Answer: The number 99.4177 rounded to the nearest hundredth is 99.42.
Step-by-step explanation:
Here's how I got my answer:
Since you need to round to the nearest hundredth, then round to the first two decimal places. So if the number is 5 or greater, then round up. If the number is 4 or lesser, then do not round up.
In this scenario:
99.4177
Round the 1 in the hundredths place up to 2, because 7 is on the greater end. Since they are just asking you for the hundredths place, then do not round anything else.
Hence, your final answer is 99.42.
Pls help!! Find the area of the lighter shaded region and round to the nearest tenth.
Answer:
5.1 cm² approximately
Step-by-step explanation:
A lighter= Area inscribed -1/2r² sin80°
A lighter=π r² (80°/360°) -1/2(5 cm)² sin 80°
A lighter=π(5cm)² (80°/360°) -1/2(5 cm)² sin 80°
A lighter=3.14*25cm²(80°/360°) - 12.5cm² sin 80°
A lighter=17.444…cm² - 12.31009... cm²
A lighter=5.13cm² approximately
Answer: =approx 5.13 cm²
Step-by-step explanation:
Lets find the area of the region that is blue ( dark blue+light blue)
S= pi*r^2/360*80=pi*25*2/9=pi*50/9
The lighter region' s area is the S- S(triangle marked with dark blue)
The area of this triangle is r^2*sin(80°)/2= 25*sin(80°)/2=
=12.5*sin(80°)
So the required area Sreg= pi*50/9-12.5*sin(80°)=
= approx 3.14*50/9-12.5*0.985=approx 5.13 cm²
Solve the equation using the Properties of Equality: 15a = – 2
Answer:
2
a = - ------
15
Step-by-step explanation:
15 a = -2 (divide 15 on each side)
15a 2
----- = - ------
15 15
2
a = - ------
15
Need Help With This Equation
Show Work
Answer:
$42
Step-by-step explanation:
Original price: $56
Discount: 25%
A discount of 25% means that the discount is 25% of the price of the item, so you need to subtract 25% of the price of the item from the original price of the item.
Let's find an expression for the amount of the discount.
25% of $56 = 25% * $56 = 0.25 * $56
The amount of discount is 0.25 * $56.
Now we subtract that amount form the original price of $56.
$56 - 0.25 * $56 = $56 - $14 = $42
Answer: The boots cost $42 on sale.
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Answer:
22 is the avrage rate of elavation change in feet per second if a sumbarine dives 440 feet in 20 seconds
-22 is the avrage temature change in degrees
440 is the avrage distance in miles
2.20 is the boys height if that makes sense
Step-by-step explanation:
if it dosent make sent om sorry
given that cos 60°= sin 30°= 1/2 and cos 30°= sin 60°= √3/2, evaluate tan 60°-1/ 1- tan 30°
Answer:
answer is on the sheet photo
exponents and power - simplify and express result with positive index
Answer :
[tex] {ab}^{3} [/tex]
the answer should look like this. (___,___) plzzz fast.
Answer:
( -1, 15/2) or ( -1, 7 1/2)
Step-by-step explanation:
Formula: ( (x1 + x2)/2, (y1 + y2)/2 )
1. ( (-4 +6)/2, (8 + 7)/2 ) Plug in
2. ( -2/2, 15/2) Add/Subtract
3. ( -1, 15/2) or ( -1, 7 1/2) Divide
Answer:
Coordinates of the midpoint are: (1, 7.5)
Step-by-step explanation:
Find the distance between the x-values of the given points,and the distance between the y-values of them:
distance between 7 and 8 (y-values of N and A respectively) is: 8-7 = 1
then half of that is 0.5, therefore, the midpoint should have for y value the value of the minimum between 7 and 8 (7) plus 0.5, that is, the y-value of the midpoint is: 7.5
Now for the x-value of the midpoint we do something similar:
The distance between 6 and -4 (x-values of B and A respectively) is: 10 units, half of this is 5, and therefore, the x-value of the midpoint should be at the minimum of those two values (-4) plus 5 units, that is: -4 + 5 = 1
Coordinates of the midpoint are: (1, 7.5)
Use the coordinate plane to plot the point (3, 6). Then complete the statements that explain how to plot the point. Start at the ____ Move 3 units ____ Move 6 units ____ Plot a point ____
Answer:
Use the coordinate plane to plot the point (3, 6). Then complete the statements that explain how to plot the point. Start at the origin. Move 3 units right Move 6 units up Plot a point there.
Step-by-step explanation:
To plot the point, start at the origin. Move 3 units right and Move 6 units upwards to plot a point (3 6).
What is a coordinate plane ?A coordinate plane is a plane in which a set of two number lines are represented, horizontal line is called x-axis and vertical line is called y-axis.
The given point is (3, 6).
The coordinate plane to plot the point (3, 6) is shown below.
To plot the graph of point (3, 6) on coordinate plane,
Start at the origin. Move 3 units right and Move 6 units upwards to plot a point (3 6).
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A basket of fruit contains 4 bananas, 3 apples, and 5 oranges. You intend to draw a piece of fruit from the basket, keep it, and then draw a 2nd piece of fruit from the basket. What is the probability of selecting two oranges in a row from the basket if you are blindfolded?
Answer: 5/33
Step-by-step explanation: There are 12 fruits and 5 are oranges.
If you draw an orange, then there are 11 fruits and 4 oranges. (5/12)x(4/11)=20/132 or 5/33 in simplest form.
change 1011 to base 10 number
Answer:
11.
Step-by-step explanation:
1011 is a number in binary.
To convert 1011 from base 2 to base 10...
1(2^3) + 0(2^2) + 1(2^1) + 1(2^0)
= 1(8) + 0 + 1(2) + 1(1)
= 8 + 2 + 1
= 11
Hope this helps!
Often, anomalous objects are known as _____, since on a scatter plot of the data, they lie far away from other data points.
Answer:
outliers
Step-by-step explanation:
An outlier is a data point that is significantly different from other observations. An outlier might be due to inconsistency in measurements, or due to an error introduced into the experiment. Outliers cans lie extremely high or low of other observation in statistics, and they usually create a big problem for proper analysis.
7 1/8 + 7 1/13= Give my answer as a mixed number
Answer:
[see below]
Step-by-step explanation:
[tex]7(1/8)+7(1/13)\\\\\text{Add Whole Numbers: }\\\\7 + 7 = 14\\\\\text {Add fractions: }\\\\ (1/8)+(1/13)\\\\LCM (8, 13): 104\\\\(13/104)+(8/104)\\\\(21/104)\\\\\\\text{Combine: }\\\\14 + (21/104)\\\\\boxed{14\frac{21}{104}}[/tex]
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
[tex]\boxed {14\frac{35}{104}}[/tex]
Step 1 : Solving the fraction parts.
[tex]\frac{71}{8} + \frac{71}{13} = ?[/tex]
Find the LCD of 71/8 and 71/13 and rewrite to solve with the equivalent fractions.
LCD = 104
[tex]\frac{923}{104} + \frac{568}{104} = \frac{1491}{104}[/tex]
Simplifying the fraction part, 1491/104,
[tex]\frac{1491}{104} = 14\frac{35}{104}[/tex]
____________________
Solution by Formulas
____________________
Using the given fractions
[tex]\frac{71}{8} + \frac{71}{13}[/tex]
Applying the fractions formula for addition,
[tex]= \frac{(71 . 13) + ( 71 . 8 ) }{8 . 13}[/tex]
[tex]= \frac{923 . 568}{104}[/tex]
[tex]= \frac{1491}{104}[/tex]
Simplifying 1491/104, the answer is:
[tex]\boxed {14\frac{35}{104}}[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
a natural number between 6 and 12
Which scenario is best represented by the graph
Answer:
A taxi travels at a constant speed of 50 miles per hour.
Hope this helps!
In May 1998, forest fires in southern Mexico and Guatemala spread smoke all the way to Austin. Those fires consumed forest land at a rate of 25200 acres/week. On the average, how many square meters of forest are burned down every minute
Answer:
On average the size of the area of the forest burnt down every minute is 10117.14 m²
Step-by-step explanation:
The given parameters are;
The rate consumption of forest land by the fire = 25200 acres/week
Therefore, we have;
The number of minutes in one week = 60 × 24 × 7 = 10080 minutes
Therefore;
The rate consumption of forest land by the fire per minute = 25200/10080 acres/minute = 2.5 acres/minute
The number of square meters in one acre is given as follows;
1 acre = 4,046.856 m²
Therefore;
2.5 acres/minute = (2.5 × 4,046.856 m²/(1 acre)) acres/minute = 10117.14 m²/minute
Which give;
The rate consumption of forest land by the fire= 10117.14 m²/minute.
