Someone plz help me I will give brainliest

To find the length of the curve given by r(t) = cos(7t) i + sin(7t) j + 7 ln(cos(t)) k, 0 ≤ t ≤ π/4, we need to use the formula for arc length:

L = ∫[a,b] √[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 dt

In this case, we have:

dx/dt = -7 sin(7t)
dy/dt = 7 cos(7t)
dz/dt = -7 sin(t) / cos(t)

So,

[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 = 49 sin^2(7t) + 49 cos^2(7t) + 49 sin^2(t) / cos^2(t)
= 49 [sin^2(7t) + cos^2(7t) + sin^2(t) / cos^2(t)]
= 49 [1 + sin^2(t) / cos^2(t)]

Now, using the identity sin^2(t) + cos^2(t) = 1, we can rewrite this as:

[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 = 49 cos^2(t)

Therefore, the length of the curve is:

L = ∫[0,π/4] √[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 dt
= ∫[0,π/4] 7 cos(t) dt
= 7 [sin(t)]|[0,π/4]
= 7 sin(π/4) - 7 sin(0)
= 7 (√2/2)
= 7√2/2

So the length of the curve is 7√2/2.

Learn more about it here:

brainly.com/question/31643763

#SPJ11

The ordered step and their justification are as follows;

Steps \({}\)                                     Justification

1. y + 15 = 9          \({}\)                     1. Given

2. y + 15 - 15 = 9 - 15  \({}\)              2. Subtraction property of equality

3. y = -6  \({}\)                                   3. Simplification

The subtraction property of equality state that if the same amount is subtracted from two equivalent expressions, the new expressions will have the same new values.

The equation in the question is a linear equation and the coefficient of y is 1.

The constants of 15 and 9 are on the left and right side of the equation

To make y the subject, and obtain the solution of the equation, the main or required operation or step is the subtraction of the constant term of 15 from both sides of the equation.

The order of the steps and their justification are as follows;

Steps \({}\)                                     Justification

y + 15 = 9          \({}\)                      Given

y + 15 - 15 = 9 - 15  \({}\)                 Subtraction property of equality

y = -6  \({}\)                                     Simplification

Learn more about the subtraction property of equality here:

https://brainly.com/question/1601404

#SPJ1

Answer:

4(9a-4)

Step-by-step explanation:

36a - 16

We can factor 4 from each expression.

4*9a - 4*4

4(9a-4)

Hola!!

5p² = 20

p² = 20/5

p² = 4

p = √4

p = 2.

El valor de p² es 4 & p es 2.

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

¡Espero que te ayude!

RainbowSalt2222 ☔

Answer:

(-3,-1)

Step-by-step explanation:

Solution of the system means where both lines intersect. Which would be at (-3,-1)

The nearest dollar that Madeline would have in her account when Andres's money has tripled in value is $5,777.

Given that Andres invested $2,400 in an account paying an interest rate of 7 3/8% compounded quarterly and Madeline invested $2,400 in an account paying an interest rate of 7 1/2% compounded continuously.

We need to find the money Madeline would have in her account when Andres's money has tripled in value.

Since we know that the money would triple, this implies that the future value (FV) of Andres's investment after some time would be thrice the principal amount, which is $2,400 * 3 = $7,200.

We can find the time period taken for Andres's investment to triple in value using the formula for the future value of an investment (FV).FV = P(1 + r/n)^(nt),where P = principal amount, r = interest rate, n = number of times compounded per year, t = time in years.

Substituting P = $2,400, r = 7 3/8% = 7.375%, n = 4, FV = $7,200 we get7,200 = 2,400(1 + 0.07375/4)^(4t)

Simplifying this equation gives:(1 + 0.0184375)^4t = 3

Taking the natural logarithm (ln) of both sides, we get: 4t ln (1.0184375) = ln (3)t = ln (3) / (4 ln (1.0184375))t = 9.88 years (approx)

Madeline invested $2,400 in an account paying an interest rate of 7 1/2% compounded continuously.

Therefore, we can calculate the future value of Madeline's investment (FV) after 9.88 years using the formula:

FV = Pe^(rt),where e = exponential function with base e = 2.71828.

Substituting P = $2,400, r = 7.5% = 0.075, t = 9.88, we get:

FV = 2,400 e^(0.075 × 9.88) = $5,777 (rounded to the nearest dollar).

