Why is it even? There is 3 arrays in total.

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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The choice that provides the best example of alliteration for the given sentence is tested terrifically on teaching. (Option C)

Alliteration is a literary device in which there is a noticeable repetition of initial consonant sounds in consecutive or nearby words in a phrase. It refers to the occurrence of the same sound or letter at the beginning of adjacent or closely connected words. Alliteration is created by repeated sound at the start of the words and not the repeated letter. For example, the phrase “kids’ coats” is alliterative, and the phrase “phony people” is not alliterative. In the given sentence, author can create alliteration by using tested terrifically in place was absolutely aced.

Note: The question is incomplete. The complete question probably is: In the sentence, the author wants to use alliteration. Which choice provides the best example of this? Ted absolutely aced his teaching exam. A) NO CHANGE B) was astounded at how well he did on C) tested terrifically on teaching.

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Answer:

We get the approximate value of [n] as 5.

What is logarithm? What is a mathematical equation and expression?

A quantity representing the power to which a fixed number (the base) must be raised to produce a given number. We can write -

$$$\log_{b}({b^x})=x$$

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions.

A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have 31,100 is rounded to the nearest power of 10 and [N] represents a power of 10.

We can write -

We can write -10ⁿ = 31100

We can write -10ⁿ = 3110010ⁿ = 311 x 10²

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)(n - 2) log 10 = log (311)

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)(n - 2) log 10 = log (311)n - 2 = log(311)/log(10)

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)(n - 2) log 10 = log (311)n - 2 = log(311)/log(10)n - 2 = 2.5

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)(n - 2) log 10 = log (311)n - 2 = log(311)/log(10)n - 2 = 2.5n = 4.5

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)(n - 2) log 10 = log (311)n - 2 = log(311)/log(10)n - 2 = 2.5n = 4.5n = 5 (approx.)

We can write -10ⁿ = 3110010ⁿ = 311 x 10²10ⁿ ⁻ ² = 311log(10ⁿ ⁻ ²) = log(311)(n - 2) log 10 = log (311)n - 2 = log(311)/log(10)n - 2 = 2.5n = 4.5n = 5 (approx.)Therefore, we get the approximate value of [n] as 5.

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Using percentages we know that the total price of the book that Tommy will pay is $131.04.

What is the percentage?

In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100.

Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most usually used to denote it.

A% is a number that has neither dimensions nor a defined unit of measurement.

For instance, if you properly answered 75 out of 100 questions on a test, you would have received a 75% grade (75/100).

So, we know that the price of the book is 180.

Sales tax is 4%. So, the total price:

180/100 * 4 = 7.2$ ⇒ $187.2

Now, there is a 30% discount:

187.2/100 * 30 = $56.16

⇒ 187.2 - 56.16 = $131.04

Therefore, using percentages we know that the total price of the book that Tommy will pay is $131.04.

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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:

Step-by-step explanation:

Answer:

The price per cup would be 0.41 cents.

Step-by step explaination:

Answer:

$0.41

Step-by-step explanation:

To find the price per cup of milk, we first need to know how many cups are in a 3-quart carton.

1 quart is equivalent to 4 cups, so a 3-quart carton contains:

[tex]\sf 3\;quarts=3 \times 4 \;cups= 12\;cups[/tex]

Now, we can calculate the price per cup by dividing the total price by the number of cups:

[tex]\begin{aligned}\textsf{Price per cup} &= \dfrac{\textsf{Total price}}{\textsf{Number of cups}} \\\\&=\sf \dfrac{\$4.92}{12}\\\\&=\sf \$0.41\end{aligned}[/tex]

Therefore, the price per cup of milk is $0.41.

