Using Squeeze theorem, the limit of the function is 0
What is the LimitThe Squeeze Theorem states that if f(x,y) <= g(x,y) <= h(x,y) for all x,y in a region around (x0,y0) and lim (x,y)->(x0,y0) g(x,y) = L, then lim (x,y)->(x0,y0) f(x,y) = lim (x,y)->(x0,y0) h(x,y) = L.
We can use the Squeeze Theorem to find the limit of the given function by finding two other functions that bound it and have known limits as (x,y) approaches (0,0).
We can see that
(x^2+y^2)/(x^2+y^2) <= 3x^2y/(x^2+y^2) <= (3xy)/(x^2+y^2)
As x,y approaches 0, the first inequality approaches 1 and the second one approaches 0, so the limit of the given function is also 0.
Therefore, lim [(x,y) -> (0,0)] (3 . x^2 . y / (x^2 + y^2)) = 0.
Learn more on limit of a function here;
https://brainly.com/question/24133116
#SPJ1
Expand and simplify
a) x(x + 2)(x + 3)
The required expression is x³ + 5x² + 6x as an expanded form.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
The expression is given in the question, as follows:
x(x + 2)(x + 3)
We have to expand and simplify the given factors.
As per the question, we have
⇒ x(x + 2)(x + 3)
Open the first parentheses, and distributes
⇒ (x² + 2x)(x + 3)
⇒ x²(x + 3) + + 2x(x + 3)
Combine the likewise terms in the above expression,
⇒ x³ + 3x² +2x² + 6x
⇒ x³ + 5x² + 6x
Thus, the required expression is x³ + 5x² + 6x.
Learn more about the algebraic expression here :
brainly.com/question/21751419
#SPJ1
What’s the diameter of O
The diameter of the circle is 16.66 units.
What is a circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the center.
Given a circle,
and two segments intersect at a point and form a right angle,
the length of the segment to the point of intersection is 6 units and 8 units as given in the figure,
and a segment pass from the center of the circle,
let the distance from point of intersection to center be x
so radius of circle be 6 + x from figure,
it forms a right triangle as shown in the figure, with hypotenuse 6 + x, base x, and perpendicular 8 units,
using Pythagoras theorem
h² = b² + p²
(6 + x)² = x² + 8²
36 + x² + 12x = x² + 64
12x = 64 - 36
12x = 28
x = 28/12
x = 2.333
radius of circle = 6 + x = 6 + 2.33 = 8.33
diameter of circle = 2r = 2 x 8.33 = 16.66 units
Hence the diameter is 16.66 units.
Learn more about circles;
https://brainly.com/question/29142813
#SPJ1
An Egg Farm
Rob lives on an egg farm with 5,287 chicken hens. Rob collects the chicken eggs every
day. One day Rob collects 4,056 eggs. The eggs are placed in egg cartons of twelve eggs
per carton and are shipped to stores. The egg cartons must be carefully placed in
shipping boxes. Each shipping box holds twenty-four egg cartons. The shipper can
deliver no more than fifteen shipping boxes of eggs at a time. Can Rob ship all 4,056
eggs in the same shipment? Show all of your mathematical thinking.
Yes, Rob can ship all 4,056 eggs in the same shipment.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, Rob lives on an egg farm with 5,287 chicken hens. Rob collects the chicken eggs every day. One day Rob collects 4,056 eggs.
The eggs are placed in egg cartons of twelve eggs per carton and are shipped to stores.
Here, number of cartons required =4,056/12
= 338 cartons
The egg cartons must be carefully placed in shipping boxes. Each shipping box holds twenty-four egg cartons.
Number of shipping boxes =338/24
= 14.08
The shipper can deliver no more than fifteen shipping boxes of eggs at a time.
Yes, Rob can ship all 4,056 eggs in the same shipment.
To learn more about the unitary method visit:
brainly.com/question/22056199.
#SPJ1
Help please!! Find the equation of the linear function represented by the table below in slope-
intercept form.
Answer:
X
1
2
3
4
y
-1
-3
-5
-7
The slope intercept form is y= 2x+1
What is slope ?
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
Let's take 2 points :
(x1,y1) = ( 1, -1)
(x2,y2) = ( 2, -3)
slope , m = (y2-y1) /(x2-x1)
= (-3-(-1))/(2-1)
= (-3+1)/1
= -2
Slope intercept form:
y-y1=m(x-x1)
y-(-1) = -2 (x-1)
y+1=-2x+2
=> y=2x+2-1
=> y= 2x+1
Thus, the slope intercept form is y= 2x+1
To learn more about the slope from the given link
https://brainly.com/question/16949303
#SPJ1
Estimating and Checking
Rashida has worked out that 21.29 x 38 = 809.02.
