Find the taylor polynomial of degree three for the function x^0.2 about the point a=7. (your answers should include the variable x when appropriate.)

Answer:

[tex]x1=\frac{-2(+)2i\sqrt{2}} {3}[/tex]

[tex]x2=\frac{-2(-)2i\sqrt{2}} {3}[/tex]

Step-by-step explanation:

we have

[tex]-3x^{2} -4x-4=0[/tex]

Rewrite (Multiply by [tex]-1[/tex] both sides)

[tex]3x^{2}+4x+4=0[/tex]

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]3x^{2}+4x+4=0[/tex]

so

[tex]a=3\\b=4\\c=4[/tex]

substitute

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

[tex]x=\frac{-4(+/-)\sqrt{-32}} {6}[/tex]

remember that

[tex]i=\sqrt{-1}[/tex]

[tex]x=\frac{-4(+/-)4i\sqrt{2}} {6}[/tex]

Simplify

[tex]x=\frac{-2(+/-)2i\sqrt{2}} {3}[/tex]

[tex]x1=\frac{-2(+)2i\sqrt{2}} {3}[/tex]

[tex]x2=\frac{-2(-)2i\sqrt{2}} {3}[/tex]

ASA

Is the answer i got on my work

Final answer:

There were 113 people who bought a ticket but did not show up to the concert, calculated by subtracting the number of attendees (587) from the total tickets sold (700).

Explanation:

To determine how many people bought a ticket but did not attend the concert, you would subtract the number of people who attended from the total number of tickets sold. In this case, 700 tickets were sold and only 587 people attended. So, the calculation would be:

700 tickets sold - 587 attendees = 113 people who did not attend

Thus, 113 people bought a ticket but did not show up to the concert.

Answer:

25

Step-by-step explanation:

Complex numbers are "binomials" of a sort, and are added, subtracted, and multiplied in a similar way. (Division, which is further down the page, is a bit different.) First, though, you'll probably be asked to demonstrate that you understand the definition of complex numbers.

To simplify complex-valued expressions, you combine "like" terms and apply the various other methods you learned for working with polynomials.

(2 + 3i) + (1 – 6i) = (2 + 1) + (3i – 6i) = 3 + (–3i) = 3 – 3i

You may find it helpful to insert the "1" in front of the second set of parentheses (highlighted in red above) so you can better keep track of the "minus" being multiplied through the parentheses.

Final answer:

To solve a complex number, understand it as a sum of a real number and an imaginary number and use operations like conjugation. For division, multiply by the conjugate to simplify. Complex numbers ensure all polynomial equations have solutions.

Explanation:

To solve a complex number, one must understand that a complex number z is the sum of a real number and an imaginary number, which is written as z = a + ib. The terms a and b represent the real and imaginary parts respectively, often notated as Re(z) and Im(z).

To divide by a complex number, you multiply the numerator and the denominator by the conjugate of the denominator, simplifying to a form without imaginary numbers in the denominator. This can be expressed as z/z' = (aa' + bb')/(a'² +b'²) + i(ba' - ab')/(a'² + b'²). The conjugate of a complex number z is written as z* or z*.

Complex numbers are crucial in solving polynomial equations as they ensure that every polynomial equation has a solution. This is shown by the Fundamental Theorem of Algebra, which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. For instance, the equation x² - 2x + 5 = 0 has no real solutions but two complex solutions, x = 1±2i.

Final answer:

To convert 6 7/9% to a decimal, we change the mixed number to an improper fraction, divide by 100 and round to the nearest thousandth, resulting in approximately 0.068.

Explanation:

To find the decimal equivalent of 6 7/9%, we must first convert the mixed number to an improper fraction and then to a decimal. To convert 6 7/9% to an improper fraction, we multiply the whole number 6 by the denominator 9 and add the numerator 7 to get 7 + (6 × 9) = 7 + 54 = 61. Then we place 61 over the original denominator to obtain 61/9. The percentage sign indicates that we are dealing with a part out of 100, so we must divide 61/9 by 100 or, equivalently, multiply by 1/100.

Therefore, the calculation to convert the percentage to a decimal is: (61/9) × (1/100) = 61/900. Using a calculator, or performing the division manually, gives us approximately 0.0677777....

Finally, to round this to the nearest thousandth, we would look at the fourth decimal place (which is 7 in this case). Since 7 is greater than 5, we round up the third decimal place, resulting in 0.068.

25 * 2.5 = 62.5 *2 = 125

8x5 = 40

125 +40 = 165 square feet

Final answer:

The standard form of the equation y = (3/8)x - 4 is 8y - 3x = -32.

