PLEASE HELP EXPLANATION 100 POIUNTS

Answer:

See below

Step-by-step explanation:

Extreme values of a function are found by taking the first derivative of the function and setting it equal to 0. To determine if it's a minimum or maximum, we set the second derivative equal to 0 and determine if its positive or negative respectively.

Let's do [tex]f(x)=3x^4+2x^3-5x^2+7[/tex] as an example

By using the power rule where [tex]\frac{d}{dx}(x^n)=nx^{n-1}[/tex], then [tex]f'(x)=12x^3+6x^2-10x[/tex]

Now set [tex]f'(x)=0[/tex] and solve for [tex]x[/tex]:

[tex]0=12x^3+6x^2-10x[/tex]

[tex]0=2x(6x^2+3x-5)[/tex]

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

[tex]x=\frac{-3\pm\sqrt{3^2-4(6)(-5)}}{2(6)}[/tex]

[tex]x=\frac{-3\pm\sqrt{9+120}}{12}[/tex]

[tex]x=\frac{-3\pm\sqrt{129}}{12}[/tex]

[tex]x=-\frac{3}{12}\pm\frac{\sqrt{129}}{12}[/tex]

[tex]x=-\frac{1}{4}\pm\frac{\sqrt{129}}{12}[/tex]

[tex]x_1=0,x_2\approx0.6965,x_3=-1.1965[/tex]

By plugging our critical points into [tex]f(x)[/tex], we can see that our extreme values are located at [tex](0,7)[/tex], [tex](0.6965,5.956)[/tex], and [tex](-1.1965,2.565)[/tex].

The second derivative would be [tex]f''(x)=36x^2+12x-10[/tex] and plugging in our critical points will tell us if they are minimums or maximums.

If [tex]f''(x)>0[/tex], it's a minimum, but if [tex]f''(x)<0[/tex], it's a maximum.

Since [tex]f''(0)=-10<0[/tex] then [tex](0,7)[/tex] is a local maximum

Since [tex]f''(0.6965)=15.822>0[/tex], then [tex](0.6965,5.956)[/tex] is a local minimum

Since [tex]f''(-1.1965)=27.18>0[/tex], then [tex](-1.1965,2.565)[/tex] is a global minimum

Therefore, the extreme values of [tex]f(x)=3x^4+2x^3-5x^2+7[/tex] are a global minimum of [tex](-1.1965,2.565)[/tex], a local minimum of [tex](0.6965,5.956)[/tex], and a local maximum of [tex](0,7)[/tex].

Hope this example helped you understand! I've attached a graph to help you visualize the extreme values and where they're located.

(9y - 6) + 51 = 90 (right angle)

9y - 6 + 51 = 90

9y - 6 = 90 - 51

9y - 6 = 39

9y = 39 + 6

9y = 45

y = 45/9

y = 5

_______

Hope it helps!

꧁✿ ᴿᴬᴵᴺᴮᴼᵂˢᴬᴸᵀ2222 ✬꧂

Answer:

15 and 5 hours.

Step-by-step explanation:

Call x the time taken by the first chap, and y the second.

[tex]\left \{ {{x+y = 20 \atop {55x+60y=1125}} \right.[/tex]

Let's divide by 5 and play with the LHS of the first equation a bit:

[tex]11x+ 11y +y = 225\\11(x+y)+y= 225[/tex] we know how much x+y is ( first equation!) let's solve.

[tex]11(20) +y = 225 \rightarrow y=5[/tex] At this point it's easy to check that [tex]x=15[/tex]

In order to graph the relationship, we will need to write the expression as the equation of a straight line as shown:

d = mt + b

d is the distance covered

t is the time taken

m is the speed

If you are skateboarding at a pace of 30 meters every 5 seconds. your friend is in-line skating at a pace of 9 meters every 2 seconds, this can be written as (5, 30) and (2, 9)

Get the slope of the line:

m = (9-30)/(2-5)

m = -21/-3

m = 7

Substitute m = 7 and the coordinate (2, 9) into the equation y = mt + b

9 = 7(2) + b

9 = 14 + b

b = -5

The required equation to plot will be expressed as y = 7t - 5

Plot the required graph

Learn more here: https://brainly.com/question/17003809

If the house is sold with a 25% profit then the purchase price of the house will be equal to $48,675.

The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.

As per the data provided in the question,

The selling price of the house = $64,900

Profit percent = 25%

The profit price of the house after selling,

64900 × 25/100

= $16225

Now,

The purchase price of the house,

$64900 - $16225 = $48675.

To know more about Percentage:

https://brainly.com/question/29306119

#SPJ2

Answer:

A    -4; -2; 0 ; 2 ; 4 ; 6 ; 8 ; 10

B   1; 2; 3; 4; 5; 6; 7; 8

Answer:

257

Step-by-step explanation:

216 + (5 x(8 + 1/5)

Answer:

45*x-10

Step-by-step explanation:

10 less than a number would give you

x - 10

and the product of a number means your multiplying and your multiplying 45 so you would get

45*x

add them together and you get

45*x-10

Answer:

c

Step-by-step explanation:

Answer:

−2.

Step-by-step explanation:

y = 4 − 2x? b is the y -intercept. Here, 4 is b and −2 is m. Therefore, the slope is −2.

Answer:

Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon and Decagon

Answer:

1.Regular Polygons.

2.Irregular Polygons.

3.Concave Polygons.

4.Convex Polygons.

5.Trigons.

6.Quadrilateral Polygons.

7.Pentagon Polygons.

