Answers
So then the limit would be 3/1 = 3.
Alternatively,
[tex]\displaystyle \lim_{x\to\infty}\dfrac{3x^2+6}{x^2-4}=\displaystyle \lim_{x\to\infty}\dfrac{3x^2+6}{x^2-4}\cdot\dfrac{1/x^2}{1/x^2}=\lim_{x\to\infty}\dfrac{3+\frac6{x^2}}{1-\frac4{x^2}} = \dfrac{3+0}{1-0}=\boxed{3}[/tex]
Hope this helps.
Final answer:
The limit of a function as x approaches negative infinity is the value that the function f(x) approaches as x becomes very large in the negative direction. For example, the limit of 1/x is 0 as x approaches negative infinity, while the limit of 1/x² approaches positive infinity. Functions that oscillate, like sin(\u03C0/x), do not have a limit at infinity.
Explanation:
When discussing the limit of a function f(x) as x approaches negative infinity, we are essentially asking what value f(x) gets closer to as x becomes very large and negative. For instance, consider the function 1/x. As x approaches negative infinity, 1/x gets closer to 0, and we say that the limit of 1/x as x approaches negative infinity is 0. Similarly, for a function like 1/x² which "blows up" or increases rapidly as x approaches 0 from either side, we notice that as x approaches negative infinity, the function approaches positive infinity since the squared term always results in a positive number.
However, not all functions have limits at infinity. For functions that oscillate, such as sin(\u03C0/x), as x approaches 0, it oscillates indefinitely between -1 and +1 and does not approach a specific value.
The formal definition of a limit at infinity states: If there is a number L such that f(x) gets arbitrarily close to L when x is sufficiently large (positively or negatively), we write lim f(x) = L as x → -∞.
Related Questions
A leak in a water tank causes the water level to decrease by 3.6×10−2 millimeters each second.
About how many millimeters does the water level in the tank decrease in 5 hours, or 1.8×104 seconds?
Drag and drop the values to the boxes to express the answer in scientific notation.
Answers
Answer:
just to sum up the answer it is 6.5*10^2
Kim's family spends $62.50 on a dinner they leave an 18% tip how much is their total bill after
Answers
1) Find the tips.
2) Add the tips to the bill.
Tips = 18% x $62.50 = 0.18 x 62.5 = $11.25
Total bill = $62.50 + $11.25 = $73.75
Answer: $73.75
total bill = dinner*(1.18)
total bill = $62.50*1.18 = $73.75
The bill with tip is $73.75.
Find the exact value of tan5x/4
Answers
5x/4
=5/4*150
=225
which is in quadrant III.
This implies that the value of tan will be positive, hence:
tan 225=tan (270-225)
tan 225=tan 45
using right angle with length of the legs being unit, then
tan 45=1
hence
tan 5x/4=1
rewrite 5/6 with the denomintaior of 12
Answers
Lot 21 is a trapezoid with the two bases
perpendicular to the road. The scale drawing
below uses the scale 1/2 inch = 40 feet.
Base 1=3.5 inches
Base 2=5 inches
height=4 inches
What is the approximate area of Lot 21?
(1 acre = 43,560 square feet)
A 1/2 acre
B 2 acres
C 2 1/2 acre
D 3 acres
Answers
but the scale is:
1/2in=40 ft
hence
1 in=80 ft
the dimensions of the trapezium is:
Base=80*3.5=280 ft
Base=80*5=400 ft
Height=80*4=320 ft
thus the area is:
A=1/2(280+400)*320
A=108,800
but
1 acre=43560 ft²
Thus:
108800 ft²=108800/435602.4977=~2.5 acres
Answer: C] 2.5 acres
In quadrilateral $ABCD$, we have $AB=3,$ $BC=6,$ $CD=4,$ and $DA=4$.
If the length of diagonal $AC$ is an integer, what are all the possible values for $AC$?
Answers
In order for ACD to be a triangle, the length of AC must lie between CD-DA=0 and CD+DA=8.
In order for ABD to be a triangle, the length of AC must lie between BC-AB=3 and BC+AB=9.
