The derivative of the function at P0 in the direction of A is,
([tex]\frac{df}{dx}[/tex])[tex]p_{0}[/tex] = -3 , ([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = -1 , ([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = 0
Geometrically, the derivative of a function can be interpreted as the slope of the graph of the function or, more precisely, as the slope of the tangent line at a point. Its calculation, in fact, derives from the slope formula for a straight line, except that a limiting process must be used for curves.
Given that,
The derivative of the function at P0 in the direction of A.
f(x, y, z) =
f(x, y, z) = (1,-1,-2)
x = 1
y = -1
z = -2
Derivative of f(x, y, z) = xy + yz + zx
[tex]\frac{df}{dx}[/tex] = y + z
[tex]\frac{df}{dy}[/tex] = x + z
[tex]\frac{df}{dz}[/tex] = x + y
We can substitute f(x, y, z) = (1,-1,-2) values,
([tex]\frac{df}{dx}[/tex])[tex]p_{0}[/tex] = y + z
([tex]\frac{df}{dx}[/tex])[tex]p_{0}[/tex] = -1 + (-2)
([tex]\frac{df}{dx}[/tex])[tex]p_{0}[/tex] = -3
([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = x + z
([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = 1 + (-2)
([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = 1-2
([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = -1
([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = x + y
([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = 1 + (-1)
([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = 1-1
([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = 0
Therefore,
The derivative of the function at P0 in the direction of A is,
([tex]\frac{df}{dx}[/tex])[tex]p_{0}[/tex] = -3 , ([tex]\frac{df}{dy}[/tex])[tex]p_{0}[/tex] = -1 , ([tex]\frac{df}{dz}[/tex])[tex]p_{0}[/tex] = 0
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The cost for printing service is $0.35 per copy plus a service fee of $2.
a. Write an equation to model the cost where t represents the total cost and c represents the number of copies.
b. How much would 120 copies cost?
Answer:
a. t = 0.35c + 2
b. 44
Step-by-step explanation:
since it is $0.35 per copy, we would put 0.35c (c represents copies)
and t is the total cost, or what we're adding to
0.35c = t
since there is an addition of a service fee (which is $2), we add that
Final Result : 0.35c + 2 = t
solve each of the following problems by realizing it as a binomial experiment. a fair six-sided die is rolled four times. what is the probability that an odd number is thrown twice?
The probability of getting two odd numbers is 1/2*1/2 = 1/4.
What are binomial experiments used for?When there are only two possible outcomes for an experiment, binomial probability may be used to estimate the likelihood of each result (success and failure).There are just two outcomes that can happen on each try in a binomial situation. You may label one of the alternatives Fail and the other Succes, depending on what you desire. A 6 on a dice is a success, whereas anything other than a 6 is a failure.A statistical experiment with the following characteristics is called a binomial experiment: There are n repeated trials in the experiment. There are only two potential results for each experiment. One of these results is referred to be a success, and the other as a failure.Making the standard assumptions (unbiased die, faces numbered 1-6), there are three odd numbers per die (1, 3 and 5), so the probability of getting an odd number on a die is 3/6 = 1/2, and the probability of getting two odd numbers is 1/2*1/2 = 1/4.
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1/2*1/2 = 1/4 is the likelihood of receiving two odd numbers.
What are the purposes of binomial experiments ?When an experiment has just two possible results, binomial probability can be used to calculate the likelihood of each outcome (success and failure).
In a binomial circumstance, there are only two outcomes that can occur on each try. Depending on what you want, you may declare one of the possibilities a failure and the other a success. Anything less than a 6 is a failure, whereas a 6 is a triumph.
A binomial experiment is a statistical test that has the following features: The experiment consists of n repeated repetitions. Each experiment has only two possible outcomes. One of these outcomes is known as a success, while the other is known as a failure.
According to the given information
The probability of receiving an odd number on a die is 3/6 = 1/2 and the likelihood of getting two odd numbers is 1/2*1/2 = 1/4 under the usual assumptions (unbiased die, faces numbered 1-6). There are three odd numbers per die (1, 3 and 5).