What calculation could you do to check that this answer is about right?
The required expression is 21.29 × 38 = 809.02. has an exact value of the given product.
What is an estimate?The estimate is a process, and it includes the rough over-calculation that makes one have a close value to the exact value.
here,
Given expression,
21.29 × 38 = (21 + 0.29) 38
Using distributive property,
= 21× 38 + 0.29 × 38
= 798 + 11.02
= 809.02
The required expression is 21.29 x 38 = 809.02. has an exact value of the given product.
Learn more about estimates here:
https://brainly.com/question/565542
#SPJ2
Audrey deposited $10,000 into a 3-year certificate of deposit that earned 10% annual interest, compounded annually. Audrey made no additional deposits to or withdrawals from the certificate of deposit. What was the value of the certificate of deposit at the end of the 3-year period?
A. $13,000
B. $13,300
C. $13,310
D. $13,401
Answer: C
Step-by-step explanation:
10000(1+0.10)³
=10000(1.10)³
=10000*1.331
=13310
help it was meant to be turned in 8 minutes ago...
The length of the car in Ivans drawing is given as 8 cm
How to find the length of the carWe are to solve for the length of this car by using the figure we have in the scale drawing. The length of car in Megan's drawing is 6 cm. The scale is 3 : 2
Ivan's drawing is in the relation of 2 : 1 cm
We would have to find the actual length of this car but by the use of Megan's ratio
This is given as
6 * 2 / 3
12 / 3
= 4 cm
Next we have to find Ivans length.
4 * (2/1)
= 8 / 1
= 8 cm
Read more on length here: https://brainly.com/question/16557738
#SPJ1
Kendra and Jamal are standing in line. The number line shows their positions in meters with
positive numbers representing positions to the right. Help please
the solution of number line is all the options are correct.
What is number line?A number line is an image of numbers plotted on a straight line, either horizontally or vertically. We can compare numbers and execute simple arithmetic operations on them easily by writing the numbers down on a number line. The starting point of a number line is often regarded as zero (0). These numbers to the left of zero are all negative while the numbers just on right of zero are all positive. As a result, we can argue that on a number line, the value of numbers grows as we approach the right. The numbers on the right are therefore larger than the ones on the left, according to this statement.
Here,
Kendra and Jamal are standing in line. The number line shows their positions in meters with positive numbers representing positions to the right.
The position of Kendra is -6 and Jamal is 0.
Kendra is 6 meters left of Jamal.
Kendra and Jamal are 1-6 meters apart.
Jamal is 6 meters right of Kendra.
Hence, all the options are correct.
Learn more about number line, by the following link
https://brainly.com/question/28726930
#SPJ1
House representatives are elected every two years the President of the United States is elected every four years both will be elected in 2004 when is the next year after 2004 for both will be elected
You are playing a card game. When you finish the game,
you receive one point for each card you played and lose two points for each card
remaining in your hand. You finish the game before three of your friends finish, so
your score is tripled. What is your final score if you play 18 cards and have 2 cards
left in your hand?
The requried, score is given as 42, as of the given condition,
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
here,
Let the total score after finishing the game be x,
Receive one point for each card you played and lose two points for each card remaining in your hand. and the score is tripled.
According to the quesiton,
x =3 [1 × 18 - 2 × 2]
x = 3[ 18 -4]
x = 3 × 14
x = 42
Thus, The requried, score is given as 42, as of the given question,
Learn more about models here:
https://brainly.com/question/22591166
#SPJ1
it is generally believed that nearsightness affects about 15% of al children. a local elementary school registered 120 incoming kindergarteners.
Note that this scenario is talking about a sampling distribution sincer this school is a sample size 120, therefopre, you will need to calculate the standard deviation using a formula before using the normalcdf aqnd invNorm commands.
(a) what is the mean of the sampling distribution of all samples like this
(b) what is the standard deviation of the sampling distributrion of all samples like this
(c) what is the probability that less tahn 10%of the incoming kindergarteneres are nearsighted?
(d) if this school measutre at the 80th percentile for all incoming kindergarten classes of size 120, what proportion of incoming kindergarteners are nearsighted?
The mean is of 0.15. The standard deviation is of 0.0326.0.1774 of incoming kindergarteners are nearsighted.