The rate of the fire consumption of the forest is 10117.14 m²/minute.
Classify the data as qualitative or quantitative. If qualitative then classify it as ordinal or categorical, and if quantitative then classify it as discrete or continuous. Variable Height (in inches) Grade (ABCDF) Weight (exact) Color Data Type a Quantitative Continuous b Quantitative Discrete c Qualitative Categorical d Qualitative Ordinal
Answer:
Explained below.
Step-by-step explanation:
Qualitative variables are categorized or labelled to belong to a certain category or group.
There are two types of qualitative variables, Categorical and ordinal.
Categorical variable are those variables that are labelled in non-numeric or numeric form, where the numbers have no value. The order also does not matters. For example, the number on the jerseys of football players. It is not necessary that the player number 1 is actually the best player.
Ordinal variables are those variables where the label or category has to be in order. For example, the rank of students in the statistics class.
Quantitative variables are in numerical form and can be measured.
There are two types of quantitative variables, discrete and continuous.
Discrete variables are those variables that assume finite and specific value. For example, the number of girls in each section of a school.
Continuous variables are those variables that can assume any number of values between a specific interval. For example, the time it takes to reach point B from A.
Variable Category Sub-Category
Height Quantitative Continuous
Grade Qualitative Ordinal
Weight Quantitative Continuous
Color Qualitative Categorical
BRAINLIEST IF RIGHT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Trevon's Custom Kitchen Supplies sells handmade forks and spoons. It costs the store $1.80 to buy the supplies to make a fork and $1.40 to buy the supplies to make a spoon. The store sells forks for $4.60 and spoons for $5.40. Last April Trevon's Custom Kitchen Supplies spent $24.60 on materials for forks and spoons. They sold the finished products for a total of $73.80. How many forks and how many spoons did they make last April? A. 8 forks and 10 spoons B. 8 forks and 8 spoons C. 9 forks and 9 spoons D. 9 forks and 6 spoons
Answer:
D. 9 forks and 6 spoons
Step-by-step explanation:
Let's calculate how many forks and spoons were made. We need to guess a pair of variable values that will add up to $24.60. We'll do this by substituting all the possible pairs in:
Here's the pair for A:
[($1.80 * a) + ($1.40 * b)]
= [($1.80 * 8) + ($1.40 * 10)]
= [$14.40 + $14]
= $28.40
Is $28.40 equal to $24.60? No, this is not correct.
Here's the pair for B:
[($1.80 * a) + ($1.40 * b)]
= [($1.80 * 8) + ($1.40 * 8)]
= [$14.40 + $10.80]
= $25.20
Is $25.20 equal to $24.60? No, this is not correct.
Here's the pair for C:
[($1.80 * a) + ($1.40 * b)]
= [($1.80 * 9) + ($1.40 * 9)]
= [$16.20 + $12.60]
= $28.80
Is $28.80 equal to $24.60? No, this is not correct.
Here's the pair for D:
[($1.80 * a) + ($1.40 * b)]
= [($1.80 * 9) + ($1.40 * 6)]
= [$16.20 + $8.40]
= $24.60
Is $24.60 equal to $24.60? Yes, this is correct.
Therefore, we know the answer is (D) 9 forks and 6 spoons
We can also check by substituting these values to find the amount Trevon's Custom Kitchen Supplies earned last April:
[($4.60 * a) + ($5.40 * b)]
= [($4.60 * 9) + ($5.40 * 6)]
= [$41.40 + $32.40]
= $73.80
This is equal to the amount of money earned last April.
I hope this helps! Tell me if I'm wrong, please!
Devon bought running shocs at a price that was 1/4 off the original price of $88. He paid a sales tax of 7% on
the discounted price and gave the clerk four $20 bills.
How much change should he receive?