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what distribution is used with the global test of the regression model to reject the null hypothesis?
F distribution is used with the global test of the regression model to reject the null hypothesis.
The hypothesis test will be conducted using a novel distribution. After the English statistician Sir Ronald Fisher, it is known as the F distribution. A ratio, the F statistic is (a fraction). One set of degrees of freedom is for the denominator, and the other set is for the numerator.
According to the null hypothesis, all group population means are equal. Because it is assumed that the populations are normal and that they have similar variances, the equal means hypothesis indicates that the populations have the same normal distribution. All groups are samples from populations with the same normal distribution, according to the null hypothesis. According to the alternative theory, at least two of the sample groups are drawn from populations with various normal distributions.
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Which equation best describes the line whose graph is shown?
A y=x+3
By = 3x
Cy=3
D x=3
Answer:
i have done this mano time ago, but problaply the answer is x=3
PLS HELP ASAP
QUESTION ON SCREENSHOT
Answer: D
Step-by-step explanation:
Drawing a straight line between the two x's would give the line bisecting MN.
For the following inequality, find a solution for the variable. Show all of your work and use complete sentences to explain the solving process that you used to find a solution for the inequality. Be sure to include at least two terms from the word bank.
Answer:
x ≤ -12
Step-by-step explanation:
We solve for x by dividing both sides by 1/4:
[tex]1/4x\leq -3\\x\leq -12[/tex]
Thus, the two sentences you need to have two words from your work bank are (1) "divide" both sides by 1/4 and (2) x is "less than or equal to" -12
a ________ value in a loop can be either a positive or a negative number.
A Increment value in a loop can be either a positive or a negative number.
Positive Increment: A positive increment is when the value of the loop increases on each iteration.
Negative Increment: A negative increment is when the value of the loop decreases on each iteration.
In a step value, the counter variable is either an increment or a decrement every time the loop is executed. If the counter variable is decreased, it can go as low as a negative number, whereas with an increment, the counter variable can be either negative or positive with each loop executed increased.
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a manufacturer of mp3 players conducts a set of comprehensive tests on the electrical functions of its product. all mp3 players must pass all tests prior to being sold. of a random sample of 500 mp3 players, 15 failed one or more tests. find a 90% confidence interval for the proportion of mp3 players from the population that pass all tests.
0.957 < p < 0983 is a 90% confidence interval for the proportion of mp3 players from the population that pass all tests
How do I calculate 90% confidence interval?Add and subtract the margin of error from the sample mean to get this confidence interval. The confidence interval's top and lower limits are represented by this result.We can be 90% certain that the interval contains the population mean,, if the degree of confidence is 90%. The associated z-scores are 1.645. In order to calculate a confidence interval, the sample mean (X) and, if applicable, the population standard deviation () must be known. When the sample size is more than 30, the sample standard deviation, s, can be used in place of the population standard deviation..Given :
a random sample of 500 mp3 players, 15 failed one or more tests.
no of passed mp3 players = 500-15 =485
p = 485/500 =0.97
q = 1-p = 1-0.97 =0.03
90% confidence interval.
1- [tex]\alpha[/tex] = 90%
[tex]\alpha = 0.1[/tex]
[tex]Z_{\alpha/2}[/tex] = [tex]z_{.05} =1.645[/tex]
[tex]\hat{p} -[/tex] [tex]Z_{\alpha/2}[/tex][tex]\sqrt{\frac{\hat p \hat q}{n} }[/tex]< p< [tex]\hat{p} +[/tex] [tex]Z_{\alpha/2}[/tex][tex]\sqrt{\frac{\hat p \hat q}{n} }[/tex]
0.957 < p < 0983
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A 90% confidence interval for the percentage of mp3 players in the population that pass all tests is 0.957 < p <0983.
How can I determine the confidence interval at 90%?To obtain this confidence interval, add and subtract the margin of error from the sample mean. This result represents the upper and lower bounds of the confidence interval.
If the level of confidence is 90%, we can be 90% confident that the interval contains the population mean. The corresponding z-score is 1.645.
