Neither of these statements are true.
x/∞ = 0 is a nonsensical statement. It's more accurate to say
[tex]\displaystyle \lim_{y\to\infty} \frac xy = 0[/tex]
for any real number x. The important bit is that y is an arbitrarily large number as it approaches ∞. To convince yourself that this expression approaches 0 as y gets larger and larger, try fixing x and pick any increasing sequence of numbers for y.
For example, let x = 1 and take y from the sequence of increasing powers of 10, {10, 10², 10³, …}, which grows without bound. Then
1/10 = 0.1
1/10² = 0.01
1/10³ = 0.001
and so on. Naturally, the larger the power of 10 and thus the larger y gets, the closer x/y gets to 0.
Similarly, x/0 is nonsense, but the "limit-ized" version of the claim is also incorrect. For any fixed real number x, the limit
[tex]\displaystyle \lim_{y\to0} \frac xy[/tex]
does not exist. Suppose x > 0. If y approaches 0 from above, then y > 0 and x/y > 0 and
[tex]\displaystyle \lim_{y\to0^+} \frac xy = +\infty[/tex]
which you can convince yourself is true by reversing the example from before. Let x = 1 and take y from the sequence of decreasing powers of 10, {1/10, 1/10², 1/10³, …}, which converges to 0. Then
1/(1/10) = 10
1/(1/10²) = 100
1/(1/10³) = 1000
and so on. The smaller y gets (while still being positive), the larger x/y becomes.
But now suppose y < 0 and that y approaches 0 from below. Then x/y < 0, and
[tex]\displaystyle \lim_{y\to0^-} \frac xy = -\infty[/tex]
The limits from either side do not match, so the limit as y approaches 0 does not exist.
You can use the same reasoning for when x < 0.
The case of x = 0 is special, however. Since y is approaching 0, it's never actually the case that y = 0. 1/y is then some non-zero real number, and multiplying it by x = 0 makes x/y = 0. Then
[tex]\displaystyle \lim_{y\to0} \frac 0y = 0[/tex]
So in general,
[tex]\displaystyle \lim_{y\to0} \frac xy = \begin{cases}0 & \text{if }x = 0 \\ \text{does not exist} & \text{otherwise}\end{cases}[/tex]
Please help me i need this finish by the hour
Answer:
60
Step-by-step explanation:
Question 11
Solve the simultaneous equations
4x + 2y = 9
x - 2y = 1
The value of x and y is (5,2)
We have given that,
4x + 2y = 9 ........(1)
x - 2y = 1.......(2)
We have to solve the simultaneous equation
What is the simultaneous equation?
A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
adding equations 1 and 2 so we get,
4x + 2y = 9
x - 2y = 1
----------------
5x-0y=10
[tex]5x=10\\x=10/2\\x=5[/tex]
Use the value of x in equation 2 so we get,
[tex]5-2y=1[/tex]
[tex]-2y=1-5[/tex]
[tex]-2y=-4[/tex]
[tex]y=-4/-2[/tex]
[tex]y=2[/tex]
Therefore the value of x and y is (5,2)
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could someone please answer this will give brainliest
There is a 30% chance that Jerry will have to wait for the bus for more than five minutes to go to office. What is the probability that he does not wait for more than five minutes all 5 days this week?
The probability that he does not wait for more than five minutes all 5 days this week is 0.16807
How to determine the probability?The probability that he waits for more than 5 minutes is:
p = 30%
This means that the probability that he does not wait for more than 5 minutes is
q = 70%
If he does not wait for more than five minutes all 5 days this week, the probability is:
P = q^5
This gives
P = (70%)^5
Evaluate
P = 0.16807
Hence, the probability that he does not wait for more than five minutes all 5 days this week is 0.16807
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The table below shows the amount of time a light stays green, red, and yellow (for one cycle) during the day and during the night. Day Night Light is green 2 minutes 3 minutes Light is red 3 minutes 4 minutes Light is yellow 20 seconds 30 seconds Is it more likely for you to have to wait at red light during the day or at night? How much more likely? Show all of your work. WRITER
The table shows that it is more likely to wait at red during daytime by 2.92%.
