If 10^x=5 what is x
1)x=log^10 5
2)x=ln 5
3)x=1/2
4)x=5/log^10 10

The interval that is graphed in the number line is the one in option D:

[-4, 1]

Here we have an interval graphed on a number line. We can see that the interval starts at x = -4 and ends at x = 1.

Notice that bot ends have closed circles. These closed circles are used when the elements belong to the interval notation, and in those cases, we use the symbols [ ] to define the interval.

If instead we had open circles, we should use the symbols ( ), in that case, the ends do not belong to the interval.

Here because both of the ends are closed, the interval will be written as [-4, 1]

Then the correct option is D.

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Answer:

Step-by-step explanation: Negatives because a number lower than 0 go like this -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 see? so the answer is Negatives.

Answer:

X

-5

-1

0

2

4

/(×)

12

0

-3

-9

-15

The expression "raise b to the 2nd power" means to multiply b by itself, which can be written as [tex]b^2[/tex]. The expression [tex](b^2)/8[/tex] represents this quotient.

When we say "raise b to the 2nd power", it means we are squaring b, which is equivalent to multiplying b by itself. So, [tex]b^2[/tex] represents the result of multiplying b by itself.

Next, the phrase "find the quotient of the result and 8" means we need to divide [tex]b^2[/tex] by 8. Dividing [tex]b^2[/tex] by 8 gives us the expression [tex](b^2)/8[/tex], which represents the quotient we are looking for. We do not simplify the expression any further, because the instructions say to "not simplify any part of the expression."

So, [tex](b^2)/8[/tex] is the final answer. This expression is still in fraction form, and it can be useful to keep it in this form if we are using it to solve a larger problem or if we want to keep the answer as precise as possible. If we want to convert it to decimal form, we can use a calculator to divide [tex]b^2[/tex] by 8.

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The data set contains no outliers since all of the values are within the bounds of 148.5 and 198.5.

The following is the five-number summary of the given data set 68, 162, 163, 167, 167, 168, 168, 169, 170, 178, 180, 180, 182, 182, 185. Identify any outliers.

The five-number summary of the data set are as follows:Minimum value = 68 First quartile = 167Median = 169Third quartile = 180Maximum value = 185 We use the following formula to find outliers in the data set:IQR = Q3 - Q1 Here, Q1 and Q3 are the first and third quartiles, respectively.So,IQR = 180 - 167IQR = 13 To find the lower and upper bounds, we use the following formulas:Lower bound = Q1 - (1.5 × IQR)Upper bound = Q3 + (1.5 × IQR)Here, the lower bound and upper bound values are calculated as follows:Lower bound = 167 - (1.5 × 13)Lower bound = 148.5Upper bound = 180 + (1.5 × 13)Upper bound = 198.5

Now, any values that are less than the lower bound or greater than the upper bound are considered outliers.The data set contains no outliers since all of the values are within the bounds of 148.5 and 198.5.

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The subgroups are as follows: (a) (±a ±b; ±b ±a), (b)  (±a 3b; ±b a),  (c) group of all 2x2 upper triangular matrices with 1's on the diagonal, (d) (a b; 0 a⁻¹), (e) (a b; b a) and (f) (a b; -b a).

(a) The subgroup generated by (0 1; -1 0) is the group of all 2x2 matrices of the form (±a ±b; ±b ±a), where a and b are real numbers.

(b) The subgroup generated by (0 1/3; 3 0) is the group of all 2x2 matrices of the form (±a 3b; ±b a), where a and b are real numbers.

(c) The subgroup generated by (1 -1; 1 0) is the group of all 2x2 upper triangular matrices with 1's on the diagonal.

(d) The subgroup generated by (1 -1; 0 1) is the group of all 2x2 matrices of the form (a b; 0 a⁻¹), where a and b are nonzero real numbers.

(e) The subgroup generated by (1 -1; -1 0) is the group of all 2x2 matrices of the form (a b; b a), where a and b are real numbers.

(f) The subgroup generated by (√3/2 1/2; -1/2 √3/2) is the group of all 2x2 matrices of the form (a b; -b a), where a and b are real numbers.