The sample mean (X) and, if relevant, the population standard deviation must be known in order to compute a confidence interval. The sample standard deviation, s, can be used in place of the population standard deviation when the sample size is greater than 30.
According to the given information
15 out of 500 mp3 players in a random sample failed one or more tests.
MP3 players that have been passed: 500-15 = 485
p = 485/500 =0.97
q = 1-p = 1-0.97 =0.03
Confidence interval of 90%.
[tex]1-\alpha[/tex] = 90%
[tex]\alpha[/tex] = 0.1
[tex]Z_{\frac{\alpha }{2} } = Z_{.05} = 1.645[/tex]
[tex]p-Z_{\frac{\alpha }{2} } \sqrt{\frac{pq}{n} }[/tex]<p<[tex]p+Z_{\frac{\alpha }{2} } \sqrt{\frac{pq}{n} }[/tex]
0.957 < p < 0983
A 90% confidence interval for the percentage of mp3 players in the population that pass all tests is 0.957 < p <0983.
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how many cups is it?
The number of cups that will be in 3 gallons is 48 cups.
How to calculate the number of cups?It is important to note that ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
Based on the information, the number of cups won a gallons will be:
= 64 / 4
= 16 cups.
Therefore, the cups that will be in 3 gallons will be:
= 3 × 16. cups
= 48 cups.
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Solve for x.
8x-3 4x + 3
When angles form a linear pair, the sum is 180°.
8x3+4x + 3 = 180
[?]x +
= 180
Hint: First we must combine like terms. Calculate the sum
of 8x and 4x and enter the value of the coefficient.
The required value of the coefficient of x is given as 12.
A simplified value of the coefficient of x is to be determined.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
In order to simplify the given expression add the like terms first,
8x-3+4x + 3 = 180
x + 4x - 3 + 3 = 180
12x = 180
Thus, the needed coefficient of x value is provided as 12.
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If the perimeter of triangle is 15 centimeters what is value of n
Answer:
5 cms
Step-by-step explanation:
This is assuming that it is equilateral and that n is the length of one side
Mawsynram, a village in India, is the wettest place on earth. It gets about 11,850 millimeters of rain per year.
About how many centimeters of rain fall in the village?
About how many inches if rain fall in the village?
Answer: 467 inches and 1185 centimeters
Step-by-step explanation:
1. Divide by 10 to find centimeters
2. Divide by 25.4 and round to find inches
Name Yala. Al Write down each of the following expressions in the form of a power of one number a) 5³x5⁴ b) (-7)² ×(-7)³ c) 3⁶x3³ d) 27⁰x27² e) (-2)² ×(-2)³ × (-2)⁴ f) 3⁴x9²x(-3)⁶ g) (-4)⁶ × (-4)⁵ (-4)³ h) (-8)x(-8)x2² i) (0.25)×(0.25)⁴ × (0.25)⁰ J) 7³x7²x7
Answer:
A. [tex] {5}^{7} [/tex]
B. [tex] ( { - 7})^{5} [/tex]
C. [tex] {3}^{9} [/tex]
D. [tex] {27}^{2} [/tex]
E. [tex] ({ - 2})^{9} [/tex]
F. [tex] {3}^{14} [/tex]
G. [tex] {( - 4)}^{14} [/tex]
H. [tex] {2}^{8} [/tex]
I. [tex] {(0.25)}^{5} [/tex]
J. [tex] {7}^{6} [/tex]
Step-by-step explanation:
A.
[tex] {5}^{3} \times {5}^{4} \\ = {5}^{3 + 4} \\ = {5}^{7} [/tex]
B.
[tex]( { - 7})^{2} \times ( { - 7})^{3} \\ = ( { - 7})^{2 + 3} \\ = ( { - 7})^{5} [/tex]
C.
[tex] {3}^{6} \times {3}^{3} \\ = {3}^{6 + 3} \\ = {3}^{9} [/tex]
D.
[tex] {27}^{0} \times {27}^{2} \\ = {27}^{0 + 2} \\ = {27}^{2} [/tex]
E.
