Answers
Step-by-step explanation:
Take the first derivative
\( \frac{d}{dx} ( {x}^{3} - 3x)\)
\(3 {x}^{2} - 3\)
Set the derivative equal to 0.
\(3 {x}^{2} - 3 = 0\)
\(3 {x}^{2} = 3\)
\( {x}^{2} = 1\)
\(x = 1\)
or
\(x = - 1\)
For any number less than -1, the derivative function will have a Positve number thus a Positve slope for f(x).
For any number, between -1 and 1, the derivative slope will have a negative , thus a negative slope.
Since we are going to Positve to negative slope, we have a local max at x=-1
Plug in -1 for x into the original function
\(( - 1) {}^{3} - 3( - 1) = 2 \)
So the local max is 2 and occurs at x=-1,
For any number greater than 1, we have a Positve number for the derivative function we have a Positve slope.
Since we are going to decreasing to increasing, we have minimum at x=1,
Plug in 1 for x into original function
\({1}^{3} - 3(1)\)
\(1 - 3 = - 2\)
So the local min occurs at -2, at x=1
Related Questions
Abe digs a hole at a steady rate of (meaning negative) 1.2 feet every hour.
Consider ground level to be 0.
What value represents the elevation of the hole relative to ground level after digging for 2.5 hours?
Enter your answer in the box.
Answers
The elevation of the hole relative to ground level after digging for 2.5 hours is -3.
Solve for h -110=13+3(4h-6)
Answers
Answer:
H= -35/4
Decimal form: -8.75
Explanation:
Subtract 13 from both sides. { -110 - 13 =3(4h - 6) }Simplify -110 -13 to -123 { -123 = 3 (4h - 6) }Divide both sides by 3 { -123/3 = 4h - 6 }simplify 123/3 to 41 { -41 = 4h - 6 }add 6 to both sides { -41 +6 = 4h }simplify -41 + 6 to -35 { -35 = 4h }divide both sides by 4 { - 35/4 = h }switch sides { h= - 35/4 }i don't understand how to do this.. can someone help, please
Answers
The possible values for angles 1, 2, and 3 given that lines a and b are parallel lines include the following:
m∠1 = 60°.m∠2 = 120°.m∠3 = 60°.What are parallel lines?In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet or intersect.
Note: Assuming angle 1 is equal to 60 degrees.
In Mathematics and Geometry, the vertical angles theorem states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other:
m∠1 ≅ m∠3 = 60°.
Based on the linear pair postulate, the measure of angle 2 can be determined as follows;
m∠1 + m∠2 = 180°
60° + m∠2 = 180°
m∠2 = 180° - 60°
m∠2 = 120°
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A rectangular box has dimensions 2ft by 4ft by 3ft. Increasing each dimension of the box by the same amount yields a new box with a volume four times the old. Use the ALEKS graphing calculator to find how much each dimension of the original box was increased to create the new box. Round your answer to two decimal places.
Answers
The increase in the dimensions of the new rectangular box is given by the equation x = 1.65 feet
What is the Volume of a Rectangle?The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle
Volume of Rectangle = Length x Width x Height
Volume of Rectangle = Area of Rectangle x Height
Given data ,
Let the dimensions of the rectangle A be 2ft x 4ft x 3 ft
So , the length of the rectangle L = 2 feet
The width of the rectangle W = 4 feet
The height of the rectangle H = 3 feet
Now , the volume of rectangle = Length x Width x Height
Substituting the values in the equation , we get
Volume of rectangle A = 2 x 4 x 3 = 24 feet³
And , let the increase in dimensions be represented as x
So , the length of the rectangle B = ( 2 + x )
The width of the rectangle B = ( 4 + x )
The height of the rectangle B = ( 3 + x )
Volume of rectangle B = ( 2 + x ) ( 4 + x ) ( 3 + x )
On simplifying the equation , we get
Volume of rectangle B = x³ + 9x² + 26x + 24
And , volume of rectangle B = 4 ( volume of rectangle A )
So , x³ + 9x² + 26x + 24 = 4 ( 24 )
x³ + 9x² + 26x + 24 = 96
Subtracting 96 on both sides of the equation , we get
x³ + 9x² + 26x + -72 = 0 be equation (1)
So , the value of x from ALEKS graphing calculator is 1.65
Hence , the increase in dimensions of the rectangle is 1.65 feet
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Desmond is 5 inches taller than Niki.
If we let
represent Niki's height in inches, write an algebraic expression for Desmond's height.
Answers
The algebraic expression for Desmond's height is x + 5.
write an algebraic expression for Desmond's height.If we let "x" represent Niki's height in inches, then Desmond's height can be represented by "x + 5", since Desmond is 5 inches taller than Niki.
So the algebraic expression for Desmond's height is x + 5.
What are algebraic expression?Algebraic expressions is consist of variables, numbers, and mathematical operations (such as addition, subtraction, multiplication, and division).
They can contain one or more variables and can be evaluated for different values of the variables.
For example, the expression 3x + 5y - 2z is an algebraic expression that contains three variables (x, y, and z) and three coefficients (3, 5, and -2) that are multiplied by those variables. Algebraic expressions are commonly used in algebra to represent mathematical relationships and solve problems.
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What is the distance from C to B
please help me
Answers
Please helppppppppppp
Answers
Answer:
1
2
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x
2
2
−
x
3
3
]
2
0
=
1
2
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(
4
2
−
8
3
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−
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=
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Step-by-step explanation:
6. A gas tank holds 450 gal. when it is filled to the height of 12 ft. How many
gallons will it hold when it is filled to 5 ft.?
Answers
Answer:
\(\huge\boxed{\sf 187.5\ gal.}\)
Step-by-step explanation:
Given that:
For,
12 ft. height, gas tank can hold 450 gal.
Using unitary method:
12 ft = 450 gal.
Divide 12 to both sides
1 ft = 450/12 gal.
1 ft = 37.5 gal.
Multiply 5 to both sides
5 ft. = 37.5 × 5 gal.
5 ft. = 187.5 gal.
So, the height of 5 ft. holds 187.5 gal.
\(\rule[225]{225}{2}\)
Answer:
187.5 gal
Step-by-step explanation:
A=lw
450=12(w)
450/12=37.5ft
A=lw
A=37.5(5)
A=187.5 gal
Hope that helps
Children 13 and over, but less than 19, where given a discount price
Answers
Children 13 and over, but less than 19, were given a discount price can be represented using inequalities as 13≤x<19 .
What are inequalities ?
An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value.
a ≠ b says that a is not equal to ba < b says that a is less than ba > b says that a is greater than b(those two are known as strict inequality)
a ≤ b means that a is less than or equal to ba ≥ b means that a is greater than or equal to b.How to form an inequality ?
At most means " no more than, " " less than or equal to, " or " not greater than"
The math symbol that you will use for at most is ≤
Children less than 19 ,hence x<19
Similarly,
At least means " no less than " or " greater than or equal to "
The math symbol that you will use for at least is ≥
Since , it is given that Children 13 and over therefore 13≤x .
On combining , we get 13≤x<19
Given question is incomplete , the complete question is given below:
Determine correct inequality for "Children 13 and over, but less than 19, where given a discounted price" .
a. 13≤x<19
b. 13≤x≤19
c. 13<x≤19
d. 13<x<19
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You have just been approved for a 30 year 5.5% fixed home mortgage. The monthly payment that you qualify for is $879.32. Use the table provided to determine the price of a home that can be purchased. A 5-column table with 4 rows titled Monthly Payments per 1000 dollars of mortgage. Column 1 is labeled Interest Rate (percent) with entries 5, 5.5, 6, 6.5. Column 2 is labeled 10 Years with entries 10.61, 10.86, 11.11, 11.36. Column 3 is labeled 20 years with entries 6.60, 6.88, 7.17, 7.46. Column 4 is labeled 30 years with entries 5.37, 5.68, 6.00, 6.33. Column 5 is labeled 40 years with entries 4.83, 5.16, 5.51, 5.86. a. $154,267 c. $156,753 b. $154,810 d. $157,153
Answers
Answer:
b. $154,810
Step-by-step explanation:
You want to know the price of a home that can be purchased for a monthly payment of $879.32 on a 30-year loan at 5.5%.