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The number 3 107/125 is greater than  3.151.

A number that is stated as bοth a whοle number and a fractiοn, such 3 1/2, is referred tο as a mixed number. A fractiοn, such as 7/2, that has the numeratοr higher than οr equal tο the denοminatοr is referred tο as an imprοper fractiοn. Yοu must multiply the whοle number by the denοminatοr, add the numeratοr, and then place it οver the οriginal   denοminatοr in οrder tο cοnvert a  mixed number tο an imprοper fractiοn.

Divide the numeratοr by the denοminatοr and then write the residue as a fractiοn with the same denοminatοr tο turn an imprοper fractiοn intο a mixed number.

The given numbers are: 3.515 οr 3 107/125.

Cοnvert 3 107/125 tο a decimal.

3 107/125 = (3 * 125 + 107)/125 = 482/125 = 3.856

Cοmparing the twο 3.515 and 3.856 we οbserve that 3.856 is greater than 3.515.

Hence, the number 3 107/125 is greater than 3.151.

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sin D is 4/5 or 0.8, sin E is 3/5 or 0.6, and cos D is 3/5 or 0.6.

Just dividing the numerator by the denominator is all that is required to convert a fraction to a decimal. Nothing else needs to be said!

Divide the opposite side by the hypotenuse to find sin D and sin E; similarly, divide the adjacent side by the hypotenuse to find cos D.

opposite/hypotenuse = 4/5 = 0.8 sin D (rounded to 4 decimal places)

opposite/hypotenuse = 3/5 = 0.6 sin E (rounded to 4 decimal places)

adjacent/hypotenuse = 3/5 = 0.6 cos D (rounded to 4 decimal places)

The resulting values for sin D, sin E, and cos D are 4/5, 0.8, 3/5, and 0.6 respectively.

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The probability that a household watches more than 3 hours of television a day is 0.0478.

The mean daily viewing time of television is 8 hours per household. Use a normal probability distribution with a standard deviation of 3 hours to answer the following questions about daily television viewing per household.

(a) Probability that a household views television between 5 and 11 hours a day:P(5 < x < 11) = P(z < (11-8)/3) - P(z < (5-8)/3) = P(z < 1) - P(z < -1) = 0.8413 - 0.1587 = 0.6826(b) Hours of television viewing must a household have in order to be in the top 3% of all television viewing households:

The top 3% of all households correspond to z = 1.88. Therefore, the number of hours that a household must watch television to be in the top 3% is:1.88 = (x - 8) / 3x - 8 = 5.64x = 13.64

(c) Probability that a household views television more than 3 hours a day:P(x > 3) = P(z < (3-8)/3) = P(z < -5/3) = 0.0478.the probability that a household watches more than 3 hours of television a day is 0.0478.

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The (1, 4), (1, 5), (1, 6), (3, 4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)Out of these possible outcomes, there are only 11 such outcomes where X1 ≠ 2 and X2 ≥ 4: (1, 4), (1, 5), (1, 6), (3, 4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 4), (5, 5)P(X1 ≠ 2 and X2 ≥ 4) = 11/36

Probability that X2 = 4:Since we rolled a fair dice, so the probability of getting a number 4 on the dice would be 1/6.P(X2 = 4) = 1/6b) Probability that X1 + X2 = 7:Now we know that the sum of the outcomes of two fair dices rolled is 7, this can be obtained by the following possibilities:(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)Since each outcome is equally likely, so each of these outcomes has a probability of 1/36.P(X1 + X2 = 7) = 6/36 = 1/6c) Probability that X1 ≠ 2 and X2 ≥ 4:

If we look at the possible outcomes of X1 and X2 then we have the following possibilities:(1, 4), (1, 5), (1, 6), (3, 4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)Out of these possible outcomes, there are only 11 such outcomes where X1 ≠ 2 and X2 ≥ 4: (1, 4), (1, 5), (1, 6), (3, 4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 4), (5, 5)P(X1 ≠ 2 and X2 ≥ 4) = 11/36

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The function that represents the estimated average price of 1 acre of land in Berrien County after x years can be written as:

[tex]$$P(x) = 6236(1 + 0.032)^x$$[/tex]

What is average?

