At the given point, find the slope of the curve, the line that is tangent to the curve, or the line that is normal to the curve, as
requested.
y5+ x3 = y2 + 12x, slope at (0, 1)
0-2
02
04

Answers

Answer 1

The slope of the curve described by the equation at the given point (0,1) as in the task content is; 4.

What is the slope of the curve, the line tangent to the curve at the given point; (0, 1)?

According to the task content, it follows that the slope of the curve can be determined by means of implicit differentiation as follows;

y⁵+ x³ = y² + 12x

5y⁴(dy/dx) -2y(dy/dx) = 12 - 3x²

(dy/dx) = (12 -3x²)/(5y⁴-2y)

Hence, since the slope corresponds at the point given; (0, 1); we have;

(dy/dx) = (12 -3(0)²)/(5(1)⁴-2(1))

dy/dx = 12/3 = 4.

Hence, slope, m = 4.

Consequent to the mathematical computation above, it can then be concluded that the slope of the curve, the line tangent to the curve at the given point is; 4.

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Related Questions

Write an equation for a rational function with: Vertical asymptotes at x = 4 and x = 1 x-intercepts at x = -3 and x = 6 y-intercept at 5

Answers

The rational equation with the desired asymptotes and intercepts is given by:

[tex]f(x) = \frac{-10(x^2 - 3x - 18)}{9(x^2 - 5x + 4)}[/tex]

What are the asymptotes of a function f(x)?

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.

The vertical asymptotes are related to the roots of the  denominator, hence:

[tex]f(x) = \frac{a}{(x - 4)(x - 1)} = \frac{a}{x^2 - 5x + 4}[/tex]

The x-intercepts are related to the numerator of the function, hence:

[tex]f(x) = \frac{a(x + 3)(x - 6)}{x^2 - 5x + 4} = a\frac{x^2 - 3x - 18}{x^2 - 5x + 4}[/tex]

The y-intercept is to find a, hence, when x = 0, y = 5, thus:

-18a/4 = 5

18a = -20

a = -10/9

Hence the function is:

[tex]f(x) = \frac{-10(x^2 - 3x - 18)}{9(x^2 - 5x + 4)}[/tex]

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Which equation represents the data shown in the table below?

Answers

Answer:

  B.  y = x +3

Step-by-step explanation:

The fastest way to find this answer is to substitute offered values of x and y into the given equations to see if they are true.

Substitution

Using the first line in the table, (x, y) = (2, 5), we have ...

  A  5 = 2(2) . . . . false

  B  5 = 2 +3 . . . . true

  C  5 = 3(2) . . . . false

  D  5 = 2 +1 . . . . false

__

Additional comment

Checking answer choices against the problem statement is one of many possible strategies for answering multiple-choice questions.

the size of the second application is 3.45 MB less than he first application. What is the size of the second application

Answers

The size of the second application given the size of the first application and the expression ( x - 3.45 mb) for the size of the second application is 293.55 MB.

Equation

Let

Size of the first application = x

Size of the second application= x - 3.45 mb

For instance,

if the size of the first application is 297 MB

Size of the second application= x - 3.45 mb

= 297 MB - 3.45 MB

= 293.55 MB

Therefore, the size of the second application given the size of the first application and the expression for the size of the second application is 293.55 MB

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If Usman buys 8 books that cost Rs. 120/- each, he will be left Rs. 140/-. If he buys 25 copies, how much he will be left with?​

Answers

He will be left no money after buying 25 copies because he has 1900 rupees less.

Given that Usman buys 8 books that cost Rs. 120/ each, he will be left Rs. 140.

The cost of 1 books is Rs 120.

The cost of 8 book is 120×8=960.

The cost of 25 books is 120×25=3000

To find the money usman will left with him is the difference between the total money and the cost of 25 books.

Total money=960+140=1100

money left=Total money -cost of 25 books

money left=1100-3000

Usman have less money to buy 25 books. He has 1900 rupees less to buy 25 books.

Hence, Usman does leave any money with even he has less money to buy 25 books

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10005²³ x + cos x = 11 sin²x = 9​

Answers

/$/$3)37Aionenejiaiaiahdhsusus

Name plane K using three noncollinear points.

Answers

Answer:

plane HNA, HMB, ANG ...

Step-by-step explanation:

Any combination of three points on plane K will work unless all three are on the same line.