TableThe given table tells you the multiplier m used to find the monthly payment p from the loan amount P for different time periods and interest rates.
p = (P/1000)×m
ApplicationThe table value for a 30-year loan at 5.5% is m = 5.68. Solving the equation for P, we have ...
1000p/m = P
1000(879.32/5.68) = P ≈ 154,809.86 ≈ 154810
You qualify for a loan of $154,810.
__
Additional comment
The multiplier 5.68 is found on row 2 (5.5%) of column 4 (30 years).
By answering the presented question, we may conclude that As a result, equation the answer is (b) $154,810.
What is equation?A mathematical equation is a formula that connects two statements and denotes equivalence with the equals symbol (=). An equation is a mathematical statement that shows the equality of two mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the variables 3x + 5 and 14. A mathematical formula describes the connection between the two sentences that occur on opposite sides of a letter. The symbol and the single variable are frequently the same. As in 2x - 4 Equals 2, for instance.
To establish the purchase price of a property, we must use the monthly payment and the table supplied to determine the mortgage amount that corresponds to the monthly payment.
According to the data, the monthly payment per $1000 of mortgage for a 30-year fixed mortgage at a 5.5% interest rate is $5.68.
Hence, to calculate the mortgage amount for a $879.32 monthly payment, we may apply the following formula:
Mortgage amount = monthly payment / mortgage payment per $1000
$879.32 mortgage amount / $5.68 per $1000
Loan amount = $154,810
As a result, the purchasing price of a house is $154,810.
As a result, the answer is (b) $154,810.
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The graph represents a relation where x represents the independent variable and y represents the dependent variable. a graph with points plotted at negative 5 comma 1, at negative 2 comma 0, at negative 1 comma 3, at negative 1 comma negative 2, at 0 comma 2, and at 5 comma 1 Is the relation a function? Explain. No, because for each input there is not exactly one output. No, because for each output there is not exactly one input. Yes, because for each input there is exactly one output. Yes, because for each output there is exactly one input.
Answers
No, the relation is not a function, because for each input there is not exactly one output.
What is graph?A graph is a visual representation of data that shows the relationship between variables or sets of data. It consists of a set of points, called vertices or nodes, which are connected by lines or curves, called edges or arcs. Graphs are commonly used to display numerical information, such as trends, patterns, or relationships, and can be used to analyze and interpret data.
The relation is not a function because for the input x = -1, there are two different output values, y = 3 and y = -2. A function is a relation where each input has exactly one output, but in this case, the input -1 has two different outputs, violating the definition of a function.
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Que es una ecuación cuadrática
Answers
Step-by-step explanation:
En álgebra, una ecuación cuadrática es cualquier ecuación que se puede reorganizar en forma estándar como ax ^ {2} + bx + c = 0 donde x representa una incógnita, y a, byc representan números conocidos, donde a ≠ 0. Si a = 0, entonces la ecuación es lineal, no cuadrática, ya que no hay término ax ^ 2.
a. (10 points) The number of brownies sold by a bakery on a random day is a random variable with a mean value of 38 and a standard deviation of 6. What is the probability that the total number of brownies sold for a random sample of 56 days is less than 2070? Explain. b. (10 Points) Let X₁, X2, X3, and X4 represent the weight of shipment packages at a certain shipment facility. Suppose they are independent normal random variables with means µ4 7.4 pounds and μ₁ = 3.6, μ₂ = 0.9, µ3 = 1.8, μ4 µ2 variances o² = 0 = 0 = 0 = 1. Find P (2X₁ + 1X₂ + 3X3 + 1X4 ≤ 17.6). -
Answers
a. The probability that the total number of brownies sold for a random sample of 56 days is less than 2070 is approximately 0.0107.
b. The probability that 2X₁ + X₂ + 3X₃ + X₄ is less than or equal to 17.6
Explain probability
Probability is the measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event will not occur, and 1 means the event will definitely occur. Probability is a fundamental concept in mathematics and is used in many fields, including statistics, science, and finance.