In mathematics, the average, also known as the mean, is a measure of central tendency that represents the sum of a set of values divided by the number of values in the set.

The current price of 1 acre of land in Berrien County is $6236. After one year, the price of land will increase by 3.2%, which is equivalent to multiplying the current price by 1.032. After two years, the price will increase by another 3.2%, which is equivalent to multiplying the price after one year by 1.032, and so on.

Therefore, the function that represents the estimated average price of 1 acre of land in Berrien County after x years can be written as:

[tex]$$P(x) = 6236(1 + 0.032)^x$$[/tex]

where [tex]$P(x)$[/tex] is the estimated average price of 1 acre of land in Berrien County after [tex]$x$[/tex] years.

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Answer:

Mean 3.125

Median 3

Step-by-step explanation:

Answer: x ∈ (10; +∞)

Step-by-step explanation:

Since x isn't the longest side of the triangle, it is one of the shorter ones, so the sum of two shorter sides must be greater than the longest side of the triangle (that's the property):

x + 16 ﹥ 26

x ﹥ 26 - 16

x ﹥ 10 (x ∈ N)

x ∈ (10; +∞)

Let's say, I chose x = 20

Since x can be on either shorter side of the triangle, she can make 2 triangles (I think)

After 10 years, the area of the forest will be approximately 1384 km² (rounded to the nearest square kilometer) assuming the decrease in area is consistent at 4% each year.

The problem provides us with the initial area of the forest which is 2100 km². It also tells us that each year the area of the forest decreases by 4%. We need to find out what will be the area of the forest after 10 years.

The initial area of the forest is 2100 km². After the first year, the area will decrease by 4%, which means it will be 0.96 times the original area:

2100 km² x 0.96 = 2016 km²

After the second year, the area will decrease again by 4%, which means it will be 0.96 times the area from the first year:

2016 km² x 0.96 = 1935.36 km²

Continuing this pattern for 10 years, the area of the forest will be:

2100 km² x [tex](0.96)^10[/tex] = 1364.59 km²

Rounding this to the nearest square kilometer, the area of the forest after 10 years will be approximately 1365 km².

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x = 2, y = 81.

u = g(x) = x^2 – 7x + 9

y = f(u) = u^4.

The inside function and outside function in a composite function can be identified by examining the structure of the function. The inside function is the function that is being acted upon by the outside function. In this case, the inside function is u = g(x) = x^2 – 7x + 9, and the outside function is y = f(u) = u^4.

To find the value of y for a given value of x, we first need to find the value of u by substituting the value of x into the inside function. Then, we can substitute the value of u into the outside function to find the value of y.

For example, if x = 2, then:

u = g(x) = x^2 – 7x + 9 = 2^2 – 7(2) + 9 = -3
y = f(u) = u^4 = (-3)^4 = 81
So, when x = 2, y = 81.

In conclusion, the inside function is u = g(x) = x^2 – 7x + 9, and the outside function is y = f(u) = u^4. To find the value of y for a given value of x, we first need to find the value of u by substituting the value of x into the inside function, and then substitute the value of u into the outside function to find the value of y.

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the 88% confidence interval for the proportion of college professors who wear eyeglasses is (0.487, 0.625).

To generate an 88% confidence interval for the proportion of college professors who wear eyeglasses, we can use the normal approximation to the binomial distribution. The formula for the confidence interval is:

p ± z*√(p(1-p)/n)

where p is the sample proportion, z is the z-score corresponding to the desired level of confidence (88% in this case), and n is the sample size.

First, we need to calculate the sample proportion:

p = 139/250 = 0.556

Next, we need to find the z-score corresponding to the 88% confidence level. We can use a standard normal distribution table or calculator to find this value. For an 88% confidence level, the z-score is approximately 1.553.

Now, we can substitute these values into the formula to calculate the confidence interval:

0.556 ± 1.553*√(0.556(1-0.556)/250)

Simplifying the expression gives us:

0.556 ± 0.069

the 88% confidence interval for the proportion of college professors who wear eyeglasses is (0.487, 0.625).  

