Find the limit, if it exists, or type dne if it does not exist.
a. \displaystyle\lim_{(x, y) \rightarrow (0, 0)} \frac{(x + 23y)^2}{x^2 + 529y^2} =

Answers

Answer 1

[tex]\displaystyle\lim_{(x,y)\to(0,0)}\frac{\left(x+23y)^2}{x^2+529y^2}[/tex]

Suppose we choose a path along the [tex]x[/tex]-axis, so that [tex]y=0[/tex]:

[tex]\displaystyle\lim_{x\to0}\frac{x^2}{x^2}=\lim_{x\to0}1=1[/tex]

On the other hand, let's consider an arbitrary line through the origin, [tex]y=kx[/tex]:

[tex]\displaystyle\lim_{x\to0}\frac{(x+23kx)^2}{x^2+529(kx)^2}=\lim_{x\to0}\frac{(23k+1)^2x^2}{(529k^2+1)x^2}=\lim_{x\to0}\frac{(23k+1)^2}{529k^2+1}=\dfrac{(23k+1)^2}{529k^2+1}[/tex]

The value of the limit then depends on [tex]k[/tex], which means the limit is not the same across all possible paths toward the origin, and so the limit does not exist.

Related Questions

In a recent year 33.2% of all registered doctors are female. If there were 56,400 female register doctors that year, what was the total number of registered doctors?

Answers

56400 ÷ 0.332
169879 total people

Hope this helps!

An object is traveling at a steady speed of 8 2/3 miles per hour. How long will it take the object to travel to 5 1/5 miles

Answers

Answer:

The answer is 36 minutes

Step-by-step explanation:

Distance is speed multiplied by time. ( when we have steady speed )

Distance=speed* time

We are looking for time.

Time=Distance /speed

Distance= 5 1/5 miles=5,20

Speed=8 2/3 miles=8,66

T=5.20/8.66666=0,60

1 hour is 60 minutes

T=0,60/60 minutes=36 minutes

The time that it'll take the object to travel in 5 1/5 miles is 36 minutes

Note that 1 hour = 60 minutes Since the object is traveling at a steady speed of 8 2/3 miles.

Let the time taken for the object be represented by x. The equation to solve the question will be:

5 1/5 / 8 2/3 = x / 60

Cross multiply

(8 2/3 × x) = (5 1/5 × 60)

8 2/3x = 312

x = 312/ 8.67

x = 36

Therefore, the time that it'll take the object to travel in 5 1/5 miles is 36 minutes.

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If it is known that a+b/a-b=c, find the following: 2a-2b/5a+5b

Answers

Final answer:

The value of (2a - 2b)/(5a + 5b) can be simplified to c.

Explanation:

To find the value of (2a - 2b)/(5a + 5b) when the equation (a + b)/(a - b) = c is given, we can substitute the value of (a + b)/(a - b) with c. Rearranging the equation, we get:

(2a - 2b)/(5a + 5b) = c

Simplifying the expression, we have:

(2(a - b))/(5(a + b)) = c

So, the value of (2a - 2b)/(5a + 5b) is c.

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Carrie buys 4.16 pounds of apples for 5.20 how much does 1 pound cost

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4.16 / 5.20 = 1 / x.....4.16 lbs to $ 5.20 = 1 lb to $x
cross multiply because this is a proportion
(4.16)(x) = (5.20)(1)
4.16x = 5.20
x = 5.20 / 4.16
x = 1.25 per lb <==

number that can be divided evenly by only itself and by the number 1 is called which of the following? Prime Variable Prime Term Prime Multiple Prime Factor

Answers

The answer is Prime Factor.

What is M-1/6-4m+5/6 simplified

Answers

-2 • (9m - 2)/6 is the final answer.

The simplified expression is -3M + 1

How did we get the value?

To simplify the expression M - (1/6) - 4M + (5/6), we can combine the like terms.

