Find the derivative of the given function. y = - 4xln(x + 12) 3х 3x A. + 3ln (x + 12) x+12 B. - 3ln (x + 12) x+12 4x 4x C. - 4ln (x + 12) D. - x+12 + 4ln (x + 12) x+12

Step-by-step explanation:

Length = Area / Width = 104in² / 16in = 6.5in²

(who knows why the width is longer...)

Answer:

6.5in

Step-by-step explanation:

Area of rectangle = \(L\)×\(W\)

\(L\)×16 = 104

\(L\) = 104 ÷ 16

= 6.5

\(\therefore\) The length of the rectangle is 6.5in

Hope this helps :)

Answer:

AC is longest

BC is middle

AB is shortest

Answer:

Step-by-step explanation:

Area of the right triangle is 63 ft²

To find the area of a right triangle, we need to multiply the lengths of its legs and divide the result by 2. So in this case:

Area = (10.5 ft) x (12 ft) / 2

Area = 63 ft²

To find how many squares with sides of 3/4 feet can fit in this area, we need to divide the area by the area of one square:

Number of squares = (63 ft²) / (3/4 ft)²

Number of squares = (63 ft²) / (9/16) ft²

Number of squares = (63 ft²) x (16/9)

Number of squares = 112

So the area of the right triangle is 63 ft² and it can be covered by 112 squares with sides of 3/4 feet.

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Answer:

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

Calculate the total number of payments:

Calculate the total amount paid:

So, the Wong family will pay a total of $358200 in principal and interest.

The total principal is $358200 and the interest is $168200.

Given that, the Wong family bought a $190,000 home in 2001.

The monthly payment, not including property taxes and insurance, is $995.

Total money for 30 years = 30×12×995

= $358200

Here, the principal =$190,000 and the interest = 358200-190,000

= $168200

Therefore, the total principal is $358200 and the interest is $168200.

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Answer:

24496

Step-by-step explanation:

40912 * (1-5%) ^10 = 24495.5

becuase they are humans, so round up to 24496

Answer:

So, Y (the up and down part of the graph) equals K (The constant of proportionality, you get it by dividing Y by X), times X (the side by side part of the graph.)

Answer:

-84

Step-by-step explanation:

The solution to the equation \((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\) is 10.3891

From the question, we have the following parameters that can be used in our computation:

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\)

Using the following trigonometry ratio

sin²(x) + cos²(x) = 1

We have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = (\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + 1 + e^2\)

The sum to infinity of a geometric series is

S = a/(1 - r)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = \frac{1/2}{1 - 1/2} + \frac{9/10}{1 - 1/10} + 1 + e^2\)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 1 + 1 + 1 + e^2\)

Evaluate the sum

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 3 + e^2\)

This gives

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 10.3891\)

Hence, the solution to the equation is 10.3891

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The expected value of the policy for the insurance company: $359.38

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

The expected value of the policy for the insurance company can be calculated as follows:

Expected value = (Probability of survival) x (Annual payment)

= 0.999057 x $360

= $359.38

So, the expected value of the policy for the insurance company is $359.38.

It's important to note that this is just an estimate based on statistical probabilities and does not guarantee the outcome. The actual value could be higher or lower than this estimate, depending on the actual lifespan of the policyholder.

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The ratio of f to g to h is:

1:3:5

First, we know that g is the 60% of h, then we can write:

g = 0.6*h

Now we can write the 0.6 as a fraction, then 0.6 = 3/5.

g = (3/5)*h

So we can write:

5*g = 3*h

So the ratio of g to h is 3:5

Now, we know that f is a third of g:

f = (1/3)*g

3f = g

So the ratio of f to g is:

1:3

notice that the value that represents the proportion of g is 3 in both ratios, so we can just write:

The ratio of f to g to h is:

1:3:5

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Answer:

y = 15x

Step-by-step explanation:

90 divided by 6 is 15 so y = 15x is the answer

Answer:313.1

Step-by-step explanation:

The existence and uniqueness theorem in the ordinary differential equations are explained below.

