i don't get it could you please help me? also please could it be quick because I have soccer practice too

ToTo find the equation of the tangent to the curve at the given point, we first need to find the coordinates of the point and the slope of the tangent. 1. Find the coordinates of the point (x, y) at t = 1: x = e√1 = e^1 = e y = 1 - ln(1^4) = 1 - ln(1) = 1 So the point is (e, 1). 2. Find the derivatives dx/dt and dy/dt: dx/dt = (d/dt) e√t = e√t * (1/2) * t^(-1/2) = (1/2) * e√t * t^(-1/2) dy/dt = 1 - (1/t) 3. Find the slope of the tangent at t = 1: dx/dt (1) = (1/2) * e^1 * 1^(-1/2) = e/2 dy/dt (1) = 1 - (1/1) = 0 4. Calculate the slope dy/dx at the point (e, 1): dy/dx = (dy/dt) / (dx/dt) = 0 / (e/2) = 0 5. Use the point-slope form to find the equation of the tangent: y - y1 = m(x - x1) y - 1 = 0(x - e) So the equation of the tangent is y(x) = 1.




The given curve is x = e√t and y = t - ln t4. To find an equation of the tangent to the curve at the point corresponding to the given value of the parameter t = 1, we will use the formula of the slope of the tangent at the given point.

Most of the times, a tangent is defined as a straight line that touches the curve at only one point. It is at a point on a curve where its gradient is equal to that of the curve itself. The slope of the tangent at a point on the curve is equal to the value of the derivative at that point.

So, let's differentiate y with respect to t to obtain the derivative of y. Then we will substitute t = 1 in the derivative to get the slope of the tangent.dy/dt = 1 - 1/t4Let t = 1,dy/dt = 1 - 1/14 = 13/4So, the slope of the tangent at the point t = 1 is 13/4.Now, to find an equation of the , we need a point on the tangent. The given point on the tangent is (e, y) where y = t - ln t4 and t = 1.

Substituting t = 1 in the equation of y,y = 1 - ln 14Thus, the point on the tangent is (e, 1 - ln 14).Using the point-slope form of the equation of a straight line,y - y1 = m(x - x1)where m is the slope of the tangent and (x1, y1) is the given point on the tangent.

Substituting the values,m = 13/4, x1 = e and y1 = 1 - ln 14,y - (1 - ln 14) = (13/4)(x - e)Expanding the above equation,y - 1 + ln 14 = 13/4 x - 13/4e.

Thus, the equation of the tangent to the curve at the point corresponding to t = 1 is y - 1 + ln 14 = 13/4 x - 13/4e.

Therefore, the correct option is C. y - 1 + ln 14 = 13/4 x - 13/4.

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Width: f(x) = 4x feet, Length: g(x) = 3x feet 1. Let's assume that the width of Emma's garden is represented by the variable x, measured in feet.

2. According to the given information, the length of the garden is three times the width. Therefore, the length can be represented as 3 times x, or 3x.

3. Now, let's consider the fencing panels that are 4 feet long. Emma plans to use x fence panels along the width of her garden.

4. To determine the width of the garden, we need to calculate the total length of the fence used for the width. Since each panel is 4 feet long, we multiply the number of panels (x) by the length of each panel (4 feet). This gives us the equation for the width:

  f(x) = x * 4 = 4x

  Hence, the expression for the width of Emma's garden is 4x feet.

5. Similarly, the length of the garden remains as 3x feet, as determined in step 2:

  g(x) = 3x

  Therefore, the expression for the length of Emma's garden is 3x feet.

In summary, the expressions for the width and length of Emma's garden are:

Width: f(x) = 4x feet

Length: g(x) = 3x feet

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Answer:

A

Step-by-step explanation:

She has 2 more nickels then dimes not 2 times more therefore answers B and D are incorrect. C is incorrect because it has that there are 2 more dimes than nickels. A is correct because it says that there are c dimes, and then c +2 nickels.

Answer:

Step-by-step explanation:

If the function has a factor of x + 9, then the function will have a zero output at x = -9

Lets verify:

Answer:

answer :

\(x > - 9\)

solution:

step 1 :

\(5x - 2x > - 4 - 23\)

step 2 :

\(3x > - 27\)

step 3 :

\(x > \frac{ - 27}{3} \)

final step :

\(x > - 9\)

Answer:

Her hourly rate is $10.7

Step-by-step explanation:

Here, we are interested in calculating Laraine hourly rate.

In the question, we are told that the overtime rate is 1.5 times the regular hours rate.

