#SPJ8

a. Null distribution is expected to be centered at the hypothesized proportion, which is 0.25.

b. Null distribution is expected to be centered at 25.

a. If you are using a proportion as your statistic, you expect the null distribution to be centered at the hypothesized proportion, which is 0.25 in this case.

b. If you are using a count as your statistic, you expect the null distribution to be centered at the expected count, which is np under the null hypothesis, where n is the sample size and p is the hypothesized proportion. In this case, np = 100 * 0.25 = 25.

To know more about null hypothesis click here:

https://brainly.com/question/11614388

#SPJ11

There are 72 multiples of 9³ that are greater than \(9^4\) and less than \(9^5\).

We have,

The values of 9³, \(9^4\), and \(9^5\):

9³ = 729

\(9^4\) = 6561

\(9^5\) = 59049

Now,

The multiples of 729 that fall within the range (6561, 59049).

The number of multiples can be calculated as follows:

Multiples = (Highest value ÷ Divisor) - (Lowest value ÷ Divisor)

= (59049 ÷ 729) - (6561 ÷ 729)

= 81 - 9

= 72

Therefore,

There are 72 multiples of 9³ that are greater than \(9^4\) and less than \(9^5\).

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ12

Answer:

\(64.147^{\circ}\)

Step-by-step explanation:

The explanation is attached below.

Answer and Step-by-step explanation:

The numbers that are irrational are the square root of 27 and the square root of 55. ( \(\sqrt{27}, \sqrt{55}\) ).

This is because those numbers don't have a perfect square root.

The square root of 16 and the square root of 64 have perfect square roots (16 having the answer as 4, and 64 having the answer as 8).

#teamtrees #PAW (Plant And Water)

Answer:

  not direct variation

Step-by-step explanation:

You want to know if the equation y = 3x +2 represents a direct variation between x and y.

Direct variation is characterized by the equation ...

  y = kx

for a constant of variation k. The point (0, 0) is on a graph of direct variation.

The given equation is not in this form, and cannot be put in this form. The value of y when x=0 is not 0, so the variation is not direct.

<95141404393>

Answer: 1 2 imm comingg for youuuuuuuuuuuuu

Step-by-step explanation:

Answer:

C. their slope are equal

Step-by-step explanation:

The general solution to the differential equation y'' + 16y = 0 is y(x) = (c₁ + c₂) * cos(4x)

To solve the differential equation y'' + 16y = 0 using reduction of order, we'll assume a second solution of the form y₂(x) = u(x) * y₁(x), where y₁(x) is a known solution and u(x) is an unknown function.

Given y₁(x) = cos(4x), we'll differentiate it to find y₁'(x) and y₁''(x):

y₁'(x) = -4sin(4x)

y₁''(x) = -16cos(4x)

Now we substitute y₂(x) = u(x) * y₁(x) into the original differential equation:

y'' + 16y = 0

(-16cos(4x)) + 16(u(x) * cos(4x)) = 0

Simplifying the equation:

-16cos(4x) + 16u(x) * cos(4x) = 0

cos(4x)(-16 + 16u(x)) = 0

For this equation to hold for all values of x, we must have (-16 + 16u(x)) = 0.

Solving for u(x):

-16 + 16u(x) = 0

16u(x) = 16

u(x) = 1

Now we have the second solution:

y₂(x) = u(x) * y₁(x)

y₂(x) = 1 * cos(4x)

y₂(x) = cos(4x)

Therefore, the general solution to the differential equation y'' + 16y = 0 is:

y(x) = c₁ * y₁(x) + c₂ * y₂(x)

y(x) = c₁ * cos(4x) + c₂ * cos(4x)

y(x) = (c₁ + c₂) * cos(4x)

Where c₁ and c₂ are arbitrary constants.

Learn more about reduction of order at

https://brainly.com/question/32250420

#SPJ11

Answer:

a) The Margin of Error = 0.26

b) The 99% Confidence Interval = ( 2.84, 3.36)

Step-by-step explanation:

a) Margin of Error

The formula for Margin of Error =

z × Standard deviation/√n

From the above question

The z score for 99% confidence interval = 2.576

Standard deviation = 0.72

n = Random number of samples = 50

Margin of Error =

2.576 × 0.72/√50

= 1.85472 /√(50)

= 0.2622970178

Approximately to 2 decimal places = 0.26

b) 99% Confidence Interval

= Mean ± Margin of Error

Mean = 3.1mm

Confidence Interval = 3.1 ± 0.26

3.1 ± 0.26

= 2.84

3.1 + 0.26

= 3.36

The 99% Confidence Interval = ( 2.84, 3.36)

The cost of each rosebush is $12.5. Her first purchase was 8 rosebushes and 4 hostas for a total of $140.

Let's assume the cost of each rosebush is represented by "r" (in dollars), and the cost of each hosta is represented by "h" (in dollars).