According to the given information
a. The total number of brownies sold for a random sample of 56 days, Y, is a normal random variable with mean µ_Y = 56µ_X = 5638 = 2128 and standard deviation σ_Y = √(56)*σ_X = √(56)*6 = 25.21.
We want to find P(Y < 2070). Standardizing Y, we get:
Z = (Y - µ_Y) / σ_Y = (2070 - 2128) / 25.21 = -2.31
Using a standard normal distribution table or calculator, we can find that P(Z < -2.31) is approximately 0.0107. Therefore, the probability that the total number of brownies sold for a random sample of 56 days is less than 2070 is approximately 0.0107.
b. 2X₁ + X₂ + 3X₃ + X₄ is also a normal random variable with mean 2µ₁ + µ₂ + 3µ₃ + µ₄ = 2(3.6) + 0.9 + 3(1.8) + 7.4 = 18.5 and variance 4o² + o² + 9o² + o² = 14o².
We want to find P(2X₁ + X₂ + 3X₃ + X₄ ≤ 17.6). Standardizing the variable, we get:
Z = (17.6 - 18.5) / √(14o²) = -0.5735 / √(o²)
To find P(Z ≤ -0.5735 / √(o²)), we need to know the value of o². If o² = 1, then P(Z ≤ -0.5735) = 0.2831. If o² is a different value, we would need to adjust accordingly.
Therefore, the probability that 2X₁ + X₂ + 3X₃ + X₄ is less than or equal to 17.6
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4. Amy, Betty and Carol have 96 books altogether. Betty has 6 books less than Amy and Carol has half as many as Betty. How many books does each girl have?
Answers
The Amy has 42 books, Betty has 36 books, and Carol has 18 books.
Let's set up equations to represent the given information:
Let A represent the number of books Amy has.
Let B represent the number of books Betty has.
Let C represent the number of books Carol has.
Let's say Amy has x books.
Betty has 6 books less than Amy, so Betty has (x - 6) books.
Carol has half as many books as Betty, so Carol has (x - 6)/2 books.
According to the problem, the total number of books they have is 96.
So, we can write the equation:
x + (x - 6) + (x - 6)/2 = 96
To solve the equation, we can simplify it by multiplying through by 2 to remove the fraction:
2x + 2(x - 6) + (x - 6) = 192
2x + 2x - 12 + x - 6 = 192
5x - 18 = 192
5x = 210
x = 42
Amy has 42 books.
Betty has (42 - 6) = 36 books.
Carol has (36)/2 = 18 books.
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CAN SOMEONE PLEASE HELP ME WITH THIS QUESTION I DONT UNDERSTAND
Answers
Answer:
40 PERCENT CORRECTLY
AND
60 PERCENT INCORRECTLY
Step-by-step explanation:
1. Rachel has $60 to spend
on lunches this week. On
Monday she spent $5, and
on Tuesday she spent $7.
Which inequality can be
used to find, x, the amount
of money she can spend
the rest of the week?
Answers
On a road map, the distance from Washington to Seattle is approximately 2 inches. The map scale is 1 in.:25 mi. Approximately how many miles is the actual distance between the two cities?
Answers
Answer: your answer would be 50 inches
Step-by-step explanation:
Arrange the following fractions in order
from least to greatest.
7 15 3 11 13
5 4 2 4 3
Answers
The order of the fraction from least of greatest are
3/11 7/154/3 4/213/5How to order the fractionsThe fractions in order from least to greatest.
7/15 3/11 13/5 4/2 4/3
converting to decimals
7/15 = 0.4667
3/11 = 0.2727
13/5 = 2.6
4/2 = 2
4/3 = 1.3333
The order is written as follows
3/11 = 0.2727
7/15 = 0.4667
4/3 = 1.3333
4/2 = 2
13/5 = 2.6
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Solve for x if 5^x=200
Answers
Answer:
x ≈ 3.29
Step-by-step explanation:
Take the logarithm of both sides of the equation to remove the variable from the exponent.