The values common to both these restrictions are numbers between 3 and 8. Assuming we don't want the diagonal to be coincident with any sides, its integer length will be one of ...
{4, 5, 6, 7}
To find the possible integer lengths for diagonal AC in quadrilateral ABCD, the Triangle Inequality Theorem is used. Possible integer values for AC are constrained between the sum and the difference of the lengths of the sides forming triangles ABC and CDA, resulting in potential lengths of 4, 5, 6, and 7.
Explanation:The question pertains to finding all possible integer values for the diagonal AC of a quadrilateral ABCD given the lengths of the sides. To determine the possible lengths of AC, we need to inspect the properties of triangles that could form within the quadrilateral upon drawing this diagonal. The quadrilateral could possibly be a rectangle, a square, or a parallelogram, but without further information, we assume it is an irregular quadrilateral.
By using the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, we can determine possible values for AC. Since ABCD is a quadrilateral with sides AB = 3, BC = 6, CD = 4, and DA = 4, diagonal AC can create two triangles, ABC and CDA. For triangle ABC, the sum of sides AB and BC is 9, so AC must be less than 9. Similarly, for triangle CDA, the sum of sides CD and DA is 8, so AC must be less than 8. Therefore, the maximum value for AC is 7. However, AC must also be greater than the difference of the sides, 3 for triangle ABC and 0 for triangle CDA. This leaves us with possible integer values of 4, 5, 6, and 7 for AC.
hello can you please help me posted picture of question
Answers
Any value outside this range cannot be a value of probability.
Values like -0.5 , 1.25 cannot be the probabilities.
So, the correct options are: B, C and E
Select all that apply. In a linear function: Δy = 0 Δx = 0 Δy = n Δx = n Δy = -n Δx = -n
Answers
Explanation:
1) Δy = 0
Means y is constant, which is also that the slope is zero.
The function is a horizontal line (paralell to the x-axis)
2) Δx = 0
Means x is constant, the slope is not defined (∞).
The function is a vertical line (parallel to the y-axis)
3) Δy = n
Means that the change in y is constant. So, only if the change in x is also constant the slope is constant and the function is linear.
This is because the slope is Δy / Δx.
4) Δx = n
Means the change in x is constant. So, only if Δy is constant it is a linear function, for the same reason explained above
5) Δy = -n and and 6) Δx = -n
Same reasoning of 3 and 4.
Answer:
All options are correct except Δx = 0.
So select: Δy = 0 Δy = n Δx = n Δy = -n Δx = -n
Step-by-step explanation:
Δy can be positive, negative, or zero. The value of Δx can be positive or negative but not zero. From Odyssey ware.
A 9 cm tall cone shaped paper cup can hold up to 58.9 cm3 of water. What is the minimum amount of paper needed to make the paper cup, assuming no overlap in the paper? Use 3.14 for π.
Answers
V=1/3πr²h
thus the radius of the cone will be:
58.9=1/3×3.14×r²×9
r²=6.25265
r~2.5 cm
thus the area of the cone will be:
A=πr(r+√(h²+r²))
A=3.14×2.5(2.5+√(2.5²+9²))
A=92.9500 cm²
Thus the area of material needed to make the cup is 92.95 cm²
Answer:
A minimum of 93 cm squared
Step-by-step explanation:
What is the surface area of the cylinder in terms of Pi? radius is 14in and height is 18 in A. 896 pi in^2 B. 504 pi in^2 C. 392 pi in^2 D. 350 pi in^2
Answers
Answer:
The answer is 896pi in.^2
Step-by-step explanation:
It may seem confusing as you get an answer in the thousands by plugging in the formula, but remember they are asking you to find the answer in "terms of pi". This means you have to divide the answer by 3.14.
2814/3.14 = 896pi in^2
Hope this helped!
A random sample of 31 charge sales showed a sample standard deviation of $50. a 90% confidence interval estimate of the population standard deviation is
Answers
[tex] \sqrt{ \frac{(n-1)s^2}{\chi^2_{1- \frac{\alpha}{2} } }} \leq\sigma\leq\sqrt{ \frac{(n-1)s^2}{\chi^2_{\frac{\alpha}{2} } }}[/tex]
Given a sample size of 31 charge sales, the degree of freedom is 30 and for 90% confidence interval,
[tex]\chi^2_{1- \frac{\alpha}{2} }=43.773 \\ \\ \chi^2_{\frac{\alpha}{2} }=18.493[/tex]
Therefore, the 90% confidence interval for the standard deviation is given by
[tex]\sqrt{ \frac{(31-1)50^2}{43.773 }} \leq\sigma\leq\sqrt{ \frac{(31-1)50^2}{18.493 }} \\ \\ \Rightarrow\sqrt{ \frac{(30)2500}{43.773 }} \leq\sigma\leq\sqrt{ \frac{(30)2500}{18.493 }} \\ \\ \Rightarrow\sqrt{ \frac{75000}{43.773 }} \leq\sigma\leq\sqrt{ \frac{75000}{18.493 }} \\ \\ \Rightarrow \sqrt{1713.38} \leq\sigma\leq \sqrt{4055.59} \\ \\ \Rightarrow41.4\leq\sigma\leq63.7[/tex]
Final answer:
The 90% confidence interval estimate of the population standard deviation is (0.97, 274).
Explanation:
To estimate the population standard deviation with a 90% confidence interval, you can use the formula:
CI = [s * sqrt(n-1) / sqrt(chi-squared lower value), sqrt(chi-squared upper value))]
where s is the sample standard deviation, n is the sample size, and chi-squared lower and upper values are obtained from a chi-squared distribution table. For a 90% confidence interval, the chi-squared lower value is 0.05 and the chi-squared upper value is 0.95 for the given sample size of 31. Plugging in the values:
CI = [50 * sqrt(31-1) / sqrt(0.05), sqrt(0.95))] = [50 * sqrt(30) / sqrt(0.05), sqrt(0.95))] = [50*5.48, 0.97] = [274, 0.97]
Therefore, the 90% confidence interval estimate of the population standard deviation is (0.97, 274).
a triangle has an area of 12 centimeters to the second power and a base of 8 centimeters what is the height of the triangle show you work will mark brainiest
Answers
A cartoon in the shape of a cube measuring 8 inches tall is filled with colored plastic cubes measuring 1 inch across each face. The cubes sell for 25cent each. How much would it cost to buy all of the cubes in the carton? Enter your answer in the box?
Answers
How many points should be plotted when creating a scatterplot from the table of values below? Pages in Book vs. Time Needed to Read Number of pages in book Time needed to read book (hours) 200 18 175 15 275 21 225 18 400 30 350 26
Answers
Answer: 6
Step-by-step explanation:
Given table: Number of pages in book Time needed to read book (hours)
200 18
175 15
275 21
225 18
400 30
350 26
The number of observations in the above table = 6
When we create a scatter-plot from the table of values the number of points should be plotted =6.
Hence, the number of points should be plotted when creating a scatter-plot from the given table of values =6
Ted determined that there are 50000 millimeters in 5 meters. Was he correct? Why or why not?
Answers
hey can you please help me posted picture of question
Answers
C (f) = (5/9) (f -32)
Clearing f we have:
(f-32) = (9/5) c
Rewriting:
f = (9/5) c + 32
f (c) = (9/5) c + 32
Answer:
The inverse function for this case is given by:
f (c) = (9/5) c + 32
option B
4/5 decomposed in 2 different ways
Answers
jenny is diving into a swimming pool from a diving board. The expression below represents Jenny's vertical height, in feet, above the surface of the water after x seconds. -16x^2 +12x+10. Which statement best describes the term 10?
A. Jenny's initial height above the surface of the water
B. The time it takes Jenny to reach the surface of the water
C. The horizontal distance from the diving board Jenny travels
D. the maximum height Jenny reaches.
Answers
Answer:
A. Jenny's initial height above the surface of the water
Step-by-step explanation:
Given : The expression below represents Jenny's vertical height, in feet, above the surface of the water after x seconds. [tex]-16x^2 +12x+10.[/tex]
To Find: Which statement best describes the term 10?
