Question 15 a) If x = sinh-¹ t², show that √₁+EA dx + + ² ( 4+ ) ² 200 -2=0 dt² dt b) A particle moves along the x-axis such that it's position at time t is given by xlt) = tan-¹ (sinht). Determine the speed of the particle in terms of x only. d² x d

Answer:

The answer is C. 1/2^4

The final number remaining in this sequence is the number 2.

We start with the first 300 natural numbers written in ascending order. We remove the numbers at odd places, which means we remove all the numbers at positions 1, 3, 5, and so on.

After the first removal, we are left with the numbers at even positions: 2, 4, 6, and so on.

Now, we repeat the process and remove the numbers at odd positions again. We remove numbers at positions 1, 3, 5, and so on from the remaining sequence.

After the second removal, we are left with the numbers at even positions again: 4, 8, 12, and so on.

We can observe that in each removal, the sequence reduces to half its size, and we are left with the numbers at even positions.

Continuing this process, we will eventually reach a point where we have only one number left.

Since we start with 300 numbers, after the first removal, we have 150 numbers. After the second removal, we have 75 numbers. After the third removal, we have 38 numbers. After the fourth removal, we have 19 numbers. After the fifth removal, we have 10 numbers. After the sixth removal, we have 5 numbers. After the seventh removal, we have 3 numbers. After the eighth removal, we have 2 numbers. Finally, after the ninth and last removal, we are left with a single number.

Therefore, the final number remaining in this sequence is the number 2.

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Answer:f

Step-by-step explanation:

Answer:

-300

Step-by-step explanation:

Step 1:  Find the amount Elmer's funds decreased after purchasing the rabbits:

Let x represent Elmer's funds.

Since Elmer bought five rabbits for $10 each, he lost $10 5 times.

x - (10 * 5)

x - 50

Thus, Elmer lost (spent) $50 for the 5 rabbits.

Step 2:  Find the amount Elmer's funds decreased after purchasing the  cupboards:

Since Elmer bought four cupboards for $70 each, he lost $70 4 times:

x - (50 + (70 * 4))

x - (50 + 280)

x - 330

Thus, after purchasing the rabbits and cupboards, Elmer lost $330.

Step 3:  Find the amount Elmer's funds increased after finding the twenty-dollar bill:

Since Elmer found a twenty-dollar bill, he gained $20

x - (330 + 20)

x - 310

Step 4:  Find the amount Elmer's funds increased after returning one rabbit:

Since Elmer returned one rabbit, he gained $10:

x - (310 + 10)

x - 300

Thus, Elmer's funds changed totally by -$300.

Putting all the information together, we have:

x - 10 - 10 - 10 - 10 - 10 - 70 - 70 - 70 - 70 + 20 + 10

x - 50 - 280 + 30

x - 330 + 30

x - $300

The perimeter of the triangle is 12 in.

What is perimeter of similar triangle?

The perimeter of similar triangle is equal to the ratio of the similar sides of the triangle.  The ratio of two similar perimeters of two similar shapes is equal to the  ratio of the lengths of their corresponding sides.

Here, perimeter of triangle PQR = sum of all the side

=12+20+16

=48

The ratio of the corresponding side = 12/3

=4/1

Hence, the perimeter of triangle xyz = ?

perimeter of triangle PQR /perimeter of triangle xyz =4/1

48/x =4/1

x = 48/4

=12

Hence, the perimeter of triangle xyz = 12

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Answer:

x = 12

Step-by-step explanation:

Step 1: Define

f(x) = 4x + 6

f(x) = 54

Step 2: Substitute variables

54 = 4x + 6

Step 3: Solve for x

Subtract 6 on both sides: 48 = 4x

Divide both sides by 4: 12 = x

Step 4: Check

Plug in x to verify it is a solution.

f(12) = 4(12) + 6

f(12) = 48 + 6

f(12) = 54

hello

f(x) = 54

4x + 6 = 54

4x = 54 -6

4x = 48

x = 12

good day

Answer: To find the equation of the tangent line y(x) of the curve r(t) = (t^9, t^5), we need to find the derivative of the curve and then evaluate it at the point where we want to find the tangent line.