Find d²y/dx² for implicitly in terms of x and y
xy-1=2x+y²

Answers

The second derivative of the implicit function x · y - 1 = 2 · x + y² is equal to y'' = [2 / (2 · y - x)] · [(2 - y) / (x - 2 · y)] · [1 - [(2 - y) / (x - 2 · y)]].

What is the second derivative of an implicit equation?

In this problem we have a function in implicit form, that is, an expression of the form: f(x, y, c) = 0, where c is a constant. Then, we should apply implicit differentiation twice to determine the second derivative of the function:

Original expression

x · y - 1 = 2 · x + y²

First derivative

y + x · y' = 2 + 2 · y · y'

(x - 2 · y) · y' = 2 - y

y' = (2 - y) / (x - 2 · y)

Second derivative

y' + y' + x · y'' = 2 · (y')² + 2 · y · y''

2 · y' - 2 · (y')² = (2 · y - x) · y''

y'' = 2 · [y' - (y')²] / (2 · y - x)

y'' = [2 / (2 · y - x)] · [(2 - y) / (x - 2 · y)] · [1 - [(2 - y) / (x - 2 · y)]]

The second derivative of the implicit function x · y - 1 = 2 · x + y² is equal to y'' = [2 / (2 · y - x)] · [(2 - y) / (x - 2 · y)] · [1 - [(2 - y) / (x - 2 · y)]].

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Which pair of words describe this system of equations
3y=9x-6
2y-6x=4

Answers

The pair of words that describe the given system of equations is: consistent and dependent.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.

It demonstrates the equality of the relationship between the expressions written on the left and the right.

Given equations:

3y=9x-6

2y-6x=4

The first equation can be simplified and written as: y=3x-2

Similarly, the second equation can be written as: y-3x=2

It can be seen that the two equations are the same. Thus, the given system of equations is consistent and dependent.

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All pies at the baked goods booth were cut into eighths. When Justina Hartley’s sift in the boot began, there were eight and one forth pies waiting to be sold. At the end of her shift there were only five pieces of apple pie left. How many pieces of apple pie were sold during Justina’s shift?

Answers

Answer: 3 1/4

Step-by-step explanation: you started with 8 1/4 subtract the 1/4 now ur left with 8-3 which equals 5

The intersection point of an angle bisectors of a triangle

Answers

Answer: The point of intersection of angle bisectors of the 3 angles of triangle ABC is the incenter . The incircle touches each side of the triangle

Question A cylinder has height 7 yards and radius 3 yards. Find the a. volume and b, surface area. Use 3.14 for . Do not round.

Answers

The volume of a cylinder is 197.82 yards³ and the surface area of ​​a cylinder is 188.4 yards².

Given a cylinder has a height of 7 yards and a radius of 3 yards.

(a) We first find the volume of the cylinder using the formula V=πr²h, where π=3.14, r=3 yards and h=7 yards.

Substitute the values ​​in the formula and we get

V=π(3)²×7

V=3.14×9×7

V = 197.82 yards³

(b) We will now find the surface area of ​​the cylinder using the formula S=2πr²+2πrh, where π=3.14, r=3 yards and h=7 yards.

Substitute the values ​​in the formula, we get

S=2π(3)²+2π×3×7

S=2×3.14×9+2×3.14×21

S=56.52+131.88

S = 188.4 square yards

Therefore, the volume and area of ​​a cylinder with a height of 7 meters and a radius of 3 meters is 197.82yards³ and 188.4 yards².

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Circle A has center of (6, 7) and a radius of 4, and circle B has a center of (2, 4) and a radius of 16. What steps will help show that circle A is similar to circle B? (5 points)

Answers

Circle A has center of (6, 7) and a radius of 4, and circle B has a center of (2, 4) and a radius of 16. Now, in order to show that circle A is similar to circle B, we will have to dilate circle A by a scale factor of 4. We can use transformations like dilation and translation to make two circles similar.

Given Information:

For circle A,

Center, C1(x, y) = (6, 7)

Radius, r1 = 4

For circle B,

Center, C2(x, y) = (2, 4)

Radius, r2 = 16

Showing the Two Circles Similar

Now, to make circles A and B similar, we will have to make their centers coincide. It can be done by following the steps listed below:

First, translate circle A using the rule (x + 4, y + 3).Then, rotate circle A by 45° about the center.In the third step, dilate circle A by a scale factor of 4 (r2/r1).Finally, Reflect circle A about the origin to make it similar to circle B

Hence, we can now see that circle A is similar to circle B.

