Using limits, it is found that the end behavior of the polynomial function for the volume of the rectangular box is:
B. down and up.
What is the volume of a rectangular prism?The volume of a rectangular prism of length l, width w and heigth h is given by:
V = lwh.
In this problem, we have that the dimensions are given by:
w = x.l = x - 1.h = x - 2.Hence the volume is given by:
[tex]V = x(x - 1)(x - 2) = x(x^2 - 3x + 2) = x^3 - 3x^2 + 2x[/tex]
What is the end behavior of a function?It is given by it's limits as x goes to infinity.
Hence:
[tex]\lim_{x \rightarrow -\infty} V(x) = \lim_{x \rightarrow -\infty} x^3 - 3x^2 + 2x = \lim_{x \rightarrow -\infty} x^3 = -\infty[/tex]
[tex]\lim_{x \rightarrow \infty} V(x) = \lim_{x \rightarrow \infty} x^3 - 3x^2 + 2x = \lim_{x \rightarrow \infty} x^3 = \infty[/tex]
Which means that option B is correct.
More can be learned about limits at brainly.com/question/22026723
the question is below
Answer:
£59.25
Step-by-step explanation:
Hello!
To solve this problem, we must:
Solve for the length of the fence (aka height)Find the area of the lawn (trapezoid)Find the number of cans neededFind the price of all the cansArea of a trapezoid, and why the formula works:
A trapezoid is a quadrilateral with one set of parallel sides known as bases. The other two sides are known as the legs.
To find the area of a trapezoid, we use the formula:
[tex]\frac{B_1 + B_2}{2}* h[/tex]
This works because if we used the formula, we would be duplicating the trapezoid to form a rectangle with a side length of B1 + B2, and a height of h. Since the trapezoid is half of that, we divide by 2.
Solve for height:
The height is unknown but can be found using the Pythagorean Theorem.
The difference between the bases is the length of the bottom leg of the right triangle, and 17 is the hypotenuse.
Difference = 20 - 12 = 8
Hypotenuse = 17
8² + fence² = 17²64 + fence² = 289225 = fence²fence = 15The height is 15
Solve for area:
Now we can solve for the area.
[tex]A = \frac{B_1 + B_2}{2} * h[/tex][tex]A = \frac{12 + 20}{2} * 15[/tex][tex]A = \frac{32}{2} * 15[/tex][tex]A = 16 * 15 = 240[/tex]The area is 240
Cans:
The area of the lawn is 240 square meters. Each can cover 100 square meters.
240 ÷ 100 = 2.4Since we can't use part of a can, we round up to three whole cans.
The price of 3 cans :
3 * 19.7559.25£59.25
The Pythagorean Theorem:
The Pythagorean theorem is a very common geometry formula used to find the length of the hypotenuse in a right triangle, given the lengths of the two other bases.
The formula is : [tex]a^2 + b^2 = c^2[/tex]
a is a legb is a legc is the hypotenuseImages attached for your reference
Camila has a coin collection. She keeps 13 of the coins in her box, which is 10% of the
collection. How many total coins are in her collection?
Answer:
130
Step-by-step explanation:
We need to keep adding 13 together until we have done this 10 times :)
10%: 13
20%: 26
30%: 39
40%: 52
50%: 65
60%: 78
70%: 91
80%: 104
90%: 117
100%: 130
Have an amazing day!!
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A theater is selling tickets for a musical. One attendee purchased 2 adult tickets and 5 student tickets, and the total cost was $64. Another attendee purchased 3 adult tickets and 4 student tickets, and the total cost was $68. Write a system of equations to find the price of an adult ticket and a student ticket. Let x be the price of an adult ticket and y be the price of a student ticket.
Answer:
Price of an adult ticket: 12$
Price of a student ticket: 8$
Step-by-step explanation:
Let x be the price of an adult ticket, and y be the price of a student ticket.
