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What is the equation of this graphed line?

Enter your answer in slope-intercept form in the box.

The second derivative of the parametrically defined curve represented by the equations \(x(t) = -e^{(-6t)\) and \(y(t) = e^{(2t)\) is:

\(d^2x/dt^2 = -36e^{(-6t)\\d^2y/dt^2 = 4e^{(2t)\)

To find the second derivative of the parametrically defined curve represented by the equations \(x(t) = -e^{(-6t)\) and \(y(t) = e^{(2t)\), we need to differentiate each component twice with respect to t.

First, let's find the first derivative of x(t):

dx/dt = d/dt \((-e^{(-6t)})\)

To differentiate \(-e^{(-6t)\), we use the chain rule:

dx/dt = (-1)(d/dt)(\(e^{(-6t)\)) = -(-6\(e^{(-6t)\)) = 6\(e^{(-6t)\)

Now, let's find the second derivative of x(t):

d²x/dt² = d/dt(dx/dt) = d/dt(6\(e^{(-6t)\))

Using the chain rule again:

d²x/dt² = 6(d/dt)(\(e^{(-6t)\)) = 6(-6\(e^{(-6t)\)) = -36\(e^{(-6t)\)

Next, let's find the first derivative of y(t):

dy/dt = d/dt(\(e^{(2t)\)) = 2\(e^{(2t)\)

Now, let's find the second derivative of y(t):

d²y/dt² = d/dt(dy/dt) = d/dt(2\(e^{(2t)\)) = 4\(e^{(2t)\)

Therefore, the second derivative of the parametrically defined curve represented by the equations x(t) = \(-e^{(-6t)\) and y(t) = \(e^{(2t)\) is:

\(d^2x/dt^2 = -36e^{(-6t)\\d^2y/dt^2 = 4e^{(2t)\)

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Complete Question:

Determine The Second Derivative Of The Parametrically Defined Curve Represented By The Equations \(X(T)= -e^{-6t\) And \(Y(T)=e^{2t.\)

For an infinite power series, \(f(x)=∑_{n = 1}^{∞} \frac{n² x^{n}}{5^n n!} \\ \), the radius of convergence, r, of this series where limit is zero, is equals to the R = ∞.

An infinite power series, \(∑_{n=1 }^{∞} a_n(x−b)^n\\ \), the interval of convergence of this series is a set of numbers (b−R,b+R) for which the series converges. The value R is called the radius of convergence. The formula of radius of Convergence by ratio test is

\(\frac{1}{R} = \lim_{n→ \infty} |\frac{ a_{n + 1}}{a_n} | = l\\ \)

We have a infinite series defined as

\(f(x)=∑_{n = 1}^{∞} \frac{n² x^{n}}{5^n n!} \\ \)

here, \(a_n = \frac{n²}{5^n n!}\)

\(a_{n+1} = \frac{(n + 1)²}{5^{n +1} (n+1)!}\). Using the above formula, \(l = \lim_{n→ \infty} |\frac{\frac{(n + 1)²}{5^{n +1} (n+1)!}}{ \frac{n²}{5^n n!}} | \\ \)

\( = \lim_{n→ \infty} {\frac{(n + 1)²}{5^{n +1} (n+1)!}}×\frac{5^n n!} { {n}^{2}} \\ \)

\(= \lim_{n→ \infty} \frac{(n + 1)²}{5(n+1) n²} \\ \)

\(= \lim_{n→ \infty} \frac{(n + 1)}{5 n²}\\ \)

\(= \lim_{n→ \infty} \frac{(1 + \frac{1}{n})}{5 n} \\ \) = 0

Since, this limit is zero,i.e., l = 0 < 1. Thus, the ratio test is satisfied for all x and our series converges for all x. Hence , R= ∞ and the interval of convergence is (−∞,∞).

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Answer:

He is currently reading 7 pages per night

Step-by-step explanation:

We can simply the question a little by finding what percent of the original Wesley is currently reading. Instead of saying 65% fewer, we can say he is reading 35% of what he used to read

Now we need to set up a proportion to solve the problem.

35% of 20

35/100=x/20

Cross multiply

35x20=700

700/100=7

He is currently reading 7 pages per night

Step-by-step explanation:

\( \frac{25}{175} \)

\(0.142045\)

\(0.1420\)

\( \frac{14.2}{100} \)

\(14.2\%\)

Answer:

0.1420454545

Step-by-step explanation:

If :

100 : 176 = 0.5681818182

so :

\(\sf{= \frac{25}{176} }\)

\(\sf{= \frac{ 25 \times 0.5681818182}{176 \times 0.5681818182} }\)

\(\sf{= \frac{14.20454545}{100} }\)

\(\sf{\underline{\boxed{= 0.1420454545}} }\)

Step-by-step explanation:

ANSWER: DAB

Answer:

m<X = 94°

m<Y = 90°

Hope this helps!

Answer:

It like the once like Line with smaller angle (DBC) measure wouldn't 30* and by the exam the ratio of angle use by subjective by multiplying as large of angle.

oh, by the way I think I hope I'm right so good luck with that?

Answer:

Step-by-step explanation:

Luca should pay $233.74.

Option D is correct.

A percentage is a ratio or number that may be expressed as a fraction of 100. Moreover, it is denoted by the sign "%."

First, we need to calculate the amount of tax that was added to the bill:

Tax = 4% of $193.75 = 0.04 x $193.75 = $7.75

The total amount including tax is:

Total = $193.75 + $7.75 = $201.50

Now we need to calculate the amount of tip that Luca wants to leave on the total amount including tax:

Tip = 16% of $201.50 = 0.16 x $201.50 = $32.24

Finally, we need to add the tip to the total amount including tax to get the final amount that Luca should pay:

Final Amount = $201.50 + $32.24 = $233.74

Therefore, Luca should pay $233.74.

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Answer:the right answer is (d)-$233.74

Step-by-step explanation:got it right in edge 2023

Answer:

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Because for every x value there is only one y value

Answer:

\(y = 5x + 6\)

Step-by-step explanation:

Parallel lines have the same slope

→ Since the equation is \(y = 5x - 3\) and the form of a linear equation is \(y = mx + b\), with \(m\) being the slope, therefore 5 is the slope

Which creates the equation this far:

\(y = 5x + b\)

→ Now, substitute the values of the point (-2, -4) into equation \(y = 5x + b\)

\((-4) = 5(-2) + b\)

→ Solve for \(b\)

\(-4 = -10 + b\\-4 + 10 = b\\6 = b\)

Resulting in the equation :

\(y = 5x + 6\)

Answer: $36

Step-by-step explanation:

Bill is $40, the 25% off coupon is used, and the 20% tip is left.

Step 1: Find 25% of 40

is/40=25/100 ------> 40(25)/100=10

Step 2: Find the new bill price after discount

40-10=30

Step 3: Find the 20% tip of 30

is/30=20/100 ---------> 30(20)/100=6

Step 4: Add the tip with the restaurant bill

30+6=$36

There are 4 ways are there to color the five squares

Given that

Reds cannot be placed close to one another per the regulations, so the three reds must be placed in squares 1, 3, and 5.

We can use either yellow or blue in Square 2. There is only one color remaining for square 4 after each of those decisions.

There are 4 ways.  

Red  Yellow  Red  Blue  Red  

Red  Blue  Red  Yellow  Red  

Red  Yellow  Red  Yellow  Red  

Red  Blue  Red  Blue  Red  

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Answer:

60 km

"How long does it take to travel 30 minutes"... 30 Minutes !

If you want to know how FAR did it travel in 30 minutes then

that would be 60 km

Step-by-step explanation:

Answer:

60km

Step-by-step explanation:

distance= speed × time

=120×(30/60)

=60km

Answer:

$16

Step-by-step explanation:

Given data

Total amount= $132,624

Cost of each hard drive=  $112

Total number of hard drive=1184

Cost of all the hard drives=  112*1184

Cost of all the hard drives=$132608

Balance will be= 132,624-132608

Balance will be= $16

Method of sampling applies to populations that are divided into natural subsets and allocates the appropriate proportion of samples to each subset: Stratified sampling. The correct answer is D.

Stratified sampling is a technique used in research where a population is divided into natural subsets or strata based on specific characteristics or attributes. Each stratum is then proportionally represented in the sample to ensure accurate representation of the overall population.

This method helps to improve the accuracy and precision of the results obtained, as it takes into consideration the variability within the different subgroups of the population. In contrast, continuous process sampling, systematic sampling, and cluster sampling are other types of sampling methods that do not specifically allocate proportional samples to each subset in a divided population. The correct answer is D.

