Use the given Maclaurin series to evaluate the limit

Answer:

A

Step-by-step explanation:

the answer is A because it is absolute so it would actually be x + 3

Answer: the first one and the third one

Step-by-step explanation:

The prime polynomials from the polynomials are:

1. [tex]x^4[/tex] + 3y²x - 1 and 3. x² - 9x + 3.

Options 1 and 3 are the correct answer.

We have,

A prime polynomial is a polynomial that cannot be factored into a product of two polynomials with integer coefficients.

Let's check each expression to see if it is a prime polynomial:

[tex]x^4[/tex] + 3y²x - 1:

This expression cannot be factored further, so it is a prime polynomial.

9y + 4y² + 12y³:

This expression can be factored as y(9 + 4y + 12y²), so it is not a prime polynomial.

x² - 9x + 3:

This expression cannot be factored further, so it is a prime polynomial.

x² - 3x - 10:

This expression can be factored as (x - 5)(x + 2), so it is not a prime polynomial.

x³ - 512y³:

This expression can be factored as (x - 8y)(x² + 8xy + 64y²), so it is not a prime polynomial.

Thus,

The prime polynomials are:

1. [tex]x^4[/tex] + 3y²x - 1 and 3. x² - 9x + 3.

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Based on the given parameters of a = 1.7 cubic feet and concrete for first 4 steps as 17 cubic feet, the concrete is required for the first 12 steps is 132.6 cubic feet

Sn = n/2 {2a + (n - 1) d}

17 = 4/2{2×1.7 + (4 - 1)d}

17 = 2{3.4 + (3)d}

17 = 2(3.4 + 3d)

17 = 6.8 + 6d

17 - 6.8 = 6d

10.2 = 6d

d = 10.2/6

Concrete required for first 12 steps;

Sn = n/2 {2a + (n - 1) d}

= 12/2{2×1.7 + (12-1)1.7}

= 6{3.4 + (11) 1.7}

= 6(3.4 + 18.7)

= 6(22.1)

= 132.6

Concrete required for first 12 steps = 132.6 cubic feet

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Answer:

132.6 cubic feet

Step-by-step explanation:

Answer:

A) -6

Step-by-step explanation:

its just by substituting 3 in place of x

3(3-4)+2(3)-(3)²

3(-1)+6-9

-3+(-3)= -6

pls gimme brailiest if it helped :)

Answer:

A. -6

Step-by-step explanation:

3(x-4) + 2x - x²

Evaluate

Let x =3

Substitute into the expression

3( 3-4) +2(3) - 3^2

Parentheses first

3( -1) +2(3) - 3^2

Exponents next

3( -1) +2(3) - 9

Multiply

-3 +6 -9

Add and subtract

-6

Answer:

Area = (a² -5a) in²

Perimeter = (4a -10) in

Step-by-step explanation:

Let the length of the rectangle be a.

Given that, its width is 5 in less than the length.

So,

length ⇒ a

width ⇒ (a - 5)

First, let's find the area of the rectangle.

Area = length × width

Area = a ( a - 5 )

Solve the brackets.

Area = (a² -5a) in²

Now, let us find the perimeter of the rectangle.

Perimeter = 2 ( l + w )

Perimeter = 2 ( a + a - 5 )

Perimeter = 2 ( 2a - 5 )

Perimeter = (4a -10) in

Answer:

A=113 cm²

Step-by-step explanation:

If the length of the rope is 6 cm

then the radius of the circle we draw is 6 cm.

Area of the circle is A = π·r²

A = π·6² ≈ 3.14· 36 ≈ 113cm²

Answer:

sheu7euw73u3hsusuuwueudhdhdhsjsjwiwuwuehehdggdhdue

Step-by-step explanation:

hzhsusududjdndjdhehhshshhdhdhdhdhdhdhdhdhbhdhdhhdhdhdudxbdhdhdhdhhshdhyehsuehduwhgduwhdydh

Answer:subtraction

Step-by-step explanation: to find out how many fewer tickets were sold on Sunday you would need to subtract 34012 by 29879. The solution would be how many fewer tickets were sold on Sunday compared to Saturday.