We have the equation:
2x + 5y = 64
3x + 4y = 68
=> x - y = 4
2x + 5y = 64
=> x = 4+y
2*(4+y) + 5y = 64
=> x = 4+y
8 + 2y + 5y = 64
=> x = 4 + y
7y = 56
=> x = 4 + y
y = 8
=> x = 12
y = 8
$1 = £0.73. Change $346 into £
Answer:
£252.58
Step-by-step explanation:
$346 × £0.73/$1 = £252.58
Please rate!! I hope this helps!!
Trigonometric equations
4sin^2(theta) + 4 = 5
Answer:
Θ = (π/6) + πn
Θ = (5π/6) + πn
Step-by-step explanation:
4sin²Θ + 4 = 5
-4 -4
4sin²Θ = 1
÷4 ÷4
sin²Θ = (1/4)
√sin²Θ = √(1/4)
sinΘ = (1/2), (-1/2)
-------------------------
Θ = arcsin (1/2)
Θ = (π/6)
to find the quadrant subtract π
Θ = π - (π/6)
Θ = (5π/6)
Find the period
2π / |b|
b = 1
2π/1 = 2π
The sin Θ function is 2π, so values will repeat 2π in both directions.
Θ = (π/6) + 2πn (n is the variable)
Θ = (5π/6) + 2πn
-------------------------------------------------------------------------------------------------------
sin Θ = (-1/2)
Θ = arcsin (-1/2)
Θ = (-π/6)
To find the second function add π
Θ = 2π + (π/6) + π
Θ = (7π/6)
Find the period
2π/|b|
2π/1
2π
(-π/6) + 2π
2π 6 π
----- × ----- - -----
1 6 6
Θ = (11π/6) will repeat every 2π in both directions
-------------------------------------------------------------------------------------------------------
Θ = (π/6) + 2πn
Θ = (5π/6) + 2πn
Θ = (7π/6) + 2πn
Θ = (11π/6) + 2πn
(π/6) + π = (7π/6)
(5π/6) + π = (11π/6)
Θ = (π/6) + πn
Θ = (5π/6) + πn
----------------------------------------------------------------------------------------------------------
I hope this helps!
Sanjay is standing on level ground 70 meters away from a flag pole. The angle of elevation to the flagpole is 38 degrees. The height of Sanjay's eyes are 167cm from the ground. How tall is the flag pole in meters?
The height of the pole is 53 m
What is the height of the pole?The angle of elevation is the angle formed between a horizontal line and a line of sight or an upwardly inclined line from an observer to an object or point. It is used to describe the angle at which an object is viewed from a particular position
Let the height of the pole be x
We know that;
Tan 38 = 1.67 + x/70
Tan 38 * 70 = 1.67 + x
x = (Tan 38 * 70 ) - 1.67
x = 53 m
Thus we can see that the height of the pole is about 53 m
Learn more about angle of elevation:https://brainly.com/question/21137209
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When asked to factor the trinomial x^2 - 18x + 81, a student gives the answer (x - 9)(x + 9). Which of the following statements is true?
A. The answer is incorrect; the trinomial cannot be factored.
B. The answer is incorrect; the plus sign should be a minus sign.
C. The answer is incorrect; the minus sign should be a plus sign.
D. The answer is correct.
Answer:
B.The answer is incorrect; the plus sign should be a minus sign.
Step-by-step explanation:
[tex]x^2-18x+81\\\\=x^2-2\cdot 9x +9^2\\\\=(x-9)^2\\\\=(x-9)(x-9)[/tex]
the sum of 3x and 1 is greater than-5 and less than or equal to 10
Answer:
x is greater than -2 and less than or equal to 3
Step-by-step explanation:
so the 3x + 1 is greater than -5
so 3x is greater than -6
we divide both sides by 3
then we find out that x is greater than -2
we also know that 3x + 1 is less than or equal to 10
so 3x is less than or equal to 9
we divide both sides by 3
then we find out that x is less or equal to 3
so we can say that x is greater than -2 and less than or equal to 3
Measurements of angles
Answer:
x = 60
Step-by-step explanation:
Since this triangle is an isosceles triangle, the angle next to the 60 degrees is 60 as well. The interior angles of a triangle adds up to 180 degrees, so:
60 + 60 + x = 180
120 + x = 180
x = 60
Hope this helps :)
Elise had 1/4 of an apple pie. She gave 1/4 of what she had to her friend Danny. What fraction of the whole pie did Danny get?