This means that we are 88% confident that the true proportion of college professors who wear eyeglasses is between 0.487 and 0.625. In other words, if we were to repeat this study multiple times, we would expect the true proportion to fall within this interval in 88% of the cases.

It is important to note that confidence intervals are a range of plausible values for the population parameter (in this case, the proportion of college professors who wear eyeglasses), and do not provide definitive answers. Therefore, it is necessary to interpret the interval in the context of the study and the research question.

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The equation of the line passing through the points (-2,-4) and (4,4) is y = (4/3)x - 4/3.

To find the equation of the line passing through the points (-2,-4) and (4,4), we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where:

m is the slope of the line

(x1, y1) are the coordinates of one of the points on the line

First, we need to find the slope of the line using the two points:

m = (y2 - y1)/(x2 - x1)

m = (4 - (-4))/(4 - (-2))

m = 8/6

m = 4/3

Now, we can choose either point to plug into the equation. Let's choose (-2,-4):

y - (-4) = (4/3)(x - (-2))

Simplifying the equation:

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

Distributing the 4/3:

y + 4 = (4/3)x + (8/3)

Subtracting 4 from both sides:

y = (4/3)x + (8/3) - 4

Simplifying:

y = (4/3)x - 4/3

Therefore, the equation of the line passing through the points (-2,-4) and (4,4) is y = (4/3)x - 4/3.

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Suppose sin t = 5/7 and cos t < 0. The exact value :
cos t = -√(1 - (5/7²)
tan t =  -(5√6)/12
csc t =7/5
sec t =  -(7√6)/12
cot t =  -12/(5√6)

Since sin t = 5/7 and cos t < 0, we can use the Pythagorean identity cos² t + sin² t = 1 to find cos t:

cos² t + (5/7)²= 1

cos² t = 1 - (5/7)²

cos t = -√(1 - (5/7)²) (since cos t < 0)

Next, we can use the definitions of the trigonometric functions to find the remaining values:

tan t = sin t / cos t = (5/7) / (-√(1 - (5/7)^2)) = -5/√24 = -(5√6)/12

csc t = 1/sin t = 7/5

sec t = 1/cos t = -1/√(1 - (5/7)²) = -7/√24 = -(7√6)/12

cot t = 1/tan t = -12/(5√6)

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Therefore, the correct answer is: "The IQR is the best measure of variability, and it equals 4."

In mathematics, a variable is a symbol or letter that represents a quantity that can vary or change. Variables are used to express mathematical relationships and to represent unknown values.

For example, in the equation "y = 2x + 3", "x" and "y" are variables. "x" represents an unknown value that can vary, while "y" represents the output value that is dependent on the input value of "x".

Variables can take on different values depending on the context of the problem being solved. In algebra, variables are commonly used to solve equations and to represent unknowns in formulas.

It's important to note that variables are not the same as constants, which are values that remain fixed throughout a mathematical expression or equation.

by the question.

The appropriate measure of variability for the data represented by the box plot is the interquartile range (IQR). The IQR is a measure of the spread of the middle 50% of the data, and it is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). In this case, the box extends from 17 to 21, with a line at 19, which means that Q1 is 17 and Q3 is 21. Therefore, the IQR is:

IQR = Q3 - Q1 = 21 - 17 = 4

So, the appropriate measure of variability for the data is the IQR, and its value is 4.

Therefore, the correct answer is: "The IQR is the best measure of variability, and it equals 4."

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John will receive a tax refund from the government because his employer withheld more taxes than he actually owes, resulting in an overpayment. The amount of John's refund is $2,082.13.

In this problem, John's employer withheld $13,956.95 in federal income tax over the course of the year. When John completed his tax return, he determined that his actual tax liability for the year was only $11,874.82. This means that John's employer withheld more than the amount of tax that John actually owes, resulting in an overpayment of taxes.

To determine whether John will receive a refund or owe the government money, we need to compare the total tax withheld to the amount of tax owed. If the total tax withheld is greater than the tax owed, then John will receive a refund. If the tax owed is greater than the total tax withheld, then John will owe the government money.

