find the absolute maximum value of g(x)=−2x2 x−1 over [−3,5].
Answers
To find the absolute maximum value of the function g(x)=−2x^2/x−1 over the closed interval [−3,5], we will use the Extreme Value Theorem (EVT).EVT states that if a function is continuous over a closed interval, then the function will have an absolute maximum and minimum over that interval.
So, for finding the absolute maximum value of the given function, we will follow these steps:Step 1: Check the function's domain.We know that the denominator of the function g(x) is x - 1, so the function is not defined at x = 1. However, the closed interval we are working with is [-3, 5], which does not include x = 1. Hence, the function is defined over this interval.Step 2: Find the critical points of the functionTo find the critical points, we need to differentiate the function g(x) and equate it to zero:g'(x) = (-4x(x-1) + 2x^2)/(x-1)^2= 2x(3-x)/(x-1)^2=0So, the critical points of g(x) are x = 0 and x = 3.Step 3: Find the end-point values of the functiong(-3) = -2/5, g(5) = -50/9.
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Related Questions
Triangle ABC has coordinates A(-2, -3), B(1, 1), and C(2, -1). If the triangle is
translated 1 unit right and 3 units up, what are the coordinates of A?
Answers
what is the value of result after the following statement executes? result = (3 * 5) 24 / (15 - (7 - 4));
Answers
The value of result after executing the statement is 30.
To evaluate the expression and find the value of result, let's break down the operations step by step, following the order of operations (PEMDAS/BODMAS):
Inside the parentheses, we have:
3 × 5 = 15
Next, the expression becomes:
15 × 24 / (15 - (7 - 4))
Inside the inner parentheses:
7 - 4 = 3
Now, the expression becomes:
15 × 24 / (15 - 3)
Inside the parentheses:
15 - 3 = 12
The expression simplifies to:
15 × 24 / 12
Multiplication:
15 × 24 = 360
Division:
360 / 12 = 30
Therefore, the value of result after executing the statement is 30.
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The mathematical expression 'result = (3 * 5) * 24 / (15 - (7 - 4))' simplifies to 'result = 15 * 24 / 12', leading to a final value of 30.
Explanation:The task here is to understand and solve the provided mathematical expression, which is result = (3 * 5) 24 / (15 - (7 - 4)). However, this expression seems to contain a typo - there's an operation missing between (3 * 5) and 24. Let's assume that the operation is multiplication, turning the expression into result = (3 * 5) * 24 / (15 - (7 - 4)).
First, solve the operations in the parenthesis. Hence, 3 * 5 equals 15 and 15 - (7 - 4) equals 12. The modified expression is now result = 15 * 24 / 12.
Then, performing the multiplication and division in order from left to right gives the result as 30.
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let f be the function with f(0)=0 and derivative f'(x) = 1/(1 + x^7) what is the meclauren series of f.
Answers
The Maclaurin series for f(x) is:
f(x) = ∑[n=1 to infinity] (x^n)/n! * P_n(0)
= ∑[n=1 to infinity] (x^n)/n! * n!/n^8
= ∑[n=1 to infinity] (x^n)/n^8
To find the Maclaurin series of f(x), we can repeatedly differentiate f(x) and evaluate it at x=0 to find the coefficients of the series.
f(0) = 0
f'(x) = 1/(1 + x^7)
f''(x) = -7x^6/(1 + x^7)^2
f'''(x) = (42x^5 + 49x^13)/(1 + x^7)^3
f''''(x) = (-210x^4 - 637x^12 - 343x^20)/(1 + x^7)^4
and so on. The general formula for the nth derivative of f(x) is given by:
f^(n)(x) = P_n(x)/(1 + x^7)^(n+1)
where P_n(x) is a polynomial of degree at most 6n-1. We can find the coefficients of P_n(x) using the formula for the nth derivative and evaluating it at x=0:
P_n(0) = n!f^(n)(0) = n!/(1+0^7)^(n+1) = n!/n^8
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The meclauren series for the function f with f(0)=0 and derivative \(f'(x) = \frac{1}{1 + x⁷}\), is equals to \(f(x) = x - \frac{ x⁸}{8} + \frac{x¹⁵}{15} - \frac{x²²}{22} + .... \).
The Maclaurin series represents a function as an infinite sum of terms, each term being a derivative of the function evaluated at x = 0, 1,... Formula is written, \(\sum_{n= 0}^{\infty}\frac{ f^{n}(0)}{n!} x^n\)
where fⁿ(0) --> derivatives of f(x) at x = 0
n --> real numbers
We have a function, f(x) such that f(0) = 0 and derivative of f(x), i.e, \(f'(x) = \frac{1}{1 + x⁷}\).