The values of a + b, 6a + 9b, |a|, and |a − b| are −3i + 16j, 0i + 108j, 15 and 17 respectively. This can be obtained by using vector addition, vector subtraction and formula to find magnitude of a vector.

Given that,

a = <−9, 12> , b = <6, 4>

These vectors can be rewritten as,

a = <−9, 12> = −9i + 12j

b = <6, 4> = 6i + 4j

a + b = −9i + 12j + 6i + 4j

a + b = −9i + 6i + 12j + 4j

a + b = (−9 + 6)i + (12 + 4)j

a + b = −3i + 16j

6a = 6 (−9i + 12j )

6a = −54i + 72j

9b = 9(6i + 4j)

9b = 54i + 36j

Now add 6a and 9b together,

6a + 9b = −54i + 72j  + 54i + 36j

6a + 9b = −54i + 54i + 72j + 36j

6a + 9b = 0i + 108j

If a = a₁i + a₂j, |a| = √a₁² + a₂²

Here, a = −9i + 12j

|a| = √(−9)² + (12)²

|a| = √81 + 144 = √225

|a| = 15

a - b = −9i + 12j - (6i + 4j)

a - b = −9i - 6i + 12j - 4j

a - b = −15i + 8j

Now use the formula to find the magnitude of a vector,

|a − b| = √(-15)² + (8)²

|a − b| = √225 + 64 = √289

|a − b| = 17

Hence the values of a + b, 6a + 9b, |a|, and |a − b| are −3i + 16j, 0i + 108j, 15 and 17 respectively.

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The value of given trigonometric value cos(22. 5°) is 0.387.

According to the statement

we have given that the trigonometric value and we have to find the exact value of that given value with the help of the half angle formula.

So, For this purpose, we know that the

The half angle formulas are used to find the exact values of the trigonometric ratios of the angles like 22.5°.

So,

The given value is :

cos(22. 5°)

Then the value of cos half angle formula is

[tex]cos (theta/2) = +- sqrt((1-cos theta) / 2)[/tex]

then

The value of θ/2 is 22.5 degree.

And θ is 22.5*2

θ = 45 degree

and cos 45 degree is 1/squareroot 2

And by this the value of given value become is

[tex]cos 22.5 = +\sqrt{((\sqrt{2} -1)/(2 \sqrt{2} )) } = + 0.3827[/tex]

So, The value of given trigonometric value cos(22. 5°) is 0.387.

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Answer:

1.0954.

Step-by-step explanation:

Standard error  =  std dev / √n

=  6 / √30

= 1.0954.

Step-by-step explanation:

This is trigonometry. Focusing on Y initially, we can see that Y is the opposite, and 32 is the hypotenuse. Therefore, we must use sin:

[tex] \sin(60) = \frac{y}{32} [/tex]

[tex]y = \sin(60) \times 32[/tex]

[tex]y \approx28[/tex]

Next X. We can see that X is the adjacent, and 32 is the hypotenuse, so we must use cos:

[tex] \cos(60) = \frac{x}{32} [/tex]

[tex]x = \cos(60) \times 32[/tex]

[tex]x = 16[/tex]

Now let's look at A. We can see that a is the adjacent, and 12 is the opposite, so we must use tan:

[tex] \tan(60) = \frac{12}{a} [/tex]

[tex]a = \frac{12}{ \tan(60) } [/tex]

[tex]a \approx7[/tex]

Now, B. We can see that B is the hypotenuse, and 12 is the opposite, so we must use sin:

[tex] \sin(60) = \frac{12}{b} [/tex]

[tex]b = \frac{12}{ \sin(60) } [/tex]

[tex]b \approx14[/tex]

Answer:

Below in bold.