Now, let the regular hours rate be $x / hour

For a total of 40 hours, the total money made will be 40 * x = $40x

Now let’s look at the overtime;

Since the overtime is 1.5 times the regular and she had 3 overtime hours;

Money obtained from overtime will be 1.5 * x * 3 = $4.5x

Let’s add this to the regular and equate to the total money made;

4.5x + 40x = 476.15

44.5x = 476.15

x = 476.15/44.5

x = 10.7

Answer: It will take approximately 30 months to pay off the $500.00.

Step-by-step explanation:

Since we have given that

Principal = $10.00

Amount = $500.00

Rate of interest = 18.24%

So, we will apply "Compound interest" to find the number of months:

\(A=P(1+\dfrac{r}{100})^n\\\\500=10(1+\dfrac{18.24}{100})^n\\\\500=11.824^n\\\\\n\approx 2.5\)

So, the number of months would be

\(2.5\times 12=30\ months\)

Hence, it will take approximately 30 months to pay off the $500.00.

Answer:

D/ h =q

Step-by-step explanation:

D = qh

Divide each side by h to isolate q

D/ h = dh/h

D/ h =q

Step-by-step explanation: To solve for q in the equation d = qh, all we have to do is get q by itself on the right side of the equation.

Since q is being multiplied by h, to get q by itself,

we simply divide both sides of the equation by h.

On the right, the h's cancel and we are re left with q.

On the left we have \(\frac{d}{h}\).

So our answer is \(\frac{d}{h} = q\).

Answer:

D (1,0)

Step-by-step explanation:

Therefore, the diagonal matrix D is [2.847 0 0; 0 -0.424 0; 0 0 -2.423], the matrix P is [1 -4 -3; 0 1 1; 0 1 1], and the matrix \(P^{(-1)}\) is [(1/9) (-2/9) (-1/3); (-1/9) (1/9) (2/3); (-1/9) (1/9) (1/3)].

To find the matrix D (diagonal matrix) and the matrix P such that A = \(PDP^{(-1)}\), we can use the diagonalization process. Given A = [1 1 4; -8 -1 -1], we need to find D and P such that \(A = PDP^{(-1).\)

First, let's find the eigenvalues of A:

|A - λI| = 0

| [1-λ 1 4 ]

[-8 -1-λ -1] | = 0

Expanding the determinant and solving for λ, we get:

\(λ^3 - λ^2 + 3λ - 3 = 0\)

Using numerical methods, we find that the eigenvalues are approximately λ₁ ≈ 2.847, λ₂ ≈ -0.424, and λ₃ ≈ -2.423.

Next, we need to find the eigenvectors corresponding to each eigenvalue. Let's find the eigenvectors for λ₁, λ₂, and λ₃, respectively:

For λ₁ = 2.847:

(A - λ₁I)v₁ = 0

| [-1.847 1 4 ] | [v₁₁] [0]

| [-8 -3.847 -1] | |v₁₂| = [0]

| [0 0 1.847] | [v₁₃] [0]

Solving this system of equations, we find the eigenvector v₁ = [1, 0, 0].

For λ₂ = -0.424:

(A - λ₂I)v₂ = 0

| [1.424 1 4 ] | [v₂₁] [0]

| [-8 -0.576 -1] | |v₂₂| = [0]

| [0 0 1.424] | [v₂₃] [0]

Solving this system of equations, we find the eigenvector v₂ = [-4, 1, 1].

For λ₃ = -2.423:

(A - λ₃I)v₃ = 0

| [0.423 1 4 ] | [v₃₁] [0]

| [-8 1.423 -1] | |v₃₂| = [0]

| [0 0 0.423] | [v₃₃] [0]

Solving this system of equations, we find the eigenvector v₃ = [-3, 1, 1].

Now, let's form the diagonal matrix D using the eigenvalues:

D = [λ₁ 0 0 ]

[0 λ₂ 0 ]

[0 0 λ₃ ]

D = [2.847 0 0 ]

[0 -0.424 0 ]

[0 0 -2.423]

And the matrix P with the eigenvectors as columns:

P = [1 -4 -3]

[0 1 1]

[0 1 1]

Finally, let's find the inverse of P:

\(P^{(-1)\) = [(1/9) (-2/9) (-1/3)]

[(-1/9) (1/9) (2/3)]

[(-1/9) (1/9) (1/3)]

Therefore, we have:

A = [1 1 4] [2.847 0 0 ] [(1/9) (-2/9) (-1/3)]

[-8 -1 -1] * [0 -0.424 0 ] * [(-1/9) (1/9) (2/3)]

[0 0 -2.423] [(-1/9) (1/9) (1/3)]

A = [(1/9) (2.847/9) (-4/3) ]

[(-8/9) (-0.424/9) (10/3) ]

[(-8/9) (-2.423/9) (4/3) ]

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Answer:

62 degrees is the 3rd angle measure.