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A large party balloon is being filled with helium at a constant rate. After 8 seconds, there is 2.5L of helium in the balloon.

b) The balloon will burst if there is more than 10 L of helium in it. How long will it take to fill the balloon with that much helium?

Answers

Answer:

32 seconds

Step-by-step explanation:

first 8 secknds gives us the value of set 2.5l

2.5L to make 10 =

10÷2.5=4

That said 2.5L fills 1pL by 4 giving us;

4×2.5= 10L

Determine the fifth term of the binomial expansion (x+y)^4

Answers

The expression, the  fifth term of the binomial expansion is y^4

Binomial expansion

Binomial expansion is a means of expanding expressions into terms

Given the expression (x+y)^4, according to the theorem, as the power of x is decreasing, the power of y will be increasing up till the power of the expression.

Expand (x+y)^4

(x+y)^4 = x^4y^0 + x^3y^1 + x^2y^2 + xy^3 + x^0y^4

Include the coefficients according to the Pascal triangle to have:

(x+y)^4 = x^4y^0 + 4x^3y^1 + 6x^2y^2 + 4xy^3 + x^0y^4

(x+y)^4 = x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4

From the expression, the  fifth term of the binomial expansion is y^4

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SOMEONE PLS HELPP ASAP

Answers

Answer:

yes

Step-by-step explanation:

f the exterior angle of a polygon is given, then the formula to find the interior angle is Interior Angle of a polygon = 180° – Exterior angle of a polygon Method 3: If we know the sum of all the interior angles of a regular polygon, we can obtain the interior angle by dividing the sum by the number of sides

f(x)=ax+b/2 then f^-1 (x-1) =2x-5/2 find a and b​

Answers

From the given inverse function, we have

[tex]f^{-1}(x-1) = 2x - \dfrac52 \\\\ \implies f^{-1}(x) = f^{-1}((x+1)-1) = 2(x+1) - \dfrac52 = 2x-\dfrac12[/tex]

By definition of inverse function,

[tex]f\left(f^{-1}(x)\right) = x[/tex]

so that

[tex]f\left(2x-\dfrac12\right) = x[/tex]

[tex]a\left(2x-\dfrac12\right) + \dfrac b2 = x[/tex]

[tex]2ax - \dfrac a2 + \dfrac b2 = x[/tex]

[tex]\implies\begin{cases}2a=1 \\\\ -\dfrac a2+\dfrac b2 = 0\end{cases}[/tex]

[tex]\implies \boxed{a=\dfrac12}[/tex]

[tex]\implies \dfrac b2 = \dfrac a2 \implies \boxed{b=\dfrac12}[/tex]

if X + Y = 212 and xy = 27 find the value of (x³+y³)

Answers

X^3 + y^3 = (x + y)(x^2 - xy +’y^2)
X^2 + y^2 = (x+y)^2 - 2xy
So
X3 +y^3 = 212((212^2-2(27)-27))
= 212(46983)
= 9,960,396

The world price of umbrellas is $20 each. The pre-trade price of baskets in England is S15 each. What would happen if England allows trade in baskets?

Answers

Answer: Ans. Option c As the price of basket in England is $15, which is less than the world

Given the property:
a = am-n, for a 0
am
an
Explain the three cases for:
a. 0 b. 0 c.m=n

Answers

Could you try reposting the question clearly

Compute the amount of interest earned in the following simple interest problem. A deposit of $1,295 at 7% for 180 days
(Note: Use 365 days in a year)

Answers

since there are 365 days in a year, so 180 days is really just 180/365 of a year, so

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1295\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\to \frac{180}{365}\dotfill &\frac{36}{73} \end{cases} \\\\\\ I = (1295)(0.07)(\frac{36}{73})\implies I\approx 44.7[/tex]

Maytag Company earns $2.60 per share. Today the stock is trading at $46. The company pays an annual dividend of $1.60 a. Calculate the price-earnings ratio (Round your answer to the nearest whole number.) Price-earings natio b. Calculate the stock yield. (Round your answer to the nearest tenth percent.) Stock yield

Answers

a. The price-earnings ratio of Maytag Company's stock is 17.

b. The stock yield of Maytag Company's stock is 3.48%.

What are the price-earnings ratio and stock yield?

The price-earnings ratio is a financial measurement of the worth of Maytag Company.

The price-earnings (P/E) ratio is computed as the current stock price divided by the company's earnings per share.