The answer to your question is =
Danny got 1/16 of the whole pie
I need help with this question really badly please help.
A runner is preparing for a marathon that is divided into 5 sections of equal distance. The Marathon is 42.195 km long. How long is each section of the marathon?
A. 210.975
B. 21.0975
C. 8.439
D. 0.8439
Answer:
8.439
Step-by-step explanation:
Since the marathon is divided on 5 EQUAL sections, and it is 42.195 km long, you only need to divide the length of the marathon by 5.
La integral indefinida de la función h(x)=2x+5x4
Answer:
x^2 + x^5 + C.
Step-by-step explanation:
∫2x + 5x^4 dx
= 2 * x^2/2 + 5 * x^5/5 + C
= x^2 + x^5 + C.
Please help me i need help!!!
Answer:
sorry cant help with that
Step-by-step explanation:
40 Points! If AD is a diameter and m∠C = 112°, what is the measure of ∠A?
Both are supplementary
<A+<C=180112+<A=180<A=180-112<A=68Which polynomial function could be represented by the graph below?
Answer:
C
Step-by-step explanation:Only one that makes sence just look at the graph
double the difference of 6 and x
Determine whether the statement makes sense or does not make sense, and explain your reasoning.
A candidate received the majority of first-place votes and lost the election.
Choose the correct answer below.
A. The statement does not make sense because the candidate with the majority of the first place votes using the plurality method is the winner.
B. The statement does not make sense because the candidate with the majority of the first place votes in an election is always the winner.
C. The statement makes sense because the Borda count method using preference ballots can result in a situation where this can happen.
D. The statement makes sense because the plurality method can result in a situation where this can happen.
A candidate received the majority of first-place votes but loses hows that A. The statement does not make sense.
What is plurality voting?It should be noted that plurality voting simply means when each voter is allowed to vote for only one candidate.
In this case, a candidate received the majority of first-place votes will win the election. Here, the majority of the first place votes using the plurality method is the winner.
Learn more about votes on:
https://brainly.com/question/3710029
Diego's recipe calls for three times as much oregano than Tracy's recipe. If Tracy only uses 0.75 tablespoons of oregano in her recipe, how many does Diego use?
Answer:
2.25 tablespoons of oregano
Step-by-step explanation:
as Diego use 3x more than Tracy, and you know that Tracy use 0.75 tablespoon, so 0.75 x 3 and you will get 2.25
3 friends share 6 pounds of grapes equally. Each pound has 40 grapes.
How many grapes does each friend get?
A.
20 grapes
B.
60 grapes
C.
80 grapes
D.
90 grapes
Answer:
C. 80 grapes
Step-by-step explanation:
6 / 3 = 2
Each person gets 2 pounds of grapes.
2 X 40 = 80
1 pound = 40 grapes
2 pound = 80 grapes
Necesito saber cual funcion es
Answer:
A function is defined as a relation between a set of inputs having one output each..
Step-by-step explanation:
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
¿Qué es la función explicar?
Una función se define como una relación entre un conjunto de entradas que tienen una salida cada una. En palabras simples, una función es una relación entre entradas donde cada entrada está relacionada exactamente con una salida. Cada función tiene un dominio y un codominio o rango. Una función generalmente se denota por f(x) donde x es la entrada.
Find the sum of the arithmetic sequence 1, 4, 7, 10, ...,94; n=32
Answer:
Step-by-step explanation:
hello :
the sum is : Sn = n/2(U1 + Un ) and U n = U1+(n-1)r
given : U1 = 1 r=4-1=7-4=...= 3 n= 32
so : U 32 = 1+(32-1)3= 94
S32 = 32/2 (1+94) = 1520
Find the derivative of the image below
[tex]~~~\dfrac{d}{dx} f(x) \\ \\=\dfrac{d}{dx} \left(x^3 \cdot \log_6 x \right)\\\\=x^3\dfrac{d}{dx} \left(\log_6 x\right) + \log_6 (x)\dfrac d{dx} x^3 \\\\=x^3 \cdot \dfrac 1{x \ln 6} + \log _6 (x) \cdot 3x^2\\\\=\dfrac{x^2}{\ln 6} + \log_6(x) \cdot 3x^2\\\\\\=x^2 \left(\dfrac 1{\ln 6} + 3\log_6 x \right)[/tex]
[tex]\text{The derivative is now in a form of}~ x^A (B + C \log_D (x))[/tex]
A footbridge is being built across the river that will connect points A and B. If the length of each box represents 2 yards, approximately what will the length of the footbridge be?