(a) "Existence" in the context of the existence and uniqueness theorem for ordinary differential equations (ODEs) refers to the guarantee that a solution to the ODE exists for a certain interval or range of values.

(b) "Uniqueness" means that there is only one solution to the ODE that satisfies certain initial conditions or constraints. It ensures that there are no multiple solutions that meet the given criteria.

(c) The equation x' = f(t, x) represents a first-order ODE, where the derivative of the function x with respect to t is equal to the function f, which depends on both t and x.

(d) The notation x(to) = xo represents the initial condition of the ODE. It specifies the value of the function x at a particular initial time to, which is equal to xo.

(e) The graph of R = {(t, x): 0 ≤ |t - to| ≤ a, 0 ≤ |x - xo| ≤ b} represents a rectangular region in the t-x plane. It includes all points (t, x) that satisfy the conditions: the absolute difference between t and to is less than or equal to a, and the absolute difference between x and xo is less than or equal to b. The point (to, xo) is included in this region.

(f) The symbol u(t) is not mentioned in the given context. Without additional information, it is not possible to provide a specific interpretation or meaning for u(t).

(g) "On some interval |t - to| < h contained in |t - to| < a" implies that there exists a smaller interval, represented by |t - to| < h, which is fully contained within the larger interval |t - to| < a. The value of h represents the size or length of the smaller interval. In the graph, h can be added as a smaller length within the interval defined by a.

The relationship between a and h is that h is a subset of a. This means that h is smaller or equal to a and is fully contained within a. In other words, h represents a sub-interval of the larger interval a.

(h) The significance of the existence and uniqueness theorem in layman's terms is that it provides a mathematical assurance that a specific type of differential equation has a unique solution that satisfies certain conditions. It gives confidence that a solution exists and is unique within a specified range or interval. This is valuable for various scientific and engineering applications, as it allows for the prediction and understanding of systems described by differential equations.

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Answer:

The slope is 30, and the y-intercept is 75.

Step-by-step explanation:

Use two points from the table, and find the equation of a line given two points.

Point 1: (1, 105)

Point 2: (3, 165)

y = mx + b

slope = m = (y_1 - y_1)/(x_2 - x_1)

m = (165 - 105)/(3 - 1) = 60/2 = 30

y = 30x + b

Use point (1, 105) for x and y.

105 = 30(1) + b

105 = 30 + b

b = 75

y = 30x + 75

The slope is 30, and the y-intercept is 75.

Answer:

3n+9

Step-by-step explanation:

So, the gradient of y = -3x^1 is -3.

The gradient of a function y = f(x) with respect to x is the derivative of the function with respect to x, denoted by dy/dx or f'(x).

In the case of y = -3x^1, the gradient is -3.

It is a constant function, thus, the slope is always the same and equal to the coefficient of the x term, which in this case is -3.

The gradient of a function tells us the rate of change of the function with respect to x. In other words, it tells us how steep the function is at any given point. A positive gradient means that the function is increasing, while a negative gradient means that the function is decreasing.

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Answer:

0033

Step-by-step explanation:

.033 of a whole number so its .033

Answer:0.375

Step-by-step explanation:

3/4=0.75

0.75/2=0.375

(3/4)/2=0.375

For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

To determine the value of n₀ for which Algorithm A is better than Algorithm B when B uses n√n operations, we need to find the point at which the number of operations for Algorithm A is less than the number of operations for Algorithm B.

Algorithm A: 10n log n operations

Algorithm B: n√n operations

Let's set up the inequality and solve for n₀:

10n log n < n√n

Dividing both sides by n gives:

10 log n < √n

Squaring both sides to eliminate the square root gives:

100 (log n)² < n

To solve this inequality, we can use trial and error or graph the functions to find the intersection point. After calculating, we find that n₀ is approximately 459. Therefore, For n ≥ 459, Algorithm A is better than Algorithm B when B uses n√n operations.