How to explain the information given?Day
Green = 2 min
Red = 3 min
Yellow = 20 sec = 0.333 min
Total day cycle time= 5.33 min
Night
Green = 3 min
Red = 4 min
Yellow = 30 sec = 0.5 min
Total night cycle time= 7.5 min
Pday= 3 min/5.33 min= 0.5625
Pnight= 4 min/7.5 min= 0.5333
Pdifference= 0.02917 = 2.92%
Therefore it is more likely to wait at red during the daytime by 2.92%.
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what is P(2 or divisor of 9)?
please explain!
The probability that a divisor of 2 or 9 is chosen when the spinner is spun once is 2/3.
What is the probability?
Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
P(2 or divisor of 9) = section that has a divisor of 2/ total number of sections + section that has a divisor of 2/ total number of sections
1/3 + 1/ 3 = 2/3
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ABCD is a quadrilateral
a) calculate the value of x.
b) when ABCD is drawn to scale would the lines be parrallel or not?
What is the area of the base of the prism?
1 square centimeters
what is the volume of the prism?
cubic centimeters
The base area of the prism is 36 square centimeters and the volume of the prism is 288 cubic centimeters
How to determine the base area?The base area is calculated as:
Base area =Length * Width
From the complete question (see attachment), we have:
Length = 12
Width = 3
So, we have:
Base area = 12 * 3
Base area = 36
How to determine the volume?The volume is calculated as:
Volume = Base area * Height
So, we have:
Volume = 36 * 8
Evaluate
Volume = 288
Hence, the volume of the prism is 288 cubic centimeters
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PLEASE HELP find the arch shown in red leave your answer in terms of pi
Answer:
Answer:1296π
Step-by-step explanation:
As we know,
Area of cicle=πr^2
= π(36)^2
=1296π
A square has a perimeter of 36x - 12. Which expression represents one side of the
square?
Answer:
9x - 3
Step-by-step explanation:
Hello!
A square has 4 sides.
We can factor out 4 from the expression to find the value of one side.
Factor:
36x - 124(9x) - 4(3)4(9x - 3)This means that each side of the square is 9x - 3 units long.
Using the 4 train car strategy for factoring polynomials, what is the green common factor for the 1st two train cars and the green common factor for the 3rd and 4th train car: . note: the answers are intermediary steps. do not enter the final step or factored form, but this question is asking what is the intermediate step as the answer.
2x^2 + 4x + 3xy + 6y
enter your answer in the boxes.
The completely factored expression of 2x^2 + 4x + 3xy + 6y is (2x + 3y)(x + 2)
How to factor the polynomial?The expression is given as:
2x^2 + 4x + 3xy + 6y
Group the expression into two
[2x^2 + 4x] + [3xy + 6y]
Factor out each group
2x(x + 2) + 3y(x + 2)
Factor out x + 2
(2x + 3y)(x + 2)
Hence, the completely factored expression of 2x^2 + 4x + 3xy + 6y is (2x + 3y)(x + 2)
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Answer:
Step-by-step explanation:
ans in picture
pleaseeee help me out
Answer:
78
Step-by-step explanation:
QT is a 180 straight line so 180-55-47
Hope its right!
Answer:
U-60
S-90
Q-80
ur welcome
Given mn, find the value of x.
(7x-7)°
(6x+11)°
Answer:
x = 18
Step-by-step explanation:
the 2 angles are alternate exterior angles and are congruent, then
7x - 7 = 6x + 11 ( subtract 6x from both sides )
x - 7 = 11 ( add 7 to both sides )
x = 18
Answer:
18
Step-by-step explanation:
(7x-7)° = (6x+11)°------ (alternate exterior angles are equal)
Alternate exterior angles are the pair of angles that are located on the outer side of the parallel lines but on either side of the transversal.therefore,
7x-7= 6x+11
collect like terms
7x-6x = 11+7
x = 18
The water was pumped out of a backyard pond. What is the domain of this
graph?