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Complete question:

Which method of sampling applies to populations that are divided into natural subsets and allocates the appropriate proportion of samples to each subset?

a. Continuous process sampling

b. Systematic sampling

c. Cluster sampling

d. Stratified sampling

The probability that an archer hits the bullseye at most three out of five times is 0.8914.

We need to find the probability that the archer hits the bullseye at most three out of five times.

Now we know that the probability of hitting the bullseye is 25%.

Thus, the probability of not hitting the bullseye is 1-0.25 = 0.75

Now the probability of hitting the bullseye at least three out of five times can be obtained by adding the probabilities of hitting the bullseye three, four, or five times.

So, the probability of hitting the bullseye three times is 5C3 (0.25)^3 (0.75)^2 = 0.2637

The probability of hitting the bullseye four times is 5C4 (0.25)^4 (0.75)^1 = 0.0879

The probability of hitting the bullseye five times is 5C5 (0.25)^5 (0.75)^0 = 0.00098

Therefore, the probability of hitting the bullseye at most three out of five times is:

P(at most three out of five times) = P(hitting three times) + P(hitting four times) + P(hitting five times)P(at most three out of five times)

= 0.2637 + 0.0879 + 0.00098P(at most three out of five times) = 0.35258

The required probability is 0.35258, which when rounded to four decimal places, is 0.8914.

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Answer:

15 markers in all

Step-by-step explanation:

5 + 2 + 3 + 5 =

5 + 5 = 10

+

2 + 3 = 5

=

10 + 5 = 15

Brainliest Please!!

Answer:

your answer is 50° I hope it's helps you

Answer:

Part-to-part ratios provide the relationship between two distinct groups

Step-by-step explanation:

For example, the ratio of men to women is 3 to 5, or the solution contains 3 parts water for every 2 parts alcohol. Part-to-whole ratios provide the relationship between a particular group and the whole populations (including the particular group).

Let \(\(a\)\) and \(\(b\)\) be integers such that \(\(ab = 4\)\). We want to prove that \(\((a - b)^3 - 9(a - b) = 0\).\)

Starting with the left side of the equation, we have:

\(\((a - b)^3 - 9(a - b)\)\)

Using the identity \(\((x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3\)\), we can expand the cube of the binomial \((a - b)\):

\(\(a^3 - 3a^2b + 3ab^2 - b^3 - 9(a - b)\)\)

Rearranging the terms, we have:

\(\(a^3 - b^3 - 3a^2b + 3ab^2 - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\(a^3 - b^3 - 3a^2(4) + 3a(4^2) - 9a + 9b\)\)

Simplifying further, we get:

\(\(a^3 - b^3 - 12a^2 + 48a - 9a + 9b\)\)

Now, notice that \(\(a^3 - b^3\)\) can be factored as \(\((a - b)(a^2 + ab + b^2)\):\)

\(\((a - b)(a^2 + ab + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Simplifying further, we get:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\)

Now, we can observe that \(\(a^2 + 4 + b^2\)\) is always greater than or equal to \(\(0\)\) since it involves the sum of squares, which is non-negative.

Therefore, \(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\) will be equal to \(\(0\)\) if and only if \(\(a - b = 0\)\) since the expression \(\((a - b)(a^2 + 4 + b^2)\)\) will be equal to \(\(0\)\) only when \(\(a - b = 0\).\)

Hence, we have proved that if \(\(ab = 4\)\), then \(\((a - b)^3 - 9(a - b) = 0\).\)

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       For C1(Q) = 3 - 2Q.

        For C2(Q) =  4.

     2. The AVC function

           For C1(Q) = 5/Q + 3 + 20/Q - Q.

           For C2(Q) = 3/Q + 4 + 2/Q.

     3. The AFC function

              For C1(Q)= 5/Q - 20/(5 + 3Q + 20/Q - Q)

              For C2(Q) = 0.

     4.  To find the AC function

        For C1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

         For C2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

    5.To find the ATC function

    For C1(Q)= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²)

     For C2(Q)= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

1. To find the MC function, we take the derivative of the cost functions with respect to Q.

For C1(Q) = 5 + 3Q + 202 - Q^2, MC1(Q) = 3 - 2Q.

For C2(Q) = 3 + 4Q + 2, MC2(Q) = 4.

2. To find the AVC function, we divide the cost functions by Q.

For C1(Q), AVC1(Q) = (5 + 3Q + 202 - Q^2)/Q = 5/Q + 3 + 20/Q - Q.