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R-1.3: For \($n \geq 14$\), Algorithm A is better than Algorithm B when B uses \($n^2$\) operations.

R-1.4: Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

R-1.3:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n^2$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n^2$\)

\($10 \log n < n$\)

\($\log n < \frac{n}{10}$\)

To solve this inequality, we can plot the graphs of \($y = \log n$\) and \($y = \frac{n}{10}$\) and find the point of intersection.

By observing the graphs, we can see that the two functions intersect at \($n \approx 14$\). Therefore, for \($n \geq 14$\), Algorithm A is better than Algorithm B.

R-1.4:

Algorithm A: \($10n \log n$\) operations

Algorithm B: \($n\sqrt{n}$\) operations

We want to determine the value of \($n_0$\) such that Algorithm A is better than Algorithm B for \($n \geq n_0$\).

We need to compare the growth rates:

\($10n \log n < n\sqrt{n}$\)

\($10 \log n < \sqrt{n}$\)

\($(10 \log n)^2 < n$\)

\($100 \log^2 n < n$\)

To solve this inequality, we can use numerical methods or make an approximation. By observing the inequality, we can see that the left-hand side \($(100 \log^2 n)$\) grows much slower than the right-hand side \($(n)$\) for large values of \($n$\).

Therefore, we can approximate that:

\($100 \log^2 n < n$\)

For large values of \($n$\), the left-hand side is negligible compared to the right-hand side. Hence, for \($n \geq 1$\), Algorithm A is better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

So, for R-1.4, the value of \($n_0$\) is 1, meaning Algorithm A is always better than Algorithm B when B uses \($n\sqrt{n}$\) operations.

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Answer:

82 bags

Step-by-step explanation:

Since we know that one cubic yard of topsoil is 4128 pounds to find how many 50 pound bags we can fill we just need to divide 4128 by 50 to get how many bags and we get 82 (82 is not the exact number the exact number is 82.56)

Answer:

83

Step-by-step explanation:

83 bags

Explanation:

All the soil is placed in the bags. So we need to know how many lots of 50 will fit into 4128.

There will be a remainder and this will need to be put into a bag without filling it up. So that bag will weigh less than 50 pounds.

4128 ÷ 50=82.56

By calculator this is  

82  1 /2 lots of 50 pounds

So we have 82 full bags and 1 that is  

1 /2  full

Total count of bags is 83

Answer: 1/12

Step-by-step explanation:

First make all the fractions have the same denominator. To do that, multiply the fractions by a number that will get them the same denominator. In this case, multiply 1/4 by 3, and 2/3 by 4.

1/4 x 3/3 = 3/12

2/3 x 4/4 = 8/12

then you have 3/12 + 8/12 = 11/12

so, blue is 1/12

Answer:

1/12 of the pins are blue

Step-by-step explanation:

¼ yellow & ⅔ red

First you have to find a common denominator.

4×3 =12 & 3×4 =12 so the common denominator is 12.

Now × the numerator on the fraction with the same number that you x the denominator and you will get 3/12 and 8/12.

3/12 +8/12 = 11/12

12/12 - 11/12 = 1/12

Therefor 1/12 of the pins are blue

The distance the drone has flown after both cars get back to where they started is equal to the length of the diagonal of the square, which is approximately 0.7071.

Since the perimeter of the square is 2, each side of the square has a length of 0.5. Therefore, the total distance around the square is 2 x 0.5 = 1.

Both cars start at the same time and drive clockwise on the perimeter of the square, so they will meet each other exactly halfway around the square. At this point, the drone at the midpoint of the two cars will have flown a distance equal to half the perimeter of the square, which is 0.5.

After the cars complete one full lap around the square and return to where they started, they will have each traveled a distance of 1. Therefore, the distance the drone has flown at this point is equal to the distance between the two cars, which is also equal to the diagonal of the square. Using the Pythagorean theorem, we can calculate the length of the diagonal as follows:

d^2 = 0.5^2 + 0.5^2
d^2 = 0.25 + 0.25
d^2 = 0.5
d = sqrt(0.5)

Therefore, the distance the drone has flown after both cars get back to where they started is equal to the length of the diagonal of the square, which is approximately 0.7071.