Water Depth
110
100
90
80
70
50
40
30
20
10
1 2 3 4 5 6 7 8 9 10 11 12 13
Time (minutes)
Depth (inches)
0
Using it's concept, it is found that the domain of the function is given by:
C. Real numbers between 0 and 12.
What is the domain of a function?
The domain of a function is the set that contains all possible input values of the function. In a graph, it is given by the values of the horizontal axis.
In the graph, the function is defined for real numbers between 0 and 12, hence option C is correct.
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Maurice averaged 79 points for 6 tests. How many more points must he score in the next text to raise his average to 80.
Answer:
86 is the score that Maurice must get to average his score to 80
The midpoint of AB given A (3, -12) and B (-1, -2) is (x, y). What are the
values of x and y?
Answer:
(1, - 7 )
Step-by-step explanation:
using the midpoint formula
given endpoints (x₁, y₁ ) and (x₂, y₂ ) , then
midpoint = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
here (x₁, y₁ ) = A (3, - 12 ) and (x₂, y₂ ) = B (- 1, - 2 )
midpoint = ( [tex]\frac{3-1}{2}[/tex] , [tex]\frac{-12-2}{2}[/tex] ) = ( [tex]\frac{2}{2}[/tex] , [tex]\frac{-14}{2}[/tex] ) = (1, - 7 )
Step-by-step explanation:
[tex] x_{m} , y_{m} \: = ( \frac{x _{1} + x_{2} }{2} ,\frac{y _{1} + y_{2} }{2}) \\ [/tex]
x1 = 3, x2 = (-1)
y1 = (-12), y2 = (-2)
[tex] x_{m} , y_{m} \: = ( \frac{3+ ( - 1) }{2} ,\frac{( - 12)+ ( - 2) }{2}) \\ [/tex]
[tex]x_{m} , y_{m} \: = ( \frac{3 - 1 }{2} ,\frac{( - 12) - 2 }{2}) \\ [/tex]
[tex]x_{m} , y_{m} \: = ( \frac{2 }{2} ,\frac{- 14 }{2}) \\ [/tex]
[tex]x_{m} , y_{m} \: = 1 ,( - 7)[/tex]
Your friend simplifies the expression. Is your friend correct?
( i didnt mean to click yes )
Reason:
The friend should have multiplied the exponents.
This is what the steps should look like:
[tex](r^6)^4 = r^{6*4}\\\mbox{ \ \ \ \ \ \ } =r^{24}[/tex]
The reason for the multiplication is because we have four copies of [tex]r^4[/tex] added together. Repeated addition can be shortened to multiplication.
In other words,
[tex](r^6)^4 = (r^6)*(r^6)*(r^6)*(r^6) = r^{6+6+6+6} = r^{6*4} = r^{24}[/tex]
9 What is the next whole number after twenty thousand ? Write your answer in figures .
10 What is the next whole number after one hundred thousand ? Write your answer in figures .
11 What is the last whole number before five thousand ? Write your answer in figures .
12 What is the last whole number before one million ? Write your answer in figures .
Answer:
9. 20,001
10. 100,001
11. 4,999
12. 999,999
Step-by-step explanation:
how many whole weeks are in a year
Answer:
52 weeks are there in a year
Step-by-step explanation:
365/7
30 divided by 5 - 2 + 7 = 3
Then , write down the correct equation.
Answer:
30 : (5 - 2 + 7) = 3Step-by-step explanation:
30 divided by 5 - 2 + 7 = 3
Then , write down the correct equation.
30 : (5 - 2 + 7) = 3
30 : (3 + 7) = 3
30 : 10 = 3
3 = 3
sectors of circle. east points, this is due tomorrow help is appreciated
By knowing the circumference of the base of the cone, we see that the radius is 4 centimeters.
How to find the radius of the cone?Notice that in the first figure, the length of the arc AB is L = 8π cm.
Then, that arc will be the bottom part of the cone. Then we can see that the circumference of the base of the cone will be equal to the length of the arc.
And remember that for a circle of radius R (like the base of the cone), the circumference is:
C = 2πR.