Explanation:

The standard form of the equation y = (3/8)x - 4 is written as 8y - 3x = -32.

To convert a linear equation from slope-intercept form (y = mx + b) to standard form (Ax + By = C), you need to multiply the entire equation by the common denominator of the coefficients.

In this case, the common denominator is 8, so multiplying both sides of the equation by 8 gives us 8y = 3x - 32. Moving all the terms to one side, we have 8y - 3x = -32, which is the standard form of the equation.

To transform the equation y = 3/8x - 4 into standard form, subtract 3/8x from both sides and then multiply through by 8 to eliminate the fraction, resulting in -3x + 8y = -32.

The standard form of a linear equation is typically written as Ax + By = C, where A, B, and C are integers and A should not be negative. To convert the equation y = 3/8x - 4 to standard form, you need to manipulate the equation so that it fits the standard form criteria.

Step-by-step, we start by moving the x-term to the left side of the equation:

Therefore, the standard form of the given equation is -3x + 8y = -32.

The standard form of the equation  is:

                  [tex]x=8y^2-16y-7[/tex]

We know that the standard form of a quadratic equation is given by the expression:

[tex]x=ay^2+by+c[/tex]

where a,b and c are real numbers.

and a≠0

Here we are given the  vertex form of the equation of a parabola by:

[tex]x=8(y-1)^2-15[/tex]

Now, on expanding the parentheses term by using the formula:

[tex](a-b)^2=a^2+b^2-2ab[/tex]

Here a=y and b= 1

Hence, we have:

[tex]x=8(y^2+1-2y)-15\\\\i.e.\\\\x=8\times y^2+8\times 1-2y\times 8-15\\\\i.e.\\\\x=8y^2+8-16y-15\\\\i.e.\\\\x=8y^2-16y+8-15[/tex]

( Since, in the last step we combined the constant term i.e. 8 and -15 )

Hence, we get the standard form of the equation as:

[tex]x=8y^2-16y-7[/tex]

Answer:

the answer is B

Step-by-step explanation:

The acceptable circumferences for a woman's basketball range from 28.5 inches to 29 inches.

To find the acceptable circumferences for a woman's basketball, we need to consider the ideal circumference and the allowable variation. The ideal circumference is 28.75 inches and the actual circumference can vary by at most 0.25 inches. So, the acceptable circumferences can be found by adding and subtracting the maximum allowable variation from the ideal circumference:

Acceptable circumference = 28.75 ± 0.25 inches

This means the acceptable circumferences for a woman's basketball range from 28.5 inches to 29 inches.

300/6 = 50 mph

250/5 =50mph

 so they drove 50 miles per hour

 so 50 *3 = 150 miles in 3 hours

>First jump = 4.25 m

>Best jump = 1.12 * First jump

Best jump = 1.12 * (4.25 m)

Best jump = 4.76 m

>Best jump = 0.85 * Winning jump

Hence,

Winning jump = Best jump / 0.85

Winning jump = 4.76 m / 0.85

Winning jump = 5.6 m

Answer:

The correct answer is C.

Step-by-step explanation:

This can be done using complex numbers and its relations with plane geometry. The endpoints of the segment are X(-6,2) and Y(-1,-3). These points can be seen as complex numbers, just recall the geometric interpretation of complex numbers.

So, the complex counterpart of [tex]X(-6,2) is x=-6+2i[/tex], and the complex counterpart of [tex]Y(-1,-3) = -1-3i[/tex]. Moreover, a rotation about the origin has an interpretation as multiplication by a complex number of modulus 1. In this particular case, a rotation of 90 degrees is equivalent to multiply by the complex unit: [tex]i=\sqrt{-1}[/tex].

Then,

[tex] x' = (-6+2i)\times i = -2-6i[/tex] which gives the point [tex]X'(-2,-6)[/tex]

[tex] x' = (-1-3i)\times i = 3-1i[/tex] which gives the point [tex]Y'(2,-1)[/tex].

The other option is to use a software to make geometrical constructions as Geogebra. Bellow there is an image attached made with Geogebra with the solution of the exercise.

8.2% = 0.082

50 * 0.082 = 4.1

the answer is 4.1

Answer:

C.Less than $712.50

Step-by-step explanation:

Given details are :

Loan amount = $190,000

Rate = 4.5% or 0.045 compounded monthly.

Time = [tex]30\times12=360[/tex] months

Monthly payments are = $962.70

First month interest = $712.50

I have calculated this using excel sheet and the answer is - C.Less than $712.50 .

Please find attached the excel sheet to see the working. You can see the highlighted interest that is less than first month interest.

Answer:Less than $712.50

Step-by-step explanation: