m and p are in direct proportion.
The equation of proportionality is m = 8p.
If p increases from 3 to 7, how much will m increase by?
If your answer is a decimal, give it to 1 d.p.

The exact length of the curve is [tex]& \mathbf{L}=\mathbf{e}^5+\mathbf{4}[/tex].

Let the given equation is [tex]x=e^t-t, y=4 e^{\frac{t}{2}}, 0 \leq t \leq 5[/tex].

Length of Parametric Curve: A parametric curve is a function expressed in components form, such that x=f(t),y=g(t). The length of a parametric curve on the interval a ≤ t ≤ b is given by the definite integral [tex]$L=\int_a^b \sqrt{\left(\frac{d x}{d t}\right)^2+\left(\frac{d y}{d t}\right)^2} d t$[/tex]

Let’s begin by getting the first derivative of the components of the function with respect to the variable t.

[tex]$$\begin{aligned}x & =e^t-t, y=4 e^{\frac{t}{2}} \\\frac{d x}{d t} & =\frac{d}{d t}\left(e^t-t\right)=\frac{d}{d t}\left(e^t\right)-\frac{d}{d t}(t)=e^t-1 \\\frac{d y}{d t} & =\frac{d}{d t}\left(4 e^{\frac{t}{2}}\right)=\left(4 e^{\frac{t}{2}}\right) \frac{d}{d t}\left(\frac{t}{2}\right)=\left(4 e^{\frac{t}{2}}\right)\left(\frac{1}{2}\right)=2 e^{\frac{t}{2}}\end{aligned}$$[/tex]

Substitute the derivatives into the following definite integral which computes the length of the parametric curve on the interval [a,b]=[0,5].

[tex]$$\begin{aligned}L & =\int_a^b \sqrt{\left(\frac{d x}{d t}\right)^2+\left(\frac{d y}{d t}\right)^2} d t \\& =\int_0^5 \sqrt{\left(e^t-1\right)^2+\left(2 e^{\frac{t}{2}}\right)^2} d t \\& =\int_0^5 \sqrt{\left(e^{2 t}-2 e^t+1\right)+\left(4 e^t\right)} d t \\& =\int_0^5 \sqrt{\left(e^{2 t}+2 e^t+1\right)} d t \\& =\int_0^5 \sqrt{\left(e^t+1\right)^2} d t \\& =\int_0^5\left(e^t+1\right) d t\end{aligned}$$[/tex]

We need to find the value of the definite integral to get the exact length of the curve.

Take out the limits of integration and evaluate the resulting indefinite integral to solve.

[tex]$$\begin{aligned}L & =\left.\left[\int\left(e^t+1\right) d t\right]\right|_0 ^5 \\& =\left.\left[\int e^t d t+\int 1 d t\right]\right|_0 ^5 \\& =\left.\left[e^t+t\right]\right|_0 ^5\end{aligned}$$[/tex]

Evaluate the solution at the limits of integration to get the length.

[tex]$$\begin{aligned}& L=\left[e^{(5)}+(5)\right]-\left[e^{(0)}+(0)\right] \\& L=\left(e^5+5\right)-\left(e^0+0\right) \\& L=e^5+5-(1+0) \\& L=e^5+5-1 \\& \mathbf{L}=\mathbf{e}^5+\mathbf{4}\end{aligned}$$[/tex]

Therefore, the exact length of the curve is [tex]& \mathbf{L}=\mathbf{e}^5+\mathbf{4}[/tex].

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The area of the region bounded by the given curves is 0.7123 square units

In this question we have been given two curves y = sin^2(x), y = sin^3(x), 0 ≤ x ≤ π

We need to find the area of the region bounded by the given curves.

We know that the formula for the area between two curves f and g :

A = |∫_[a to b] [f(x) - g(x)] dx|

here, a = 0, b = π, f(x) = sin^2(x) and g(x) = sin^3(x)

So, A = |∫_[0 to π] [sin^2(x) - sin^3(x)] dx|

A = |∫_[0 to π] sin^2(x) dx - ∫_[0 to π] sin^3(x) dx|

consider ∫_[0 to π] sin^2(x) dx

= ∫_[0 to π] (1 - cos(2x) / 2) dx

= π/2

Now consider ∫_[0 to π] sin^3(x) dx

= ∫_[0 to π] (1 - cos^2(x)) sin(x)  dx

= 4/3

So A = |π/2 - 4/3|

        = 3π - 8/2

        = 0.7123

Therefore, the required area: 0.7123 square units

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The constant rate of change and initial value for the given graph are 40 and 20 respectively. the initial value might represent the fixed cost of the soil.

The slope of a straight line is the tangent of the angle formed by it with the positive x axis as the reference. The negative slope indicates the rate of decrease while the positive shows the rate of increase.

The given problem can be solved as follows,

(a) The graph given is a straight line that passes through (0, 40) and (10, 240).

The constant rate of change is equivalent to the the slope of the line given as,

⇒ (240 - 40)/(10 - 0) = 20

(b) The initial value of the graph is given as the y-intercept of the line.

Which is given as 40.

It might represent the fixed cost.

Hence, the constant rate of change is given as 40 and the initial value is 20 which might represent the fixed cost.

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The missing graph is attached here.

The total annual salary with a festive bonus is Rs (12r+2000)

In maths, multiply means the repeated addition of groups of equal sizes.

Given that, there is an annual salary at r rupees per month along with a Christmas bonus of, Rs 2000.

Here, a person is getting monthly salary  = Rs r

Therefore, his annual salary = Rs r × 12

= Rs 12r

He is also getting a bonus for Christmas = Rs 2000

So, in total, he will get =  Rs (12r+2000)

Hence, The total annual salary with a festive bonus is Rs (12r+2000)

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Answer:

120°

Step-by-step explanation:

125° + ( y + 5 )° + y = 360°

or, 125° + y + 5° + y = 360°

or, 2y + 130° = 360°

or, 2y = 360° - 130°

or, 2y = 230

or, y = 230/ 2

. y = 115°

. .

. ( y + 5 )°

. . ( 115 + 5 )°

.

. . 120°

Option are wrong.

Answer:

50000

Step-by-step explanation:

If the degree on x in the denominator is larger than the degree on x a bigger leading exponent than the polynomial in the numerator.

After then the graph to the value found by dividing the leading coefficients of the two polynomials.

To find horizontal asymptotes:

1.  If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0).

2.  If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote.

3. Rational functions (a polynomial divided by a polynomial) and exponential functions have horizontal asymptotes.

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Answer:

22 degrees

Step-by-step explanation:

D=B and C=A

To determine if a misspelled name is repeated throughout a dataset, a data analyst can use the COUNT function. This function counts the number of occurrences of a value in a range of cells.

Alternatively, the data analyst could use the COUNTA function, which counts the number of cells in a range that contain data (including text and numbers, but not empty or blank cells). The COUNTA function would also count the number of occurrences of the misspelled name in the dataset.

What is a dataset, using an example?

A collection of numbers or values pertaining to one subject constitutes a data set. An example of a data set might be each student's test scores for a certain class. The amount of fish that each dolphin eats in an aquarium is a data set.

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Answer:

25 and 37

Step-by-step explanation:

x+y=62

y-x=12

 +x. +x

y=12+x

x+(12+x)=62

2x+12=62

   -12. -12

2x=50

/2. /2

x=25

25 is one of the numbers

y-25=12

+25 +25

y=37

hopes this helps

Answer:

2 apples = 0.24 kg

12 apples = 1.44 kg

Step-by-step explanation:

Find the weight of one apple.

If 5 apples weigh 0.60 kg, then 1 apple weighs:

[tex]\implies \sf 1\;apple=\dfrac{0.60}{5}=0.12\; kg[/tex]

Therefore:

Answer:

-3

Step-by-step explanation:

x² + x = 3

3 - 6 = -3

Answer:

Step-by-step explanation:

The change per week in the amount of money in the account is 40

The starting amount of money in the account is 550.

The statement that exemplifies the provided variables is called an equation. In this instance, the scenario is described by taking into account two or more factors. The definition of an equation as a mathematical statement that consists of two expressions joined by an equal sign must be understood.

In this instance, x and y are connected by the formula y=550 + 40x. In light of this, the weekly change in the account's balance is 40 dollars, while the initial balance was 550.

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The power of the lens is 2.5D

The focal length of 40 cm and a diameter of 5.0 cm.

Optical power (also referred to as dioptric power, refractive power, focusing power, or convergence power) is the degree to which a lens, mirror, or other optical system converges or diverges light. It is equal to the reciprocal of the focal length of the device: P = 1/f.

Power of lens = 1 / focal length (in meters)

For a thin lens in air, the focal length is the distance from the center of the lens to the principal foci (or focal points) of the lens. For a converging lens (for example a convex lens), the focal length is positive and is the distance at which a beam of collimated light will be focused to a single spot.

we have focal length 40cm (.4 m)

so

Converging lenses have positive optical power, while diverging lenses have negative power.

Power of lens = 1/0.4 m

=2.5 D  [The unit of Power of lens is Dioptre]

Therefore, the power of the lens that has a focal length and a diameter of 5.0 cm is 2.5D

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Answer:

....................

Answer: There are 4.3 hours * 60 minutes per hour = 4.360=258minutes in 4.3 hours.

There are 258 minutes * 60 seconds per minute = 25860=15480 seconds in 258 minutes.

Therefore, the printer at Seneca office can print out 15,480 pages / 5 seconds per page =15480/5=3096 pages in 4.3 hours. Answer: 3096

Step-by-step explanation:

To calculate Keith's equivalent rate with simple compounding, we need to use the following formula:

r = (e^(i/n) - 1) * n

where r is the equivalent rate with simple compounding, i is the interest rate with continuous compounding, and n is the number of compounding periods per year.

In this case, we are given that i = 8.27% and we can assume that the number of compounding periods per year is 12, since many loans are compounded monthly. Plugging these values into the formula, we get:

r = (e^(0.0827/12) - 1) * 12

= (1.0082 - 1) * 12

= 0.0082 * 12

= 0.0984 or 9.84%

Therefore, Keith's equivalent rate with simple compounding is [B] 0.0998 or 9.98%.

Answer:

x = 11

Step-by-step explanation:

the sum of the 3 angles in the triangle = 180°

sum the 3 angles and equate to 180

80 + 60 + 3x + 7 = 180

147 + 3x = 180 ( subtract 147 from both sides )

3x = 33 ( divide both sides by 3 )

x = 11

Answer:

x = 11

Step-by-step explanation:

The sum of the angles of a triangle is 180 degrees

60 + 80 + 3x+7 = 180

Combine like terms

3x+147=180

Subtract 147 from each side

3x+147-147=180-147

3x = 33

Divide each side by 3

3x/3 = 33/3

x = 11

y = e is the equation of the tangent line to the given curve at the specified point , y = [tex]e^{x}[/tex] / x , (1, e)

Through the coordinate geometry formal of point-slope form, the equation of tangent and normal can be calculated.

The tangent has the equation (y - y1) = m(x - x1), and a normal travelling through this point and perpendicular to the tangent has the equation (y - y1) = -1/m (x - x1).

thus , y' =  [tex]\frac{e^{x}-xe^{x} }{x^{2} }[/tex]

y'(1) = 0 = m

Our slope is indicated by the horizontal line.

y−[tex]y_{1}[/tex]=m(x−[tex]x_{1}[/tex])

Our line will simply be our y-coordinate because our slope(m) is 0:

e

Therefore:

The tangent line's equation is y=e.

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Answer:

9.42cm

Step-by-step explanation:

according to fig :

diameter (d) =3cm so ,

radius (r) = d/2 =3/2 = 1.5cm

solution:

as we know that ,

circumference of a circle = 2πr

=2×3.14×1.5

=9.42 cm

Answer:

21.98 cm

Step-by-step explanation:

The circumference formula is [tex]2\pi r[/tex] which can be expressed as [tex]\pi d[/tex], where r is radius and d is the diameter length.

Since we know the diameter is 3 cm, that means we can plug in that value for d and get [tex]7 \pi[/tex] as the circumference

However, the question tells us to use 3.14 for [tex]\pi[/tex], so we must find the value of [tex]7 * 3.14[/tex]. By doing mental math or by using a calculator we can find this value to be 21.98.

Thus, the circumference of the circle is 21.98 cm

To answer this question, we need to first multiply the left side of the given equation and write it as the difference of two squares. This can be done by using the difference of squares formula, which states that the difference of two squares can be written as the product of the square of the sum and the square of the difference.

The left side of the given equation can be written as:

(csc0+ cot 0)(csc0- cot0)

We can then apply the difference of squares formula to this expression to get:

(csc0+ cot 0)(csc0- cot0) = (csc0+ cot 0)(csc0- cot0)

Now, we can see that this expression is equivalent to 1 using the Cancellation Property. This property states that if two numbers or expressions are equal, then their corresponding parts are also equal. In this case, since 1 = (csc0+ cot 0)(csc0- cot0), we can cancel out the corresponding parts on both sides of the equation to get 1 = 1.

Therefore, the correct answer is D. Cancellation Property.

The number on the third term and the eleventh term will be 22 and 46, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

In a game, the number of dominos in different lines structures an A.P. Assuming that the quantity of dominos in the third and eleventh cell together is 68 and the quantity of dominos in the eleventh cell is 24 a bigger number than of the third cell.

Let 'x' be the third number and 'y' be the eleventh number. Then the equations are given below.

x + y = 68          ...1

y = x + 24          ...2

From equations 1 and 2, then we have

x + x + 24 = 68

2x = 44

x = 22

Then the value of the variable 'y' will be given as,

y = 22 + 24

y = 46

The number on the third term and the eleventh term will be 22 and 46, respectively.

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The probability that molly will roll the die less than four times before stopping is 91/216

Probability is the calculation of an outcome or the chance of an event ever happening.

Probability determines the likelihood of an event occurring: P(A) = f / N.

Probability(Event) = Favorable Outcomes/Total Outcomes

She can do this in 1 roll, 2 rolls, or 3 rolls.

Probability of getting 1 in the first roll: 1/6

Probability of getting 1 on the second roll: 5/6∗1/6=5/36

Probability of 1 on the third roll: 5/6∗5/6∗1/6=25/216

As it can happen in 1, 2, or 3 rolls we add the probabilities: 1/6+5/36+2/52

⇒26/216+30/216+25/216

⇒91/216

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The difference between  51th term of a and 51th term of b is 1000.

nth term of an arithmetic series is given by [tex]a_n = a_0 +( n-1)* d[/tex]

where [tex]a_0[/tex] is first term of arithmetic series , [tex]a_n[/tex] is nth term of the series and d is the common difference

given [tex]a_0 = b_0 = 30[/tex]

and given that both series have common difference have absolute value of 10.

common difference of series a is 10 as this series is increasing

similary common difference of series b is -10 as it is decreasing

putting the values in the above equation we get:

[tex]a_5_1[/tex]  = [tex]a_0[/tex] +(n-1)*d

=> 30 + (51-1)*10

=> 30 + 500

so [tex]a_5_1[/tex] = 530

[tex]b_5_1[/tex]  = [tex]b_0[/tex] +(n-1)*d

=> 30 + (51-1)*-10

=> 30 -500

so [tex]b_5_1[/tex] = -470

so we have to find value of [tex]a_5_1 - b_5_1[/tex] which is 530 - (-470) =530 +470 =1000

so the differnce of 51th term of a and b is 1000

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Answer:

z > 1 1/3

Step-by-step explanation:

See picture

The bakery sold total 200 cupcake in that day.

The word percent means per hundred and percent value of a quantity refers to the hundred parts of that quantity. Percent value is expressed by sign %.

In order to determine a percent value of a quantity, we divide the quantity by the total quantity and finally the resultant value is multiplied by 100.

In the other hand, when we need to calculate total quantity from a percentage value, we multiply the specific quantity by 100 and finally the resultant is divided by the percentage value.

Given, Number of cupcakes sold at a specific time =26 which was 13 percent of total number of cupcakes sold in that day.

Therefore, number of total cupcakes sold in that day = 26× 100/13 =200

    the total number is 200

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An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a fixed number, called the common difference, to the previous term. For example, the sequence 1, 2, 3, 4, … is an arithmetic sequence because each term is obtained by adding 1 to the previous term, which is the common difference.

Out of the four given options, only the sequence 1/2, 1/4, 1/6, 1/8, … is an arithmetic sequence. The common difference of this sequence is 1/4-1/2 = -1/4, so each term is obtained by subtracting 1/4 from the previous term. The other three sequences, 3, 5, 7, 9, 11, …, 2, 6, 18, 54, …, and 64, 32, 16, 8, … are not arithmetic sequences because the difference between each consecutive pair of terms is not constant. Therefore, the correct answer is a.

Answer:

y= 14.875

x= 16.875

Step-by-step explanation:

simultaneous equation

substitution method