8.Hexagon Polygons.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

[tex]\dfrac{13}{24}< \dfrac 7{12} < \dfrac 34[/tex]

[tex]7(\frac{9}{4}x- \frac{18}{7})= -\frac{5}{21} +\frac{17}{7}x <=> \frac{63}{4}x-18 =-\frac{5}{21}+ \frac{17}{7}x\\ <=>\frac{63}{4}x - \frac{17}{7}x = 18-\frac{5}{21}<=>\frac{373}{28} =\frac{373}{21} <=>x=\frac{4}{3}[/tex]

ok done. Thank to me :>

Step-by-step explanation:

I=PTR/100

cross multiply to get 100I= PTR

Put 100I/PR and PTR/PR

HENCE u get 100I/PR=T

THIS is because the PR cancelled from PRT to remain with T

Answer:

Step-by-step explanation:

Altitude or height

Answer

It is known as altitude

There are three such altitudes and the point of intersection of these altitudes

is called as orthocentre

Please find attached photograph for your answer.

Hope it helps.

Do comment if you have any query.

[tex]\\ \sf\longmapsto \sqrt{X^{a-b}}\times \sqrt{X^{b-c}}\times \sqrt{X^{c-a}}[/tex]

[tex]\\ \sf\longmapsto X^{\frac{a-b}{2}}\times X^{\frac{b-c}{2}}\times X^{\frac{c-a}{2}}[/tex]

[tex]\\ \sf\longmapsto X^{\frac{a-b}{2}+\frac{b-c}{2}+\frac{c-a}{2}}[/tex]

[tex]\\ \sf\longmapsto X^{\frac{a-b+b-c+c-a}{2}}[/tex]

[tex]\\ \sf\longmapsto X^{\frac{a-a+b-b+c-c}{2}}[/tex]

[tex]\\ \sf\longmapsto X^{\frac{0}{2}}[/tex]

[tex]\\ \sf\longmapsto X^0[/tex]

[tex]\\ \sf\longmapsto 1[/tex]

Step-by-step explanation:

the most common form of line equation is

y = ax + b

a is the slope of the line. it is expressed as the ratio

y coordinate change / x coordinate change

when going from one point to the other.

b is the y-intercept (the y value when x = 0).

once we have the slope, we get b by using the coordinates of one of the given points as x and y in the equation and since for b.

for the slope a :

x changes by +5 (from -3 to 2)

y changes by -15 (from 10 to -5)

so, the slope is -15/+5 = -3

the equation looks now like

y = -3x + b

let's use the first point

10 = -3×-3 + b = 9 + b

1 = b

so, the equation is

y = -3x + 1

Answer:

98

Step-by-step explanation:

It is 98! x and the 98 degree angle are corresponding angles and m is parallel to n. dw I hate geometry too.

Answer:

16c+24

Step-by-step explanation:

4c+4c+7+7+8c+10=16c+24

Answer: fraction:47/200 desimal:0.235

Step-by-step explanation:

Refer to the attachment

Answer:

[tex]\sqrt[2]{225} =15[/tex], [tex]\sqrt[2]{961} =31[/tex], [tex]\sqrt[2]{3969} =69[/tex], [tex]\sqrt[2]{10404} =102[/tex]

Step-by-step explanation:

[tex]\sqrt[2]{225} =\sqrt{15*15}=15[/tex]

[tex]\sqrt[2]{961}=\sqrt{31*31} =31[/tex]

[tex]\sqrt[2]{3969} =\sqrt{69*69} =69[/tex]

[tex]\sqrt[2]{10404} =\sqrt{102*102}=102[/tex]

Answer:

the shape of the graph is a vertical straight line. So the angle is 90°

So tan 90° = infinite

Answer:  The slope is undefined.

Step-by-step explanation:

The slope is undefined because it is based on the Rise (y) over the Run (x) of the data points.  X is not changing even as y goes from -2 to 8.  If we took the first and last points, (-1,-2) and (-1,8) and go from left to right, y increases by (8-(-2)) = 10 while x is unchanged, or o.  Rise/Run therefore becomes 10/0.  Division by 0 is undefined in math, so the slope is undefined.

This is a straight vertical line going through x = -1.  All y's are on this line.  Undefined slope.

Answer:

Step-by-step explanation:

Answer:

n = 8

Step-by-step explanation:

Both given angles are verticale angles therefore they are congruent, so;

9n = 8n + 8

(9n - 8n) = 8

n = 8

Hope this helps!

Answer:

Number 4

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

C. y = 1/4 x - 3

Step-by-step explanation:

Answer:

7 5/12

Step-by-step explanation:

first, subtract 4 5/6 from 6 2/3 by converting 6 2/3 to 6 4/6

5 3/4 + (6 4/6 - 4 5/6) = 5 3/4 + 1 4/6

* I borrowed 6/6 or '1' from the 6 and made 4/6 into 10/6

5 3/4 equals 5 9/12 and 1 4/6 equals 1 8/12

adding them gives you:

6 17/12 which is the same as 6 + 1 5/12, or 7 5/12

Answer:

The answer would be 26

Step-by-step explanation:

First I divided the shape to make a rectangle and a right  angle triangle, then i calculated the shape of the rectangle which came out to be 20. After that I calculated the area of the right angle triangle which is 6. So The answer would be 6 + 20 = 26

Answer:

47.5 minutes

Step-by-step explanation:

40 min = 80

x min = 95

40/80 = x/95

3800 = 80x

x = 47.5

-Chetan K