Find the first five non-zero terms of taylor series centered at x=3x=3 for the function below. f(x)=6x−x2−−−−−−√ f(x)=6x−x2
a carpenter and helper can do a certain job in 18 days if the carpenter takes walks 1.5 times as fast as the helper how long would it take each working alone?
Answer:
i dunno know
Step-by-step explanation:
2+2=FISH
Find the 5th partial sum of the arithmetic sequence an=2n–3.
A container shape as a rectangular prism can hold 840 wooden cube blocks with edge lengths of 1/2 feet. What is the volume of the container?
Which logarithmic equation is equivalent to 3^2 = 9?
Answer:
[tex]log_3(9)=2[/tex]
Step-by-step explanation:
[tex]3^2 = 9[/tex]
Logarithmic form is the reverse of exponential form
To convert exponential form in to log form we use a rule
[tex]b^x=a[/tex] can be written as [tex]log_b(a)=x[/tex]
WE apply the same rule in our exponential equation to convert it into log form
[tex]3^2 = 9[/tex]
The base of exponent is the base of log
[tex]log_3(9)=2[/tex]
A hotel is in the shape of a square pyramid. Each side of the base is 183 meters long and the height is 110 meters. What is the hotel's volume? Enter your answer in the box
Answer:
1,227,930 m²
Step-by-step explanation:
We are given that,
Base of the pyramid = 183 meter
Height = 110 meter.
Since, we know,
Volume of a square pyramid = [tex]Base^2\times \frac{Height}{3}[/tex]
We have,
Volume of the square pyramid = [tex]183^2\times \frac{110}{3}[/tex]
i.e. Volume of the square pyramid = [tex]33489\times 36.667[/tex]
i.e. Volume of the square pyramid = 1,227,930 m²
Hence, the volume of the square pyramid is 1,227,930 m².
Analyze the key features of the graphs of the functions below. Select all of the quadratic functions that open down, have a vertex that is a maximum and a positive y-intercept.
The Choices are
F(x)=2x^2-4x-3
G(x)= -x^2+x+1
H(x)= -2x^2+3x-1
M(x)=x^2-9
N(x)= -3x^2+7
Out of the options provided, only G(x) = -x^2 + x + 1 fits the conditions asked in the question. It is a quadratic function that opens downward, has a vertex that is a maximum, and a positive y-intercept.
Explanation:The key features of a quadratic function are determined by its equation: f(x) = ax2 + bx + c. The sign of 'a' determines whether the function opens up or down. If 'a' is positive, the graph opens up, and if 'a' is negative, it opens down. The vertex of a quadratic function is given by the formula (-b/2a , f(-b/2a)). If 'a' is negative, this vertex will be a maximum. The y-intercept of the function is the value of 'c' in the quadratic equation. According to the conditions provided, we can classify the given functions.
f(x) = 2x2 - 4x - 3 opens upward and has a negative y-intercept; it’s not in the selection.G(x) = -x2 + x + 1 opens downward, has a maximum vertex, and a positive y-intercept. It fits the conditions.H(x) = -2x2 + 3x - 1 opens downward and has a maximum vertex, but has a negative y-intercept, so it’s not in the selection.M(x) = x2 - 9 opens upward and has a negative y-intercept; it’s not in the classification.N(x) = -3x2 +7 opens downward and has a maximum vertex, but it does not mention whether there is a positive y-intercept; so it’s unclear.
Learn more about Quadratic Functions here:
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Olive has read 79 pages of her book. Which equation shows how many more pages she has to read?
which method could be used to factor 4x^2-50
The correct factorization for [tex]\(4x^2 - 50\) is \(2(x\sqrt{2} - 5)(x\sqrt{2} + 5)\)[/tex], where [tex]\(\sqrt{2}\)[/tex] is included in each term.
The given quadratic expression [tex]\(4x^2 - 50\)[/tex] can be factored using the difference of squares method.
The difference of squares formula is[tex]\(a^2 - b^2 = (a + b)(a - b)\).[/tex]
In this case, a = 2x and [tex]\(b = \sqrt{50}\).[/tex]
1. Identify the expression as a difference of squares: [tex]\(4x^2 - 50 = (2x)^2 - (\sqrt{50})^2\).[/tex]
2. Apply the difference of squares formula:[tex]\(4x^2 - 50 = (2x + \sqrt{50})(2x - \sqrt{50})\).[/tex]
3. Further simplify by factoring out 2: [tex]\(4x^2 - 50 = 2(2x + \sqrt{50})(2x - \sqrt{50})\).[/tex]
The correct factorization for [tex]\(4x^2 - 50\) is \(2(x\sqrt{2} - 5)(x\sqrt{2} + 5)\)[/tex], where [tex]\(\sqrt{2}\)[/tex] is included in each term.
A circle is divided into parts. Which sum could represent the angle measures that make up the circle?
A circle is always going to be 360°.
Write, and show on a number line, the set of all the numbers that are:
greater than (−3) and less than 3.
Each term in a binomial expansion has degree n; therefore, the product of the exponents of each term is n.
true
or
false
Answer:
False
Step-by-step explanation:
In any binomial expansion of the form
[tex](x+a)^n = \Sigma_0^n nCr x^{n-r} a^{r}[/tex]
We find that each term has decreasing powers of x by 1 and increasing powers of a by 1, such that the sum of exponents is always n
Hence product of exponents of each term cannot be n.
The given statement is false.
Only the sum of the exponents of each term in a binomial expansion has degree n
what is community property and associative property
Final answer:
The associative property in mathematics states that the way in which numbers are grouped or associated does not affect the result of the operation. Community property refers to the legal framework in which the ownership of property is divided equally between spouses in a marriage or a domestic partnership.
Explanation:
The associative property is a property in mathematics that states that the way in which numbers are grouped or associated does not affect the result of the operation. For example, for addition, the associative property states that (a + b) + c = a + (b + c). This property holds true for addition and multiplication, but not for subtraction and division.
Community property, on the other hand, is a concept in the field of law, specifically property law. Community property refers to the legal framework in which the ownership of property is divided equally between spouses in a marriage or a domestic partnership. It is most commonly associated with community property states in the United States.
How many x intercepts appear on the graph of this polynomial function? F(x)=x^4-5^2.
1 x intercept
2 x intercepts
3 x intercepts
4 x intercepts
Click on ALL the values for n that make this inequality true. There maybe more than one answer.
[tex]120 \geq 10n + 20[/tex]
Possible Answers:
You can divide by 10 and subtract 2.
12 ≥ n + 2 . . . . . . divide by 10
10 ≥ n . . . . . . . . . subtract 2
The values that will make the inequality true are those that are 10 or less, including 0 and all negative numbers.
How to find A? help please and thanks
Four runners, Fran, Gloria, Haley, and Imani, compete on a relay team. Haley is the first runner in the relay. The other runners can run in any order. What is the sample space showing the possible orders of the other three runners? S = {FGI, GFI, IFG} S = {FGI, FIG, GFI, GIF} S = {FGI, FIG, GFI, GIF, IFG, IGF} S = {FGI, FIG, GFI, GIF, HFG, HGI, IFG, IGF}
The sample space or sets showing the possible orders of the other three runners is S = {FGI, FIG, GFI, GIF, IFG, IGF}.
What are Sets?Sets are the collection of well-defined elements. A set is represented by a capital letter symbol and the number of elements in the finite set is shown as curly bracket {..}.
Four runners, Fran, Gloria, Haley, and Imani, compete on a relay team.
Haley is the first runner in the relay. The other runners can run in any order.
The sample space or sets showing the possible orders of the other three runners will be
S = {FGI, FIG, GFI, GIF, IFG, IGF}
Thus, the correct option is C.
More about the sets link is given below.
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The graph below shows the solution to a system of inequalities
Which of the following inequalities is modeled by the graph?
A. x + 4y ≥ 15; y ≥ 0
B.x − 4y ≥ 15; y ≥ 0
C.x + 4y ≤ 15; y ≥ 0
D.−x − 4y ≥ 15; y ≥ 0
Find the distance from the point p(4, −1, 1) to the line x = 1 + 2t, y = 3t, z5 − 7t
Finn imagines 1 more row of nines to find the total area of 9 * 9 rectangle. explain how this could help him solve 9 * 9
Please help with this question!
Ari has been paying attention to the number of calories she burns while exercising. One day she spent 3 hours hiking, and 4 canoeing, and she calculated that she burned 2338 calories. The next day, she hiked for 7 hours and canoed for one hour, and she calculated that she burned 3322 calories. How many calories per hour does Ari burn doing each exercise?