[tex]( { - 2})^{2} \times ( { - 2})^{3} \times ( { - 2})^{4} \\ = ( { - 2})^{2 + 3 + 4} \\ = ({ - 2})^{9} [/tex]
F.
[tex] {3}^{4} \times {9}^{2} \times ( { - 3})^{6} \\ = {3}^{4} \times {3}^{2 \times 2} \times {3}^{6} \\ = {3}^{4} \times {3}^{4} \times {3}^{6} \\ = {3}^{4 + 4 + 6} \\ = {3}^{14} [/tex]
G.
[tex] {( - 4)}^{6} \times {( - 4)}^{5} \times {( - 4)}^{3} \\ = {( - 4)}^{6 + 5 + 3} \\ = {( - 4)}^{14} [/tex]
H.
[tex] ( - 8) \times ( - 8) \times {2}^{2} \\ = 8 \times 8 \times {2}^{2} \\ = {2}^{3} \times {2}^{3} \times {2}^{2} \\ = {2}^{3 + 3 + 2} \\ = {2}^{8} [/tex]
I.
[tex] 0.25 \times {(0.25)}^{4} \times {(0.25)}^{0} \\ = {(0.25)}^{1} \times {(0.25)}^{4} \times {(0.25)}^{0} \\ = \times {(0.25)}^{1+4+0} \\ = \times {(0.25)}^{5} [/tex]
J.
[tex] {7}^{3} \times {7}^{2} \times 7 \\ = {7}^{3} \times {7}^{2} \times {7}^{1} \\ = {7}^{3+2+1} \\ = {7}^{6} [/tex]
Please help, giving thanks and brainliest:) (Please give an explanation if possible and please dont give a fake answer)
The angle of x in the triangle is 30 degrees.
How to find angles of a triangle?The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
In other words, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles of the triangle.
Therefore, the value of x can be found using the exterior angle theorem as follows:
x + 45 = 2x + 15
x - 2x = 15 - 45
- x = - 30
divide both sides by - 1
Therefore,
x = 30
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Solve for X. Please help me
Answer:
x = 9
Step-by-step explanation:
g(n)=n² +4n
h(n)=-3n-3
Find (g+h)(n-4)
The function (g+h)(n-4) is the sum of the function g(n-4) and h(n-4) will be written as (g+h)(n-4) = n² - 7n + 9.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The functions are given below.
g(n) = n² + 4n
h(n) = - 3n - 3
The function (g+h)(n) is calculated as,
(g+h)(n) = g(n) + h(n)
(g+h)(n) = n² + 4n - 3n - 3
(g+h)(n) = n² + n - 3
Put n = n - 4, then we have
(g+h)(n-4) = (n - 4)² + (n - 4) - 3
(g+h)(n-4) = n² + 16 - 8n + n - 4 - 3
(g+h)(n-4) = n² - 7n + 9
The function (g+h)(n-4) will be (g+h)(n-4) = n² - 7n + 9.
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Suppose we select every fifth invoice in a file. What type of sampling is this? Multiple Choice Cluster Simple random Stratified random Systematic
This is an example of Systematic sampling.
Here we are drawing out every fifth invoice from the file available. Hence here we create an order where every fifth item is selected.
Hence this is called systematic sampling.
This is a type of probability sampling. In this method, samples are selected by the researcher at regular intervals.
This type of sampling is most suitable when we want to conduct a sampling method similar to simple random sampling but the list of population is unknown to us. However, this can also be used when the list of the same is available to us.
Another important condition is the order os the population, i.e ow it is spread must be random and not in some particular order or sample. Else the reult obtained will lose its credibility.
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What is the value of m?
The value of m in the diagram is 18°
What is a right-angle?
A right angle is an angle of 90°. When two rays intersect and form a 90˚ angle or are perpendicular to each other at the intersection, they are said to form a right angle.
A right angle is an angle that measures 90 degrees. It is the most commonly seen angle in our day-to-day life.