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To find all the values of k for which the matrix is not diagonalizable over C, we first find the characteristic equation of the matrix.Let A be the given matrix. Then, the characteristic equation is given by| A - λI | = 0where λ is the eigenvalue and I is the identity matrix.

Therefore, we have\begin{align*} \begin{vmatrix} 1 - \lambda & 0 & B \\ 0 & 1 - \lambda & k \\ -9 & -k+10 & -\lambda \end{vmatrix} &= 0 \\ (1 - \lambda) \begin{vmatrix} 1 - \lambda & k \\ -k+10 & -\lambda \end{vmatrix} + B \begin{vmatrix} 0 & k \\ -9 & -\lambda \end{vmatrix} &= 0 \\ (1 - \lambda)[(\lambda - 1)^2 + k(-k+10)] - B(-9k) &= 0 \end{align*}Expanding and simplifying, we get the following cubic equation in λ:\begin{align*} f(\lambda) &= \lambda^3 - 12 \lambda^2 + (46 - k^2) \lambda - 9k + Bk \end{align*}

If A is diagonalizable, then f(λ) must have three distinct roots in C. That is, the discriminant of f(λ) must be nonzero. Therefore,\begin{align*} \Delta &= (46 - k^2)^2 - 4(1)(-12)(9k - Bk) > 0 \\ 46^2 - 2k^2 + k^4 - 432k + 36Bk > 0 \end{align*}This is a quartic inequality in k. To solve it, we first find the roots of the quartic polynomial, g(k) = k^4 + 36k - 46^2.  

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Answer: a

Step-by-step explanation:

Answer:

A. 3(7-3) < 6 + 21

Step-by-step explanation:

A. 3(7-3) < 6 + 21

21-9 < 27

12 < 27

True

B. ??

C. 3(7-3) = 6 + 21

21 - 9 = 27

12 = 27

False

D. 3(7-3) < 6 + 21

21-9 > 27

12 > 27

False

Therefore, the correct answer is A

Hope this helps!

Answer:

after 25 minutes the temperature was at 78 degrees

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want two methods of choosing points on the line with slope 1/2 through A(-1, 2).

Writing the equation in standard form, we can find the x- and y-intercepts. To get there, we can start from point-slope form:

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y -2 = 1/2(x -(-1)) . . . . . using given slope and point

  2y -4 = x +1 . . . . . . . . . . multiply by 2

  x -2y =  -5 . . . . . . . . . . . . add -1 -2y

Setting x=0 tells us the y-intercept is ...

  0 -2y = -5

  y = -5/-2 = 5/2

So, the y-intercept is (0, 5/2).

Setting y=0 tells us the x-intercept is ...

  x -2(0) = -5

  x = -5

So, the x-intercept is (-5, 0).

It will be convenient to choose an arbitrary y-value to find another point on the line. We can pick y = 6, for example, Then the corresponding x-value is ...

  x -2y = -5

  x = -5 +2y = -5 +2(6) = 7

Another point on the line is (7, 6).

__

Additional comment

If we were to choose an arbitrary value for x, we would want it to be odd, so the corresponding y-value would be an integer. We chose to pick an arbitrary value of y so we didn't have to worry about how to make the x-value an integer.

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Answer:

1

Step-by-step explanation:

so you want to input the numbers into variables so for (p+q)^2 you input p as 4 and q as 8 (4+8)^2 and then you add 4+8 which is 12. Then you have to do 12 to the power of 2 which is 12x12 and the answer to that is 144. For the bottom you input p as 4 and then for -2q you have to input the 8, -2(8) and that equals to -16 so then it's 4-16 so it equals to -12. Then you have to do -12 divided by 12 which equals to 1.