Solution:
[tex]h(x)=-16x^2 +12x+10.[/tex]
Substitute x = 0 i.e.time = 0 seconds
[tex]h(x)=-16x^2 +12x+10.[/tex]
[tex]h(0)=-16(0)^2 +12(0)+10.[/tex]
[tex]h(0)=10[/tex]
so, at time 0 the height was 10
So, 10 is the initial height.
Thus Option A is correct.
A. 10 is Jenny's initial height above the surface of the water.
Q # 7 please solve. the math
Answers
12 in by 22 in by 4 in
the explanation is as shown in the figure
The dimension will be x , 20 - 2x , 30 -2x
the volume= v = x(20-2x)(30-2x) = 4x³ - 100x² + 600x
differentiating with respect to x and equating to zero
dv/dx = 12x² - 200x + 600 = 0
solve for x using calculator
x = 12.7 (unacceptable) or x = 3.92 ≈ 4
∴ The dimension will be 4 , 12 , 22
Solution:The dimension = x , 20 - 2x , 30 -2x
the volume=
v = x(20-2x)(30-2x)
= 4x³ - 100x² + 600x
dv/dx = 12x² - 200x + 600 = 0x = 12.7
x = 3.92
≈ 4
Dimension: 4 , 12 , 22
Is 0.6 and 0.60 equal to each other
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QM Q4.) Find the solution set
Answers
First you find the least common multiplier which is 2x(x + 2)
[tex] \frac{1}{x} * 2x(x + 2) + \frac{1}{x + 2} * 2x(x + 2) = \frac{1}{2} * 2x(x + 2)[/tex]
Simplify
2(x + 2) + 2x = x(x + 2)
Now you solve it algebraically
Distribute the 2
2x + 4 + 2x = x(x + 2)
Distribute the x
[tex]2x + 4 + 2x = x^{2} +2x[/tex]
Combine like terms
[tex]4x + 4 = x^{2} +2x[/tex]
Subtract 4 from both sides
[tex] x^{2} + 2x - 4 = 4x[/tex]
Subtract 4x from both sides
[tex] x^{2} - 2x - 4 = 0[/tex]
Now you put this into the quadratic formula
[tex]x = \frac{-(-2) + and - \sqrt{(-2)^{2}- 4 * 1 * (-4) } }{2 * 1} [/tex]
Simplify
[tex]x = \frac{2 + and - \sqrt{20} }{2} [/tex]
Factor the sqrt of 20
[tex]x = \frac{2 + and -2 \sqrt{5} }{2} [/tex]
Factor 2 + and - the 2 * sqrt of 5
[tex] \frac{2(1 + and - \sqrt{5}) }{2} [/tex]
The 2's cancel each other other
[tex]x = 1 + and - \sqrt{5} [/tex]
The answers are [tex]x = 1 + \sqrt{5} and x = 1- \sqrt{5} [/tex]
Hope this helps!
The square root of a negative number is imaginary, there are no real solutions to the equation x² - x = 2.
The equation using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
Where:
a is the coefficient of the x² term
b is the coefficient of the x term
c is the constant term
In the equation x² - x = 2, we have:
a = 1
b = -1
c = 2
Plugging these values into the quadratic formula, we get:
x = (1 ± √((-1)² - 4(1)(2))) / 2(1)
Simplifying the expression, we get:
x = (1 ± √(1 - 8)) / 2
Evaluating the square root, we get:
x = (1 ± √(-7)) / 2
Since the square root of a negative number is imaginary, there are no real solutions to the equation x² - x = 2.
For similar question on quadratic formula.
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A tank with a capacity of 100 gallons initially contains 50 gallons of water with 10 pounds of salt in solution. fresh water enters at a rate of 2 gallons per minute and a well-stirred mixture is pumped out at the rate of 1 gallon per minute. compute the amount of salt (in pounds) in the tank at the first moment when the tank is filled.