Find the mean and S.D ?The central limit theorem and the normal distribution are used to determine that:
a) A 0.15 is the mean.
b) A standard deviation of 0.0326 is present.
c) There is a 0.063 = 6.3% chance that fewer than 10% of the kindergarten applicants have nearsightedness.
d) 0.1774 percent of kindergarten students have nearsightedness.
The mean is of 0.15.
Item b:
s = p (1-p)/n = 0.15(0.85)/120
= 0.0326.
The standard deviation is of 0.0326.
Item c:
The probability is the p-value of Z when X = 0.1.
By the Central Limit Theorem
Z= 0.1 -0.15/ 0.0326.
= -1.53
Z = -1.53 has a p-value of 0.063.
There is a 0.063 = 6.3% probability that less than 10% of the incoming kindergarteners are nearsighted.
Item d:
X = 0. 1774
The proportion is X when Z has a p-value of 0.8, so X when Z = 0.84.
0.1774 of incoming kindergarteners are nearsighted.
To learn more about normal distribution refer
https://brainly.com/question/27130932
#SPJ1
If a1=3 and an=-2an find f 8
Answer:
a₄ = 25
Step-by-step explanation:
using the recursive formula [tex]a_{n}[/tex] = 2[tex]a_{n-1}[/tex] and a₁ = 4 , then
a₂ = 2a₁ - 1 = 2(4) - 1 = 8 - 1 = 7
a₃ = 2a₂ - 1 = 2(7) - 1 = 14 - 1 = 13
a₄ = 2a₃ - 1 = 2(13) - 1 = 26 - 1 = 25
function f(x)=7^x represent exponential growth, decay or neither?
Answer:
exponential growth
Step-by-step explanation:
The announcer said, ‘Ingrid won the 100 metre race in 13.9 seconds.’
Her time was originally measured to 2 decimal places.
What was the slowest time she could have run?
Answer:
So the slowest time she could have run is 13.99 seconds, as any time greater than that would have been rounded up to 14 seconds.
Step-by-step explanation:
Ingrid's time of 13.9 seconds was originally measured to 2 decimal places, which means that her actual time could be rounded to 13.9 seconds. To find the slowest time she could have run, we need to find the greatest value that could have been rounded down to 13.9 seconds.
Since the time was measured to 2 decimal places, this means that the hundredths place is known and the thousandths place can be anything between 0 and 9. So the slowest time she could have run is 13.99 seconds, as any time greater than that would have been rounded up to 14 seconds.
Find the place value of the 4 in the the number 16,952,874.
Answer:
one's place
Step-by-step explanation:
Carlos is building a prop for the school play and he needs to calculate the amount of lumbet needed to make it. the prop is shaped like a tower and the radius of the base of the tower is 2.5 feet. if the tower is hollow and has no base, what is the approximate surface area of the tower? round your answer to the nearest tenth.
The approximate surface area of the tower is 156.33 feet².
What is Surface Area?The area of a three dimensional object on it's outer surface is called the surface area of the object.
The given tower is a composite of a cylinder and a cone.
But cylinder does not have the bases and cone also does not have it's base.
Surface area of the curved surface of cylinder = 2π r h
where r is the radius of the base and h is the height of the cylinder.
Given h = 8 feet and r = 2.5 feet
Curved surface area of cylinder = 2π × 2.5 × 8 = 40π feet²
Surface area of the curved surface of the cone = π r √(h² + r²)
where r is the radius of the base of the cone and h is the perpendicular height of the cone.
Given r = 2.5 feet and h = 3 feet
Curved surface area of cone = π × 2.5 [√(2.5² + 3²)]
= 9.76π feet²
Total surface area = 40π + 9.76π
= 156.33 feet²
Hence the total surface area of the tower is approximately 156.33 feet².
Learn more about Surface Area here :
https://brainly.com/question/29298005
#SPJ1
in the fruit bowl that are 10 times. 5 peachse and 2 mangoes select the correct choice from the drop down
The probability of randomly picking a peach from from the fruit bowl is 29 %
How to find the probability ?To find the probability of picking a peach from the fruit bowl at random, you first need to sum up the number of fruit :
= 10 Limes + 5 peaches + 2 mangoes
= 17 fruit
The probability of picking a peach from the fruit bowl can then be found to be :
= Number of peaches in fruit basket / Number of fruit in the fruit basket
= 5 / 17
= 29 %
Find out more on probability at https://brainly.com/question/9738029
#SPJ1
The rest of the question is:
The probability of randomly picking a peach from from the fruit bowl is _________.