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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Answer:

22 degrees

Step-by-step explanation:

D=B and C=A

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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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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[tex]\frac{2}{243} (82^\frac{3}{2} -1)[/tex] is the required length of the curve y = 4 + 6[tex]x^\frac{3}{2}[/tex]

Given equation of curve:

y = 4 + 6[tex]x^\frac{3}{2}[/tex]

length of the curve is given by L= [tex]\int\limits^a_b {\sqrt{1+(y^')^2} } \, dx[/tex]

where [tex]y^'[/tex] is derivative of y with respect to x

so [tex]y^'[/tex] = 6*(3/2) * [tex]\sqrt{x}[/tex]

=> 9 [tex]\sqrt{x}[/tex]

given a=1 and b=0

so L= [tex]\int\limits^1_0 {\sqrt{1+(9\sqrt{x})^2 } } \, dx[/tex]

L=  [tex]\int\limits^1_0 {\sqrt{1+81x } } \, dx[/tex]

let 1+81x be t

81dx = dt

as the value of x changes after the substitution of the value.

so now the L changes as:

L= 1/81 [tex]\int\limits{\sqrt{t } } \, dt[/tex]

L=1/81* [tex]\left \{ {{t=82} \atop {t=1}} \right.[/tex]  [tex]\frac{t^\frac{3}{2} }{\frac{3}{2} }[/tex]

the min value of t=1 and max value of t=82

L=[tex]\frac{2}{243} (82^\frac{3}{2} -1)[/tex]

so the exact length of the curve is given by L=[tex]\frac{2}{243} (82^\frac{3}{2} -1)[/tex]

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The function f(x,y) is at origin [tex]\left|\frac{\sin x y}{x y}-1\right| < \varepsilon[/tex].

We can treat this function as h=xy and then it will looks like sin h/h because if we choose any path passing through original it will always continuous so above f(x,y) is continuous

[tex]$$f(x, y)= \begin{cases}\frac{\sin x y}{x y,} & \text { if } x y \neq 0 \\ 1, & \text { if } x y=0\end{cases}$$[/tex]

Choose y=mx path y→0, x→0

[tex]$$\begin{aligned}\lim _{\substack{x \rightarrow 0 \\y=\infty}} f(x, x) & =\lim _{x \rightarrow 0} \frac{\sin m x^2}{m x^2} \\& =\lim _{x \rightarrow 0} \frac{\cos m x^2 \cdot 2 m x}{2 m x}=1\end{aligned}$$[/tex]

Now consider,

[tex]$|f(n, y)-L 1=| \frac{\sin x-1}{n y}-1 \mid < \varepsilon$[/tex]

[tex]$$$\forall \varepsilon > 0$, and $|n| < \delta,|y| < d$$$=\left|\frac{\sin x y}{x y}-1\right| < \varepsilon$$[/tex]

Hence f(x,y) is continues at origin.

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Discuss the continuity of the function:

[tex]$$f(x, y)= \begin{cases}\frac{\sin x y}{x y,} & \text { if } x y \neq 0 \\ 1, & \text { if } x y=0\end{cases}$$[/tex]

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.

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 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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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%.

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 value of α + β  is 4. Then the value of the expression 2⁻¹ x (α + β)² will be 8.

Let the equation be ax² + bx + c = 0 and the roots are α and β.

Then the sum of the roots will be

α + β = - b / a

And the product of the roots will be

α · β = c / a

The quadratic equation is given below.

x² - 4x + 1 = 0

The sum of the roots of the equation is given as,

α + β = - (-4) / 1

α + β = 4

Then the value of the expression will be given as,

⇒ 2⁻¹ x (α + β)²

⇒ 2⁻¹ x (4)²

⇒ 16 / 2

⇒ 8

The value of the expression 2⁻¹ x (α + β)² will be 8.

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Answer:

-3

Step-by-step explanation:

x² + x = 3

3 - 6 = -3

Answer:

Step-by-step explanation:

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:

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

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

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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Answer: (x- 1/4)^2=9/16

Step-by-step explanation:

x^2 -1/2x =8/16

(x^2-1/2x +1/16)^2= 8/16+1/16)

(x- 1/4)^2=9/16

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:

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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