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The rate at which the amount of salt in the tank changes is given by the ODE
[tex]A'(t)=\dfrac{2\text{ gal}}{1\text{ min}}\cdot\dfrac{0\text{ lb}}{1\text{ gal}}-\dfrac{1\text{ gal}}{1\text{ min}}\cdot\dfrac{A(t)\text{ lb}}{50+(2-1)t\text{ gal}}[/tex]
[tex]A'(t)+\dfrac{A(t)}{50+t}=0[/tex]
[tex](50+t)A'(t)+A(t)=0[/tex]
[tex]\bigg((50+t)A(t)\bigg)'=0[/tex]
[tex](50+t)A(t)=C[/tex]
[tex]A(t)=\dfrac C{50+t}[/tex]
Given that [tex]A(0)=10[/tex], we find that
[tex]10=\dfrac C{50+0}\implies C=500[/tex]
so that the amount of salt in the tank is described by
[tex]A(t)=\dfrac{500}{50+t}[/tex]
The tank will be filled when [tex]50+t=100[/tex], or after [tex]t=50[/tex] minutes. At this time, the amount of salt in the tank is
[tex]A(50)=\dfrac{500}{50+50}=5\text{ lb}[/tex]
Final answer:
The amount of salt in the tank, described by the differential equation, reaches 5 pounds after 50 minutes with an initial amount of 10 pounds and a rate of change defined by the given equation.
Explanation:
Let's start with the given differential equation: A'(t) = (2 gal/1 min) * (0 lb/1 gal) - (1 gal/1 min) * A(t) / (50 + (2 - 1)t gal).
By simplifying the equation, we get A'(t) + A(t) / (50 + t) = 0. Multiplying through by (50 + t) gives (50 + t)A'(t) + A(t) = 0. Recognizing that ((50 + t)A(t))' equals zero, we integrate to find (50 + t)A(t) = C, where C is a constant.
With the initial condition A(0) = 10, we find 10 = C / (50 + 0), which simplifies to C = 500. So, the equation describing the amount of salt in the tank is A(t) = 500 / (50 + t).
To determine when the tank will be filled, we solve 50 + t = 100, which gives t = 50 minutes. Plugging this into A(t) yields A(50) = 500 / (50 + 50) = 5 lb.
Hi please help :)
What is the value of b in the given quadratic regression equation?
Y= -0.139x^2 + 1.667x
A. 1
B. 1.667
C. 0
D. -0.139
Answers
Answer:
The answer on edge 2021 is 1.667
Step-by-step explanation:
I got a 50% and it showed the answer
The value of b in the quadratic regression equation is 1.667.
The value of b in the given quadratic regression equation is 1.667.
To find the value of b, you can look at the coefficient of the linear term in the quadratic equation ,, In this case, the linear term is 1.667x, so the value of b is 1.667.
21$is 75% of what amount?
Answers
divide both sides by 3
7cents= 25%
multiply each side by 4
28=100%
Answer=28
System.out.print((k%3) + " "); if ((k % 3) == 0) k = k + 2; else k++; } what is printed as a result of executing the code segment? question 21 options:
a. 0 2 1 0 2
b. 0 2 0 2 0 2
c. 0 1 2 1 2 1 2
d. 0 2 0 2 0 2 0
e. 0 2 1 0 2 1 0
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What is the measure of < L ? Need help
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Looking at the image above, we can see that the two “legs” of the triangle both have a length of 7 units. Consequently, this triangle can be classified as an isosceles triangle. An isosceles triangle has two sides of equal length (in this case, KJ and KL) and two corresponding angles of equal measure (in this case, ∠J and ∠L).
∠J has a measure of 25 degrees. Consequently, with our knowledge of isosceles triangles, we can conclude that ∠L has a measure of 25 degrees as well.
I hope this helps!
Length contraction is the shortening of an object's measured length when it is moving relative to the observer's frame. The formula for length contraction is L = L0√(1 - (v^2/c^2)).
Explanation:Length contraction (L) is the shortening of the measured length of an object moving relative to the observer's frame. It occurs when an object is moving at a significant fraction of the speed of light. The formula for length contraction is L = L0√(1 - (v2/c2)), where L0 is the rest length of the object, v is its velocity, and c is the speed of light.
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Law of cosines: a2 = b2 + c2 – 2bccos(A). What is the measure of S to the nearest whole degree?