From the diagram, the two angles sum up to 90°
∠WZX + ∠XZY = ∠WZY
3m + 3 + 33 = 90
3m + 36 = 90
3m = 90 - 36
3m = 54
m = 54/3
m = 18°
In conclusion the value of m is 18°
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you flip a fair coin 10 times (i.e. probability of tossing a head is the same as the probability of tossing a tail and is equal to 0.5). answer the next five questions. flag question: question 10 question 105 pts what is the probability of getting exactly 8 heads? group of answer choices 0.064 0.044 0.034 0.054
Apply the Binomial Probability Distribution, The Answer is 0.044.
What is Binomial Probability Distribution?The discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome is known as the binomial distribution with parameters n and p in probability theory and statistics.
What is the formula to calculate Binomial Probability Distribution?The required formula is:
[tex]P(x)= C(n,x) p^{x}q^{n-x}[/tex]
n=10
x=8
p(8)= [tex]C(10,8) * 0.5 ^ {8} *0.5 ^{2}[/tex]
=0.044
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A pizza lover wants to compare the average delivery times for four local pizza restaurants. Over the course of a few weeks, he orders a number of pizzas from each restaurant, and he records the time it takes for each pizza to be delivered.
a) When performing an ANOVA with this data, what is the alternative hypothesis?
- All of the restaurants have different mean delivery times
- At least two of the restaurants have different mean delivery times
- Two of the restaurants have different mean delivery times
- One of the restaurants has a different mean delivery time than the others
b) A partial ANOVA table for his data is shown below. What is the value of B?
Source DF SS MS F P-value
Treatment B 19.31 D F G
Error C 15.667 E
Total 18 34.977
What is the value of C in the ANOVA table?
d) What is the value of D in the ANOVA table? Give your answer to three decimal places.
e) What is the value of E in the ANOVA table? Give your answer to three decimal places.
f) What is the value of F in the ANOVA table? Give your answer to two decimal places.
g) What is the value of G in the ANOVA table? Give your answer to four decimal places.
h) Using a 0.1 level of significance, what should his conclusion be in this case?
- He should conclude that at least two of the restaurants have different mean delivery times because the P-value is less than 0.1.
- He should fail to reject the claim that at all of the restaurants have the same mean delivery times because the P-value is greater than 0.1.
- He should conclude that at least two of the restaurants have different mean delivery times because the P-value is greater than 0.1.
- He should conclude that at all of the restaurants have the same mean delivery times because the P- value is less than 0.1.
(a) When performing an ANOVA with the data the alternative hypothesis is at least two of the restaurants have different mean delivery times.
(b)75.8
Analysis of variance. or ANOVA, is a statistical method that separate observed variance data into different components to use for additional tests. A one way ANOVA is used for three or more groups of data, to gain information about the relationship between the dependent and independent variables.
The ANOVA table shows how the sum of squares are distributed according to source of variation, and hence the mean sum of squares.
It is given that a pizza lover wants to compare the average delivery times.
Therefore the null hypothesis and alternate hypothesis implies that,
H₀ = all restaurants have equal mean delivery time
Hₐ = at least two restaurants have different two deliveries
Hence the alternate hypothesis for performing an ANOVA with the data is at least two of the restaurants have different mean delivery times.
The alternate hypothesis (Hₐ) defines that there is a statistically important relationship between two variables. Whereas null hypothesis states that is no statistical relationship between the two variables.
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Gabriella owned so many CDs that she gave 64 of them away. After donating the CDs she had 147 left. Write an equation to find the number of CDs c gabriella had originaly
Answer:
147+64=c
Step-by-step explanation:
you would add the two numbers together to get the original.
How many packages does Ellis need to buy to build the extension?
Answer:
To find out how many tiles Ellis will need, we first need to find the total area of the extension that she plans to build. To do this, we can find the area of each of the three sides of the extension separately and then add them together.The extension will have a length of 6.25 m and a width of 1.5 m, so its area will be 6.25 m * 1.5 m = 9.375 m^2.There will be three sides of the extension, so the total area of the extension will be 3 * 9.375 m^2 = 28.125 m^2.Each tile has an area of 0.25 m * 0.25 m = 0.0625 m^2.Therefore, Ellis will need a total of 28.125 m^2 / 0.0625 m^2 = 448 tiles. Since each package contains 25 tiles, she will need to buy 448 tiles / 25 tiles/package = 18 packages of tiles.