A. $ 4.62
B. $ 7.84
C. $ 9.38
D. $12.46
E. $18.62
The correct answer is C. $ 9.38
Explanation:
The first step to solve this mathematical problem is to know the price of the shoes. About this, we know the price is 1/4 of $88 plus taxes. You can find how much is 1/4 of $88 by following this process:
1. Write the amounts given
[tex]\frac{1}{4}[/tex] of [tex]88[/tex]
2. Divide the number by the denominator (bottom number) and then multiply by the numerator
[tex]88[/tex] ÷ [tex]4 = 22[/tex]
[tex]22 x 1 = 22[/tex]
This means the discount was $22 and $88- $22 = $66, which is the price with the discount. Now, it is necessary to add the sales tax, which can be done by finding the 7% of $66 and adding this number to $66 (the price of the shoes including the 1/4 discount)
1. Write the values
66 = 100 (66 represents the total or 100%)
x = 7 (7% is the value you want to know and the x represents the value is not known)
2. Cross multiply
x 100 = 462
3. Find x
x = 462 ÷ 100
x = 4. 62 ( value of taxes)
Now, add the taxes to the price $66 + $ 4.62 = $70.62 (price with taxes). Finally, we know Devon paid using four $20 bills. This means he gave the clerk $80 ($20 x 4 = $80). Finally, to know how much is the change subtract the price of the shoes from the money Devon gave the clerk $80 - $70.62 = $9.38
In the problem below, what is the SECOND operation that should be performed:
42 - (28 + 7) + 111
Answer:
Add -28 and -7 (2nd operation)
Step-by-step explanation:
42-(28+7)+111
Step 1: Remove the brackets
42-28-7-11
Step 2: Add 42 and 111( 1st operation ) you can also rewrite to avoid confusion
42+111-28-7
= 153-28-7
Step 3: Add -28 and -7 (2nd operation)
153-28-7
=153-35
Step 4 : Subtract
153-35
=118
student/dashboard/home
Dan sees the following number pattern on the chalkboard.
5, 10, 20, 40...
What is the rule for this pattern?
1)) add 5, then add 10
(1) multiply by 10
1) multiply by 2
Answer:
multiply by 2
Step-by-step explanation:
5x2=10
10x2=20
Answer:
multiplying by 2 ........
The expression 3r - 6 can be written as _____. A:3(r - 2) B:3(r - 6) C:3(3r - 6)
Answer:
[tex] \boxed{ \bold{ \sf{ \boxed{3(r - 2)}}}}[/tex]Option A is the correct option.
Step-by-step explanation:
[tex] \sf{3r - 6}[/tex]
▪️If there is a common factor in each term of an expression, the common factor can be taken as the factor with the remaining terms.
Here, taking 3 common
[tex] \sf{3(r - 2)}[/tex]
Hope I helped!
Best regards!!
Answer: 3(r - 2)
Step-by-step explanation: First, determine the Greatest Common Factor between the different terms in the polynomial.
The Greatest Common Factor between 3r and 6 is 3.
So a 3 factors out.
Inside the parenthses, we are left with each term divided by 3.
So we have 3(r - 2) as our final answer.
When a vehicle is in motion, it has _____. A. no weight B. no inertia C. potential energy D. kinetic energy
Answer:
D kinetic energy
Step-by-step explanation:
When a vehicle is in motion, it has kinetic energy. Option C is correct.
The statement is given, When a vehicle is in motion, it has _____.
Blank statement to be filled from the options A. no weight B. no inertia C. potential energy D. kinetic energy.
When an object is subjected to perform a motion by the action of force induced by external means the object's potential energy transforms into kinetic energy. Or kinetic energy is half the product of mass and square of the velocity.
When a vehicle is in motion. it has both kinetic energy and inertia because a vehicle has velocity and weight respectively. Since kinetic energy is directly proportional to the square of velocity, inertia is directly proportional to weight. In option, we have only kinetic energy options.
Thus, When a vehicle is in motion, it has kinetic energy. Option C is correct.