First, let's combine the terms with M:

M - 4M = -3M

Now, let's combine the constant terms:

(1/6) + (5/6) = (1 + 5)/6 = 6/6 = 1

Putting it all together, the simplified expression is:

-3M + 1

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There are 44 colas and 22 lemon lime soda is in the cooler. Whatis the ratio of colas to lemon lime sodas?

Answers

The ratio would be 44 / 22 = 2 / 1 or we could say 2:1

1 point) use the inner product ⟨f,g⟩=∫10f(x)g(x)dx ⟨f,g⟩=∫01f(x)g(x)dx in the vector space c0[0,1]c0[0,1] of continuous functions on the domain [0,1][0,1] to find ⟨f,g⟩⟨f,g⟩, ‖f‖‖f‖, ‖g‖‖g‖, and the angle αf,gαf,g between f(x)f(x) and g(x)g(x) for f(x)=10x2−3 and g(x)=6x−9.

Answers

[tex]f(x)=10x^2-3[/tex]
[tex]g(x)=6x-9[/tex]

[tex]\langle f,g\rangle=\displaystyle\int_0^1(10x^2-3)(6x-9)\,\mathrm dx=3[/tex]

[tex]\|f\|=\sqrt{\langle f,f\rangle}=\sqrt9=3[/tex]

[tex]\|g\|=\sqrt{\langle g,g\rangle}=\sqrt{39}[/tex]

[tex]\cos\alpha=\dfrac{\langle f,g\rangle}{\|f\|\|g\|}=\dfrac3{9\sqrt39}=\dfrac1{3\sqrt{39}}\implies \alpha=\cos^{-1}\dfrac1{3\sqrt{39}}[/tex]

Final answer:

The norms and the inner product of f and g can be calculated using the given inner product definition and the knowledge that the norm of a vector (here, function) is the square root of its inner product with itself. Then, the cosine of the angle between f and g can be found by dividing their inner product by the product of their norms.

Explanation:

The problem is asking us to compute certain components in the context of a vector space of continuous functions, namely inner product ⟨f,g⟩, norms ‖f‖, ‖g‖, and angle between them for f(x) and g(x). Since the functions are given as f(x)=10x^2-3 and g(x)=6x-9, these can be used in the provided inner product definition ⟨f,g⟩=∫from 0 to 1f(x)g(x)dx.

The norm of a vector, in this case, the function f or g, is the square root of the inner product of the function with itself. The cosine of the angle α between the functions f and g is given by the ratio of the inner product of f and g to the product of their norms.

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If the heights of 300 students are normally distributed with mean 68.0 inches and standard deviation 3.0 inches, how many students have heights (a) greater than 72 inches, (b) less than or equal to 64 inches, (c) between 65 and 71 inches inclusive, (d) equal to 68 inches? assume the measurements to be recorded to the nearest inch.

Answers

Given:
μ = 68 in, population mean
σ = 3 in, population standard deviation

Calculate z-scores for the following random variable and determine their probabilities from standard tables.

x = 72 in:
z = (x-μ)/σ = (72-68)/3 = 1.333
P(x) = 0.9088

x = 64 in:
z = (64 -38)/3 = -1.333
P(x) = 0.0912

x = 65 in
z = (65 - 68)/3 = -1
P(x) = 0.1587

x = 71:
z = (71-68)/3 = 1
P(x) = 0.8413

Part (a)
For x > 72 in, obtain
300 - 300*0.9088 = 27.36

Answer: 27

Part (b)
For x ≤ 64 in, obtain
300*0.0912 = 27.36

Answer: 27

Part (c)
For 65 ≤ x ≤ 71, obtain
300*(0.8413 - 0.1587) = 204.78

Answer: 204

Part (d)
For x = 68 in, obtain
z = 0
P(x) = 0.5
The number of students is
300*0.5 = 150

Answer: 150

Final answer:

The student can use the normal distribution and z-scores to estimate the number of students in different height ranges. The heights were estimated to be: about 28 students over 72 inches, 28 students less or equal to 64 inches, roughly 205 students between 65 and 71 inches, and it is statistically impossible to determine exactly 68 inches from the data given.