Answer:
4 yards
Step-by-step explanation:
IG;youngdestinyofficial
What is the mean absolute deviation of the following set
of data?
9
2
9
9
5
4.
9
1
4
10
Answer:
3
Step-by-step explanation:
You want the mean absolute deviation of the set of numbers ...
{9, 2, 9, 9, 5, 4, 9, 1, 4, 10}
MADThe mean of this 10-number set of data is 6.2. The mean absolute deviation (MAD) is found by subtracting that from the members of the dataset, taking the absolute values of the result, and finding the means of those.
The attachment shows those calculations.
The MAD of this set of data is 3.
__
Additional comment
The period (decimal point) in the column of numbers suggests this is a 6-number dataset, and the last 4 numbers are answer choices. If that is the case, none of those answer choices is correct. That is why we assumed that this problem has a 10-number dataset.
When you're calculating this by hand, you only need to consider the values for which the deviation is negative. The MAD is twice their total absolute value, divided by the number of numbers in the dataset. Here, that is 2(4.2+2.2+5.2+2.2+1.2)/10 = 3. (Numbers 2, 5, 4, 1, 4 are less than the mean of 6.2.)
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The Han family just enjoyed dinner at Mizumi restaurant. The bill was $160.18. The tax rate is 8.25% and the restaurant charges a 15% service fee on each bill, not including the tax.
a) what was the total amount the Han family paid for dinner?
Answer:
$198.62
Step-by-step explanation:
The dinner itself is $160.188.25% tax on $160.18 is approximately $13.21A 15% service fee on $160.18 is approximately $25.23**You only apply the 15% service fee to $160.18 and not 173.39 (dinner and tax) because the problem says the service fee is applied before tax.
160.18 + 13.21 + 25.23 = 198.62
Hope this helps!
solve the equation
answer: x=
Answer:
Hope the picture will help you
For a sample of n = 16 scores, what is the value of the population standard deviation (o) necessary to produce each of the following standard error values?
a. Ом = 8 points
b. Ом =4 points
с. Ом = 1 point
Using the Central Limit Theorem, it is found that the values of the population standard deviation [tex]\sigma[/tex] needed are given by:
a) [tex]\sigma = 32[/tex]
b) [tex]\sigma = 16[/tex]
c) [tex]\sigma = 4[/tex]
What does the Central Limit Theorem state?By the Central Limit Theorem, the sampling distribution of sample means of size n has standard error [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this problem, we have that n = 16.
Item a:
s = 8, hence:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]8 = \frac{\sigma}{\sqrt{16}}[/tex]
[tex]\sigma = 32[/tex]
Item b:
s = 4, hence:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]4 = \frac{\sigma}{\sqrt{16}}[/tex]
[tex]\sigma = 16[/tex]
Item c:
s = 1, hence:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]1 = \frac{\sigma}{\sqrt{16}}[/tex]
[tex]\sigma = 4[/tex]
More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213
7. SHORT ANSWER Determine whether the
relationship between the two quantities
in the table is proportional. Explain
your reasoning.
Answer:
it is proportional because there is a roc of +5 bc as one hour increases 5 dollars is added to the initial cost
what is 1/4 - 41 1/4 + 3
Answer:
-38
Step-by-step explanation:
i hope this helps you
good luck on your quiz or lesson!
Answer:
-38
Step-by-step explanation:
[tex]\frac{1}{4} = 0.25[/tex]
[tex]\frac{1}{4} -41\frac{1}{4} +3[/tex]
[tex]0.25-41.25+3[/tex]
[tex]-41+3[/tex]
[tex]-38[/tex]