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Tom can type 120 words in 3 minutes. What is the ratio of words typed to minutes? Question 2 options: A. 1 : 117 B. 1 : 40 C. 40 : 1 D. 117 : 1
Answer:
C
Step-by-step explanation:
Since he writes 120 words in 3 minutes, we know that Tom will write 120 / 3 = 40 words in 1 minute, therefore the ratio is 40 : 1. It's not 1 : 40 because the question is asking for the ratio of words typed to minutes, not minutes to words typed.
A piece of rope falls out of a hot air
balloon from a height of 5,184 ft. If the
equation for height as a function of time
is h(t) = -16t2 - initial height where t is
time in seconds and h(t) is height in feet,
how many seconds will it take for the
piece of rope to hit the ground?
Answer:
18 seconds
Step-by-step explanation:
Given the equation for height as a function of time expressed as
h(t) = -16t² - initial height, if initial height is 5,184ft, the expression will become;
h(t) = -16t² - 5,184
t is time in seconds
h(t) is height in feet
The height of the rope on the ground is zero. In order to calculate the amount of seconds it will take the piece of rope to hit the ground, we will substitute h(t) = 0 into the modeled equation as shown:
Since the body falls downwards (negative direction), initial height = -5184 ft
h(t) = -16t² - -(5,184)
0 = -16t² + 5,184
0+16t² = 5184
16t² = 5184
16t²/16 = 5184/16
t² = 324
t = √324
t = 18 seconds
Hence, it will take the rope 18seconds to hit the ground.
Answer:18 seconds
Step-by-step explanation:just did the assignment
The graphs below have the same shape. Complete the equation of the blue
graph. Enter exponents using the caret (-); for example, enter x2 as x^2.
The answer : (x-5)^2 .....................................(x-5)square
For example, for f(x)= x square . For x=1 ,then, y=1 .
But consider the g function. the minimum value that g function has is x is 5. When x is 5, y is 0 . So (x-5)square is the equation of this function.
The complete equation of the blue graph is (x-5)^2.
What is a function?
Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
Linear function is a function whose graph is a straight line
We are given that;
Red graph equation= X^2
Now,
In blue graph it shifted by 5 units to the right
For blue graph
x=5
Putting the value of x in red graph equation
=(x-5)^2
=x^2 + 25 - 10x
Therefore, by the given graph function will be (x-5)^2.
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2. Which scales are equivalent to 1 inch to 1 foot? Select all that apply.
A. 1 to 12
B. 1 to 1
C. 100 to 0.12
. D. 5 to 60
E. 36 to 3
F. 9 to 108
Answer:
A option is correct
Step-by-step explanation:
We know that one foot contain 12inches so 12 inches is equal to one foot
There are 36 inches is equivalent to 3 feet which scales is the correct answer would be option (E).
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
The operator that performs the arithmetic operation is called the arithmetic operator.
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
/ Division operation: Divides left-hand operand by right-hand operand
For example 4/2 = 2
We know that one foot contains 12 inches.
Therefore 12 inches equal one foot
According to option (E),
36 inches is equivalent to 3 feet.
Therefore, the correct answer would be an option (E).
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"If the average cholesterol level is 194 with a standard deviation of 15, what percentage of children have a cholesterol level lower than 199? Answers are rounded to the nearest whole percent."
Answer:
63%
Step-by-step explanation:
Given the following :
Average cholesterol level or mean (m) = 194
Standard deviation (sd) = 15
what percentage of children have a cholesterol level lower than 199?
P(X < 199)
Assume a normal distribution :
Find the z-score :
Z = (score - mean) / standard deviation
Score = 199
Z = (199 - 194) / 15
Z = 5 / 15
Z - score = 0.3333
P(Z < 0.33) :
Using the z - table ; 0.33 = 0.6293
P(Z < 0.33) = 0.6293
0.6293 * 100% = 62.93%
= 63% (nearest whole percent)
Solve the system by substitution. x= x= \,\,-y-5 −y−5 -3x+7y= −3x+7y= \,\,-45 −45
Answer:
(1, -6)
Step-by-step explanation:
the layout of your question is kind of confusing, but i'm guessing this is the system of equations
x = -y - 5
-3x + 7y = -45
plug in x to the second equation
-3(-y - 5) + 7y = -45
distribute
3y + 15 + 7y = -45
combine like terms
10y = - 60
divide by 10
y = -6
plug y into first equation
x = -(-6) - 5
x = 6 - 5
x = 1
Consider the same rectangle of the preceding 8 units. Squares of x by x units are cut out of each corner, and then the sides are folded up to create an open box. Express the volume of the box as a polynomial function in terms of x problem. Squares of 2x by 2x units are cut out of each corner. Express the volume of the box as a polynomial in terms of x.