Then we will get:
8π cm = C = 2πR
( 8π cm)/ 2π = R
4cm = R
The radius of the cone is 4cm.
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口 6. Write the following inequality in slope-intercept form.
-6x + 3y ≥ -45
O
O
O
O
y≤ 2x + 15
y≤ 2x - 15
y≥ 2x - 15
y≥ 2x + 15
Answer:
[tex]y = mx + b[/tex]
[tex]y \geqslant 2x - 15[/tex]
I hope this helps
What is the area of the figure? The figure is not drawn to scale.
05.1 cm²
011.7 cm²
027.72 cm²
O55.44 cm²
Answer:
27.72 cm^2
Step-by-step explanation:
Parallelogram's area = base x height
= 3.3 x 8.4
= 27.72 cm^2
30 In right triangle PRT, m/P = 90°, altitude PQ is drawn to hypotenuse RT. RT = 17, and
PR = 15.
Determine and state, to the nearest tenth, the length of RQ
Using the cosine ratio formula, the length of RQ to the nearest tenth is: 13.2.
What is the Cosine Ratio Formula?The cosine ratio formula is given as, cos ∅ = length of adjacent side / length of hypotenuse.
Find m∠PRT in ΔPRT using the cosine ratio formula:
cos(m∠PRT) = 15/17
m∠PRT = cos^(-1)(15/17)
m∠PRT ≈ 28.07°
Find RQ in ΔPRQ using the cosine ratio formula:
cos(28.07) = RQ/15
RQ = cos(28.07) × 15
RQ ≈ 13.2
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What is the perimeter of triangle ABC? Round answer to the nearest tenth.
A. 12 meters
B. 20.5 meters
C. 22.4 meters
D. 18 meters
Step-by-step explanation:
this is an isoceles, right-angled triangle.
but legs are equally long (6 m), and the baseline is per Pythagoras
baseline² = leg1² + leg2² = 6² + 6² = 36 + 36 = 72
baseline = sqrt(72) = 8.485281374... m
so, the perimeter is
6 + 6 + 8.485281374... = 20.485281374... ≈ 20.5 m
so, B is the right answer.
The Perimeter of Triangle is 6(2 + √2).
what is Trigonometry?A branch of mathematics called trigonometry examines connections between triangles' sides and angles. Due to the fact that every straight-sided form can be decomposed into a group of triangles, trigonometry may be found across all of geometry.
The area of mathematics known as trigonometry examines the link between the ratios of a right-angled triangle's sides to its angles. Trigonometric ratios, such as sine, cosine, tangent, cotangent, secant, and cosecant, are employed to analyse this relationship.
Given:
Perpendicular = 6 m
Using Trigonometry
sin 45 = P/H
1/√2 = 6/ H
H= 6√2
and, tan 45 = P/ B
1= 6/ B
B= 6
So, the perimeter of triangle
= 6 + 6 + 6√2
= 12 +6√2
= 6(2 + √2)
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8. What value of n makes the equation below have
infinitely many solutions?
-2(6x+2)=nx-4
Answer:
[tex]n=-12[/tex]
Step-by-step explanation:
[tex]\text{When}~ n = -12,\\\\~~~~~-2(6x+2) = -12x-4\\\\\implies -12x -4 = -12x -4 \\\\\text{Since both sides are equal for all values of x, there are infinitely many solutions.}[/tex]
Miguel wants to build a container out of sheet metal that has a volume of about 320 cubic inches . He
can choose from the following designs listed below.. Which of the objects described requires the lea
amount of sheet metal? Assume that no sheet metal will be wasted in the construction. Explain why
your answer is correct and why other options are incorrect. (Show the volume of each described objer
in your explanation).
a) A rectangular prism with length 8 in., width 8 in., and height 5 in.
b) A rectangular prism with length 10 in., width 8 in., and height 4 in.
c) A cylinder with radius 5 in., and height 4 in.
d) A square pyramid with base length 10 in., height 10 in., and slant height about 14 in.