The P/E ratio shows the potential investor how much to pay per share for each $1 of earnings.

The stock yield is a financial measurement that shows the dividends paid relative to the market value per share.

Data and Calculations:

Earnings per share = $2.60

Current share price = $46

Annual dividend = $1.60

a. Price-earnings ratio = Price per share/earnings per share

= 17 ($46/$2.60).

b. Stock yield = Annual dividend per share/Current stock price x 100

= 3.48% ($1.60/$46 x 100)

Thus, while the price-earnings ratio is 17, the stock yield is 3.48%.

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solve for x in the diagram

Answers

sorry its a little messy!! not good at drawing with a finger haha. all you need to do is follow pedmas and isolate, knowing that a right angle=90°. hope this helps!<3<3

Answer: [tex]\Large\boxed{x=12}[/tex]

Step-by-step explanation:

Given information

∠1 = x + 42°

∠2 = 3x°

Total Angle = 90° (Right Angle)

Derived formula from the given information

∠1 + ∠2 = Total Angle

Substitute values into the given formula

(x + 42) + (3x) = (90)

Combine like terms

x + 3x + 42 = 90

4x + 42 = 90

Subtract 42 on both sides

4x + 42 - 42 = 90 - 42

4x = 48

Divide 4 on both sides

4x / 4 = 48 / 4

[tex]\Large\boxed{x=12}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Earlier in this course, you explored Euclidean geometry, which is the study of flat space. This approach follows the teachings of Euclid, in which he describes the relationships between points, lines, and planes without any numerical measurement. You saw evidence of Euclidean geometry inside several proofs and geometric constructions.

In contrast, the focus of this unit is understanding geometry using positions of points in a Cartesian coordinate system. The study of the relationship between algebra and geometry was pioneered by the French mathematician and philosopher René Descartes. In fact, the Cartesian coordinate system is named after him. The study of geometry that uses coordinates in this manner is called analytical geometry.

It’s clear that this course teaches a combination of analytical and Euclidean geometry. Based on your experiences so far, which approach to geometry do you prefer? Why? Which approach is easier to extend beyond two dimensions? What are some situations in which one approach to geometry would prove more beneficial than the other? Describe the situation and why you think analytical or Euclidean geometry is more applicable.

Answers

Based on my experiences so far, an approach to geometry which I prefer is Euclidean geometry because it's much easier than analytical geometry. Also, an approach that is easier to extend beyond two-dimensions is Euclidean geometry because it can be extended to three-dimension. A situation in which one approach to geometry would prove to be more beneficial than the other is when dealing with flat surfaces.In Euclidean geometry, a correspondence can be established between geometric curves and algebraic equations.

What are the Elements?

The Elements can be defined as a mathematical treatise which comprises 13 books that are attributed to the ancient Greek mathematician who lived in Alexandria, Ptolemaic Egypt c. 300 BC and called Euclid.

Basically, the Elements is a collection of the following geometric knowledge and observations:

DefinitionsPostulatesPropositionsMathematical proofs of the propositions.

Based on my experiences so far, an approach to geometry which I prefer is Euclidean geometry because it's much easier than analytical geometry.  Also, an approach that is easier to extend beyond two-dimensions is Euclidean geometry because it can be extended to three-dimension.

A situation in which one approach to geometry would prove to be more beneficial than the other is when dealing with flat surfaces. In Euclidean geometry, a correspondence can be established between geometric curves and algebraic equations.

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the set of integers less than -20

Answers

{-∞,..........,-22,-21}

In mathematical notation, the set of integers less than -20 as follows:

{-21, -22, -23, -24, -25, ...}

The set of integers less than -20 is the set of all whole numbers that are smaller than -20. Integers include both positive and negative whole numbers, as well as zero.

In mathematical notation, we can represent the set of integers less than -20 as follows:

{-21, -22, -23, -24, -25, ...}

The set includes all numbers that are smaller than -20, going indefinitely in the negative direction. Each number in the set is obtained by subtracting 1 from the previous number in the set.

For example:

-21 is the integer immediately smaller than -20, so it is included in the set.

-22 is the next integer, smaller than -20, so it is also included in the set.

And this pattern continues indefinitely, encompassing all the integers less than -20.

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Question: You can work 40 hours per pay period while attending school earning $12.50 an hour. There are two pay periods per month. NOW Assume you have deductions for health care of $25 per pay period and 401K deduction of $50 per pay period. These deductions are pretax.

Gross Pay per pay period: $
Taxable Income per pay period:

You pay 11% in federal taxes. Federal tax withholding per pay period: $

___

Use the state tax rates below and calculate State tax withholding per pay period: $
(round to two decimals)

_____

From the image:

Calculate FICA withholding per pay period: $

Calculate Medicare withholding per pay period: $
(round to two decimals)

What is your Net pay per pay period: $
​​​​​​​(round to two decimals)

Answers

1) Based on the information, the following taxation calculations can be made:

a) Gross Pay per pay period: $500

b) Taxable Income per pay period: $425

c) Since you pay 11% in federal taxes, the Federal tax withholding per pay period is $46.75.

2) The State tax withholding per pay period is $20.

3) The calculation of FICA, Medicare, and the Net Pay per pay period is as follows:

FICA withholding per pay period: $25.50

Medicare withholding per pay period: $6.16

Net Pay per pay period = $326.59

Data and Calculations:

Total hours worked per pay period = 40 hours

Rate per hour = $12.50

Pay periods per month = 2

Gross pay per pay period = $500 (40 x $12.50)

Deductions per pay period:

Health care = $25

401K deduction = $50

Total deductions per pay period = $75

Taxable income per pay period = $425 ($500 - $75)

Federal taxes = 11%

Federal tax withholding per pay period: $46.75 ($425 x 11%)

Annual taxable income = $10,200 ($425 x 24)

State withholding tax (annual) = $480 {$120 + ($10,200 - $5,000) x 5%}

State withholding tax per pay period = $20 ($480/24)

FICA withholding per pay period: $25.50 ($425 x 6.2%)

Medicare withholding per pay period: $6.16 ($425 x 1.45%)

Net Pay per pay period:

Gross Pay $500

Total deductions $75

Taxable income = $425

Federal Withholding = $46.75

State Withholding = $20

]FICA Withholding = $25.50

Medicare Withholding = $6.16

Net Pay per pay period = $326.59

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Heyy i just need some help with questions 29 if anyone could help me and show the work that would be amazing thank you!!

Answers

Step-by-step explanation:

if we are taking in terms of domain.. is d set of number that we can put to the function with get division by zero .. squaroot of negative number,log of zero e.t.c

A) p(x)/m(x)= 1/squaroot(x) ÷ x²-4 which we know that x²-4 must not be equal to zero

because if is equal to zero we will have division by zero, which have contradicted the hypothesis of law of domain

x²-4 =! 0

(x-2)(x+2)=!0

x=!2 or x=!-2 because if is equal to that it's has contradicted d hypothesis

the answer is all real number except -2 and -

2

B)p(m(x))=p(x²-4) =1/squaroot of x²-4

note they are two things involve we must not get division by zero and root of negative number

we have all real number expect from -2 to 2

C)m(p(x))=m(1/root of (x))=(1/root of (x))²_4)

we have 1/x-4

so the answer is all real number expect zero

Find the value of x.
Round to the nearest tenth.
A
X
29
B
50
26
C

x = [?]°

Answers

Answer:

Below

Step-by-step explanation:

Using the given law of cosines    c = 26   a = 50   b = 29

      and cos c   is  cos x  

26^2 = 50^2 + 29^2 - 2(50)(29) cos x

-2665 = -2900 cos x

cos x = 2665/2900

x = arc cos ( 2665/2900) = 23.2°

PLEASE HELP ASAPP PLEASE

Answers

Answer: Interior Angle

Step-by-step explanation:

The angle BAD is fully enclosed, it is on the inside

Calculus HW , will someone please teach me how to do this problem. I'm struggling, thanks! 10 Points

Answers

Compute the first two derivative.

[tex]f(x) = x \sqrt{16 - x^2} = x (16 - x^2)^{1/2}[/tex]

[tex]f'(x) = x \dfrac{d}{dx} (16 - x^2)^{1/2} + (16 - x^2)^{1/2} \dfrac{d}{dx} x \\\\ ~~~~ = \dfrac x2 (16 - x^2)^{-1/2} \dfrac{d}{dx} (16-x^2) + (16 - x^2)^{1/2} \\\\ ~~~~ = \dfrac x2 (16 - x^2)^{-1/2} (-2x) + (16 - x^2)^{1/2} \\\\ ~~~~ = (16-x^2)^{-1/2} \left(-x^2 + (16 - x^2)\right) \\\\ ~~~~ = \dfrac{16 - 2x^2}{(16 - x^2)^{1/2}}[/tex]

[tex]f''(x) = \dfrac{(16-x^2)^{1/2} \frac d{dx} (16-2x^2) - (16-2x^2) \frac{d}{dx} (16-x^2)^{1/2}}{\left((16-x^2)^{1/2}\right)^2} \\\\ ~~~~ = \dfrac{(16-x^2)^{1/2} (-4x) - (8-x^2) (16 - x^2)^{-1/2} \frac{d}{dx} (16-x^2)}{16 - x^2} \\\\ ~~~~ = \dfrac{-4x (16-x^2) - (8-x^2) (-2x)}{(16 - x^2)^{3/2}} \\\\ ~~~~ = \dfrac{2x^3-48x}{(16 - x^2)^{3/2}}[/tex]

Take note of the domain of [tex]f(x)[/tex]. We must have [tex]16-x^2\ge0[/tex] for the square root to be defined, so

[tex]16 - x^2 \ge 0 \implies x^2 \le 16 \implies |x| \le 4[/tex]

and [tex]f(x)[/tex] exists only for [tex]-4 \le x \le 4[/tex].

Intercepts

Set [tex]x=0[/tex] to find the [tex]y[/tex]-intercepts. The only one is (0, 0), since

[tex]f(0) = 0 \sqrt{16-0^2} = 0[/tex]

The first intercept you listed is not a valid intercept. One or both coordinates must be 0.

Set [tex]f(x)=0[/tex] and solve for [tex]x[/tex] to find [tex]x[/tex]-intercepts. We already found (0, 0); there are two others at (-4, 0) and (4, 0).

[tex]f(x) = x \sqrt{16 - x^2} = 0 \\\\ x = 0 \text{ or } \sqrt{16 - x^2} = 0 \\\\ x = 0 \text{ or } 16 - x^2 = 0 \\\\ x = 0 \text{ or } x^2 = 16 \\\\ x = 0 \text{ or } x = \pm4[/tex]

The instructions say to list these in order from smallest to largest by [tex]x[/tex]-coordinate first, then by [tex]y[/tex]-coordinate. So the proper order of the intercepts would be (-4, 0), (0, 0), and (4, 0).

Relative minima/maxima

Find the critical points. We have [tex]f'(x) = 0[/tex] when

[tex]f'(x) = \dfrac{16 - 2x^2}{(16 - x^2)^{1/2}} = 0 \\\\ 16 - 2x^2 = 0 \\\\ x^2 = 8 \\\\ x = \pm2\sqrt2 \approx \pm 2.83[/tex]

and [tex]f'(x)[/tex] is undefined when

[tex](16 - x^2)^{1/2} = 0 \\\\ 16 - x^2 = 0 \\\\ x^2 = 16 \\\\ x = \pm4[/tex]

Check the sign of the second derivative at the first two critical points.

[tex]f''(-2\sqrt2) = 4 > 0 \implies \text{rel. min. at }  f(-2\sqrt2) = -8[/tex]

[tex]f''(2\sqrt2) = -4 < 0 \implies \text{rel. max. at } f(2\sqrt2) = 8[/tex]

For posterity, we should also check the value of [tex]f(x)[/tex] at the endpoints of the domain.

[tex]f(-4) = f(4) = 0[/tex]

So [tex]f(x)[/tex] has a relative minimum at (-2.83, -8) and a relative maximum at (2.83, 8).

Inflection points

We have [tex]f''(x) = 0[/tex] for

[tex]f''(x) = \dfrac{2x^3-48x}{(16 - x^2)^{3/2}} = 0 \\\\ 2x^3 - 48x = 0 \\\\ 2x (x^2 - 24) = 0 \\\\ 2x = 0 \text{ or } x^2 - 24 = 0 \\\\ x = 0 \text{ or } x = \pm2\sqrt6\approx\pm4.90[/tex]

The two non-zero solutions fall outside the domain, so the only inflection point is (0, 0).

Find the magnitude of −1−5i

Answers

The magnitude of -1-5i is √26.

What is the magnitude of -1-5i ?

Given the complex expression; -1 - 5i

To find the magnitude, we use the formula;

| a+bi | = √[ a² + b² ]

a = -1b = -5

| a+bi | = √[ a² + b² ]

| -1-5i | = √[ (-1)² + (-5)² ]

| -1-5i | = √[ 1 + 25 ]

| -1-5i | = √26

Therefore, the magnitude of -1-5i is √26.

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