From the given information, we can create a system of equations:

Equation 1: 8r + 4h = 140 (total cost of 8 rosebushes and 4 hostas)

Equation 2: 4r + 3h = 80 (total cost of 4 additional rosebushes and 3 additional hostas)

To solve this system, we can use the method of elimination. Multiply Equation 1 by 3 and Equation 2 by 4 to eliminate the "h" term:

Equation 1: 24r + 12h = 420

Equation 2: 16r + 12h = 320

Subtract Equation 2 from Equation 1:

(24r + 12h) - (16r + 12h) = 420 - 320

8r = 100

Divide both sides by 8:

r = 100 / 8

r = 12.5

Therefore, the cost of each rosebush is $12.5.

Learn more about cost here

https://brainly.com/question/2292799

#SPJ11

Answer:  x  is 9° ,  y is 21°. The measure of angle ABE is 48°.

Step-by-step explanation:

First we will solve for x.  

The variable x appears in the angle 8x + 18   and that angle is a right angle.

Right angles have the measure of 90 degrees so we will set the angle equal 90  and solve for x.

8x + 18 = 90    Subtract 18 from both sides

      - 18   -18  

8x = 72     divide both sides by 8

x = 9  

y is also on the right side and the combination of both angles has to also equal 90 degrees because they form a right angle.

Since we already know x is 9 we will input it into the left side for x and solve for y.

y + 3(9) + 2y = 90

3y + 27= 90

    -27     -27

3y = 63

 y = 21  

Now we need to find the measure of angle ABE.

ABE is represented by  y + 3x  so since we know the value of y and x we will input it into the expression and solve for the angle.

21 + 3(9) = m∠ABE

21 + 27= m∠ABE

48 = m∠ABE

This means the measure of angle ABE is 48°

The explicit rule for the sequence is f(n) = 6 - 4(n - 1)

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

a1 = 6

a(n) = a(n - 1) - 4

In the above sequence, we can see that -4 is added to the previous term to get the new term

This means that

First term, a = 6

Common difference, d = -4

The nth term is then represented as

f(n) = a + (n - 1) * d

Substitute the known values in the above equation, so, we have the following representation

f(n) = 6 - 4(n - 1)

Hence, the explicit rule isf(n) = 6 - 4(n - 1)

Read more about sequence at

brainly.com/question/30499691

#SPJ1

To answer the questions related to the probability of droplet sizes, we'll use the normal distribution with the given mean and variance. Let's solve each part of the question:

a. Probability that the size of a single droplet is less than 1500 μm:

To find this probability, we need to calculate the cumulative distribution function (CDF) of the normal distribution up to 1500 μm. We'll use the z-score formula:

z = (x - μ) / σ

Where:

x = droplet size (1500 μm)

μ = mean (1050 μm)

σ = standard deviation (square root of the variance, which is sqrt(22500 μm))

Calculating the z-score:

z = (1500 - 1050) / sqrt(22500)

= 450 / 150

= 3

Using the z-score table or a calculator, we can find that the cumulative probability corresponding to z = 3 is approximately 0.9987.

Therefore, the probability that the size of a single droplet is less than 1500 μm is approximately 0.9987.

b. Probability that the size of a single droplet is between 1000 and 1500 μm:

Similar to part (a), we need to calculate the cumulative probability for two values: 1000 μm and 1500 μm. Let's calculate the z-scores for both values:

For 1000 μm:

z_1000 = (1000 - 1050) / sqrt(22500)

For 1500 μm:

z_1500 = (1500 - 1050) / sqrt(22500)

Once we have the z-scores, we can find the corresponding cumulative probabilities using the z-score table or a calculator. Then, we subtract the probability for 1000 μm from the probability for 1500 μm to find the probability between the two values.

c. Characterizing the smallest 2% of all droplets:

To characterize the smallest 2% of droplets, we need to find the droplet size that corresponds to the 2nd percentile of the normal distribution. In other words, we need to find the value x such that the cumulative probability up to x is 0.02. We can use the z-score formula to solve for x:

z = (x - μ) / σ

We'll find the z-score corresponding to the cumulative probability 0.02 using the z-score table or a calculator. Then, we can rearrange the formula to solve for x:

x = z * σ + μ

d. Probability that at least one of five independently selected droplets exceeds 1500 μm:

To find this probability, we'll use the complement rule. The probability that none of the five droplets exceed 1500 μm is the complement of the probability that at least one of them exceeds 1500 μm. We can calculate this probability by subtracting the probability of none from 1. We'll use the probability obtained in part (a) for a single droplet.

Learn more about probability  here:

https://brainly.com/question/31828911

#SPJ11

Answer:

It can always be written as a fraction.

Step-by-step explanation:

The importance of this question is to differentiate rational and irrational numbers.

Rational numbers can be written as a ratio, hence a fraction, or a repeating or terminating decimal.

Irrational numbers cannot be written as a ratio and will not have a terminating or repeating decimal.