Explanation:

This question is dealing with a concept in statistics known as the normal distribution. In this context, we are asked to find the proportion of students whose heights fall into various ranges, based on a known mean and standard deviation. With a mean of 68 inches and a standard deviation of 3 inches, we can calculate the z-score for each scenario:

Greater than 72 inches: Z = (72-68)/3 = 1.33. Looking at the z-table, the proportion associated with 1.33 is 0.9082, but we want greater than, so we subtract from 1, giving approximately 0.0918, or 9.18%. Multiply this percentage by the total number of students (300) to estimate the number of students taller than 72 inches. This yields an approximate total of 27.54, but since we cannot have fractional students, we would say approximately 28 students.Less than or equal to 64 inches: Z = (64-68)/3 = -1.33. The proportion for -1.33 on the z-table is 0.0918, which we interpret as 9.18%. This would amount to approximately 27 or 28 students.Between 65 and 71 inches: Calculate two z-scores: Z1 = (65-68)/3 = -1.00 and Z2 = (71-68)/3 = 1.00. Using the z-table, we find that the proportions for z-scores of -1.00 and 1.00 are approximately 0.1587 and 0.8413. So, the proportion between these two z-scores is 0.8413 - 0.1587 = 0.6826, or 68.26%. This correlates to roughly 205 students.Equal to 68 inches: It's impossible to exactly determine the number of students who are exactly 68 inches tall from the data given. The normal distribution is a continuous distribution, and the probability of any single, specific value (like exactly 68 inches) is technically zero. However, you can determine the number of students likely to be in a small range around 68 inches.

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Which of the following numbers is a factor of 49 ?

Answers

Seven 77777777777777

30 POINTS: Dalton's Diner offers its clients a choice of regular and diet soda. Last night, the diner served 200 sodas in all, 20% of which were regular. How many regular sodas did the diner serve?

Answers

200/100=2
1%=2
20%=40
Dalton's Diner served 40 regular sodas.

Hope this helps! :)

You anticipate that a $2000 investment in a local business will pay an average of 4% interest in each of the next 5 years. Determine to the nearest dollar the amount of the investment at the end of 5 years.

Answers

Since this is a problem in exponential growth/decay, y = ab^x is the formula that will be used to solve this problem.

The initial value, "a", is the value you start out with and in this case, it is $2000.

The growth/decay factor is what "b" represents, and it is 4%. We need to change the percentage into a decimal, so we will take the percent symbol, change it into a decimal, and move it two places to the left. This is make it 0.04. The problem also mentions interest, implying an exponential growth. Therefore, you will add 0.04 by 1: 1+0.04 = 1.04.

The "x" represents an amount of time. It is 5 years. The equation should be written like this:

y = 2000(1.04)^5
y = 2433.30. When rounded to the nearest dollar, it is $2433.

How can you decompose the composite figure to determine its area?

Answers

answer is the last one (D)
semicircle, trapezoid, and 2 rectangles.

Answer:

D. As a semicircle, a trapezoid and two rectangles.

Step-by-step explanation:

Please find the attachment.

We have been given a composite figure. We are asked to decompose our given figure to determine its area.

Upon looking at attachment for our given composite figure, we can see that it consists one semicircle on top, one trapezoid in middle and two rectangles on bottom. So we can decompose our composite figure as a semicircle, a trapezoid and two rectangles.

Therefore, option D is the correct choice.

help me out some one

Answers

y = mx + b is the slope-intercept form of the equation of a line,
where m = slope, and b = y-intercept.

In problems 1 and 3, your equations are written in the y= mx + b form, so you can read the slope and y-intercept directly.