We have to determine the meclauren series of function f(x). First we determine the value of f(x), so, expand the \(\frac{1}{1 + x⁷}\) as meclauren series. The meclauren series for \(\frac{1}{1 + x}\) is written, \( \frac{1}{1 + x} = 1 - x + x² - x³ + ......\)
Replace the x by x⁷, we result
\( \frac{1}{1 + x^{7} } = 1 - {x}^{7} + {x}^{14} - {x}^{21} + ......\)
Now, integrating the above series expansion, \(\int f'(x) dx= \int ( 1 - x⁷ + x¹⁴ - x²¹ + ......) dx\)
\(f(x) = x - \frac{ x⁸}{8} + \frac{x¹⁵}{15} - \frac{x²²}{22} + .... + c \\ \)
Using f(0) = 0
=> f(0) = 0 = 0 + 0 + 0 +.... + c
=> c = 0
Hence, required series is \(f(x) = x - \frac{ x⁸}{8} + \frac{x¹⁵}{15} - \frac{x²²}{22} + .... \).
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Each time any customer enters a coffee shop, there
is a probability of that their order will include a
latte.
3
If the order includes a latte, there is a probability of
3 that it will also include a cookie.
4
If the order does not include a latte, there is a
2
probability of that it will include a cookie.
What is the probability that the next customer to
enter the shop will order a cookie?
Answers
The probability that the next customer to enter the shop will order a cookie is given as follows:
31/60.
How to calculate a probability?The parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
The outcomes in which a cookie is ordered are given as follows:
3/4 of 1/3 -> includes a latte.2/5 of 2/3 -> does not include a latte.Hence the probability is obtained as follows:
3/4 x 1/3 + 2/5 x 2/3 = 1/4 + 4/15 = 15/60 + 16/60 = 31/60.
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Use the drawing below to answer the questions that follow.
16 feet
8 feet
11 feet
2 feet
Part A
What is the scale factor used when going from the larger rectangle to the smaller one?
-
Part B
What is the length of the missing side?
feet
Answers
you have to multiple 16 i think
Answer:
\(\left(A\right)\frac{1}{2}\)
\(\left(B\right)x=5.5\ feet\)
Step-by-step explanation:
\(\left(A\right)\ Scale\ factor\ =\frac{8}{16}=\frac{1}{2}\)
\(\left(B\right)\ Sides\ are\ propertional\ for\ similar\ polygon\)
\(\frac{8}{16}=\frac{x}{11}\)
\(x=\frac{11}{2}\)
\(x=5.5\ feet\)
I hope this helps you
:)
Helpp please! Explain it too!!
Which sign makes the statement true?
6.70 × 10^3 ___ 6.7 × 10^3
> < =
Answers
Answer:
6.70E3=6.7E3
Step-by-step explanation:
Since the exponents are the same, all we have to do is use the bases.
6.70 {>,<,=} 6.7
6.7 equals 6.70 because the 0 after the 6.7 means nothing.
A scientist illegally introduces new species of honey bees in their labs. The growth of the population of this new species is modeled by the equation below, where x is the time in weeks following the introduction of the species. If the lab contains 450 bacteria after 2 weeks, how many bacteria did the scientist initially create?
A,30
b.40
c.50
d.60
Answers
Does this graph show a function? Explain how you know.
Answers
Answer:
there is no picture sir
What is the yield on a corporate bond with a $1000
face value purchased at a discount price of $950, if
it pays 6% fixed interest for the duration of the
bond?
Answers
The yield on a corporate bond with a face value of $1000 after removal of discount would be =$60.
What is interest rate?Interest rate can defined as the payment received by an individual after investing a particular amount of money for a given period of time.
The principal amount after removal of $950 discount = $1000
The rate of interest (R) = 6%
The time of investment (T) = 1
Then the simple interest;
= P × T × R/100
= 1000 × 1 × 6/100
= 6000/100 = $60
Therefore, the yield of the corporate bond would be extra $60.
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if I have one broccoli and my teacher gives me two broccolis how many broccolis do I have
Answers
Answer:
Step-by-step explanation:
I'm sure of it i even used my calculatr... it 13
Write Expression from Context (mx+b)
Tyee signed up for a streaming music service that costs $6 per month. The service allows Tyee to listen to unlimited music, but if he wants to download songs for offline listening, the service charges $0.75 per song. How much total money would Tyee have to pay in a month in which he downloaded 10 songs? How much would he have to pay if he downloaded ss songs?
Answers
Answer:
Total cost for 10 songs = 6 + [0.75 × 10]
= $13.5
Step-by-step explanation:
Which function is a second-degree function? Responses A. y = xy = x B. y = 3x - 7y = 3 x - 7 C. y = x2 y = x 2 D. y = 3
Answers
In the given options, only option C has the form of a second-degree function, y = x², where a=1, b=0, and c=0.