The derivative of r(t) is:

r'(t) = (9t^8, 5t^4)

To find the equation of the tangent line at a specific point (x0, y0), we need to evaluate r'(t) at the value of t that corresponds to that point. Since r(t) = (t^9, t^5), we can solve for t in terms of x0 and y0:

t^9 = x0

t^5 = y0

Solving for t, we get:

t = (x0)^(1/9)

t = (y0)^(1/5)

Since these two expressions must be equal, we have:

(x0)^(1/9) = (y0)^(1/5)

Raising both sides to the 45th power, we get:

(x0)^(5/9) = (y0)^(9/45)

(x0)^(5/9) = (y0)^(1/5)

(x0)^(9/5) = y0

So the point where we want to find the tangent line is (x0, y0) = (t0^9, t0^5) = (x0, x0^(5/9 * 9/5)) = (x0, x0).

Now we can evaluate r'(t) at t0:

r'(t0) = (9t0^8, 5t0^4) = (9x0^(8/9), 5x0^(4/9))

The slope of the tangent line at (x0, y0) is given by the derivative of y(x) with respect to x:

y'(x) = (dy/dt)/(dx/dt) = (5t^4)/(9t^8) = (5/x0^4)/(9/x0^8) = 5x0^4/9

So the equation of the tangent line is:

y - y0 = y'(x0) * (x - x0)

y - x0 = (5x0^4/9) * (x - x0)

y = (5/9)x + (4/9)x0

Therefore, the equation of the tangent line y(x) of the curve r(t) = (t^9, t^5) at the point (x0, y0) = (x0, x0) is y = (5/9)x + (4/9)x0.

To find the equation of the tangent line at a point on the curve, we need to find the derivative of the curve at that point. So, we start by finding the derivative of r(t):

r'(t) = (9t^8, 5t^4)

Now, let's find the tangent line at the point (1, 1):

r'(1) = (9, 5)

So, the slope of the tangent line at (1, 1) is 5/9. To find the y-intercept, we can use the point-slope form:

y - y1 = m(x - x1)

where (x1, y1) is the point on the curve. Plugging in (1, 1) and the slope we just found, we get:

y - 1 = (5/9)(x - 1)

Simplifying, we get:

y = (5/9)x + 4/9

So, the equation of the tangent line at the point (1, 1) is y = (5/9)x + 4/9.

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Answer:

2500

Step-by-step explanation:

there you go haha

Answer:

m FGJ = m IJL

( they are pair of corresponding angles )

so, FGJ = 65°

Answer:

n=5

Step-by-step explanation:

i hope this helps :)

To find the inverse function of F(x) = 2x - 3, we replace F(x) with y, swap the positions of x and y, and solve for y. The inverse function is f⁻¹(x) = (x+3)/2.

To find the inverse function of F(x) = 2x - 3, follow these steps

Replace F(x) with y. The equation now becomes y = 2x - 3.

Switch the positions of x and y, so the equation becomes x = 2y - 3.

Solve for y in terms of x. Add 3 to both sides: x + 3 = 2y.

Divide both sides by 2 (x + 3)/2 = y.

Replace y with the notation for the inverse function, f⁻¹(x): f⁻¹(x) = (x + 3)/2.

So, the inverse function of F(x) = 2x - 3 is f⁻¹(x) = (x + 3)/2.

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--The given question is incomplete, the complete question is given

" How do I find the inverse function of F(x) = 2x - 3"--

The statement “there exists a function f such that f(x) < 0, f’(x) > 0, and f”(x) < 0 for all x” is false.

To understand why this statement is false, we must first understand what the symbols mean. The symbol f(x) refers to a function of x, and the symbols f’(x) and f”(x) refer to the first and second derivatives of the function, respectively.

The statement is saying that for all x, the function f(x) will be less than 0, the first derivative f’(x) will be greater than 0, and the second derivative f”(x) will be less than 0.

To show that this statement is false, we need to find an example of a function where this is not the case. Let’s consider the function f(x) = x³. At x = 0, this function is equal to 0, and so f(x) < 0 is not true. Additionally, the first derivative at x = 0 is f’(0) = 0, which is not greater than 0. Thus, the statement is false.

We can also show that this statement is false by looking at the graph of the function f(x). A function with the properties given in the statement would have a graph that looks like a “U” shape, with a minimum point at the origin. However, this is not the case for the function f(x) = x³. The graph of this function is a parabola, which does not have the desired shape.

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Answer:

x + y = 2

y = 2 - x

so it is a linear equation.

2x + 5 = 11

2x = 11 - 5

2x = 6

x = 3

it is not a function because for just one x we have many y

Answer: Center: (9,-5), Radius = 9

Answer:

centre = (9, - 5 ) and radius = 9

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

given

x² + y² - 18x + 10y + 25 = 0

subtract 25 from both sides and collect x / y terms together

x² - 18x + y² + 10y = - 25

using the method of completing the square

add ( add half the coefficient of the x/ y terms )² to both sides

x² + 2(- 9)x + 81 + y² + 2(5)y + 25 = - 25 + 81 + 25

(x - 9)² + (y + 5)² = 81 = 9²

then

centre = (9, - 5 ) and radius = 9

If the scale of drawing is 1 inches : 250 inche and the real horse height is 15 inche, then the height of the horse in drawing is 0.06 inches.

The ratio that describes the relationship between the true figure itself and model is called the scale. It serves as a representation of the real statistics in smaller units on maps. A scale of 1:5, for instance, indicates that 1 on the map is approximately the size of 5 in the actual world.

The scale of drawing the horse = 1 inch :

Therefore in scale

Horse height in drawing equals one inch

The  height of the horse = 250 inche

The original height of the horse = 15 inche

The height in the picture = x inches

To find the height the horse in the picture, we have to use proportion

1 inch : 250 inche = x inches : 15 inche

1 / 250 = x / 15

1 × 15= 250x

250x = 15

x = 15/250

x = 0.06 inches

Therefore, the height of the horse in drawing is 0.06 inches

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Answer:

x^4y^9, the second option.

Step-by-step explanation:

A radical sign over an expression also means the expression is to the power of 1/2. In other words, the square root of n=n^1/2

(x^8y^18)^1/2

You divide the powers by 2

x^4y^9 is the answer

Answer:

b

Step-by-step explanation:

Answer: 1kg = 1,000,000mg

Step-by-step explanation:

You know that 1kg = 1,000g

If you know that 1g = 1,000mg,

then it follows that 1,000g = 1,000,000mg

but since 1,000g = 1kg,

you can substitute: 1kg = 1,000,000mg

And theres your answer :)

If we have coins = [1, 2, 5] and amount = 5, then the function should return 4, because there are four combinations of coins that make up an amount of 5: [1, 1, 1, 1, 1], [1, 1, 1, 2], [1, 2, 2], and [5].

This problem can be solved using dynamic programming. Let's define dp[i][j] as the number of combinations of coins using the first i coins to make up an amount j. Then we can use the following recurrence relation:

dp[i][j] = dp[i-1][j] + dp[i][j-coins[i]]

The first term on the right-hand side of the equation corresponds to the case where we don't use the i-th coin, while the second term corresponds to the case where we use the i-th coin at least once. Note that we only need to consider cases where j >= coins[i], because it's impossible to make up an amount less than the value of the i-th coin using that coin.

We can initialize dp[0][0] = 1, because there is exactly one way to make up an amount of zero using no coins. Finally, the answer to the problem is dp[n][amount], where n is the total number of coins.

Here's the Python code:

def change(amount, coins):

   n = len(coins)

   dp = [[0] * (amount+1) for _ in range(n+1)]

   dp[0][0] = 1

   for i in range(1, n+1):

       dp[i][0] = 1

       for j in range(1, amount+1):

           dp[i][j] = dp[i-1][j]

           if j >= coins[i-1]:

               dp[i][j] += dp[i][j-coins[i-1]]

   return dp[n][amount]

For example, if we have coins = [1, 2, 5] and amount = 5, then the function should return 4, because there are four combinations of coins that make up an amount of 5: [1, 1, 1, 1, 1], [1, 1, 1, 2], [1, 2, 2], and [5].

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Answer:

25/28 (Decimal: 0.892857 )

Branliest?

Answer:

\(\frac{25}{28}\)

Step-by-step explanation:

Combine the fractions by finding a common denominator.

6(x-2) > 15

6x - 12 > 15

6x > 27

x > 27/6

Hope it helps!

Answer:

x>4.5

Step-by-step explanation:

6(x-2)>15

We do this is as if it were an equation:

6(x-2)>15

Expand the brackets:

6x-12>15

Add 12 to both sides:

6x-12+12>15+12

Simplify:

6x>37

Now we divide both sides by 6:

6x÷6>37÷6

x > 4.5

If we put 5 into the original equation as it is more than 4.5, we get:

6(5-2)>15

We can simplify the brackets or expand first:

Simplifying the brackets first:

6(3)>15

18>15 ✅

Expanding first:

6(5-2)>15

30-12>15

18>15 ✅

Answer:

$37.76

Step-by-step explanation:

32*1.18=37.76.

Hope this helps!

Answer:

B

Step-by-step explanation:

On a graph you go rise over run (or Y divided by X) which in this equation is 1 divided by 2 which equals 1/2. You also need to look at what number is being crossed on the y axis, which in this case is 1. Slope intercept form is y=mx+b with m being the slope (1/2) and b being the y intercept (1)

Answer:

B. y = 1/2x + 1

Step-by-step explanation:

I went ahead and graphed each of the answer options for you and when I graphed for B it gave me:

Answer:

10

Step-by-step explanation:

let s = total songs sung at the concert

If it took 1/8 to sing one song, it would take 1/8 x s hours to sing s songs

\(\frac{1}{8}s\) = \(1\frac{1}{4}\)

1/8 s = 5/4

Divide both sides of the equation by 8

s = 5/4 x 8

s = 10

To prove that ∠DBC ≅ ∠DCB, we can utilize the given information that AB ≅ AC and DA bisects ∠BAC. By using the properties of congruent triangles and the angle bisector theorem, we can establish the congruence of the angles.

In triangle ABC, we are given that AB ≅ AC. Since the sides AB and AC are congruent, we can conclude that the angles opposite those sides are also congruent by the isosceles triangle theorem. Therefore, ∠BAC ≅ ∠BCA.

Next, we are given that DA bisects ∠BAC. By the angle bisector theorem, we know that the bisector of an angle divides the opposite side into two segments that are proportional to the adjacent sides. Therefore, AD/DB = AC/BC.

Since AB ≅ AC, we can substitute AC for AB in the equation AD/DB = AC/BC, giving us AD/DB = AB/BC. Since AD is common to both sides of the equation, we can cancel it out, resulting in DB/BC = AB/BC.

From this, we can conclude that DB ≅ AB. Now, in triangle DBC, we have DB ≅ AB and ∠DBC = ∠BAC. Therefore, by the angle-side-angle (ASA) congruence criterion, we can conclude that ∠DBC ≅ ∠DCB.

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Answer:

The amount of interest paid over the time of the mortgage is $176,800.

Step-by-step explanation:

To solve this problem, we will use the mortgage formula to find the time it will take to pay off the mortgage.

First, we need to convert the annual rate to a monthly rate by dividing by 12:

r = 9% / 12 = 0.75%

Next, we can plug in the values we know into the mortgage formula and solve for t:

$800 = P = 100000[r(1 + r)^nt]/[(1 + r)^nt - 1]

$800 = 100000[(0.0075)(1 + 0.0075)^12t]/[(1 + 0.0075)^12t - 1]

Multiplying both sides by [(1 + 0.0075)^12t - 1], we get:

(1 + 0.0075)^12t - 1 = 100000(0.0075)(1 + 0.0075)^12t

Dividing both sides by 100000(0.0075), we get:

(1 + 0.0075)^12t - 1 / 100000(0.0075) = 1

Now we can use logarithms to solve for t:

log(1 + 0.0075)^12t - 1 / 100000(0.0075) = log(1)

[(12t)log(1 + 0.0075) - log(1 - $800/100000(0.0075))] / 12log(1 + 0.0075) = 0

[(12t)log(1.0075) - 0.23074] / 12log(1.0075) = 0

12t = 0.23074 / (log(1.0075))

t = 0.23074 / (12log(1.0075))

t ≈ 346 months

Therefore, it will take approximately 346 months, or 28.83 years, to pay off the mortgage.

To find the amount of interest paid over this period, we can subtract the total amount paid from the original mortgage amount:

Total amount paid = $800 x 346 = $276,800

Interest paid = $276,800 - $100,000 = $176,800

Therefore, the amount of interest paid over the time of the mortgage is $176,800.

Empirical likelihood estimation can be enhanced by incorporating auxiliary summary information with different covariate distributions through the use of weighted estimation. This can lead to more accurate parameter estimates in situations where the covariate distributions vary.

Empirical likelihood estimation is a statistical method used to estimate parameters in a model based on observed data. It is often used when the underlying distribution is unknown or difficult to specify.

When auxiliary summary information with different covariate distributions is available, it can be incorporated into the empirical likelihood estimation process.

To do this, we can first estimate the parameters of the auxiliary covariate distribution using the available summary information. Then, we can use these estimated parameters to construct weights for the empirical likelihood estimation.

These weights take into account the differences in the covariate distributions and help improve the accuracy of the parameter estimation.

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The amount that one family paid is 25 pound

Here two families had dinner and bill was 100 pound

They used the coupon on which they got 50% off

To find the percentage we have to use percentage formula:

\(=\frac{Value}{Total \ Value} *100\)

\(=\frac{50}{100} *100\)

\(= 50 \ Pounds\)

The remaining bill was 50 pound

Now this amount is divided between the 2 families

\(=\frac{50}{2}\)

\(= 25 \ pound\)

So one family has to pay 25 pounds

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