1.
m = -5/2
b = -5

3.
m = -1
b = 3

5.
For problem 5, you need to solve for y to put the equation
in y = mx + b form. Then you can read m and b just like we did
for problems 1 and 3.

4x + 16y = 8

16y = -4x + 8

y = -4/16 x - 8/16

y = -1/4 x - 1/2

m = -1/4

b = -1/2

Can anyone figure this out for me please? It would be greatly appreciated.

Answers

check the picture below.

now, to get how much is the area of the tiled section, we simply get the area of the whole pool, 53x26, which includes the tiles, and then subtract the area without the tile, the rectangle in the middle, and what's leftover, is the area of the tiled area.

[tex]\bf 53-4\frac{1}{2}-4\frac{1}{2}\implies 53-9\implies \boxed{42} \\\\\\ 26-4\frac{1}{2}-4\frac{1}{2}\implies 26-9\implies \boxed{17} \\\\\\ \textit{so the area of the rectangle in the middle is}\implies 42\cdot 17\implies 714 \\\\\\ \textit{and the area of the whole pool is}\implies 53\cdot 26\implies 1378[/tex]

[tex]\bf \stackrel{\textit{area of the whole pool}}{1378}~~-~~\stackrel{\textit{area of the middle rectangle}}{714}\implies \stackrel{\textit{area of the tiles}}{664}\\\\ -------------------------------\\\\ \textit{we know that is }\$5\frac{1}{2}\textit{ for a foot of tile, then}\stackrel{\textit{price of the tiles}}{664\cdot 5\frac{1}{2}}\implies 3652[/tex]

Which of the following expression has a value less than 0.7? A) 0.7×4/3. B) 0.7×3/3 C) 0.7×1/3

Answers

C: is your Answer 0.7×1/3 = 02333333333..........................

C) 0.7 x 1/3

is your answer

0.7 x 1/3 =
0.7 x 0.33 = 0.231

0.231 < 0.7

hope this helps

A car rental agency currently has 44 cars available, 28 of which have a gps navigation system. one of the 44 cars is selected randomly. find the probability that this car

Answers

propability of pick car randomly is 1/44

Hannah wishes to find the vertex of the function x2 + 3x - 28 = 0 by completing the square. Which of the following equations may be used to identify the coordinates of the vertex?

A. (x + 1.2)2 = 30.25
B. (x + 2.25)2 = 30.5
C. (x + 2.5)2 = 30.75
D. (x + 2.75)2 = 32.5

Answers

x²+3x-28=0

(x+1.5)² - 1.5² - 28 = 0
(x+1.5)² - 25.75 = 0
(x+1.5)² = 25.75

Note: The answer is not listed on the option given. Maybe worth checking the if the original equation has been copied correctly.

Sonny substituted 5 for x in the proportion 16/x=48/15 and cross multiplied to get 240=240. Why is this?

A.because the cross sums of the proportion are equal

B.because the cross differences of the proportion are equal

C.because the cross products of the proportion are equal

D.because the cross quotients of the proportion are equal

Answers

the answer is c i just took the test

Answer:

i agree c

Step-by-step explanation:

because 16 times 15 = 240

and 48 times 5 =240

If I Row my canoe at 5 mph and I travel upstream at 3 mph, how fast will I be traveling downstream if I am rowing at the same rate ?

Answers

is the same as the one you just did.

keep in mind that, going against the current, the current's speed erodes speed from your regular speed, whilst if you're going with the current, the current's speed adds to it.

now, in this case, you row 5mph, going upstream you're only doing 3mph, whatever happened to the other 2mph? well, the current speed eroded them, meaning the speed of the river is 2mph.

now, going downstream with the current, your regular speed is 5mph, and the current is 2mph, since the current adds to yours, then you're going 5 + 2, mph.

Find the z-score such that: (a) the area under the standard normal curve to its left is 0.5

Answers

This question out to be one that we could all answer almost instantly. If the area under the std. norm. curve to the left of z is 0.5 (exactly half of that area), the z value is zero (0).

Only the Fahrenheit one plz

Answers

The formula given is:
F = 1.8C + 32
The temperature C is given as -20
So, all you have to do is plug the given C temperature in the formula to get the corresponding F temperature as follows:
F = 1.8(-20) + 32 = -36 + 32 = -4 degrees Fahrenheit

What is the value of mc011-1.jpg?
–4
–2
2
4

the pic is the .jpg

Answers

Final answer:

The question is unclear as it references links rather than providing a specific mathematical problem to solve. A correct answer cannot be given.

Explanation:

It appears there has been a misunderstanding. The actual mathematical question has not been provided in the text. Instead, there are references to image sources, licenses, and websites that do not contain a clear mathematical question to answer. Therefore, I'm unable to provide a value or solve the equation.

Final answer:

The value of the expression -2(7-15)/4 simplifies to 4 after following the order of operations: first subtracting inside the brackets, then multiplying by -2, and finally dividing by 4.

Explanation:

The value of the given expression -2(7-15)/4 when simplified is computed in the following steps:

Calculate the value inside the brackets: 7 - 15 = -8.Multiply this result by -2: -2 * (-8) = 16.Divide the product by 4: 16 / 4 = 4.

Therefore, the value of the entire expression is 4, which corresponds to answer option d)4.

an electrician cuts a 136-ft piece of cable. one piece is 16 feet less than 3 times the length of the other piece. Find the length of each piece.

Answers

1st piece = x

2nd piece = 3x-16

x +3x-16 = 136

4x-16 = 136

4x = 152

x = 152/4 = 38

1st piece = 38 feet

2nd piece = 136 -38 = 98 feet

A cube has a volume of 125 cubic inches. What is the length of each edge? Enter your answer in the box.

Answers

Answer: 5 cm

Step-by-step explanation:

Given : The volume of a cube = 125 cubic inches.

The formula for the volume of a cube is :

[tex]V=s^3[/tex], where s is the side-length .

Substitute V= 125 in the above formula ,

[tex]125=s^3[/tex]

Taking cube root on both the sides , we get

[tex]\sqrt[3]{125}=s\\\\\Rightarrow\ s= \sqrt[3]{5^3}=5[/tex]

Hence, the side length of cube= [tex]5\ cm[/tex]

Each edge will be 5 inches.

Volume of the cube = 125 cubic inches

It should be noted that a cube's volume is gotten by multiplying the side thrice. In this case, let's say the value of each side is a. Therefore, based on the information given above:

a × a × a = 125

a³ = 125

a = 3✓125

a = 5

Therefore each edge is 5 inches.

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The quotient of a number and ten increased by eleven

Answers

Final answer:

The expression 'The quotient of a number and ten increased by eleven' is written as (x/10) + 11 in mathematical terms. Understanding the role of exponents, such as in the expression 10² equals 100, helps in grasping concepts like scientific notation, where large or small numbers are expressed as the product of a number and a power of ten, such as 1.372568 × 10⁶.

Explanation:

The question 'The quotient of a number and ten increased by eleven' translates to a mathematical expression. This expression can be represented as (x/10) + 11, where 'x' is the number in question. It's a simple algebraic expression where you first divide the number by ten and then add eleven to the result.

When discussing multiplication and division by powers of 10, it's important to understand the concept of an exponent. The exponent is a raised number to the right of the 10, indicating the number of factors of 10 in the original number. For example, in the expression 10², the exponent 2 indicates that ten is multiplied by itself once, resulting in 100. This is consistent with the way our numbering system works, with each place value being ten times greater than the one to its right.

The utility of using exponents is highlighted in scientific notation, which simplifies large or small numbers by representing them as a product of a number and a power of ten. This is particularly useful in fields like science and engineering, where very large or very small numbers are common. For example, the number 1,372,568 can be written in scientific notation as 1.372568 × 10⁶, representing the number as a manageable base multiplied by ten raised to the sixth power.

Joe and Ella combine their photos. Then they put an equal number on each page of an 8-page photo album. How many photos are on each page?

Answers

2 pictures I’m pretty sure

2 pictures are on each page.

The sum of the reciprocals of two consecutive integers is -9/20. Find the two integers

Answers

suppose the first integer is x, the second one is then x+1
reciprocals are 1/x and 1/(x+1)
1/x +1/(x+1)=-9/20
make the denominators the same:
1(x+1)/x(x+1) + 1x/x(x+1)=-9/20
simplify the demonstrator and add up the numerators: (2x+1)/(x^2+x)=-9/20
20(2x+1)=-9(x^2+x)
40x+20=-9x^2-9x
9x^2 +49x+20=0
factor: (1+5)(9x+4)=0
x=-5 or x=-4/9 (this one doesn't work because it is not an integer)
so the first integer is -5, the second integer is -4

solve the system of linear equations. separate the x- and y- values with a coma.
14x-4y=74
7x-7y=7

Answers

The Answer is x=7, y=6

Solve the following system:
{14 x - 4 y = 74 | (equation 1)
{7 x - 7 y = 7 | (equation 2)
Subtract 1/2 × (equation 1) from equation 2:
{14 x - 4 y = 74 | (equation 1)
{0 x - 5 y = -30 | (equation 2)
Divide equation 1 by 2:
{7 x - 2 y = 37 | (equation 1)
{0 x - 5 y = -30 | (equation 2)
Divide equation 2 by -5:
{7 x - 2 y = 37 | (equation 1)
{0 x+y = 6 | (equation 2)
Add 2 × (equation 2) to equation 1:
{7 x+0 y = 49 | (equation 1)
{0 x+y = 6 | (equation 2)
Divide equation 1 by 7:
{x+0 y = 7 | (equation 1)
{0 x+y = 6 | (equation 2)
Collect results:
Answer: {x = 7
{y = 6

P{lease note the brackets are supposed to go over both equations but I haven'y been able to find a way to make it work, see attachment.

Peter is a painter, and he wonders if he would have time to catch a paint bucket dropped from his ladder before it hits the ground. He drops a bucket from the top of his 9-foot ladder. The height, h, of the bucket can be represented by the equation, h= -16t^2 + 9, where the height is measured in feet from the ground, and the time since the bucket was dropped, t, is measured in seconds. After how many seconds does the bucket hit the ground? Do you think he could catch the bucket before it hits the ground.

Answers

Final answer:

The paint bucket dropped from the 9-foot ladder would hit the ground in approximately 0.75 seconds, according to the equation given for free fall. Given this quick time frame, it might be difficult for Peter to catch the bucket before it hits the ground.

Explanation:

The situation described involves a physical phenomenon known as free fall, under the influence of gravity. In the case of the paint bucket, when it is dropped from the top of the ladder, the height h of the bucket from the ground at any time t is given by the equation h = -16t^2 + 9. The bucket hits the ground when h = 0.

To find when the bucket hits the ground, we solve the equation -16t^2 + 9 = 0 for t. Using the quadratic formula, we find the roots to be t = -0.75s and t = 0.75s. Since time cannot be negative in this situation, we discard the negative root. Thus, the bucket hits the ground after 0.75 seconds.

As to whether Peter could catch the bucket before it hits the ground, it does depend on his reflexes and agility, but generally it may be difficult to react and move quickly enough within such a brief time frame.

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Other Questions

Find the limit, if it exists, or type dne if it does not exist. a. \displaystyle\lim_{(x, y) \rightarrow (0, 0)} \frac{(x + 23y)^2}{x^2 + 529y^2} =

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Find the limit, if it exists, or type dne if it does not exist.
a. \displaystyle\lim_{(x, y) \rightarrow (0, 0)} \frac{(x + 23y)^2}{x^2 + 529y^2} =