29%14%52%32%In triangle ABC, the measure of angle B is 21 less than four times the measure of angle A and the measure of angle C is more than five times the measure of angle A. Find the measure, in degrees, of each angle of triangle ABC.
Answer:
Step-by-step explanation:
Becky's dinner would have cost $30 but she had a 40% off coupon. How much did Bedky pay for dinner?
Answer:
If Becky had a 40% off coupon, that means she saved 40/100 = 0.4 of the original price.
To find how much she paid for dinner, we can multiply the original price by the percentage of the price that she paid:
30 * (1- 0.4) =30*0.6 = $18
Becky paid $18 for her dinner.
Decide whether parallelogram JKLM is a rectangle, a rhombus, or a square. Give all names that apply.
J(-2,7), K(7, 2), L(-2,-3). M-11,2)
rectangle
rhombus
square
Explain your reasoning.
The diagonals are neither perpendicular nor congruent.
The diagonals are perpendicular but not congruent.
The diagonals are congruent, but not perpendicular.
The diagonals are congruent and perpendicular.
Answer:
rhombus
(b) The diagonals are perpendicular but not congruent.
Step-by-step explanation:
You want to know what sort of figure the parallelogram JKLM is, given the vertices J(-2,7), K(7, 2), L(-2,-3), M(-11,2).
ObservationThe x-values of points J and L on diagonal JL are the same, so that diagonal is a vertical line. Its length is 7 -(-3) = 10.
The y-values of points K and M on diagonal KM are the same, so that diagonal is a horizontal line. Its length is 7 -(-11) = 18.
The diagonals are perpendicular and not congruent, so the parallelogram is a rhombus.
ANOTHA ONE LETS GOOOOOO
Answer:
1/560
Step-by-step explanation:
So the x input which is the top row the numbers increase by 1 so that is your top number of your slope (rate of change)
And your bottom row increases by 560 so that is your bottom number of your slope
So your rate of change is 1/560
How do I know where to get these numbers?
Well if you take the first 2 numbers from the top row (in your case 1 and 2) and subtract them from each other (2-1=1) you get your first number. Then you do the same for the bottom (in your case 560 and 1120) subtract them (1120-560=560) and get your bottom....If needed you can simplify your fraction but sometimes your slope can come out as a whole number instead of a fraction but in your case you have a fraction.
That is where you get 1/560
Hope this helped!
Height of a hot air balloon. As a hot air balloon began to ride, the ground crew drove 1.2mi to an observation station. The initial observation from the station estimated the angle between the ground and the line of sight to the balloon to be 30. Approximately how high was the balloon at that point
Answer:
0.7 mile high
Step-by-step explanation:
tan 30 = height /1.2
so height =1.2 *tan30 = 1.2*0.58 = 0.7
Simplify the expression in the exact terms ( no decimals): (2/3)^3
Answer:
[tex]\frac{8}{27}[/tex]
Step-by-step explanation:
This means
[tex]\frac{2}{3}[/tex] x [tex]\frac{2}{3}[/tex] x [tex]\frac{2}{3}[/tex] = [tex]\frac{8}{27}[/tex]
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{(\dfrac{2}{3})^3}[/tex]
[tex]\mathsf{= \dfrac{2}{3}(\dfrac{2}{3})(\dfrac{2}{3})}}[/tex]
[tex]\mathsf{= \dfrac{2(2)(2)}{3(3)(3)}}[/tex]
[tex]\mathsf{= \dfrac{4(2)}{9(3)}}[/tex]
[tex]\mathsf{= \dfrac{8}{27}}[/tex]
[tex]\huge\text{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\mathsf{\dfrac{8}{27}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
If Csc(x)=-2 , what is Cot (x/2)?
Do you know how to do it on a calculator using 1/sin(x) and 1/ tan(x)?
The value of cot(x/2) is -3.73
What are trigonometric ratios?The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Given that, Csc(x) = -2
Since,
cscx = 1/sinx
Therefore,
1/sinx = -2
sinx = -1/2
sinx = -sin30°
x = -30°
Therefore,
cot (x/2) = cot(-15)
= -1/tan15
= -3.73
Hence, the value of cot(x/2) is -3.73
Learn more about trigonometric ratios, click;
https://brainly.com/question/25122825
#SPJ1
Derive by means of the direct formulas the following functions
So on solving the provided question we can say that - the function is y = (-8x + - 74) and y = -82
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
here, we have
y = (-8x + - 74)
and from data we have x = 1
so, y = (-8-74)
y = -82
To know more about function visit:
https://brainly.com/question/28193995
#SPJ1
The product of 46 and a number added to the reciprocal of a number squared
The required equation modeled as of the given condition is 46x + 1 / x².