In this case, John's refund can be calculated as the difference between the total tax withheld and the tax owed:

Refund = Total Tax Withheld - Tax Owed

Refund = $13,956.95 - $11,874.82

Refund = $2,082.13

Since the refund amount is positive, it means that John overpaid his taxes and is entitled to receive a refund from the government.

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[tex] \green{ \underline{ \underline{\mathsf{ {(x - y)}^{2} }}}}[/tex]

We have the values of x and y:

Plug in the values~

[tex] \green{\mathfrak{ {(5 -( - 1))}^{2} }}[/tex]

[tex] \green{\mathfrak{ {(5 + 1)}^{2} }}[/tex]

Use the identity:

[tex] \red{ \mathsf{(x + y)^{2} = {x}^{2} + {y}^{2} + 2xy }}[/tex]

[tex] \green{\mathfrak{ {5}^{2} + {1}^{2} + 2 \times 5 \times 1 }}[/tex]

[tex] \green{\mathfrak{ 25 + 1 + 10 }}[/tex]

[tex] \boxed{\green{\mathfrak{36 }}}[/tex]

Answer:

To subtract vectors, we subtract corresponding components.

Step-by-step explanation:

-w = <-(-5), -3> = <5, -3>

-w-z = <5, -3> - <1, 4> = <5-1, -3-4> = <4, -7>

z-w = <1, 4> - <(-5), -3> = <1+5, 4+3> = <6, 7>

w-z = <-5, 3> - <1, 4> = <-5-1, 3-4> = <-6, -1>

The solution to the differential equation dy/dx = x/y^x, which passes through the point (1,0) is (1/(x+1))y^(x+1) = (1/2)x^2 - 1/2.

To find the solution to the differential equation dy/dx = x/y^x, which passes through the point (1,0), we can use the method of separation of variables. This involves separating the variables x and y on opposite sides of the equation and then integrating both sides.

First, we can rewrite the differential equation as:
y^x dy = x dx

Next, we can integrate both sides of the equation:
∫y^x dy = ∫x dx
(1/(x+1))y^(x+1) = (1/2)x^2 + C

Now, we can use the initial condition (1,0) to solve for the constant C:
(1/(1+1))0^(1+1) = (1/2)(1)^2 + C
0 = 1/2 + C
C = -1/2

Therefore, the solution to the differential equation is:
(1/(x+1))y^(x+1) = (1/2)x^2 - 1/2

This is the solution to the differential equation dy/dx = x/y^x, which passes through the point (1,0).

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Thus,  the ratio of height of the model of the statue of liberty is:  5.08 ft .

In maths, a ratio is the comparison of two like or corresponding values. Both a part-to-part and a part-to-whole comparison are possible.

Consider various types of information when computing a ratio. Analyze the ratio to see if it calls for a part-to-part or part-to-whole ratio.

Ratio does not imply multiplication. Fractions can be used to represent ratios, and the fraction's simplest form is division. Divided means a ratio. The ratio 1 to 3, for example, is 1 divided by 3.

Given data:

Height statue of liberty = 305 feet

Height of model of the statue = 60 inches.

Thus, Ratios of their heights.

Height statue of liberty/ Height of model of the statue = 305 feet / 60 inches.

= 5.08 ft / 1 in

Thus,  the ratio of the height of the given model of the statue of liberty is:  5.08 ft .

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The vendοr shοuld sell the remaining 595 bananas fοr a tοtal price οf 595 x $1.20 = $714.

In mathematics, prοfit is the amοunt by which revenue exceeds the cοst οf gοοds sοld, while lοss is the amοunt by which cοst exceeds revenue.

There are 50 dοzen bananas, which means there are 50 x 12 = 600 bananas in tοtal.

Five bananas gοt rοtten and cοuld nοt be sοld, sο the vendοr has 600 - 5 = 595 bananas tο sell.

The cοst price οf 50 dοzen bananas is $600, which means the cοst price οf οne dοzen bananas is $600/50 = $12.

The cοst price οf οne banana is $12/12 = $1.

Tο get a prοfit οf 20%, the vendοr needs tο sell the bananas at a price that is 20% higher than the cοst price.

The selling price οf οne banana is $1 + ($1 x 20%) = $1.20.

