What's the difference between an ABSOLUTE extrema and a RELATIVE extrema? ...?
Final answer:
Absolute extrema refer to the highest or lowest points on the entire domain of a function, while relative extrema are high or low points within a specific region. Calculus techniques such as finding derivatives are used to identify these points.
Explanation:
The concepts of absolute extrema and relative extrema are important in the context of mathematics, specifically in calculus and the study of functions. An absolute extrema (or global extrema) refers to the highest or lowest point over the entire domain of a function. Relative extrema (or local extrema), on the other hand, are points where the function takes on a maximum or minimum value within a particular region or interval, but not necessarily the highest or lowest over the entire function. More formally, an absolute maximum is the largest function value and an absolute minimum is the smallest function value in the entire domain; relative maximums and minimums may not be the absolute highest or lowest, but are higher or lower than points immediately around them. To find extrema, calculus students typically use techniques involving derivatives to identify where function values change from increasing to decreasing or vice versa.
For example, let's consider the function f(x) = x^2 on the interval [-1,1]. The absolute extrema of this function would be the global maximum and minimum values, which occur at x = -1 and x = 1, respectively. The relative extrema of this function would be the local maximum and minimum values, which occur at x = 0.
Brady Seitz’s charge account statement showed a previous balance of $1,247.55, a finance charge of $4.72, and new purchases of $112.50. What is the new balance? A. $1,364.77 B. $1,987.00 C. $987.66 D. None of the above.
a building with a height of 14 m casts a shadow that is 16m long while a taller building casts a 24 meter long shadow. what is the height of the taller building
What is the value of f(0)
For the given function f(x) = 10x + 20, substituting 0 for x yields f(0) = 20. Graphically, this corresponds to the point (0, 20) on the function's line, illustrating that the output is 20 when the input is 0.
Find the value of f(0) for the function f(x) = 10x + 20:
1: Understand the function:
We are given that f(x) is defined as 10x + 20. This means that for any input value (x), the function outputs the result of multiplying x by 10 and adding 20.
2: Substitute x with 0:
We are asked to find the value of f(0). This means we need to plug in 0 for x in the function equation.
f(0) = 10 * 0 + 20
3: Simplify the expression:
Multiplying 10 by 0 gives us 0. Therefore, the equation becomes:
f(0) = 0 + 20
4: Evaluate the expression:
Adding 0 and 20 gives us:
f(0) = 20
Therefore, the value of f(0) is 20.
This means that when you input 0 into the function f(x) = 10x + 20, the function outputs 20.
To visualize this geometrically, you can imagine the function as a straight line on a coordinate plane. The point (0, 20) would lie on this line, indicating that the function output is 20 when the input is 0.
Complete question:
What is the value of f(0)?
If f(x) = 10x + 20
The value of ( f(0) ) is 5. To calculate it, we substitute ( x = 0 ) into the expression [tex]\( 3x^{2x} + 5 \)[/tex]ero number raised to the power of 0 is 1, the simplified result is [tex]\( f(0) = 3 \cdot 1 + 5 = 8 \).[/tex]
Explanation:The expression for ( f(x) ) is given as [tex]\( 3x^{2x} + 5 \)[/tex] , we substitute ( x = 0 ) into the expression:
[tex]\[ f(0) = 3 \cdot 0^{2 \cdot 0} + 5 \][/tex]
Since any non-zero number raised to the power of 0 is 1, the term [tex]\( 0^{2 \cdot 0} \)[/tex]re,
[tex]\[ f(0) = 3 \cdot 1 + 5 \][/tex]
Simplifying further,
f(0) = 3 + 5
Combining like terms,
f(0) = 8
So, the final answer is ( f(0) = 8 ).
In summary, when evaluating ( f(0) ), we substitute 0 for ( x ) in the given expression. The calculation involves raising 0 to the power of 0, which results in 1. The remaining terms are simplified to arrive at the final answer of 8. This process follows the principles of algebraic substitution and simplification, providing a clear understanding of how the value of ( f(0) ) is determined.
Complete Question:
Consider the function f(x) with the following expression: ( f(x) = [tex]3x^2[/tex]x + 5 ). Calculate the value of f(0).
By selling old cd's, sarah has a store credit card for $153.a new cd costs $18 .what are the possible numbers of new cd's sarah can buy
For what value(s) of r is 5r-6=7+5r?
Christopher is a graphic designer who creates business websites. It takes him 2.4 hours to complete one website page. He finds out about a new software program that will cut his time in half for completing one page, but it will take him 15 hours to learn the new program.
Which equation can be used to find the number of website pages, x, that Christopher needs to create so that his time spent using the new program will be the same as his current time?
Answer:
1. 2.4x=1.2x+15
2. 13
Step-by-step explanation:
Could a reflection followed by a rotation ever be described as a single rotation?
what is the relationship between area and square units
Lola bought x pencils that cost $0.25 each and y erasers that cost $0.50. She spent less than $3. Which graph represents Lola’s purchase?
Answer with explanation:
Cost of a Pencil = $ 0.25
Cost of a Eraser = $ 0.50
⇒Total Amount Spent on Pencil and Eraser < 3.
⇒Cost of x Pencil +Cost of y Eraser < 3
⇒ 0.25 x + 0.50 y < 3
[tex]\Rightarrow \frac{25 x}{100}+\frac{50y}{100}< 3\\\\\Rightarrow 2 5 x +50 y < 300\\\\\Rightarrow x +2 y < 12\\\\\Rightarrow \frac{x}{12}+\frac{2y}{12}<1\\\\\Rightarrow \frac{x}{12}+\frac{y}{6}<1[/tex]
⇒Put, x=0 and y=0,to know which side of the graph you have to shade.
0+0< 12⇒0< 12
Shade that part under line, which contains origin.
Multiply, expressing the product in scientific notation. (9.16X10−3)(5.5X1016)
To multiply numbers in scientific notation, multiply the coefficients and add the exponents.
Explanation:To multiply numbers in scientific notation, we multiply the coefficients and add the exponents.
In this case, we have (9.16 × 10-3) multiplied by (5.5 × 1016).
The product of the coefficients is 9.16 × 5.5 = 50.38.
The sum of the exponents is -3 + 16 = 13.
Therefore, the product in scientific notation is 5.038 × 1013.
I'm bad at word problems. Natasha had 7/8 gallon of paint. her brother ivan took 1/4 gallon to paint his model boat. natasha needs at least 1/2 gallon to paint her bookshelf. did ivan leave her enough paint? ...?
Write some multiples of 5 and 8. Use the least common multiple to simplify 120\160
By decreasing each side of a rectangle by 1 unit, the area decreased from 60 square feet to 44 square feet. Find the perfect decrease in area. ...?
Answer:
Decrease in area would be 26.67%
Step-by-step explanation:
By decreasing each side of a rectangle by 1 unit area of the rectangle decreases from 60 square feet to 44 square feet.
So decrease in area = 60 - 44 = 16 square feet.
Percentage decrease in the area will be = [tex]\frac{\text{Decrease in area}}{\text{Area before decrease}}\times 100[/tex]
= [tex]\frac{16}{60}\times 100[/tex]
= [tex]\frac{160}{6}[/tex]
= 26.67%
Decrease in area would be 26.67%
The perfect decrease in area of the rectangle when each side is decreased by 1 unit, resulting in a decrease from 60 square feet to 44 square feet, is 16 square feet.
The question asks to calculate the perfect decrease in area of a rectangle when each side is decreased by 1 unit, resulting in a change in area from 60 square feet to 44 square feet. To solve for this, let's assign variables to the original dimensions of the rectangle. Let the length be L and the width be W.
The original area A1 is given by L imes W = 60. After reducing each dimension by 1, the new length and width are L - 1 and W - 1, respectively, so the new area A2 is (L - 1) imes (W - 1) = 44. The perfect decrease in area is the difference between the original and new areas, which is 60 - 44 = 16 square feet.
Write two mixed numbers between 3 and 4 that have the product between 9 and 12???
PLZ HELP!!!
Answer:
The product of two mixed fraction lies between 9 and 12.
Step-by-step explanation:
We are given the following information in the question:
Two mixed fractions between 3 and 4.
[tex]3\displaystyle\frac{1}{6} = \frac{19}{6} = 3.17\\\\3\displaystyle\frac{1}{2} = \frac{7}{2} = 3.5\\\\[/tex]
Product of the mixed fraction:
[tex]3\displaystyle\frac{1}{6}\times 3\frac{1}{2} = \frac{19}{6}\times \frac{7}{2}\\\\= \frac{133}{12} = 11\frac{1}{12} = 11.084[/tex]
Hence, the value of the product of two mixed fraction lies between 9 and 12.
In the Diagram, rectangle ABCD is split in half by like AC. What is the value of tan X?
A. 3/4
B. 4/5
C. 3/5
D. 5/4
E. 4/3
The answer is E)4/3
That is because tangent X = a/b
Since this is a rectangle, the parallel sides are equal.
In this case, a=4, B=3, and C=5.
So, tanX = 4/3
Hope this helps!
A two-digit number from 10 to 99, inclusive, is chosen at random. What is the probability that this number is divisible by 5?
The probability a two-digit number to be divisible by 5 from 10 to 99 inclusive and chosen at random is 1/5 or 0.2.
How to find the probability of an event?Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
As the probability of an event can not be more than the number 1. Thus he probability of failure of a event is equal to the difference of the 1 to the success of the event.
A two-digit number from 10 to 99, inclusive, is chosen at random. The probability that this number is divisible by 5 has to be find out.
The number of two-digit numbers which is divisible b 5 from 10 to 99 are 18.
[tex](10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95)[/tex]
There are total number from 10 to 99 are 90. Thus, the probability that the chosen number is divisible by 5
[tex]P=\dfrac{18}{90}\\P=\dfrac{1}{5}\\P=0.2[/tex]
Hence, the probability a two-digit number to be divisible by 5 from 10 to 99 inclusive and chosen at random is 1/5 or 0.2.
Learn more about the probability here;
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Final answer:
The probability that a randomly chosen two-digit number from 10 to 99 is divisible by 5 is 1/5 or 20%.
Explanation:
To find the probability that a randomly chosen two-digit number from 10 to 99 is divisible by 5, we first establish the total number of two-digit numbers, which is 99 - 10 + 1 = 90. Numbers divisible by 5 end in either 0 or 5, so we can count how many of these there are within our range. Starting from 10, the first such number, we have 10, 15, 20, ..., 95. We clearly have two of such numbers per every 10 numbers, resulting in a total of 90/10 * 2 = 18 numbers divisible by 5 between 10 and 99. Hence, the probability is the number of favorable outcomes (numbers divisible by 5), divided by the total number of possible outcomes (two-digit numbers), which gives us a probability of 18/90 = 1/5 or 20%.
What is the solution of the system? use the substitution method. {y−2x=816 4x=2y the only solution is (24, 0) . the only solution is (1, 10) . there is no solution. there are an infinite number of solutions.?
Final answer:
The system of equations given has no solution because substitution leads to a contradiction, indicating that the lines are parallel and do not intersect.
Explanation:
To solve the given system using the substitution method, we start with the two equations:
y − 2x = 8164x = 2yFrom the second equation, we can express y in terms of x by dividing by 2:
y = 2x
Now, we substitute this expression for y into the first equation:
2x − 2x = 816
This simplifies to:
0 = 816
This is a contradiction since 0 cannot equal 816. Therefore, there is no solution to the system of equations. This means that the two lines represented by these equations are parallel and never intersect.
if m1 = 40 what is the measure of 4
Eight scores have an average of six. Scores of 15 and x increase the average to 7. Find x
Final answer:
To find the value of x, multiply the original average of 6 by the original number of scores (8) to find the initial total. Then, use the new average of 7 to find the new total when the two scores (15 and x) are added. Solve for x to find that it equals 7.
Explanation:
The question asks to find the value of x such that when two new scores, 15 and x, are added to a set of eight scores with an average of six, the new average for all ten scores is seven.
To solve this, first calculate the total sum of the original scores by multiplying the average by the number of scores: 6 × 8 = 48. Adding the two new scores, the equation to find the new total sum is 48 + 15 + x = 7 × 10 (since there are now ten scores). Simplify this to get 63 + x = 70, therefore x equals 7.
The angles of a triangle are 2x, 3x, and 4x degrees. Find the value of x.
A) 20
B) 30
C) 40
D) 50
Answer:
Option A) 20 ... ... ... ✔
Step-by-step explanation:
[tex] \underline{\tt{❖ \: Given \: \: ❖}}[/tex]
interior angle of triangle 2x,3x4x[tex] \underline{\tt{❖ \: Solution \: ❖}}[/tex]
We know that interior sum of all angle is 180°
[tex]\; \;\dashrightarrow \;\pmb {2x+3x+4x=180°}[/tex]
[tex]\; \;\dashrightarrow \;\pmb {9x=180°}[/tex]
[tex]\; \;\dashrightarrow \;\pmb {x = \dfrac{180}{9} }[/tex]
[tex] \; \;\dashrightarrow\; \; {\pmb{\underline{\boxed{\red{\frak { x = 20 }}}}}} \; \green\bigstar[/tex]
Factor completely: 12a3b + 8a2b2 - 20ab3 ...?
Using the completing-the-square method, find the vertex of the function f(x) =- 3x2 + 6x − 2 and indicate whether it is a minimum or a maximum and at what point.
To find the vertex of the quadratic function using the completing-the-square method, rearrange the equation in vertex form, complete the square, and simplify. The vertex of the given function is located at (1, 1) and represents a maximum point.
Explanation:To find the vertex of the function f(x) = -3x^2 + 6x - 2 using the completing-the-square method, follow these steps:
Start by rearranging the equation in the form f(x) = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex.Factor out the coefficient of x^2. In this case, factor out -3: f(x) = -3(x^2 - 2x) - 2.Complete the square by adding and subtracting the square of half the coefficient of x. In this case, add and subtract (2/2)^2 = 1: f(x) = -3(x^2 - 2x + 1 - 1) - 2.Simplify: f(x) = -3((x - 1)^2 - 1) - 2.Expand and simplify: f(x) = -3(x - 1)^2 + 3 - 2.Final vertex form: f(x) = -3(x - 1)^2 + 1.The vertex of the function is at the point (1, 1). Since the coefficient of x^2 is negative, the vertex represents a maximum point. Therefore, the vertex is a maximum point located at (1, 1).
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What is the explicit rule for this geometric sequence?
4,4/5,4/25,4/125,…
Bianca has 25¢ she has some nickles an. d pennies how many different combonation of nickles and pennies could bianca have?
Charlie, who is 4 feet tall, walks away from a streetlight that is 16 feet high at a rate of 4 feet per second, as shown in the figure. Express the length s of Charlie's shadow as a function of time. (Hint: First use similar triangles to express s as a function of the distance d from the streetlight to Charlie.) ...?
The sum of three consecutive even integers is 36. Let x represent the first integer, x + 2 represent the second integer, and x + 4 represent the third integer.
Which equation can be used to find the first integer?
3x = 2x + 6
2x + 6 = 36
3x + 6 = 36
3x + 36 = 2x + 6
Answer:
C. [tex]3x+6=36[/tex]
Step-by-step explanation:
Let x represent the first integer, [tex]x+2[/tex] represent the second integer, and [tex]x+4[/tex] represent the third integer.
The sum of these integers would be [tex]x+x+2+x+4[/tex].
We have been given that the sum of three consecutive even integers is 36. We can represent this information in an equation as:
[tex]x+x+2+x+4=36[/tex]
Combine like terms:
[tex]3x+6=36[/tex]
Therefore, the equation [tex]3x+6=36[/tex] can be used find the first integer.
. Store E offers a book that Karen wants for 20% off its regular price of $15.00. Store F sells the same book for $15, before a $3.00 mail-in rebate. Where should Karen purchase the book? Explain your reasoning.
In one community ,84% of the animals shelters microchip cats and dogs before adoption. if 21 shelters in the community microchip cats and dogs, how many animal shelters are in that community
The graph shows the production of cars per day at a factory during a certain period of time. What is the domain of this function during this period?
The domain is all real numbers 0 through 9.
The domain is all integers 0 through 9.
The domain is all positive real numbers.
The domain is all positive integers.
Answer:
The domain is all real integers 0 through 9.
I've done the test, hope this helps