Step-by-step explanation:

A triangles angles must add up to 180 degrees.

A right triangle has a right angle which is 90 degrees

It also has a 28 degree angle so ...

90+28=118

180-118=62

or

180-90-28=62

Answer:

B hope that help

Step-by-step explanation:

Answer:

Step-by-step explanation:

The race car is doing 8 laps in 1/3 hour, in one hour the car is doing:

8laps * (1/3) hour) = 8*3 laps / 1hour = 24 laps/hour.

Now, to complete one lap, the car will it take:

1 lap * (1 hour / 24 laps) = 1/24 hours the race car requires to complete 1 lap. Right answer is:

Answer:

D

Step-by-step explanation:

Answer:

Human rights include the right to life and liberty, freedom from slavery and torture, freedom of opinion and expression, the right to work and education, and many more. Everyone is entitled to these rights, without discrimination.

Step-by-step explanation:

these are the 5 basic rights, most of them were taken for george floyd

hope this helped

Danika walks 50 blocks in one week.

Multiplication is a mathematical operation that embodies the fundamental concept of repeated addition of the same integer. The multiplied numbers are known as the factors, and the outcome of the multiplication of two or more numbers is known as the product of those numbers. Multiplication is used to make repetitive adding of the same number easier. It is used for combining groups of identical size.

As per the data given,

We have,

Danika lives at 5 blocks from her school.

As Danika walks 5 blocks to and from school, making her round trip

So, total distance covered by Danika will be: 5 blocks + 5 blocks = 10 blocks.

As Danika walks to and from school 5 days a week,

Hence, she walks 10 blocks * 5 days = 50 blocks in one week.

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Answer:

I think they are.

Step-by-step explanation:

Because they are both 39 and 34 degrees so if x and y are the same number they are similar.

Answer:

hi my name is chelsea and i wiuld like ti thank yiu fir the points

Answer:

180 deg rotation

Step-by-step explanation:

You can't simply translate the original figure into its image. You'd need a reflection or a rotation. For example, if you reflected triangle HTY over the x-axis, and then reflected it over the y-axis, you'd get triangle H'T'Y. The problem does not allow for reflections, so this cannot be used. That means you must use a rotation.

Use the origin as the center of rotation.

Rotate triangle HTY 180 degrees clockwise or counterclockwise.

You end up with the image.

Answer: 180 deg rotation

Answer:

help with what?

Step-by-step explanation:

Answer:

It’s b

Step-by-step explanation

Answer: B

Step-by-step explanation:

Null Hypothesis is the claim that no difference or relationship exists between two sets of data or variables being analyzed.

Type I error: A. Reject the null hypothesis that the percentage of high school students who graduate is equal to 55% when that percentage is actually equal to 55%.

Type II error: D. Fail to reject the null hypothesis that the percentage of high school students who graduate is equal to 55% when the percentage is actually different from 55%.

In statistics, the null hypothesis is a statement that there is no significant difference between two populations or sets of data. It is a hypothesis that is assumed to be true until proven otherwise. The null hypothesis is often denoted as H0 and is used to test the validity of an alternative hypothesis (Ha). The goal of hypothesis testing is to determine whether the evidence supports rejecting the null hypothesis in favor of the alternative hypothesis.

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It is concluded that the null hypothesis H0 is rejected. Therefore, there is enough evidence to claim that some of the population proportions differ from those stated in the null hypothesis, at the α=0.05 significance level.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

H0: P1 = \(9/16,P_2-3/16, P_3-3/16,P_4-1/16\)

Some of the population proportions differ from the values stated in the null hypothesis

This corresponds to a Chi-Square test for Goodness of Fit.

(2) Test Statistics

The Chi-Squared statistic is computed as follows:

\(4.356 + 0 + 11.267 + 0.2 = 15.822\)

(3) Decision about the null hypothesis

Since it is observed that χ2=15.822>χc2​=7.815, it is then concluded that the null hypothesis is rejected.

(4) Conclusion

It is concluded that the null hypothesis H0 is rejected. Therefore, there is enough evidence to claim that some of the population proportions differ from those stated in the null hypothesis, at the α=0.05 significance level.