Therefore, the nearest dollar that Madeline would have in her account when Andres's money has tripled in value is $5,777.

For more question on interest rate

https://brainly.com/question/25720319

#SPJ8

You can find the coefficient of variation for your data set using a TI-84 calculator by following the below steps.

To find the coefficient of variation (CV) using a TI-84 calculator, follow these steps:

1. Enter the data set values into a list on your calculator. For example, if your data is stored in the list L1, enter the values into L1.

2. Calculate the mean of the data set using the calculator's statistical functions. Press the [STAT] button and navigate to the "Calc" menu. Choose the appropriate mean function (e.g., "1-Var Stats" or "mean") and select the list that contains your data (e.g., L1).

3. Calculate the standard deviation of the data set using the calculator's statistical functions. Press the [STAT] button, navigate to the "Calc" menu, and choose the appropriate standard deviation function (e.g., "1-Var Stats" or "stdDev"). Select the list containing your data (e.g., L1).

4. Divide the standard deviation by the mean and multiply by 100 to calculate the coefficient of variation. Store the standard deviation and mean values in variables if necessary. Use the formula CV = (stdDev / mean) * 100 to calculate the coefficient of variation.

By following these steps, you can find the coefficient of variation for your data set using a TI-84 calculator.

Learn more about TI-84 calculator here

https://brainly.com/question/32748414

#SPJ4

To find the coefficient of variation on a TI-84 Plus calculator, enter the dataset into a list, calculate the mean and standard deviation, and then divide the standard deviation by the mean and multiply by 100.

To find the coefficient of variation on a TI-84 Plus calculator, follow these steps:

By following these steps, you can find the coefficient of variation for a dataset using a TI-84 Plus calculator.

About coefficient of variation here:

https://brainly.com/question/30783938

#SPJ11

   "

The variance is 7.2, the mean is 16, and the standard deviation is approximately 2.68.

Given that thirty-six of the staff of 80 teachers at a local intermediate school are certified in cardiopulmonary resuscitation (CPR).

We want to find the mean, variance, and standard deviation of the number of days

We can expect that the teacher on bus duty will likely be certified in CPR.

Since there are 180 days of school, the probability of any teacher being on bus duty on any particular day is 1/180.

The expected number of days that the teacher on bus duty is certified in CPR is

E(X) = np = 80 * 36/180 = 16

Mean μ = E(X) = 16

Variance σ^2 = np(1-p)

= 80 * 36/180 (1 - 36/80)

= 7.2

Standard deviation σ = √σ = √7.2 ≈ 2.68

Therefore, we can expect that the teacher on bus duty will likely be certified in CPR for 16 days on average. The variance is 7.2, and the standard deviation is approximately 2.68.

To learn more about the standard deviation here:

https://brainly.com/question/24298037

#SPJ11

answer is in the photo. lmk if you want the solution steps.

The equation of the line is y = 2x + 8 that is parallel to the given line y = 2x + 2 and passes through the point (−3, 2)

An equation is an expression that shows the relationship between two or more numbers and variables.

The equation of a straight line is:

y = mx + b

Where m is the rate of change and b is the y intercept.

Two lines are parallel if they have the same slope.

Let us assume that the line is parallel to y = 2x + 2 and passes through the point (−3, 2).

The slope of the line y = 2x + 2 is 2, Since it is parallel, the slope is also 2. hence:

y - y₁ = m(x - x₁)

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

y - 2 = 2(x + 3)

y = 2x + 8

The equation of the line is y = 2x + 8

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

An equation of the line that is parallel to the given line and passes through the point (−3, 2) is: 4x + 3y = -6.

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

By critically observing the graph (see attachment), we can logically deduce that the line passes through the following points:

Points (x, y) = (3, -1)

Points (x, y) = (0, 3)

Substituting the given parameters into the formula, we have;

Slope, m = (3 + 1)/(0 - 3)

Slope, m = 4/-3

Slope, m = -4/3.

In Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂ ⇒ -4/3 = -4/3

Note: m represents the slope.