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
here,
Let the number be x, and its reciprocal is 1/x
According to the question, the product of 46 and a number added to the reciprocal of a number squared is given as,
= 46 × x + 1/x²
= 46x + 1/x²
Thus, the required equation modeled as of the given condition is 46x + 1 / x².
Learn more about models here:
https://brainly.com/question/22591166
#SPJ1
Larry has some money that he has saved. He starts a new job. The graph shows the total amount of money Larry will have y after working x hours. Find and interpret the rate of change and initial value.
The rate of change is $6 per hour while the initial value is $20
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
The slope intercept form of a linear equation is:
y = mx + b
Where m is the slope (rate of change) and b is the y intercept.
Let y represent the total amount of money that Larry would have after working x hours.
From the graph, the y intercept is at (0, 20). Using point (0, 20) and (5, 50):
Slope = (50 - 20)/(5 - 0) = 6
The slope is $6 per hour
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Suppose a parabola has an axis of symmetry at x = 6, a maximum height of 6 and also passes through the point (7, 5). Write the equation of the parabola in vertex form.
Answer:
[tex]y=-(x-6)^2+6[/tex]
Step-by-step explanation:
Vertex Form:Vertex form of a parabola is expressed as: [tex]y=a(x-h)^2+k[/tex]
(h, k) = vertex"a" determines vertical stretch/compression and directionIt's also important to note that the axis of symmetry is a vertical line which passes through vertex, so in this form, that axis of symmetry can be defined as such: [tex]x=h[/tex]
So if we're given the axis of symmetry we know the x-coordinate of the vertex.
Solving the Problem:Since we're given the axis of symmetry to be: [tex]x=6[/tex] then that means the x-coordinate of the axis of symmetry is six. Another important thing to note about the vertex is it's y-value is either a minimum or maximum depending on whether it's opening up or down. So when we're given the maximum height to be 6, that's the y-coordinate of the vertex.
So now we know the coordinates to the vertex: [tex](6, 6)[/tex]. Using this we can plug in some values into the vertex form: [tex]y=a(x-6)^2+6[/tex], but we still don't know the "a" value in front (besides that it's negative). Luckily we're given a point on the equation! We can plug in the coordinates given: [tex](7, 5)[/tex] into the vertex form as (x, y) to solve for the "a" value, so let's do that.
Original Equation:
[tex]y=a(x-6)^2+6[/tex]
Passes through the point (7, 5), so substitute it for (x, y)
[tex]5=a(7-6)^2+6[/tex]
Simplify inside parenthesis:
[tex]5=a(1)^2+6[/tex]
Square the one:
[tex]5=a+6[/tex]
Subtract 6 from both sides:
[tex]-1=a[/tex]
So now let's plug this back into our equation: [tex]y=-1(x-6)^2+6[/tex], although we don't have to explicitly put the one, and just put the negative sign which does the same thing: [tex]y=-(x-6)^2+6[/tex]
Gerber Product's Gerber Mixed Cereal for Baby contains, in each serving, 60 calories and 11 grams of carbohydrates.† Gerber Mango Tropical Fruit Dessert contains, in each serving, 80 calories and 21 grams of carbohydrates.† If you want to provide your child with 340 calories and 75 grams of carbohydrates, how many servings of each should you use?
Gerber Mixed Cereal for Baby
serving(s)
Gerber Mango Tropical Fruit Dessert
serving(s)
3 of mixed cereal and 2 of tropical fruit
Carlos wants to finish a 7.5-mile trail walking at a constant rate. The remaining distance, d, that Carlos has left to finish the trail after h hours walking is
15.
represented by the function 5h+2d-
Part A
Select the correct domain of the function in terms of the context.
{h/hER}
{h/h>0}
{h|0
{h|0 ≤h≤15}
Part R
W
Type here to search
ii
20
3
hip
7:51 AM
1/17/2023
The domain of the function 5h + 2d = 15 is [0, 3].
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The function 5h + 2d = 15
Where h is the number of hours and d is the distance remaining after h hours.
Now,
5h + 2d = 15
2d = 15 - 5h
d = (15 - 5h)/2
For h = 0, d = 15/2 = 7.5
For h = 1, d = (15 - 5)/2 = 10/2 = 5 miles.
For h = 2, d = (15 - 10)/2 = 5/2 = 2.5 miles.
For h = 3, d = (15 - 15)/2 = 0 miles
The domain of the function is [0, 3].
Thus,
The domain is [0, 3].
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ1
