Answer:
When we have a function g(x)
We will have a maximum at x when:
g'(x) = 0
g''(x) < 0.
Now we start with:
g(x) = 3*x^4 - 8*x^3
The first derivation is:
g'(x) = 4*3*x^3 - 3*8*x^2
g'(x) = 12*x^3 - 24*x^2
We can rewrite this as:
g'(x) = x^2*(12*x - 24)
Now we want to solve:
g'(x) = 0 = x^2*(12*x - 24)
We have one trivial solution, that is when x = 0.
The other solution will be when the term inside of the parentheses is equal to zero.
Then we need to solve:
12*x - 24 = 0
12*x = 24
x = 24/12 = 2
Then g'(x) is equal to zero for x = 0, and x = 2.
Notice that both of these points are included in the interval [ -2,2 ]
Now we need to look at the second derivative of g(x):
g''(x) = 3*12*x^2 - 2*24*x
g''(x) = 36*x^2 - 48*x
Ok, now we need to evaluate this in the two roots we found before:
if x = 0:
g''(0) = 36*0^2 - 48*0 = 0
g''(0) = 0
Then we do not have a maximum at x = 0, this is a point of inflection.
if x = 2:
g''(2) = 36*(2^2) - 48*2 = 48
then:
g''(2) > 0
This is an absolute minimum.
Now let's look only at the interval [ -2,2 ]
We know that:
g''(0) = 0
g''(2) > 0
Then at some point, we should have g''(x) < 0 in our interval.
We need to find the first point such that happens, so let's try with the lower limit of the interval but with the first derivation, if g'(x) < 0, this means that the function is decreasing from that point on, then that point will be a maximum in our interval.
x = -2
g'(-2) = (-2)^2*(12*-2 - 24) = -192
And if we look at the function:
g'(x) = x^2*(12*x - 24)
We can easily see that it is negative unitl x = 0, and then it keeps being negative until x = 2.
So in the interval [ -2,2 ], the function g'(x) is always negative or zero, this means that in the interval [ -2,2 ], the function g(x) is always decreasing or constant.
Then the absolute maximum of g(x) in the interval [ -2,2 ] will be x = -2
this means that:
g(-2) ≥ g(x) for all x ∈ [ -2,2 ]
a line that has (1,0) and (1,7) as endpoints
A factory can fill 225 bottles of orange juice each hour. Each bottle of orange juice contains 24 fluid ounces. Each bottle of juice sells for $5.50. How many fluid ounces of juice are filled in each 12-hour shift?
Answer:
27 i think
Step-by-step explanation:
I divided them to make sure its right im not 100 percent sure tho
Sweet Treats Bakery is placing an order for 6,795 kilograms of sugar. That is 25% less than the bakery requested in its last order. How much sugar did Sweet Treats Bakery order then?
Answer:
9060
Step-by-step explanation:
let s be the amount of sugar the bakery ordered in the last order
s - 0.25s = 6795
0.75s = 6795
divide both sides by 0.75
9060
Don deposited $3,500 for 5 years on 2.40 pa interest rate in his savings account how much simple interest will he earn
Find the probability of rolling a 3 when you toss two fair 6-sided dice and add the result from each die.
Answer:
would it be 2/12 or 1/6 of a chance of getting a three
Find the indicated term of each sequence by repeatedly multiplying the first term by the common ratio. Enter your answer to 7 decimal places if necessary. Use a calculator. 12, −2.4, 0.48, ...; 7th term The 7th term of the sequence is
Answer:
The 7th term of the sequence is 0.000768
Step-by-step explanation:
As given, the sequence is : 12, -2.4 , 0.48, ....
The first term = 12
Second term = -2.4
Third term = 0.48
Common ratio = [tex]\frac{-2.4}{12} = \frac{0.48}{-2.4} = -0.2[/tex]
Fourth term = 0.48(-0.2) = -0.096
Fifth term = -0.096(-0.2) = 0.0192
Sixth term = 0.0192(-0.2) = -0.00384
Seventh term = -0.00384(-0.2) = 0.000768
A 180 foot length of fence is placed around a three-sided animal pen. Two of the sides of the pen are 72 feet and 78 feet. Does the fence form a right triangle?
Answer:
Yes
Step-by-step explanation:
Length of the third side
[tex]180-(72+78)=30\ \text{ft}[/tex]
The hypotenuse is always the longest side of a right triangle.
So, the hypotenuse here is [tex]c=78\ \text{ft}[/tex]
[tex]a=72\ \text{ft},b=30\ \text{ft}[/tex]
[tex]c=\sqrt{a^2+b^2}\\\Rightarrow c=\sqrt{72^2+30^2}\\\Rightarrow c=\sqrt{6084}\\\Rightarrow c=78\ \text{ft}[/tex]
The Pythagoras theorem applies so the fence does form a right triangle.
for each ordered pair determine whether it is a solution to 4x-7y=19
Answer:
No Solution
Step-by-step explanation:
all the ordered pair doesn't satisfy the equation.
HELP PLS ASAP i’ll mark as brainliest if correct !
Need help with this.
Answer:
try restart it and charge it to the max and then try change the internet source likeopen hotspot and see
4. David makes $ 16,000 a year. He gets paid SEMIMONTHLY (24 times a year). What is the amount
per pay?*
Answer:
$384,000
Step-by-step explanation:
Answer: Well if we have to round up i would say he makes about 6660.60 dollars a day
If there are any answer choices maybe i could help a bit morec
Step-by-step explanation:
What is this number in standard form?
(5×1,000)+(7×10)+(8×1)+(4×110)+(1×11,000)
Standard form of given expanded form of a number is 16518.
What is meant by expanded form?The expanded form of the number is the splitting of numbers based on the place value, such as ones, tens, hundreds, thousands, ten thousand, and so on. The number that is represented by the sum of each digit multiplied by its place value is called the expanded form of the number.
Given
Expanded form = (5×1,000)+(7×10)+(8×1)+(4×110)+(1×11,000)
We have to convert the expanded form into standard form
= 5000 + 70 + 8 + 440 + 11000
= 16518
Thus, standard form of given number is 16518.
Find out more information about expanded form here
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Answer:
16,518
(or 1.6518 x 10⁴)
Step-by-step explanation:
Expanded form: The digits of a number are split into individual digits based on their place value. Each digit of a number can be written in multiple of 1, 10, 100, 1000, etc.
Standard form: The combination of digits written together as a single number.
The given number is not quite, but almost, written in expanded form:
(5 × 1,000) + (7 × 10) + (8 × 1) + (4 × 110) + (1 × 11,000)
For it to truly be written in expanded form, the (4 × 110) would be written as (4 × 10) + (4 × 100) and the (1 × 11,000) would be written as either (11 × 1,000) or (1 × 10,000) + (1 × 1,000).
If the number should be written in standard form as defined above, carry out the operations in the parentheses, then add them together:
[tex]\large\begin{array}{l c r}8 \times 1 & = & 8\\7 \times 10 & = & 70\\4 \times 110 & = & 440\\5 \times 1000 & = & 5000\\1 \times 11000 & = & 11000\\\cline{3-3}& & 16518\end{array}[/tex]
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However, in math there is another type of Standard Form (also called "Scientific notation") that is written in the form of [tex]a \times 10^n[/tex], where [tex]1\leq a < 10[/tex] and [tex]n[/tex] is any positive or negative whole number.
To convert a number into standard form, move the decimal point to the left or right until there is one digit to the left of the decimal point.
The number of times you have moved the decimal point is the power of 10 ([tex]n[/tex]).
If the decimal point has moved to the left, the power is positive.
If the decimal point has moved to the right, the power is negative.
To convert 16518 into standard form:
Move the decimal point 4 places to the left and multiply by 10 to the power of the number of places the decimal was moved (4):
⇒ 1.6518 x 10⁴
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**I have provided both standard forms, as it is not clear from the question which is required.**
Zainab has 25 beads.
She gives 6 of the beads to Lucy.
What fraction of the 25 beads does Zainab have now?
Give your answer in its simplest form.
Answer:
19/25 it cant simplified
Step-by-step explanation:
Lawrence deposits 512$ in saving account that earns 1.5% commission how much money would be in his account after 2 years
Answer:
$519.68
Step-by-step explanation:
(512$ × 1.5)/100
=$7.8
512$+ $7.8
= $519.68
Can you please answer it tysm
If Isabelle chooses to read 5 books
with a total of 1260 pages, how much would she earn? And also I need the equation someone help I have to submit it by 10:30 :(
Answer:
I really don't know I just wanna know to
Please I really need help fast
Select the compound inequality shown on the graph.
+++
-5 -4 -3 -2 -1 0 1
N
3
4 5
A. x < -1 and x 24
B. x>-1 and x 34
C. -13x34
D. -13x<4
Answer:
B
Step-by-step explanation:
there is a hole at -1, so -1 is less than x and x is greater than or equal to 4
The compound inequality shown on the graph is x < -1 and x≥4.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
We have the graph for the inequality.
The first part of the inequality is
x < -1
and, the second part of inequality x≥4
So, the compound inequality is x < -1 and x≥4.
Learn more about Inequality here:
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Solve each system of equations algebraically
y=x+2
y=-3x
Answer:
Your answer is: (-1/2, 3/2)
Step-by-step explanation:
y = x + 2
y = -3x
Use substitution by plugging the second equation into the first.
-3x = x +2
Subtract x from both sides to combine the variables.
-4x = 2
Divide both sides by -4 to isolate the variable x.
x = 2/-4
Simplify.
x = -1/2
Plug x into one of the equations to find y.
y = (-1/2) + 2
y = 3/2
Plug x into the other equation to confirm your answer.
y = -3(-1/2)
y = 3/2
Your answer is: (-1/2, 3/2)
Solve the system of linear equations using Substitution
5x + 2y= 9
y = -x-3
Answer:
(5, -8)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsCoordinates (x, y)Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
5x + 2y = 9
y = -x - 3
Step 2: Solve for x
Substitution
Substitute in y: 5x + 2(-x - 3) = 9[Distributive Property] Distribute 2: 5x - 2x - 6 = 9Combine like terms: 3x - 6 = 9[Addition Property of Equality] Add 6 on both sides: 3x = 15[Division Property of Equality] Divide 3 on both sides: x = 5Step 3: Solve for y
Define original equation: y = -x - 3Substitute in x: y = -5 - 3Subtract: y = -8any help *more than one answer*
Answer:the first one and the fourth one
Step-by-step explanation:
help me just onen question
Answer:
maybe 58 im not sure sorry
Step-by-step explanation:
Answer:
yeet
Step-by-step explanation:
Write the equation of the line perpendicular to y = -31 - 1 that passes through the point (3,4).
y= (1/3)x+3
Step-by-step explanation:
i think u mean y= -3x-1
the line perpendicular to the given line is -3.m2= -1
m2=1/3 y-4=1/3(x-3)
y= (1/3)x+3
help Video
What is an equation of the line that passes through the points (2, 2) and (-2,8)?
please help and show work
Answer:
[tex]since \: the \: three \: sides \: are \: not\: equal : \\ its \: a \to \:\underline{\boxed{scalene}} \\ line \: \overline{AB} = 2 \\ line \: \overline{AC}= 6 \\ line \: \overline{BC} = 2 \sqrt{10} [/tex]
Step-by-step explanation:
[tex]to \: prove \: this \to \: we \: will \: need \: to \: find \\ \: the \: lenghts \: of \: the \: sides \: of \: \\ this \: triangle \to \\ using \: the \: shortest \: distance \: between \: \\ two \: points \to \: d \: = \sqrt{( {x_2 -x_1) }^{2} + (y_2 - y_1)^{2} } \\ \\ \underline{ \boxed{\overline{AB}}} \\ line \: \overline{AB} \: has \: points \to: ( - 3, - 3) \: and \:( 3, 5) \\ d \: = \sqrt{ (( - 3) - ( - 3))^{2} +( 5 - 3))^{2} } \\ d = \sqrt{(0) + (4)} \\ d = \sqrt{4} \\ \boxed{ d = 2 = AB} \\ \\ \underline{ \boxed{\overline{AC}}} \\ line \: \overline{AC} \: has \: points \to: ( - 3, - 3) \: and \:( 5, - 1) \\ d \: = \sqrt{ (( - 3) - ( - 3))^{2} +(( - 1) - 5)^{2} } \\ d = \sqrt{(0) + ( - 6) {}^{2} } \\ d = \sqrt{36} \\ \boxed{ d = 6 = AC} \\ \\ \underline{ \boxed{\overline{BC}}} \\ line \: \overline{BC} \: has \: points \to: ( 3, 5) \: and \:( 5, - 1) \\ d \: = \sqrt{ (5 - 3)^{2} +(( - 1) - 5)^{2} } \\ d = \sqrt{(2) {}^{2} + ( - 6) {}^{2} } \\ d = \sqrt{40} \\ \boxed{ d =2 \sqrt{10} = BC} \\ its \: a \: scalene : since \: the \: three \: sides \: are \: not\: equal[/tex]
Hiro painted his room. After 3 hours of painting at a rate of 8 meters per hour, he head 28 square meters left to paint.
Answer:
3 hours x 8 meters = 24 meters + 28 meters = 52 meters
52 / 3 = 17 and 1/3 hours.
Brainiest plz? :)
What is the value of x? Enter your answer in the box.
I forgot how to find a function in a graph
Answer:
This graph is NOT a function.
Step-by-step explanation:
A graph is a function only if there is exactly one y-value for every x-value. In this case, there are many x-values that have two y-values, making this graph not a function.
Let me know if this helps!
At the mall in Miami, Roberto found a jacket he liked. The normal price was $120, but the jacket was on sale for 40% off. If Roberto has $50 to spend, does he have enough to buy the jacket? If not, how much more money does he need?
Answer: No, He will need $22 to add to his money to buy jacket.
Step-by-step explanation:
Normal price of jacket =$120,
New price = 40% off which means 40% Less than the Normal price
= 40/ 100 x 120
=0.4 x 120 = 48; 120 -48= $72
New Price = $72
Therefore Roberto with $50 to spend does not have enough to buy the jacket
He will need $72- $50 =$22 to add to his money to buy jacket.
PLSSSS HELP CORRECT ANSWER GETS BRAINLIEST
Answers
1.A
2.B
3.C
Answer:
C
Step-by-step explanation:
Simplify the following
16a^2b^3c^6/48ab^5c^6
Answer:
a/3b^2
Step-by-step explanation:
16a^2b^3c^6/48ab^5c^6
the c^6 cancel out, then simplify a^2 and a: 16a^2b^3/48ab^5 = 16ab^3/48b^5
Then divide 48 and 16 you get 3 16ab^3/48b^5 = ab^3/3b^5
And lastly, simplify b^3 and b^5 ab^3/3b^5 =
a/3b^2