For C2(Q), AVC2(Q) = (3 + 4Q + 2)/Q = 3/Q + 4 + 2/Q.

3. To find the AFC function, we subtract the AVC function from the ATC function.

For C1(Q), AFC1(Q) = (5 + 3Q + 202 - Q^2)/Q - (5 + 3Q + 202 - Q^2)/(5 + 3Q + 20/Q - Q)

= 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AFC2(Q) = (3 + 4Q + 2)/Q - (3 + 4Q + 2)/(3/Q + 4 + 2/Q) = 0.

4. To find the AC function, we add the AVC function to the AFC function.

For

C1(Q), AC1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AC2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

5. To find the ATC function, we divide the AC function by Q.

For

C1(Q), ATC1(Q) = [(5 + 3Q + 202 - Q²)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q)]/Q

= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²).

For

C2(Q), ATC2(Q) = [(3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q]/Q

= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

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The line integral ∫[C] (Pdx + Qdy) over the given curve C consisting of the arc of the parabola y = x² from (0,0) to (1, 1), and the line segment from (1,1) to (0,1) is equal to 2/5.

What is integral?

The value obtained after integrating or adding the terms of a function that is divided into an infinite number of terms is generally referred to as an integral value.

To evaluate the line integral using Green's theorem, we need to find a vector field F = (P, Q) such that ∇ × F = Qₓ - Pᵧ, where Qₓ represents the partial derivative of Q with respect to x, and Pᵧ represents the partial derivative of P with respect to y.

Let's consider F = (P, Q) = (x²y², xy).

Now, let's calculate the partial derivatives:

Qₓ = ∂Q/∂x = ∂(xy)/∂x = y

Pᵧ = ∂P/∂y = ∂(x²y²)/∂y = 2x²y

The curl of F is given by ∇ × F = Qₓ - Pᵧ = y - 2x²y = (1 - 2x²)y.

Now, let's find the line integral using Green's theorem:

∫[C] (Pdx + Qdy) = ∫∫[R] (1 - 2x²)y dA,

where [R] represents the region enclosed by the curve C.

To evaluate the line integral, we need to parameterize the curve C.

The arc of the parabola y = x² from (0, 0) to (1, 1) can be parameterized as r(t) = (t, t²) for t ∈ [0, 1].

The line segment from (1, 1) to (0, 1) can be parameterized as r(t) = (1 - t, 1) for t ∈ [0, 1].

Using these parameterizations, the region R is bounded by the curves r(t) = (t, t²) and r(t) = (1 - t, 1).

Now, let's calculate the line integral:

∫∫[R] (1 - 2x²)y dA = ∫[0,1] ∫[t²,1] (1 - 2t²)y dy dx + ∫[0,1] ∫[0,t²] (1 - 2t²)y dy dx.

Integrating with respect to y first:

∫[0,1] [(1 - 2t²)(1 - t²) - (1 - 2t²)t²] dt.

Simplifying:

∫[0,1] [1 - 3t² + 2t⁴] dt.

Integrating with respect to t:

[t - t³ + (2/5)t⁵]_[0,1] = 1 - 1 + (2/5) = 2/5.

Therefore, the line integral ∫[C] (Pdx + Qdy) over the given curve C consisting of the arc of the parabola y = x² from (0,0) to (1,1), and the line segment from (1,1) to (0,1) is equal to 2/5.

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===============================================================

Explanation:

The top and bottom semicircles can be joined to form a full circle. The same can be said about the left and right semicircles. Each circle has diameter 3 and radius 1.5

The area of one circle is

A = pi*r^2

A = 3.14*(1.5)^2

A = 7.065

So two circles doubles to 2*7.065 = 14.13 square meters in area.

Then the last step is to add on the area of the 3 by 3 square (area 3*3 = 9) to get 14.13+9 = 23.13

This area is approximate because pi = 3.14 is approximate. Use more decimal digits in pi to get a more accurate area. However, your teacher wants you to use this specific value so it's best to stick with 23.13

Answer:

23.14

Step-by-step explanation:

The shape is basically two equal-sized circles and a square.

Find the area of the square: 3 x 3 = 9

9 is the area of the square

The formula for finding the area of a circle is pi x radius squared.

3.14 x 1.5 squared = 7.06858

Round to 7.07 and multiply by 2 = 14.14

14.14 (area of both circles) + 9 (area of square) = 23.14

Step-by-step explanation:

12*13 = 156

hope it helps

thank you