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Answer:

4.4

Step-by-step explanation:

x / 4 = 11 / 10

x = ( 4 x 11 ) / 10

= 44 / 10

x = 4.4

Answer:

5

Step-by-step explanation:

To measure scale factors, you have to measure how much units apart each triangle is, and apply the same length to x on figure A.

Here is the equation I used:

10-4=6

11-6=5

Both triangles are 6 units in difference.

Answer:

7. The Puerto Rican Parrot's are the limiting factor in this scenario. 8. Yes because the hurricanes are limiting the Parrots population. 9. Other ways species can be limited because of the weather are either any natural disasters.

Step-by-step explanation:

Hope this helped : )

I have no idea what to do in problem 1

but I will do problem 2

A. 2⁵ = 32 (2×2×2×2×2=32)

B. 4³/2 = 32 (4×4×4=64 and then 64÷2=32

the others are not equal to 32

Answer:

100

tvtvtvtcxtexxxtuncd,d,w

Answer:

100

Step-by-step explanation:

because 50 + 50 = 100

Answer: B coordinate (-24, 18.8)

Step-by-step explanation:

If point B lies on the segment AC at the midpoint, find the slope of the linear line.

distance between 2 and -30 is 32 on the x and 24 on the y

24 dived by -30 gives slope = -.8

AB should be 1/8 of AC therefore, 1/8 times 32, and add it to the -30 giving you the x value of B.

32 times 1/8 is 4

4 plus -30 is -24 giving the x value for b

using the slope of -.8 multiplied by 4 to get -3.2

22 plus -3.2 gives you 18.8

B's coordinates of (-24, 18.8)

The ordered pairs for t = 0.2, 1.2, and 2.2 are (27, 9.62), (162, 25.86), and (297, 11.06), respectively.

The baseball does travel over the fence.

The rectangular equation representing the plane curve is y = 3.3 + (38/135)x - (16/135²)x².

We have,

Part A:

To find the ordered pairs (x, y) when t = 0.2, 1.2, and 2.2, we substitute the respective values of t into the given parametric equations.

For t = 0.2:

x = 135 x 0.2 = 27

y = 3.3 + 38 x 0.2 - 16 x (0.2)² = 3.3 + 7.6 - 1.28 = 9.62

So the ordered pair is (27, 9.62).

For t = 1.2:

x = 135 x 1.2 = 162

y = 3.3 + 38 x 1.2 - 16 x (1.2)² = 3.3 + 45.6 - 23.04 = 25.86

So the ordered pair is (162, 25.86).

For t = 2.2:

x = 135 x 2.2 = 297

y = 3.3 + 38 x 2.2 - 16 x (2.2)² = 3.3 + 83.6 - 75.84 = 11.06

So the ordered pair is (297, 11.06).

Part B:

The fence is 10 feet tall and located 320 feet away from the home plate. We need to determine if the baseball's y-coordinate when x = 320 is greater than 10, which would indicate that the ball clears the fence.

For x = 320:

x = 135t

320 = 135t

t ≈ 2.37

Now, substitute t ≈ 2.37 into the equation y = 3.3 + 38t - 16t² to find the y-coordinate at x = 320:

y = 3.3 + 38 x 2.37 - 16 x (2.37)² ≈ 53.83

The y-coordinate when x = 320 is approximately 53.83.

Since 53.83 is greater than 10 (the height of the fence), the baseball does travel over the fence.

Part C:

To write a rectangular equation to represent the plane curve, we eliminate the parameter t from the given parametric equations.

From x = 135t, we can solve for t: t = x / 135

Substitute this value of t into the equation y = 3.3 + 38t - 16t²:

y = 3.3 + 38(x / 135) - 16(x / 135)²

y = 3.3 + (38/135)x - (16/135²)x²

Thus,

The ordered pairs for t = 0.2, 1.2, and 2.2 are (27, 9.62), (162, 25.86), and (297, 11.06), respectively.

The baseball does travel over the fence.

The rectangular equation representing the plane curve is

y = 3.3 + (38/135)x - (16/135²) x².

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The nurse should run the pump at 111.1 ml/hr.

To infuse a 1000ml bag of lactated ringers over 9 hours, the nurse must determine the hourly rate at which the fluid should be infused. This can be done by dividing the total volume of the fluid (1000 ml) by the number of hours it will take to infuse it (9 hours).

So, the hourly rate would be:

1000 ml ÷ 9 hours = 111.1 ml/hr.

Therefore, the nurse should run the pump at 111.1 ml/hr in order to infuse the 1000ml bag of lactated ringers over 9 hours.

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