Answers
Answer:
I think the answer is 77.
Step-by-step explanation:
hello can you please help me posted picture of question
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Number of medals to be awarded = 6
We have to distribute (arrange) the 6 medals among 28 students, so this is a problem of permutations. This means we have to find the permutations of 28 objects taken 6 at a time. This can be expressed as 28P6
[tex]28P6= \frac{28!}{22!} \\ \\ =271252800 [/tex]
This means, there are 271252800 ways to award the medals.
So, the correct option is C
Let f = ay i + bz j + cx k where a, b, and c are positive constants. let c be the triangle obtained by tracing out the path from (7, 0, 0) to (7, 0, 2) to (7, 6, 2) to (7, 0, 0). find f · dr
c.
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The curl of the given vector field is
[tex]\nabla\times\mathbf f(x,y,z)=-b\,\mathbf i-c\,\mathbf j-a\,\mathbf k[/tex]
Parameterize the triangular surface bounded by [tex]\mathcal C[/tex] - I'll call it [tex]\mathcal S[/tex] - by
[tex]\mathbf s(u,v)=7\,\mathbf i+6v\,\mathbf j+2(u+v-uv)\,\mathbf k[/tex]
with [tex]0\le u\le1[/tex] and [tex]0\le v\le1[/tex]. By Stokes' theorem, we have
[tex]\displaystyle\int_{\mathcal C}\mathbf f(x,y,z)\cdot\mathrm d\mathbf r=\iint_{\mathcal S}\nabla\times\mathbf f(x,y,z)\cdot\mathrm d\mathbf S[/tex]
where [tex]\mathcal S[/tex] is positively oriented; that is, every vector normal to [tex]\mathcal S[/tex] is pointed in the positive [tex]x[/tex] direction. The surface element is given by
[tex]\mathrm d\mathbf S=\mathbf s_u\times\mathbf s_v\,\mathrm du\,\mathrm dv[/tex]
So our integral is
[tex]\displaystyle\int_{v=0}^{v=1}\int_{u=0}^{u=1}(-b\,\mathbf i-c\,\mathbf j-a\,\mathbf k)\cdot((12v-12)\,\mathbf i)\,\mathrm du\,\mathrm dv[/tex]
[tex]\displaystyle=12b\int_{v=0}^{v=1}(1-v)\,\mathrm dv=6b[/tex]
The task involves evaluating the line integral of a vector field along a path to determine the work done by the field. Since the path does not traverse in the x-direction, only the y and z components of the vector field contribute to the integral. The calculation involves parameterizing each segment and summing up the individual integrals.
Explanation:The student's question involves finding f · dr along a path c in a vector field. The vector field is given as f = ay i + bz j + cx k, and the path c is a triangle with vertices at (7, 0, 0), (7, 0, 2), and (7, 6, 2). The dot product of a vector field with a differential displacement vector (dr) represents the work done by the field along that path.
To find the integral of f · dr along the path c, we would parameterize each segment of the path and evaluate the line integral. However, since the vector field has constants multiplied by either i, j, or k, and the path only moves parallel to the y and z axes, the components involving x do not contribute to the integral. Therefore, for each segment of the path, we will only consider the y and z components of the vector field. The line integral along the path is then the sum of the integrals over each segment of the triangle.
In this example, since the x-component of the field does not change and the path does not move in the x direction, the integral over the x components will be zero.
Calculation Steps:
Parameterize each segment of the path.Evaluate the integral of f · dr over each segment.Add the integrals from each segment to get the total work done by the field along path c.
In a large population, very close to 25% of the observations will fall below the 25th percentile (Q1), and close to 75% fall below the 75th percentile (Q3). The Web site of the Educational Testing Service reports that on the SAT Verbal test, with a possible perfect score of 800, the 89th percentile of 1,475,623 scores nationwide is a score of 670. What is the best estimate of exactly how many scores were below 670?
Answers
.89 * 1,475,623 = 1,313,304.47
So, the answer would be:
approximately equal to 1,313,305 number of scores were below 670
Answer:
1,313,000
Step-by-step explanation: