Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = 10 cos(t), y = 10 sin(t), z = 2 cos(2t), 5 3 , 5, 1

The functions in ascending orders are:

1. 3x

2. 3x + 8

3. x^2

4. x^2 + 6

5. 4^x

6. 4^x + 3

A function is known to be that relation that is said to exist between a set of numbers that is known to be having one output each.

Note that in the above such as 3x, 3x + 8, the  functions in ascending orders as it start with the function that has it least value.

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Answer:

54z+88

Step-by-step explanation:

To find the perimeter, add up the length of the sides

P = 27z+ 20+ 9z+ 24+ 12z+ 30+ 6z+ 14

Combine like terms

P = 27z+9z+12z+6z+20+24+30+14

P =54z+88

The mean length of this type of telephone conversation is E(X) = 7/5.

This means that on average, these conversations last 7/5 units of time. Additionally, the variance of X is Var(X) = 49/25, which indicates the amount of variation in the lengths of these conversations. The standard deviation, σ, is equal to 7/5, which is a measure of how spread out the data is.

Furthermore, if we add 5 to each conversation length, square the result, and take the expected value, we get E((X+5)2) = 949/25.

This calculation gives us an idea of the expected value of the squared deviations of the conversation lengths from their mean value, after adding 5 to each length.

This value can be used to assess the variability of the data and its potential impact on the outcomes of interest. Overall, these statistical measures provide useful information about the distribution of conversation lengths, and can inform decision-making in various contexts.

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Answer:

300

Step-by-step explanation:

2252÷7≈2250÷7

            ≈300

The solution to the differential equation D²y(t) + 12 Dy(t) + 36y(t) = 2 \(e^{(-5t)}\), with initial conditions y(0) = 1 and Dy(0) = 0, is \(y(t) = (1 + 6t) e^{(-6t)}\).

To solve the given differential equation using the classical method, we can assume a solution of the form \(y(t) = e^{(rt)}\) and find the values of r that satisfy the equation. We then use these values of r to construct the general solution.

Using the classical method:

Substitute the assumed solution \(y(t) = e^{(rt)}\) into the differential equation:

D²y(t) + 12 Dy(t) + 36y(t) = \(2 e^{(-5t)}\)

This gives the characteristic equation r² + 12r + 36 = 0.

Solve the characteristic equation for r by factoring or using the quadratic formula:

r² + 12r + 36 = (r + 6)(r + 6)

= 0

The repeated root is r = -6.

Since we have a repeated root, the general solution is y(t) = (c₁ + c₂t) \(e^{(-6t)}\)

Taking the first derivative, we get Dy(t) = c₂ \(e^{(-6t)}\)- 6(c₁ + c₂t) e^(-6t).\(e^{(-6t)}\)

Using the initial conditions y(0) = 1 and Dy(0) = 0, we can solve for c₁ and c₂:

y(0) = c₁ = 1

Dy(0) = c₂ - 6c₁ = 0

c₂ - 6(1) = 0

c₂ = 6

The particular solution is y(t) = (1 + 6t) e^(-6t).

Using the Laplace transform method:

Take the Laplace transform of both sides of the differential equation:

L{D²y(t)} + 12L{Dy(t)} + 36L{y(t)} = 2L{e^(-5t)}

s²Y(s) - sy(0) - Dy(0) + 12sY(s) - y(0) + 36Y(s) = 2/(s + 5)

Substitute the initial conditions y(0) = 1 and Dy(0) = 0:

s²Y(s) - s - 0 + 12sY(s) - 1 + 36Y(s) = 2/(s + 5)

Rearrange the equation and solve for Y(s):

(s² + 12s + 36)Y(s) = s + 1 + 2/(s + 5)

Y(s) = (s + 1 + 2/(s + 5))/(s² + 12s + 36)

Perform partial fraction decomposition on Y(s) and find the inverse Laplace transform to obtain y(t):

\(y(t) = L^{(-1)}{Y(s)}\)

Simplifying further, the solution is:

\(y(t) = (1 + 6t) e^{(-6t)\)

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Answer:

First on is 0.75

Second is 22/52 (not sure about this one though)

Step-by-step explanation:

For the first one:

P(aUb) = p(a) + p(b) - p(a^b)

0.6 = 0.4 + 0.5 - p(a^b)

p(a^b) = 0.3

P(a/b)= p(a^b)/p(a)

P(a/b)= 0.3/0.4

P(a/b)= 0.75

For the second one:

Total of the cards are 52

Diamonds are 13 out of that 52

Face cards are 12 out of that 52

Diamond OR face cards means p(aUb)

And that equals p(a)+p(b)-p(a^b)

p(a^b) means the intersection between the two, there are three common cards between diamonds and face cards, so p(a^b)=3

13/52 + 12/52 - 3/52= 22/52

Answer:

\(y<-\dfrac{1}{4} x+1\\OR\\ 4y<-x+4\)

Step-by-step explanation:

First of all, let us try to find out the equation.

We can easily observe from the graph the values of x and y intercept.

x intercept is the value where y coordinate is 0.

We can see that y is 0 at x  = 4

So, x intercept (4, 0)

y intercept is the value where x coordinate is 0.

We can see that y is 1 at x  = 0

So, x intercept (0, 1)

Now, we have 2 points for the equation of line.

Slope intercept form:

\(y=mx+c\)

Slope of a line:

\(m=\dfrac{y_2-y_1}{x_2-x_1}\)

\(x_1 = 0\\x_2 = 4\\y_1 = 1\\y_2 = 0\)

\(m=\dfrac{0-1}{4-0}\\\Rightarrow m =-\dfrac{1}{4 }\)

\(y=-\dfrac{1}{4} x+c\)

Putting the point (0, 1):

\(1=-\dfrac{1}{4} \times 0+c\\\Rightarrow c = 0\)

So, the equation becomes:

\(y=-\dfrac{1}{4} x+1\)

Let us try to put a point (0, 0) in the equation.

LHS becomes 0.

RHS becomes 1.

LHS < RHS (Only less than sign used because the line is dashed not solid)

So, the inequality is:

\(y<-\dfrac{1}{4} x+1\\OR\\ 4y<-x+4\)

Answer:

\(\frac{5}{3}\)

Step-by-step explanation:

Scale factor: \(\frac{5}{3}\)

Answer:

yo no se pero ahorita yo te ayudo

Answer:

\(\boldsymbol{2.5}\)

Step-by-step explanation:

Hi student! Let me help you out on this question.

____________

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

 When rounding numbers, it's important that you remember these two rules:

  \(\boldsymbol{3.51=== > 3.5}\) (Rounded to 1 D.P.)

     2. If the digit you are asked to round is followed by a digit

          greater than or equal to 5, you round up. An example is given

             below.

\(\boldsymbol{6.25=== > 6.3}\)

\(\boldsymbol{2.16=== > 2.2}\)

                                     ↪

Now that we know these two rules, let's round the given number.

\(\boldsymbol{2.51=== > ?}\)

The digit we are asked to round to (5) is followed by a number less than 5.

\(\sf{\therefore,\:we\:round\:down.}\)

Thus,

\(\boldsymbol{2.51=== > \not? \:2.5}\). Which is our answer.

Hope that this helped you out! Have a nice day ahead.

Best Wishes!

◈◈-Greetings!-◆◆

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

___________________

the answer is 240

because 4% of 2000 is 80 so you just times 80 by 3 then you get 240

Answer:

144/200 can be simplified to 72/100, which is equal to 0.72 or 72%

225/100 is equal to 2.25 or 225%

42/50 can be changed into 84/100 which would then be .84 or 84%

Step-by-step explanation:

If you give something a denominater of 100 then to find the decimal you just move the decimal place over 2 spots to the left, and it is just the numerator for the percent

The correct option is B) Not valid. Consider the statement “Since some shoes are sneakers, some non-sneakers are non-shoes.”

We know that all sneakers are shoes, but all shoes are not sneakers.  Hence, some shoes are sneakers. But, this statement does not imply that “some non-sneakers are non-shoes.” This inference cannot be drawn by contraposition. So, it is not valid.Inferences cannot be drawn in contraposition all the time. Contraposition is a type of logical statement that involves reversing and negating the terms of an original proposition. It is a logical relationship between a proposition and its converse. If a proposition is true, the contrapositive is always true.An example of contraposition can be shown as follows:“If a person is a human, then they are mortal.”We can write the contrapositive of this statement as:“If a person is not mortal, then they are not human.”

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Using visual interpretation of the plot trend, the scatter plot shows positive correlation.

A positive correlation is depicted by a positive slope or trend line on a scatter plot. The trend of the scatter plot slopes upward which establishes a positive association.

If the slope is otherwise negative, such that the trend line slopes downward, then we have a negative association or relationship.

Therefore, the scatter plot shows positive relationship.

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Answer:

By Day 10

Step-by-step explanation:

Day 1:     12 + 8 = 20

Day 2:    12 + 8 + 20 = 40

Day 3:    12 + 8 + 40 = 60

Day 4:    12 + 8 + 60 = 80

Day 5:    12 + 8 + 80 = 100

Day 6:    12 + 8 + 100 = 120

Day 7:    12 + 8 + 120 = 140

Day 8:    12 + 8 + 140 = 160

Day 9:    12 + 8 + 160 = 180

Day 10:   12 + 8 + 180 = 200

So they were 195 kilometers away before the 10th day ended.

Answer:

True

Step-by-step explanation:

This is the case when the result is True. The substituted variables in the argument must equal a conclusion that is also True. For example, if the premises are True, then the conclusion of the valid argument form needs to output a True conclusion as well. This makes the argument valid. Otherwise, the argument would be invalid if two True premises output a conclusion that is equal to False.

The probability is 0.4647.

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Answer:

The y intercept is 4

Step-by-step explanation:

Given:

-Given point: (-5,-6)

-Slope of 2

1) Put the equation into point-slope form y - y1 = m(x - x1)

With the given, we can plug it all in using this formula!

-y1 = -6

-x1 = -5

m = 2

(you would change these negative numbers into positives because the equation shows them being subtracted! remember that two negatives make one positive!)

y+6= 2(x+5)

2) Simplify

y+6= 2(x+5)

y+6=2x+10

y=2x+4

With y=2x+4, set x to 0 because the y intercept is where x is equal to 0 and you get 4!

Answer:

15+x=23

Step-by-step explanation:

Answer:

63 cents

Step-by-step explanation:

Suppose that 13 inches of wire costs 39 cents. At the same rate, how many inches of wire can be bought for 21 cents?​

0.39/13 = 0.03in

o.03 X 21 = 0.63

so 63 cents  check

63/21 should equal 39/13

63/21 = 39/13

63 X 13  = 39 X21

21 X 3 X 13 = 3 X 13 X 21

yes

21 X 3 X 13 = 21 X 3 X 13

Step-by-step explanation:

so sorry

don't know but please mark me as brainliest please

Answer:

\(\frac{20}{23}\)

Step-by-step explanation:

10/23+10/23=20/23

The probability with replacement is 0.6.

We have given that Susan has a jar of jellybeans. She has 10 yellow, 5 green, 3 red, and 2 black jellybeans.

We have to find the probability that she will get a yellow jellybean on her first grab, replace it, and then grab a black jellybean on her second

grab

\(P=\frac{number of favorable outcome }{total number of outcomes}\)

Total number of jellybeans are

10 yellow+5 green +3 red+2 black=20 jellybeans

For yellow jellybeans

The number of ways =10/20

Replace it into the grab therefore again the total number of are jellybeans are 20

So,we have to find the probability for black jellybeans

There are 2 black out of 20 we have to find to getting black therefore the probability is 2/10.

Therefore  probability for yellow and black jellybeans is,

10/20+2/20=12/20=6/10=3/5=0.6

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Answer:

5

Step-by-step explanation:

The function f is continuous on the interval (-∞, ∞) if c = 2. This is because this value of c ensures that the limits of f as x approaches 2 and as x approaches -0 from the left are equal to the function values at those points.

To determine the value of the constant c that makes the function f continuous on the interval (-∞, ∞), we need to consider the limit of f as x approaches 2 and as x approaches -0 from the left.

First, let's consider the limit of f as x approaches 2 from the left. This means that y is approaching 2 from values less than 2. In this case, the function takes the form cy + 7, and we need to ensure that this expression approaches the same value as f(2), which is 2-c. Therefore, we need to solve for c such that:

lim y→2- (cy + 7) = 2 - c

Using the limit laws, we can simplify this expression:

lim y→2- cy + lim y→2- 7 = 2 - c

Since lim y→2- cy = 2-c, we can substitute this into the equation:

2-c + lim y→2- 7 = 2 - c

lim y→2- 7 = 0

Therefore, we need to choose c such that:

2 - c = 0

c = 2

Next, let's consider the limit of f as x approaches -0 from the left. This means that y is approaching -0 from values greater than -0. In this case, the function takes the form 2 - c, and we need to ensure that this expression approaches the same value as f(-0), which is 2 - c. Since the limit of f(x) as x approaches -0 from the left is equal to f(-0), the function is already continuous at this point, and we do not need to consider any additional values of c.

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(a) tangent line to the graph of f(x) = x^3 at the point (4,2).

(b) equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12).

(a) To find the equation of the tangent line to the graph of f(x) = x^3 at the point (4,2), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of f(x) with respect to x and evaluating it at x = 4. The derivative of f(x) = x^3 is f'(x) = 3x^2. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line.

(b) Similarly, to find the equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12), we differentiate f(x) to find the derivative f'(x). The derivative of f(x) = x^2 - x is f'(x) = 2x - 1. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Using the point-slope form, we can write the equation of the tangent line.

In both cases, the equations of the tangent lines will be in the form y = mx + b, where m is the slope and b is the y-intercept.

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