At point (-3, 2), an equation of the other line can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

Where:

Substituting the given points into the formula, we have;

y - y₁ = m(x - x₁)

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

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

y - 2 = -4x/3 - 4

y - 2 = -4x/3 - 4 + 2

y = -4x/3 - 2

Multiplying all through by 3, we have:

3y = -4x - 6

Rearranging the equation, we have:

4x + 3y = -6

Read more on slope here: brainly.com/question/3493733

#SPJ1

Answer: 66

Step-by-step explanation:

I did it on khan

Answer:

39.69%

Step-by-step explanation:

Hope this helps!!

The value of X = 25.

Solution:

The two equations are

(i) the first condition is difference of x and y is 14

x - y = 14 ---------equation 1

(ii) the second condition of the given data is value of x is 3 times more than two times of y value.

x - 2y = 3 --------equation 2

From equation 2, we have to separate two variables x and y,

x = 3 + 2y  --------equation 3

We have to Substitute equation 3 in equation 1

3 + 2y - y = 14

3 + y = 14

y = 14 - 3

y = 11

Substitute y = 11 in equation 1........

x - 11 = 14

x = 14 + 11

x = 25

So, the value of x is 25 and y is 11.

To learn more about equations refer to:

https://brainly.com/question/2972832

#SPJ1

Answer:

Step-by-step explanation:

Given the difference of x and y is 14, and the difference of x and 2y is 3, you want two equations, their graph, and the value of x.

The difference of 'a' and 'b' is (a -b). Here, the two differences are expressed as the equations ...

The attachment shows a graph of these equations. Their point of intersection is (25, 11), meaning the value of x is 25.

The graph of the first equation is easily drawn by recognizing the x- and y-intercepts are 14 and -14, respectively.

The graph of the second equation will go through the x-intercept point of (3, 0) and the y-intercept point of (0, -3/2). It is probably easier to graph this by hand by considering the x-intercept point and the slope of 1/2.

Since we're only interested in the value of x, it is convenient to eliminate the variable y. We can to that by subtracting the second equation from twice the first:

  2(x -y) -(x -2y) = 2(14) -(3)

  x = 25 . . . . . . . . . simplify

Answer:21 Inches

Step-by-step explanation:

Answer:

no clue

Step-by-step explanation:

The curve y = 5 ln(x) has maximum curvature at the point  (2.122, 5 ln(2.122)).

explanation; -

step1:-To find the maximum curvature of the curve y = 5 ln(x), we need to find the second derivative of y with respect to x:

y' = 5/x (first derivative)

y'' = -5/x^2 (second derivative)

step2:-The curvature of the curve at a given point is given by the formula:

k = |y''| / (1 + y'^2)^(3/2)

Substituting y'' and y' from above, we get:

k = |(-5/x^2)| / (1 + (5/x)^2)^(3/2)

  = 5 / (x^2 * (1 + (5/x)^2)^(3/2))

step3:- To find the point where the curvature is maximum, we need to find the value of x that maximizes k. We can do this by taking the derivative of k with respect to x, setting it to zero, and solving for x:

dk/dx = (-10/x^3 * (1 + (5/x)^2)^(3/2)) + (15x/((1 + (5/x)^2)^(5/2))) = 0

Simplifying this expression, we get:

-10/x^3 * (1 + (5/x)^2)^(3/2) = -15x/((1 + (5/x)^2)^(5/2))

Multiplying both sides by (1 + (5/x)^2)^(5/2), we get:

-10(1 + (5/x)^2)^(2) = -15x^4

Simplifying further, we get:

5x^4 - 2x^2 - 25 = 0

This is a quadratic equation in x^2, which we can solve using the quadratic formula:

x^2 = (2 ± sqrt(4 + 500)) / 10

= (1 ± sqrt(126)) / 5

Since x^2 must be positive, we can discard the negative solution, and we get:

x^2 = (1 + sqrt(126)) / 5

Taking the square root of both sides, we get:

x ≈ 2.122

Therefore, the point where the curvature is maximum is approximately (2.122, 5 ln(2.122)).

As x approaches infinity, the curvature approaches zero. This is because as x gets larger, the second derivative of y with respect to x (which is negative) gets smaller and smaller, while the first derivative of y with respect to x (which is positive) gets larger and larger. This means that the curve becomes flatter and flatter as x increases, so its curvature approaches zero.

know more about the maximum curvature of any curve click here;

https://brainly.com/question/8570736

#SPJ11

Answer:

a. \(-\frac{576}{365}\)

b. \(\frac{23}{16}\)

Step-by-step explanation:

The image below shows step-by-step using Order of Operations (PEMDAS) to solve both of them.