So the first statement is true since the sum of two rational numbers will be rational.

The second statement is false since the sum of two rational numbers can absolutely be represented by a fractional ratio.

The third statement is false since the sum of two rational numbers is not always a repeating decimal.

The fourth statement is false since the sum of two rational numbers could be written as a terminating decimal.

Cheers.

I agree with the other person's response. The sum is always rational (it can always be written as a fraction of integers)

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

Here's a proof:

Let x and y be two rational numbers. This means

x = a/b

y = c/d

where a,b,c,d are integers. The denominators b and d cannot be 0.

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

Let's add x and y, then simplify

x+y = (a/b) + (c/d)

x+y = (ad/bd) + (bc/bd)

x+y = (ad+bc)/(bd)

This last expression is in the form p/q

p = ad+bc is an integer

q = bd is also an integer

we have a ratio or fraction of integers, therefore x+y is also rational

Answer:

D

Step-by-step explanation:

You have to use pythagorean theorem to solve this.

Answer:

D

Step-by-step explanation:

use pytherogream theory

sides, 5 and 12

pytherogream triple 5, 12, 13

The slope of the graph is the same positive value that is 0.75.

Hence the correct option is (1).

We know that the equation of a straight line with slope 'm' and y intercept 'c' is given by,

y = mx + c

Here the model equation

c = 0.75h, where c is the total cost to buy hotdogs

h is the number of hotdogs bought

And 0.75 is the price of one hotdog

Now we can clearly say that c = 0.75h will make a straight line coordinate plane.

Now comparing the equation with slope intercept equation of straight line we get,

m = 0.75 and c = 0

So the slope of the line represented by model equation = 0.75 which is a positive number.

y intercept  = 0.

We know that the slope of one particular straight line on cartesian plane is unique.

So, the slope of the graph is the same positive value.

Hence the correct option is (1).

To know more about slope here

https://brainly.com/question/3493733

#SPJ1

Answer:

B

Step-by-step explanation:

0.25=1/4=15/60

3/20=9/60

20%=1/5=12/60

1/3=20/60

Now we can easily put them in order since they have a common denominator.

9<12<15<20

Now let's bring back the original numbers in the same order as shown above.

3/20, 20%, 0.25, 1/3

Choice B matches this order.

The linear regression model for the weekly cost data is given by C(z) = ma + k, where z is the independent variable representing the weekly demand.



The values of m and k are determined through the regression analysis. Using this model, we can estimate the total weekly cost for a given weekly demand and calculate the per unit variable cost and weekly fixed cost.To find the linear regression model, we need to perform a regression analysis on the given weekly cost data. This analysis will determine the values of m and k in the equation C(z) = ma + k, where C(z) represents the weekly cost and z represents the weekly demand.

Once the values of m and k are obtained, we can use the model to estimate the total weekly cost when the weekly demand is 210. By plugging in z = 210 into the equation C(z) = ma + k, we can calculate the total weekly cost rounded to the nearest dollar.The per unit variable cost can be determined by the value of m in the model. It represents the change in cost per unit change in demand. By rounding m to one decimal place, we can obtain the per unit variable cost rounded to one decimal place.

The weekly fixed cost can be determined by the value of k in the model. It represents the cost that does not depend on the weekly demand. By rounding k to the nearest integer, we can obtain the weekly fixed cost rounded to the nearest dollar.Overall, by applying the linear regression model to the given data, we can estimate the total weekly cost, calculate the per unit variable cost, and determine the weekly fixed cost of producing sleeping bags.

Learn more about linear regression model here: brainly.com/question/30470285
#SPJ11

The derivative function is dy/dx = (1 - t) / (\(6t^3\)) and \(d^2y/dx^2\) = \((-1 / (6t^3))\)- (3 / \((2t^4)\)

To find dy/dx, we need to differentiate y with respect to t and x with respect to t, and then divide the two derivatives.

Given:

\(x = 3t^4 + 7\)

\(y = 2t - t^2\)

Differentiating y with respect to t:

dy/dt = 2 - 2t

Differentiating x with respect to t:

\(dx/dt = 12t^3\)

Now, to find dy/dx, we divide dy/dt by dx/dt:

\(dy/dx = (2 - 2t) / (12t^3)\)

To simplify this expression further, we can divide both the numerator and denominator by 2:

\(dy/dx = (1 - t) / (6t^3)\)

The second derivative \(d^2y/dx^2\)represents the rate of change of the derivative dy/dx with respect to x. To find \(d^2y/dx^2\), we differentiate dy/dx with respect to t and then divide by dx/dt.

Differentiating dy/dx with respect to t:

\(d^2y/dx^2 = d/dt((1 - t) / (6t^3))\)

To simplify further, we can expand the differentiation:

\(d^2y/dx^2 = (-1 / (6t^3)) - (3 / (2t^4))\)

learn more about differentiation here:

https://brainly.com/question/24062595

#SPJ11