Step-by-step explanation:
car rental company a charges an $80 service fee plus $22 per day. car rental company b does not have a service fee and charges $32 per day. which equation will help determine how many days it will take for the average charge per day for company a to be the same as the average charge per day for company b?
It will take 8 days for the average charge per day for company a to be the same as the average charge per day for company b.
The charges incurred by these companies are given by the word expression -
Total charge = Service fee + Fee per day. Equating the expressions by keeping values of both companies. Let us represent each day by z.
80 + 22x = 0 + 32x
Rewriting the equation
32x - 22x = 80
Performing subtraction on Left Hand Side of the equation
10x = 80
Shifting 10 to Right Hand Side of the equation
x = 80/10
Performing division on Right Hand Side of the equation x = 8
On eight days, the charge will be equal.
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what are the numbers for h?
Answer:
0,1
2,2
4,3
6,4
Step-by-step explanation:
Some Examples
4 = 1/2 (6) + 1
4 = 3 + 1
4=4
----------
2 = 1/2 (2) + 1
2 = 1 + 1
2 = 2
h
0
2
4
6
...................
Which of the following is true about k-means clustering Group of answer choices A tree diagram is used to illustrate the steps in the clustering analysis We choose the value for k before doing the clustering analysis It is a type of hierarchical clustering The cluster analysis will give us an optimum value for k In a cluster analysis, the distance between the clusters should be: Group of answer choices Maximized Minimized Even Zero THANK YOU :)
Prior to performing the clustering analysis, we choose the value for k. In a cluster analysis, the distance between the clusters should be minimized.
K-means clustering is an unsupervised machine learning technique used to identify clusters of data points. Before performing the clustering analysis, we must first choose the value of k (the number of clusters we wish to identify). The cluster analysis will then attempt to find the k clusters by minimizing the distances between the data points in each cluster. Once the clusters have been identified, the distance between them should be minimized to ensure that the clusters are as distinct as possible.
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pls help tyyy!!!!!
.
Answer: Those both would be 21 with work ....
Find the derivative of this with respect to x
For any data set, which measures of central location have only one value? A. Mode and median B. Mode and mean C. Mode and standard deviation D. Mean and median
Any data collection whose metrics of central placement only have the letter A as a value.Mode and median
For any given data set, the mode and median are the two measures of central location that have just one value. The mode is the most commonly occurring value in a given data set, while the median is the middle value in the data set when it is sorted in order from least to greatest. The mean, on the other hand, is an average of all the values in the data set, and the standard deviation is a measure of how much the values in the data set differ from each other. So, the answer is A. Mode and median.
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A relative frequency table is made from data in a
frequency table.
S
T
Total
Frequency Table
U
LO
5
4
9
V
8
2
10
Total
13
6
19
What is the value of k in the relative frequency table?
Round the answer to the nearest percent.
O 2%
O 11%
O-20%
O 33%
Answer:sorry i just need some poinpoint
Step-by-step explanation:
point) The number of Drosophila fruit flies in controlled experiment assumes the following growth pattern when the food source is limited: 600 N(t) 1+ Me-0.3t where measured in days. A. How many fruit files were there in the beginning? What is the limiting number of fruit flies 600 C.At what time was the population increasing most rapidly? D. At what rate is the number of fruit flies increasing after days? 600/(1+11e
time was the population increasing most rapidly. At rate is the number of fruit flies increasing after days A. 600 B. 600 C. t=0 D. 0.09
The equation 600/(1+Me-0.3t) is a model for the population of Drosophila fruit flies, with time representing the number of days the experiment has gone on for. A. The population of fruit flies in the beginning is given by the equation as 600. B. The limiting number of fruit flies is also given by the equation as 600. C. The population is increasing most rapidly when t=0. D. After days, the number of fruit flies is increasing at a rate of 0.09, which can be calculated by taking the derivative of the equation with respect to t.
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