Step-by-step explanation:

The first triangle is a 30-60-90 triangle,

so the sides are in the ratio 2 : 1 : √3,  where 2 is the hypotenuse, the 1 is adjacent to 60 degree angle and the √3 is opposite the 60 degree angle.

So x = 1/2 * 32 = 16

and y = 16√3  or 27.71 to nearest hundredth.

The second one is the same special triangle, so

√3/2 = 12/b

b = 24/√3

 = 8√3  or 13.86  to nearest hundredth.

a = 1/2 b = 4√3 or 6.93 to nearest hundredth.

The angle between the two extreme vectors of Sofia bats is 74.60 degrees.

In this question,

The angle between two vectors will be deferred by a single point, which is called as the shortest angle at which we have to turn around one of the vectors to the position of co-directional with another vector.

The extreme vectors of Sofia bats are  [tex]\vec u = < -8, 12 >[/tex] and [tex]\vec v = < -8, 12 >[/tex]

The angle between the vectors is

[tex]\theta = cos^{-1} \frac{\vec u.\vec v}{||\vec u|| ||\vec v||}[/tex]

The dot product is calculated as

[tex]\vec u. \vec v = (-8)(13)+(12)(15)[/tex]

⇒ [tex]-104+180[/tex]

⇒ 76

The magnitude can be calculated as

[tex]||\vec u|| = \sqrt{(-8 )^{2} +(12)^{2} }[/tex]

⇒ [tex]\sqrt{64+144}[/tex]

⇒ [tex]\sqrt{208}[/tex]

[tex]||\vec v|| = \sqrt{(13 )^{2} +(15)^{2} }[/tex]

⇒ [tex]\sqrt{169+225}[/tex]

⇒ [tex]\sqrt{394}[/tex]

Thus the angle between the vectors is

[tex]\theta = cos^{-1} \frac{76}{(\sqrt{208} )(\sqrt{394} )}[/tex]

⇒ [tex]\theta = cos^{-1} \frac{76}{\sqrt{81952} }[/tex]

⇒ [tex]\theta = cos^{-1} \frac{76}{286.27 }[/tex]

⇒ [tex]\theta = cos^{-1} (0.2654)[/tex]

⇒ [tex]\theta=74.60[/tex]

Hence we can conclude that the angle between the two extreme vectors of Sofia bats is 74.60 degrees.

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Answer: [tex]\huge\boxed{\boxed{15}}[/tex]

Step-by-step explanation:

Given expression

[tex]\large\boxed{\frac{12[30 - (9+4^2)]}{|10|-|-6| } }[/tex]

Simplify the exponents

[tex]\large\boxed{=\frac{12[30 - (9+16)]}{|10|-|-6| } }[/tex]

Simplify values in the parenthesis

[tex]\large\boxed{=\frac{12[30 - 25]}{|10|-|-6| } }[/tex]

[tex]\large\boxed{=\frac{12[5]}{|10|-|-6| } }[/tex]

Simplify absolute values (all positive)

[tex]\large\boxed{=\frac{12[5]}{10-6 } }[/tex]

[tex]\large\boxed{=\frac{12[5]}{4 } }[/tex]

Simplify by division

[tex]\large\boxed{=3~[5]}[/tex]

Simplify by multiplication

[tex]\huge\boxed{\boxed{=15}}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

[tex]\cos(x)[/tex] is an even function, while [tex]\sin(x)[/tex] is odd. This means

[tex]\cos(-x) = \cos(x) \text{ and } \sin(-x) = -\sin(x)[/tex]

[tex]\cot(x)[/tex] is defined by

[tex]\cot(x) = \dfrac{\cos(x)}{\sin(x)}[/tex]

so it is an odd function, since

[tex]\cot(-x) = \dfrac{\cos(-x)}{\sin(-x)} = \dfrac{\cos(x)}{-\sin(x)} = -\cot(x)[/tex]