Answer:
V(x) = l*w*x - 2*l*x² - 2*w*x² + 4*x³
Step-by-step explanation:
The volume of any box is:
a * b * h where a is the length, b is the wide and h is the height
Assuming we have cardboard of dimensions: l * w
l - 2*x will be length of the box and
w - 2*x will be wide of the box
h = x the height, then:
V(x) = ( l - 2*x ) * ( w - 2*x ) * x
V(x) = [ ( l*w - 2*l*x - 2*w*x + 4*x² ] * x
V(x) = l*w*x - 2*l*x² - 2*w*x² + 4*x³
A graphing calculator is recommended. A function is given. g(x) = x4 − 5x3 − 14x2 (a) Find all the local maximum and minimum values of the function and the value of x at which each occurs. State each answer rounded to two decimal places.
Answer:
The local maximum and minimum values are:
Local maximum
[tex]g(0) = 0[/tex]
Local minima
[tex]g(5.118) = -350.90[/tex]
[tex]g(-1.368) = -9.90[/tex]
Step-by-step explanation:
Let be [tex]g(x) = x^{4}-5\cdot x^{3}-14\cdot x^{2}[/tex]. The determination of maxima and minima is done by using the First and Second Derivatives of the Function (First and Second Derivative Tests). First, the function can be rewritten algebraically as follows:
[tex]g(x) = x^{2}\cdot (x^{2}-5\cdot x -14)[/tex]
Then, first and second derivatives of the function are, respectively:
First derivative
[tex]g'(x) = 2\cdot x \cdot (x^{2}-5\cdot x -14) + x^{2}\cdot (2\cdot x -5)[/tex]
[tex]g'(x) = 2\cdot x^{3}-10\cdot x^{2}-28\cdot x +2\cdot x^{3}-5\cdot x^{2}[/tex]
[tex]g'(x) = 4\cdot x^{3}-15\cdot x^{2}-28\cdot x[/tex]
[tex]g'(x) = x\cdot (4\cdot x^{2}-15\cdot x -28)[/tex]
Second derivative
[tex]g''(x) = 12\cdot x^{2}-30\cdot x -28[/tex]
Now, let equalize the first derivative to solve and solve the resulting equation:
[tex]x\cdot (4\cdot x^{2}-15\cdot x -28) = 0[/tex]
The second-order polynomial is now transform into a product of binomials with the help of factorization methods or by General Quadratic Formula. That is:
[tex]x\cdot (x-5.118)\cdot (x+1.368) = 0[/tex]
The critical points are 0, 5.118 and -1.368.
Each critical point is evaluated at the second derivative expression:
x = 0
[tex]g''(0) = 12\cdot (0)^{2}-30\cdot (0) -28[/tex]
[tex]g''(0) = -28[/tex]
This value leads to a local maximum.
x = 5.118
[tex]g''(5.118) = 12\cdot (5.118)^{2}-30\cdot (5.118) -28[/tex]
[tex]g''(5.118) = 132.787[/tex]
This value leads to a local minimum.
x = -1.368
[tex]g''(-1.368) = 12\cdot (-1.368)^{2}-30\cdot (-1.368) -28[/tex]
[tex]g''(-1.368) = 35.497[/tex]
This value leads to a local minimum.
Therefore, the local maximum and minimum values are:
Local maximum
[tex]g(0) = (0)^{4}-5\cdot (0)^{3}-14\cdot (0)^{2}[/tex]
[tex]g(0) = 0[/tex]
Local minima
[tex]g(5.118) = (5.118)^{4}-5\cdot (5.118)^{3}-14\cdot (5.118)^{2}[/tex]
[tex]g(5.118) = -350.90[/tex]
[tex]g(-1.368) = (-1.368)^{4}-5\cdot (-1.368)^{3}-14\cdot (-1.368)^{2}[/tex]
[tex]g(-1.368) = -9.90[/tex]