Answer:
cylinder, has the least surface area
Step-by-step explanation:
We are to choose the shape that has the least surface area for the approximate volume desired. In general, the least area for the volume will be provided by a sphere, a "square" cylinder with height equal to diameter, and a cube, in order of increasing area.
__
We are asked to find the area and volume of two rectangular prisms, a cylinder, and a square pyramid. Then, we are to identify the shape with the least surface area. Volume and area formulas will be used for the purpose.
Rectangular PrismThe relevant formulas are ...
V = LWH
A = 2(LW +H(L +W))
for length L, width W, and height H.
a) prism 1
The given dimensions are L = W = 8 in, H = 5 in. Then the volume and area are ...
V = (8 in)(8 in)(5 in) = 320 in³
A = 2((8 in)(8 in) +(5 in)(8 in +8 in)) = 2(64 in² +80 in²) = 288 in²
b) prism 2
The given dimensions are L = 10 in, W = 8 in, H = 4 in. Then the volume and area are ...
V = (10 in)(8 in)(4 in) = 320 in³
A = 2((10 in)(8 in) +(4 in)(10 in +8 in)) = 2(80 in² +72 in²) = 304 in²
__
CylinderThe relevant formulas are ...
V = πr²h
A = 2πr(r +h)
for radius r and height h.
c) The given dimensions are r = 5 in, h = 4 in. Then the volume and area are ...
V = π(5 in)²(4 in) = 100π in³ ≈ 314 in³
A = 2π(5 in)(5 in +4 in) = 90π in² ≈ 283 in²
__
Square PyramidThe relevant formulas are ...
V = 1/3s²h
A = s(s +2H)
for base side dimension s, vertical height h, and slant height H.
d) The given dimensions are s = 10 in, h = 10 in, H = 14 in. Then the volume and area are ...
V = 1/3(10 in)²(10 in) = 1000/3 in³ ≈ 333 in³
A = (10 in)(10 in + 2×14 in) = 380 in²
__
SummaryThe proposed figures have volume and area (rounded to the nearest unit) as follows:
[tex]\begin{tabular}{|c|c|c|c|}\cline{1-4}&shape&V (in^3)&A (in^2)\\\cline{1-4}a&rect prism&320&288\\b&rect prism&320&304\\c&cylinder&314&\bf283\\d&pyramid&333&380\\\cline{1-4}\end{tabular}[/tex]
The proposed cylinder requires the least amount of sheet metal for its construction. It has the least surface area of all of the shape choices offered.
_____
Additional comment
For a volume of 320 in³, a cube would have a surface area of 280.7 in². A "square" cylinder would have an area of 260.0 in². A sphere would have an area of 226.2 in². The above areas are somewhat larger because the shapes depart from the ideal aspect ratio.
−−→
A
B
=
(
x
y
)
What values should
x
and
y
take?
−−→
A
B
=
(
x
y
)
What values should
x
and
y
take?
Note: Each horizontal or vertical division represents one unit.
X=
Y=
Answer:
X=1 and Y=4
By counting eacht vetmrtical divided units
What is the measure of the arc from A to B that does not pass through C?
(Fill in the blanks)
Applying the inscribed angle theorem, the measure of the arc from A to B is: 100 degrees.
What is the Inscribed Angle Theorem?The inscribed angle theorem states that an inscribed angle in a circle is half the central angle.
Angle BAC = 40 degrees, so, central angle = 80 degrees. Arc BC would also be 80 degrees.
Measure of arc AC through point B = 180 degrees.
Arc AB = 180 - 80 = 100 degrees.
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Drag each tile to the correct box.
A data set that consists of many values can be summarized using the five-number summary. Arrange these five values in order from least to greatest.
maximum
minimum
Q3
Q1
median
< < <
The five-number summary as displayed in a box plot attached below, from the least to the greatest is: Minimum < Q1 < Median < Q3 < Maximum
What is the Five-number Summary?The five-number summary can be described as a set of data points or values that summarizes the distribution of a data.
The diagram attached below shows the five-number summary as displayed by a box plot.
From the least to the greatest, the five-number summary consist of:
Minimum < Q1 < Median < Q3 < Maximum
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