Putting everything together, it follows that

[tex]\cot(-x) \cos(-x) \sin(-x) = (-\cot(x)) \cos(x) (-\sin(x)) \\\\~~~~~~~~= \cot(x) \cos(x) \sin(x) \\\\ ~~~~~~~~= \cos^2(x)[/tex]

Answer:

r = 3.75

Step-by-step explanation:

C = 2(pi)r (write equation)

r = c / 2pi (rearrange for r)

r = 23.55 / 2(3.14) (plug in variables)

r = 23.55 / 6.28 (simplify)

r = 3.75 (solve)

Answer:

B.) x + 4y = 7

Step-by-step explanation:

(Step 1) ----------------------------------------------------------------------------------------------

To find the equation, we first need to find the slope using the point-slope form:

y₁ - y₂ = m(x₁ - x₂)

In this form, "m" represents the slope, "x₁" and "y₁" represent the values from the first point, and "x₂" and "y₂" represent the values from the second point.

Point 1: (-1, 2)                     Point 2: (3, 1)

x₁ = -1                                   x₂ = 3

y₁ = 2                                   y₂ = 1

y₁ - y₂ = m(x₁ - x₂)                                  <----- Point-slope form

2 - 1 = m(-1 - 3)                                      <----- Insert values

1 = m(-4)                                                <----- Subtract

-1/4 = m                                               <----- Divide both sides by -4

(Step 2) ---------------------------------------------------------------------------------------------

The given equations are in the slope-intercept form. The general structure looks like this:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept. To find the y-intercept, you can plug the newfound slope and values from one point into the equation.

x = -1

y = 2

m = -1/4

y = mx + b                                              <----- Slope-intercept form

2 = (-1/4)(-1) + b                                       <----- Insert values

2 = 1/4 + b                                              <----- Multiply -1/4 and -1

8/4 = 1/4 + b                                           <----- Make common denominators

7/4 = b                                                    <----- Subtract both sides by 1/4

(Step 3) ---------------------------------------------------------------------------------------------

The equation in slope-intercept form is thus: y = -1/4x + 7/4.

While this equation is accurate, it seems that it must be slightly manipulated. Therefore, we need to alter this equation to look like one of the answer choices. For instance, we can multiply the entire equation by 4 to remove the denominator.

y = -1/4x + 7/4                                         <----- Equation

4y = -x + 7                                               <----- Multiply all terms by 4    

x + 4y = 7                                               <----- Add "x" to both sides

Step-by-step explanation:

step 1: multiply [tex]2^m[/tex] by [tex]3^n[/tex]

2 × 3 = 6

to times power you must add them

[tex]2^m[/tex] × [tex]3^n[/tex] = [tex]6^{m+n}[/tex]

step 2: rearrange

[tex]6^{m+n}[/tex] = 108

can you do this step by yourself

Answer:

10 degrees

Step-by-step explanation:

8x = 2x + 60

6x = 60

x = 10

109x is the expression that could be used to determine the total number of cupcakes made given that a parent made x cupcakes for each of the 109 students in the fourth grade. This can be obtained by forming the algebraic expression for the given conditions.

Given that,

A parent made x cupcakes for each of the 109 students in the fourth grade.

The total number of students in the class = 109

The number of cupcakes one student gets = 1 × x = x

⇒ The number of cupcakes 109 student gets = 109 × x = 109x

Hence 109x is the expression that could be used to determine the total number of cupcakes made given that a parent made x cupcakes for each of the 109 students in the fourth grade.

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Compute the speed of the car:

[tex]\dfrac{2\pi\,\rm ft}{1\,\rm rev} \cdot \dfrac{13\,\rm rev}{1\,\rm s} \cdot \dfrac{1\,\rm mi}{5280\,\rm ft} \cdot \dfrac{3600\,\rm s}{1\,\rm h} = \dfrac{195\pi}{11} \dfrac{\rm mi}{\rm h} \approx 55.6919 \dfrac{\rm mi}{\rm h}[/tex]

So after 1 hour, Sal will have driven about 56 mi.