Therefore, the correct answer is C.
What is the polynomial equation?
A polynomial equation is an equation in which the variable is raised to a power, and the coefficients are constants. A polynomial equation can have one or more terms, and the degree of the polynomial is determined by the highest power of the variable in the equation.
The function y = x² is a second-degree function because it contains a variable, x, raised to the second power.
Option A, y = x, is a first-degree function because it contains a variable, x, raised to the first power.
Option B, y = 3x - 7, is a first-degree function because it contains a variable, x, raised to the first power.
Option D, y = 3, is a constant function because it does not contain any variable raised to any power.
Therefore, the answer is option C, y = x² has the form of a second-degree function.
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Assume you wanted to save $2,000 to buy a used car 18 months from now. How much money do you need to save every week to accomplish you goal
Answers
PLEASE NO LINKS AND NO NEGATIVITY
Answers
Answer:
Answer is 15-r .Hope it will help you
Abed says he has written a system of two linear equations that has an infinite number of solutions. One of the
equations of the system is y = 3x - 1. Which could be the other equation?
A. y = 3x + 2
B. 3x - y = 2
C. 3x - y = 1
D. 3x + y = 1
Answers
Answer:
3x - Y = 1
Explanation : None
BRIDGES The lower arch of the Sydney Harbor Bridge can be modeled by g(x) = - 0.0018 * (x - 251.5) ^ 2 + 118 where in the distance from one base of the arch and g(x) is the height of the arch. Select all of the transformations that occur in g(x) as it relates to the graph of f(x) = x ^ 2
Answers
The transformations to the graph of the quadratic function are given as follows:
The graph stretches vertically because of the multiplication by 3.The graph is translated left because x -> x + 7.The graph is translated down because y -> y - 6.What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.Additionally, when the function is multiplied by |a| > 1, it is said that the function is vertically stretched by a factor of a.
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just designed a cloister (a rectangular garden surrounded by a covered walkway on all four sides). the outside dimensions of the garden are 12 feets by 8 feet, and the area of the garden and the walkway together are 252 square feet. what is the width of the walkway?
Answers
The width of the rectangular walkway is 3 feet around.
The walkway has a uniform width around the rectangle.
Let the width of walkway be x
The total length of the garden and walkway will be (12+2x) feet
The total width of the walkway and garden would be (8+2x) feet
Area of the garden and the walkway together are 252 square
Let’s express this mathematically:
(8+2x)(12+2x) = 252
Let’s open the brackets;
96+ 16x+ 24x + 4x^2 = 252
4x^2 + 40x + 96 = 252
4x^2 + 40x + 96-252 = 0
4x^2 + 40x - 156 = 0
Let’s divide all through by 10. We have;
x^2 + 10x -39 = 0
X^2 +13x-3x-39 = 0
x(x + 13) -3(x+ 13) = 0
(x-3)(x + 13) = 0
x -3 = 0 or x + 13 = 0
x = 3 or -13
We ignore x = -13 since width cannot be negative in size
Therefore, the width of the rectangular walkway is 3 feet around.
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What type of number is 12i+360
Answers
Answer:
Complex number.
Step-by-step explanation:
can the √42 be √ 2 x √ 45 ??? why not and how
Answers
On comparing the above two equations we can conclude that \(\sqrt{42}\) cannot be expressed as \(\sqrt{2} * \sqrt{45}\).
What are irrational numbers?
The ratio of two whole numbers cannot be used to express irrational quantities. As opposed to this, rational numbers can and often are stated as the ratio of two whole numbers, such as 2, 7, one-fifth, and -13/9. Irrational numbers never repeat after the decimal point when stated as a decimal.
What are square and square roots?
Squares are the results of multiplying an integer by itself. The original value is revealed by multiplying the square root of an integer by itself. Both are hence vice-versa approaches. For instance, 2 is squared to provide 4, and 2 is the square root of 4, giving 2.
\(\sqrt{42}= \sqrt{2*3*7}\)
\(\sqrt{2} * \sqrt{45} = \sqrt{5*3*3} * \sqrt{2}\)
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The 19.9 foot ladder leans against a wall from a point that 2.7 feet
away from the wall on the ground. What is the angle between the
ladder and the wall to the nearest tenth of the degree?
Answers
Answer: 5.7 degrees to the nearest tenth of a degree
Step-by-step explanation:
We can use trigonometry to find the angle between the ladder and the wall. Let's call this angle θ. The ladder, the wall, and the ground form a right triangle, where the ladder is the hypotenuse, the wall is one leg, and the distance from the base of the ladder to the wall is the other leg.
Using the Pythagorean theorem, we can find the length of the ladder:
ladder^2 = wall^2 + distance^2
ladder^2 = (2.7)^2 + (19.9)^2
ladder^2 = 776.3
ladder = sqrt(776.3)
ladder ≈ 27.9 feet
Now we can use the sine function to find the value of the angle θ:
sin(θ) = opposite / hypotenuse
sin(θ) = wall / ladder
sin(θ) = 2.7 / 27.9
Taking the inverse sine (or arcsine) of both sides, we get:
θ = sin^(-1)(2.7 / 27.9)
Using a calculator, we find:
θ ≈ 5.7 degrees
Therefore, the angle between the ladder and the wall is approximately 5.7 degrees to the nearest tenth of a degree.
why can’t you use the product of powers rule to simplify this expression? explain. 34 · 28
Answers
You cannot use the product of powers rule to simplify 34 · 28.
The product of powers rule states that when you multiply two powers with the same base, you can add the exponents. For example, 23 · 25 = 28 because 2+3=5 and 5+3=8.
In the expression 34 · 28, the bases are different. 34 means 3 raised to the power of 4, and 28 means 2 raised to the power of 8. Since the bases are not the same, you cannot simplify the expression using the product of powers rule.
Hence, The product of powers rule only applies when the bases of the powers are the same, so it cannot be used to simplify expressions with different bases, such as 34 · 28.
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determine the equation of a parallel line to x=5
Answers
Answer:
x = constant ( other than 5)
Step-by-step explanation:
The slope of a line x=5 is undefined
Parallel lines have the same slope
So any line that is vertical ( slope undefined) will be parallel
Subtract 1/8 minus 3/4
Answers
Answer: 5/8
Step-by-step explanation:
Identify the rational exponent expression for V10°.
Answers
Answer:
The square root of 16 is rational.
Step-by-step explanation:
Answer:
Step-by-step explanation:
V10,000 20.5121/3 21. 41/2. 22. 11/3. 23.
What is in the blank? -11 + ____ = 15
Answers
Answer
-11 + 26 = 15
hope it's right
Give me three sides to a right triangle. Explain how you can use the Pythagorean theorem to know that your three sides will create a right triangle.
Answers
Applying these number to Pythagorean theorem…
a2+b2=c2
So,
12^2+35^2=37^2
144+1225=1369
1369=1369
As you can see both are equal (1369=1369), so we have a right angle triangle. If both sides are not equal then it is not classified as a right angle triangle.
PLZZ HELP 50 POINTS!!!
How could you change the equation from Part B so it has infinitely many solutions? What would infinitely many solutions mean in terms of the situation?
Answers
Answer: To change the equation from Part B so it has infinitely many solutions, you could make the equation equal to itself 5x + 2 = 5x + 2
Step-by-step explanation:
5x + 2 = 5x + 2
5x + 2 - 5x = 5x + 2 - 5x
2 = 2
2 - 2 = 2 - 2
0 = 0
When a number is equal to itself, and it cancels out to 0 = 0, then the equation will have infinitely many solutions.
-----true or false? prove
There exists a matrix A \in{R}^{4 \times 6} with \operatorname{rank}(A)=5
Answers
The statement "There exists a matrix A ∈ R4×6 with rank(A)=5" is True.
What is matrix rank? The rank of a matrix is defined as the maximum number of linearly independent columns (or rows) in the matrix. It is represented by the r(A) symbol.
We need to prove the existence of a matrix A ∈ R4×6 with rank(A)=5
If rank(A) = 5, then it means that there are 5 linearly independent rows or columns of matrix A. This means that either the rows or columns can be expressed as a linear combination of other rows or columns. Hence, the rank of matrix A cannot be more than 5. Let's take an example of such matrix A.
Consider a matrix A as follows:
\(\left[\begin{array}{cccccc}1&0&0&0&0&0\\0&1&0&0&0&0\\0&0&1&0&0&0\\0&0&0&1&0&0\\0&0&0&0&1&0\end{array}\right]\)
In this case, the first five columns of A are linearly independent and rank(A) = 5.
Hence, the statement is true.
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help me please!!!!!!!!!!!!!!!!!
Answers
im not for sure but Step-by-step explanation: 3,000=102938884.00919377299
Answer:
3,000=102938884.00919377299
Step-by-step explanation:
What method of assigning probabilities to a simple event uses relative frequencies?
Answers
The empirical method is the right answer.
Empirical probability is calculated by dividing the number of times an event was seen in your data by the entire sample size. An event's relative frequency is strongly connected to an empirical probability, also known as an experimental probability.
Empirical probability bases its estimation of the likelihood that a specific result will recur on the number of instances of that outcome within a sample set. In short, the empirical method uses relative frequencies to determine probabilities.
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