By setting up a system of equations, we find that Ari burns 438 calories per hour hiking and 256 calories per hour canoeing.
To determine the number of calories Ari burns per hour doing each exercise, we need to set up a system of equations based on the given information. Let x represent the number of calories burned per hour hiking, and y represent the number of calories burned per hour canoeing.
We are given two situations:
3 hours of hiking and 4 hours of canoeing burn 2338 calories: 3x + 4y = 2338.
7 hours of hiking and 1 hour of canoeing burn 3322 calories: 7x + y = 3322.
We have the following system of equations:
3x + 4y = 2338
7x + y = 3322
To solve the system, we can first multiply the second equation by 4 to eliminate y:
4(7x + y) = 4(3322)
28x + 4y = 13288
Now, subtract the first equation from this result:
(28x + 4y) - (3x + 4y) = 13288 - 2338
25x = 10950
x = 10950 / 25
x = 438
Ari burns 438 calories per hour hiking.
To find y, substitute x = 438 into the first equation:
3(438) + 4y = 2338
1314 + 4y = 2338
4y = 2338 - 1314
4y = 1024
y = 256
Ari burns 256 calories per hour canoeing.
Thus, the results reveal that Ari burns 438 calories per hour hiking and 256 calories per hour canoeing.
select all expressions thr equal 3.15/0.45
Which model shows the correct factorization of x2 + 2x - 8
The correct answer is D.
I just took the test.
Compare the two fractions. Use >, <, or =.
1st fraction, 2/3
2nd fraction, 4/6
The figures shows the show the dimension of a tennis court and a basketball court given in term of the width x in feet.
help please...........
Given the volume of Wesley's cube = 8 cubic centimeters.
We know the formula for volume of cube is given as follows :-
Volume of cube = (side) x (side) x (side)
8 = (side)³
side = [tex]\sqrt[3]{8} =\sqrt[3]{2*2*2} =2[/tex]
Hence, Wesley's cube dimensions are 2 centimeters.
The square must have side length as 2 centimeters.
If smallest square G represents 1 centimeters, then clearly it is H = 2 centimeters.
So, square H is the final answer.
Use the zero product property to find the solutions to the equation 6x^2-5x=56
6x² -5x -56 = 0 . . . . . subtract the constant
(3x +8)(2x -7) = 0 . . . .factor*
The zero product property says the product will be zero only when one (or both) of the factors is zero.
First Factor
... 3x +8 = 0
... x + 8/3 = 0 . . . . divide by the coefficient of x
... x = -8/3 . . . . . . subtract 8/3
Second Factor
... 2x -7 = 0 . . . . . . set the factor to zero
... x -7/2 = 0 . . . . . divide by the coefficient of x
... x = 7/2 . . . . . . . add 7/2
_____
*Comment on factoring
There are various ways to do this. In basic terms, we want to find numbers that are factors of the product 6·(-56) whose sum is -5. We found those numbers to be -21 and 16. Then we can rewrite the -5x term using these numbers and factor by grouping.
... 6x² -5x -56 = (6x² -21x) +(16x -56) = 3x(2x -7) +8(2x -7) = (3x +8)(2x -7)
Answer:
B. x = -8/3, or x= 7/2
Step-by-step explanation:
Using the tables found in the textbook, determine the difference between the monthly payments on a $120,000 home at 6½% and at 8% for 25 years.
Answer:115.20
Step-by-step explanation:
margaret purchased a doormat measuring 1/2 yard by 2/3 yard for her back door step. If the step is 1/4 square yard, will the mat fit? explain
Final answer:
The doormat measuring 1/2 yard by 2/3 yard will not fit on a step that is 1/4 square yard because the doormat's area, 1/3 square yard, is larger than the step's area.
Explanation:
The question "Will a doormat measuring 1/2 yard by 2/3 yard fit on a step that is 1/4 square yard?" involves understanding of measuring areas in yards and comparing the area of the doormat with that of the step. First, we calculate the area of the doormat by multiplying its length and width (1/2 yard * 2/3 yard = 1/3 square yard).
Next, we compare the area of the doormat, which is 1/3 square yard, to the area of the step, which is 1/4 square yard. Since 1/3 square yard is larger than 1/4 square yard, the doormat will not fit perfectly on the step as it is too big.
A punch recipe requires 4/5 of a cup of pineapple juice for every 2 1/2 cups of soda. What is the unit rate of soda to pineapple juice in the punch?