Therefοre, the vendοr shοuld sell the remaining 595 bananas fοr a tοtal price οf 595 x $1.20 = $714.

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Miranda took 28.5 minutes to finish the race according to the give time about the race.

Given,

Ella finished a bike race = 37.6 minutes

Let 'x' be the time taken for finishing the bike race.

Miranda finished the race sooner than Ella = [tex]9 \frac{1}{10}[/tex] = 91/10

Miranda finished the race sooner than Ella = 9.1 min

Now, we need to find the minutes did it take Miranda to finish the race.

From the statement,  9.1 minutes sooner than Ella finished it while Ella finished the same bike race in 37.6 minutes.

So, from the expression

time taken by Miranda to finish the race:

[tex]Miranda[/tex] [tex]finished[/tex] [tex]the race[/tex] = (Ella finished a bike race - 9.1)

x = 37.6 - 9.1

x= 28.5 minutes

Therefore, Miranda finished the bike race in 28.5 minutes.

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Answer:

x1 = √3/3 - 1 or -0.42

x2 = -√3/3 - 1 or -1.58

Step-by-step explanation:

(3x + 3)^2 - 42 = -39

9x^2 + 18x + 9 - 42 + 39 = 0

9x^2 + 18x + 6 = 0

divide both sides by 3:

3x^2 + 6x + 2 = 0

Using quadratic equation

x = [-b ± √(b^2 - 4ac)] / 2a

x = [-6 ± √(6^2 - 4(3)(2))] / 2(3)

x = [-6 ± √(36 - 24)] / 6

x = [-6 ±√12] / 6

x = [-6 ±2√3] / 6

x = [-3 ±√3] / 3

x = -3/3 ± √3/3

x = ± √3/3 - 3/3

x1 = √3/3 - 1 = -0.42

x2 = -√3/3 - 1 = -1.58

Hope this help

Answer:

There is only one solution.  
The solution is -7

Step-by-step explanation:

x - 3 = -10   Add 3 to both sides

x - 3 + 3 = -10 + 3

x = -7

Helping in the name of Jesus.

Answer:

b is the required ans of Qust

(a) The unit tangent and unit normal vectors T(t) and N(t) is ⟨-sin t, 0, -cos t⟩.

(b) The curvature is 3/(9 cos² t + 4 + 9 sin² t)

To find T(t), we first take the derivative of r(t) with respect to t, which gives us the velocity vector v(t) = ⟨3 cos t, 2, -3 sin t⟩. Then, we divide this vector by its magnitude to get the unit tangent vector T(t) = v(t)/||v(t)||, where ||v(t)|| is the magnitude of v(t). This gives us:

T(t) = ⟨(3/√(9 cos² t + 4 + 9 sin² t)), 2/√(9 cos² t + 4 + 9 sin² t), (-3/√(9 cos² t + 4 + 9 sin² t)))⟩

To find N(t), we take the derivative of T(t) with respect to t, and divide by the magnitude of this derivative:

N(t) = T'(t)/||T'(t)||, where T'(t) is the derivative of T(t) with respect to t.

After some algebraic simplification, we find that T'(t) = ⟨-3 sin t, 0, -3 cos t⟩, so

||T'(t)|| = 3, and

N(t) = ⟨-sin t, 0, -cos t⟩.

Now that we have the unit tangent and unit normal vectors, we can move on to finding the curvature, denoted k(t).  Specifically, the curvature is given by the formula:

k(t) = ||T'(t)||/||v(t)||²

where ||T'(t)|| is the magnitude of the derivative of the unit tangent vector, and ||v(t)||² is the square of the magnitude of the velocity vector.

We already found ||T'(t)|| and ||v(t)|| in the previous steps, so we can plug these values into the formula to get:

k(t) = 3/(9 cos² t + 4 + 9 sin² t)

This gives us the curvature for every value of t.

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Complete Question:

Consider the vector function given below. r ( t ) = ⟨ 3 sin t , 2 t , 3 cos t ⟩ Do the following:

(a) Find the unit tangent and unit normal vectors, T(t) and N(t).

(b) Find the curvature, k(t).