Hope this helps my friend! :)

Step-by-step explanation:

Domain tells us all the possible x values or inputs of a function.

Here the input is n.

The domain here is defined on the interval [-1,3) so the domain can be notated in 3 ways.

Interval Notation: [-1,3]

Words: All inputs that is between -1 and 3, exclusively.

Sign Notation:

\( - 1 \leqslant x \leqslant 3\)

The Range of a function is possible y values or outputs of a function.

For the range, plug in x values to find the y values.

Since the range in this problem, is only defined for -1 to 3. Plug in -1 for n in the function.

\(2( - 1) - 1 = - 3\)

\(2(3) - 1 = 5\)

So the range of is

[-3,5]

Or could be stated

All outputs between -3 and 5 exclusively

\( - 3 \leqslant x \leqslant 5\)

Here's a graph. Look Above

Answer:

58 weeks

Step-by-step explanation:

Water tank A = 522 - 4x

Water tank B = 696 - 7x

Where,

x = number of weeks

Equate both equations

522 - 4x = 696 - 7x

Collect like terms

522 - 696 = -7x + 4x

-174 = -3x

Divide both sides by - 3

x = -174/-3

x = 58 weeks

The amount of water in the two tanks will be the same in 58

weeks

Answer: (b/2)^2 = \(\frac{289}{4} or 72.25\)

Step-by-step explanation:

x^2 = a

17x = b

-22 = c

To find which number would have been added use the following formula:

\((\frac{b}{2} )^{2}\)

\((\frac{17}{2} )^{2} = \frac{289}{4}\)

If solving this equation the easier way would be to use the quadratic formula instead of completing the square.

Answer:

I don't know

Step-by-step explanation:

Gloria will knit 1 scarf in 3 hours.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

Gloria likes to knit scarves to give as gifts to her friends and family.

She can knit 1 over 4 of a scarf in 3 over 4 of an hour.

Simplifying,

She can knit 1/4 of a scarf in 3/4 of an hour.

To find the time:

1/4 of a scarf in 3/4 of an hour.

Multiply by 4,

4 x 1/4 of a scarf in 4 x 3/4 of an hour.

1 scarf in 3 hours.

Therefore, she will take 3 hours to knit 1 scarf.

To learn more about the multiplication;

https://brainly.com/question/19634536

#SPJ5

For the given matrix [2 7; 2 6]  [x; y] = [8; 6], the value of y  is 2.

Given the matrices in the correct form, we can write the problem as follows:

[2 7; 2 6]  [x; y] = [8; 6]

which translates into the system of equations:

2x + 7y = 8 (equation 1)

2x + 6y = 6 (equation 2)

Let's solve for y.

Subtract the second equation from the first:

(2x + 7y) - (2x + 6y) = 8 - 6

=> y = 2

Find more exercises on matrix;

https://brainly.com/question/28180105

#SPJ1

Answer:

gradient = 2

Step-by-step explanation:

Calculate the gradient (slope) using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (G (4, - 2 ) and (x₂, y₂ ) = H (7, 4 )

m = \(\frac{4-(-2)}{7-4}\) = \(\frac{4+2}{3}\) = \(\frac{6}{3}\) = 2

Answer:

V = 1/10 cm^3

Step-by-step explanation:

The volume of a rectangular prism is given by

V = l*w*h  

where l is length, w is width and h is height

V = 1/4 * 1/2 * 4/5

V = 1/10 cm^3

10%+50%=60%

60% of 6000=3600

a)3600 people had left the match when it ended

b)6000-3600=2400

40% of the crowd was still there

Answer:

the value of the test statistic.

The t-critical value is used to determine whether the results of a statistical test are statistically significant. In order to calculate the t-critical value, the following information is needed: the level of significance (often denoted as alpha or p-value), the degrees of freedom, the sample size, and whether the test is one-tailed or two-tailed. The value of the test statistic is not needed to compute the t-critical value. The t-critical value is based on the level of significance, the degrees of freedom, and the sample size, and it is used to compare the test statistic to determine whether the results are statistically significant.

Ref:

https://brainly.com/question/2656465?referrer=searchResults

#SPJ4

Answer:

\( {3}^{3} \\ {g}^{5 } \\ a \\ {y}^{ - 2} \\ 1\)