Exact Form:
x = \(\frac{ln(200)}{ln(5)}\)
Decimal Form:
x = 3.29202967 … ≈ 3.29 (Round to what the question asks, in this case, I rounded to 2 decimal places)
Answer:
ln200/ln5
Step-by-step explanation:
ln5^x=ln200
xln5=ln200
x=ln200/ln5
Calculate the geometric center of the grapg under the function
Answers
The geometric center of the graph under the function is 5/3
How to determine the geometric center of the graph under the function?The equation of the function is given as:
f(x) = 3 - |x - 2|
The interval is given as:
x ∈ [0, 3]
The geometric center (gc) of the graph under the function is calculated using
gc = ∫x f(x) dx/∫f(x) dx
Substitute the known values in the above equation
gc = ∫x * (3 - |x - 2|) dx/∫3 - |x - 2| dx
Integrate the numerator and the denominator of the above equation
gc = [-1/6(x - 2)((2|x -2| - 9)x + 2|x - 2| - 18)]/[3x - 1/2[|x - 2|(x - 2)]]
Recall that the interval is given as x ∈ [0, 3]
Substitute the interval values in the above equation.
The equation is then simplified using a graphing calculator.
So, we have
gc = (65/6)/(13/2)
Express the quotient expression as a product
gc = (65/6) * (2/13)
Divide 65 by 13
gc = 5/6 * 2
Divide 2 by 6
gc = 5/3
Hence, the geometric center of the graph under the function is 5/3
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Classify triangle please
Answers
Answer:
Step-by-step explanation:
Peter wants to test an assumption on the number of trees that tested positive for a particular infestation. He decides to focus his efforts on examining if more than 12% of trees have been infested. What should Peter state for the null hypothesis and alternative hypothesis
Answers
Answer:
H0 : P ≤ 0.12
H1 : P > 0.12
Step-by-step explanation:
12% = 12/ 100 = 0.12
Given the population proportion, P = 0.12
The claim is the alternative hypothesis, H1 ; which is to test if more than 12% of trees have been infested.
Hence, the alternative hypothesis will be ;
H1 : P > 0.12
The null hypothesis which is the initial truth is always the opposite of the alternative hypothesis, Therefore, we write our null as ;
The null hypothesis ; H0 : P ≤ 0.12
Therefore, we have :
H0 : P ≤ 0.12
H1 : P > 0.12
Answer:
Null hypothesis: p equals 0.12
Alternative hypothesis: p greater than 0.12
Step-by-step explanation:
Since we are focusing on testing if the proportion of is greater than 12%, we can only reject the null hypothesis if the value is larger. This would be a one-tailed right test. So the null hypothesis and alternative hypothesis would be:
Null hypothesis: p = 0.12
Alternative hypothesis: p > 0.12.
help my sister with this pls
Answers
Answer:
23
Step-by-step explanation:
i think
The radius of the circle whose equation is (x - 3)2 + (y + 1)2 = 16 is
04
00
O 16
Answers
Square root of 16 is 4
So, the radius is 4
Please i need the answer fast k12
Answers
(A) The range and IQR for boxplot 1 is 10 and 6 respectively.
(B) The range and IQR for boxplot 2 is 12 and 7 respectively.
What is the IQR?The interquartile range defines the difference between the third and the first quartile.
The formula for the interquartile range is given below.
Interquartile range = Upper Quartile – Lower Quartile = Q3 – Q1
What is the range?The range is the difference between the lowest and highest values.
The formula for the interquartile range is given below.
Range = Maximum – Minimum
(A) For boxplot 1, we need to find the range and IQR from the given data set.
So, let 34 be the maximum and 24 be the minimum.
\(\text{Range}=\sf 34-24\)
\(\text{Range}=\sf10\)
Therefore, the range is 10.
Now time to find the IQR.
So, let 33 be Q3 and 27 be Q1.
\(\text{IQR}=\sf 33-27\)
\(\text{IQR}=\sf 6\)
Therefore, the IQR is 6.
(B) Now for boxplot 2, we will do the same thing as from part A.
Let's find the range.
So, let 24 be the maximum and 12 be the minimum.
\(\text{Range}=\sf 24-12\)
\(\text{Range}=\sf12\)
Hence, the range is 12.
Now for the IQR.
So, let 22 be Q3 and 15 be Q1.
\(\text{IQR}=\sf 22-15\)
\(\text{IQR}=\sf 7\)
Hence, the IQR is 7.
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These two graphs show the same data. What is
different about the two graphs?
the vertical scale
the horizontal scale
the width of intervals
the starting values of the intervals
Answers
Answer:
A. (the vertical scale)
2nd part is the Bottom graph
Step-by-step explanation:
Answer:
A. The Vertical Scale
Step-by-step explanation:
the other one has more value than the other....And i got it right from
---------------------------------------E D G E N U I T Y 2 0 2 0--------------------------------------
hope this helps. :P
Aris and Josiah are reading a 50-page book for their ELA class. Aris wants to know what page Josiah is reading. Josiah gives her two hints: 1. The product of the two page numbers he can see is 930. 2. The page he is reading is an odd numbered page.
Answers
Answer:
31
Step-by-step explanation:
Let x and (x + 1) be the page numbers Josiah can see
Hint 1: x(x + 1) = 930
⇒ x² + x = 930
⇒ x² + x - 930 = 0
Using quadratic formula,
\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)
a = 1, b = 1 and c = -930
\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)
\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)
Sice x is a page number, it cannot be negative
⇒ x = 30 and
x + 1 = 31
The two pages Josiah can see are pg.30 and pg.31
Hint 2: The page he is reading is an odd number
Out of the pages 30 and 31, 31 is an odd number
Thereofre, Josiah is reading page 31
Use the Laws of logarithms to rewrite the expression
Answers
The expression log₃(x²∛y²) using the laws of logarithms is 2log₃(x) + 2/3log₃(y)
Rewriting the expression using the laws of logarithmsFrom the question, we have the following parameters that can be used in our computation:
log₃(x²∛y²)
The product law of logarithms states that
log(ab) = log(a) + log(b)
Using the above as a guide, we have the following:
log₃(x²∛y²) = log₃(x²) + log₃(∛y²)
The power law of logarithms states that
log(aᵇ) = blog(a)
Using the above as a guide, we have the following:
log₃(x²∛y²) = 2log₃(x) + 2/3log₃(y)
This means that the values of A and B are A = 2 and B = 2/3
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Raoul has 72 wristbands and 96 movie passes to put in gift bags. The greatest common factor for the number of wristbands and the number of movie passes is qual to the number of gift bags. Raoul needs to make. Then find how many wristbands and how many movie passes raoul can put in each gift bag if he evenly distributes the items.
Please help I am stuck I am doing work nonstop on all weekends if I don’t get this right and done please help and will give brainlesst for the correct answer
Answers
Answer:
Step-by-step explanation:
I do know give me brainliest first
Answer:
24 gift bags
Step-by-step explanation:
Well first the question says to find the GCF and you find that by finding prime factors in each number. Then you would want to subtract 96-72 and get the answer of 24 so you would be able to make 24 gift bags. Hope this helps!!
May I have heart, 5 star, and brainliest please?
Please solve the problems below and follow instructions given.
Answers
What is a Right Angle Triangle?
A Right Angle Triangle is a triangle where one of the angles is equal to 90 degrees.
To calculate the values using SOHCAHTOA
SOHCAHTOA calculate the angles and sides of the right triangle, using trigonometric function sine, cosine, and tangent. There are two triangles in which the adjacent and opposite changes based on which angle is in question, the hypotenuse always stays the same.
Where Sin A = Opposite/ Hypotenuse
Cos A = Adjacent / Hypotenuse
And Tan A = Opposite / Adjacent
For question 1,
If Opposite = PR
Adjacent = PQ
Hypotenuse = QR
Sin A = 14/50
Cos A = 48/50
Tan A = 14/48
For question 2,
If Opposite = PQ
Adjacent = PR
Hypotenuse = QR
Sin A = 48/50
Cos A = 14/50
Tan A = 48/14
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