Work Shown:

k = scale factor

k = (A'B')/(AB)

k = 8/12

k = (4*2)/(4*3)

k = 2/3

Triangle A'B'C' (image) has side lengths that are 2/3 as long compared to the side lengths of triangle ABC (preimage).

The equation of the vertical asymptote of the function [tex]g(x)=4log_{2} (x-2)+5[/tex] is x=2.

Vertical asymptotes are vertical lines that represent the zeros of a rational function's denominator. Asymptotes can also occur in other situations, such as logarithms. It occurs at the x-value that is outside the domain of the function, therefore the graph can never cross it.

There may be a vertical asymptote along the vertical line if a portion of the graph is about to turn vertical. At the point of x along which you discovered the vertical asymptote, the function's value changes to either ∞ or -∞. A vertical asymptote, however, must never touch the graph.

Graph the function [tex]g(x)=4log_{2} (x-2)+5[/tex]

(x,y)= (3,5), (4,9), (6,13)

From graph we can see that the graph is turning to be vertical from x=2. So, the equation of vertical asymptote of the function is x=2.

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The complete question is:

“What is the equation of the vertical asymptote of [tex]g(x)=4log_{2} (x-2)+5[/tex]? enter your answer in the box.”

Answer: $200

Step-by-step explanation:

       We will find 66⅔% of $300 to see how much Jay received. A percent divided by 100 becomes a decimal.

               66⅔% / 100 ≈ 0.667

               0.667 * $300 = $200

Question The price of a sofa is Sx. A man buys the sofa on hire purchase according to the following terms:

a downpayment of 25 % and the remaining to be paid in monthly instalments over 30 months at a

simple interest rate of 12 % per annum. Given that his monthly instalment is $52, find the value of x.

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

As you can see in the quadrilateral ABCD, the two angles measure 90° (as they are tangents to circle c) and one of them is given 124°

we need to find the Angle BAD : let it be x ~

By angle sum property of Quadrilaterals,

[tex]\qquad \sf  \dashrightarrow \: 90 + 90 + 124 + x = 360[/tex]

[tex]\qquad \sf  \dashrightarrow \: x+30 4 = 360[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 360 - 304[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 56 \degree[/tex]

Hence, Angle m A = 56°

Answer: c

Step-by-step explanation:

The five number summary and interquartile range for the data-set is given by:

In this problem, we have that:

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The average selling price of a ticket at the Algal Rhythms concert is $25

The given parameters are:

75% of the tickets were sold for $30.

The remaining 25% were sold for $10.

The average selling price of a ticket at the Algal Rhythms concert is calculated using

Average = Sum of (Price * Percentage)

So, we have

Average = 30 * 75% + 10 * 25%

Evaluate the expression

Average = 25

Hence, the average selling price of a ticket at the Algal Rhythms concert is $25

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La ecuación estándar de la circunferencia es (x - 0.5)² + y² = 2.5².

En este problema debemos derivar la ecuación estándar de la circunferencia, cuyo diámetro está comprendido por el segmento de recta entre los puntos A(x, y) = (3, - 4) y B(x, y) = (- 2, - 4). La ecuación estándar de la circunferencia se presenta a continuación:

(x - h)² + (y - k)² = r²     (1)

Donde:

El centro de la circunferencia es el punto medio del segmento de recta AB:

(h, k) = 0.5 · (3, - 4) + 0.5 · (- 2, 4)

(h, k) = (1.5, - 2) + (- 1, 2)

(h, k) = (0.5, 0)

Y el radio de la circunferencia es la mitad de la longitud del segmento de recta AB:

[tex]r = \frac{1}{2}\cdot \sqrt{(-2 - 3)^{2}+[-4 - (-4)]^{2}}[/tex]

r = 2.5

Por tanto, la ecuación estándar de la circunferencia es (x - 0.5)² + y² = 2.5².

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