Answers
Answer:
[tex]\lim_{x\to3^-}\sin{\frac{\pi}{\floor[x]}=1[/tex]
[tex]\lim_{x\to3^+}\sin{\frac{\pi}{\floor[x]}=\frac{\sqrt3}{2}[/tex]
[tex]\lim_{x\to3}\sin{\frac{\pi}{\floor[x]}=\frac{\sqrt3}{2}[/tex]
Step-by-step explanation:
So we want to left and right hand limits of the function:
[tex]f(x)=\sin{\frac{\pi}{\floor[x]}[/tex]
as x approaches 3.
Note that the [x] means the floor function a.k.a the greatest integer function. In other words, the value of the function will be the greatest integer less than or equal to x.
1) Left
So we have the limit:
[tex]\lim_{x\to3^-}\sin{\frac{\pi}{\floor[x]}[/tex]
Note that since we're coming from the left, the values are 2.9, 2.99, and 2.999...
As I mentioned previously, the floor function outputs the greatest integer less than or equal to x.
With 2.9, 2.99, and 2.999, the greatest integer less than or equal to x is 2.
Therefore:
[tex]=\sin{\frac{\pi}{2}[/tex]
Simplify:
[tex]=1[/tex]
So:
[tex]\lim_{x\to3^-}\sin{\frac{\pi}{\floor[x]}=1[/tex]
2) Right:
[tex]\lim_{x\to3^+}\sin{\frac{\pi}{\floor[x]}[/tex]
Since we're coming from the right this time, the values are going to be 3.01, 3.001, 3.001.
And, the greatest integer less than or equal to 3.01, 3.001, and 3.001... is 3.
Therefore:
[tex]=\sin{\frac{\pi}{3}[/tex]
Simplify:
[tex]=\frac{\sqrt3}{2}[/tex]
So:
[tex]\lim_{x\to3^+}\sin{\frac{\pi}{\floor[x]}=\frac{\sqrt3}{2}[/tex]
At 3:
So we have:
[tex]\lim_{x\to3}\sin{\frac{\pi}{\floor[x]}[/tex]
The greatest integer of 3 is just 3. So:
[tex]=\sin{\frac{\pi}{3}\\[/tex]
Simplify:
[tex]=\frac{\sqrt3}{2}[/tex]
So:
[tex]\lim_{x\to3}\sin{\frac{\pi}{\floor[x]}=\frac{\sqrt3}{2}[/tex]
Related Questions
Haley had 2 blue marbles, 2 red marbles, and 4 green marbles. She gave 1 4 of her marbles to Amy and 2 4 of her marbles to Sue. What is the total number of marbles that Haley gave to Amy and Sue?
Answers
Hope you have a nice day.
On Friday there were 8 snowboarders for every 3 skiers at Slovak ski resort. On Saturday the ratio of the number of snowboarders to the number of skiers was 4:7 there were 168 snowboarders at the ski resort on Friday there were the same number of people at the ski resort on Saturday as there were on Friday how many more skiers were there than snowboarders at the ski resort on Saturday
Answers
Answer:
There are 46 more skiers than snowboarder
Step-by-step explanation:
Given
Ratio of Snowboarders to Skiers
On Friday:
[tex]Ratio = 8 : 3[/tex]
On Saturday:
[tex]Ratio = 4 : 7[/tex]
Population = 168
Required
Determine the difference in the number of skiers and snowboarders on Saturday
On Saturday, we have
[tex]Ratio = 4 : 7[/tex]
Calculate Total
[tex]Total = 4 + 7[/tex]
[tex]Total = 11[/tex]
Calculate the number of skiers
[tex]Skiers = \frac{7}{11} * 168[/tex]
[tex]Skiers = \frac{1176}{11}[/tex]
[tex]Skiers = 107[/tex] (Approximated)
Calculate the number of snowboarders
[tex]Snowboarders = \frac{4}{11} * 168[/tex]
[tex]Snowboarders = \frac{672}{11}[/tex]
[tex]Snowboarders = 61[/tex] (Approximated)
Calculate the difference
[tex]Difference = 107 - 61[/tex]
[tex]Difference = 46[/tex]
Hence, there are 46 more skiers than snowboarder
Answer:63
Step-by-step explanation:
A basketball player scored 351 points last year. If the player plays 18 games this year, how many points will he need to average per game to beat last year’s total?
Answers
Answer:
The answer is C in my opinion and it is one of confusing question i have ever seen
Step-by-step explanation:
If he scored 351 points last years and he plays 18 games this year and if we want to know the points that he need to beat last year score in thsi year we need to divide 351÷18=19.5 so he will need to have no morethan 20 points because 19.5 is also enough to get the score
I hope u like it
Four times the sum of half a number and 6 is 48.
How do you put this as an equation?
Answers
Answer:
make x the subject of formula then = 6/48
divide 9y power 2 by 3
divide (8x power 2 +4x ) by 2x
Answers
Answer:
1=27
2=34
Step-by-step explanation:
1)9y power 2÷3
or, y=9 power 2÷3
or, y=9×9÷3
or, y=81÷3
or, y=27
2) (8x power 2+4x)÷2
=(8x×8+4x)÷2
=(64x+4x)÷2
=68x÷2
or, x=68÷2
or, x=34
z = 73i - 32
What is the real part of z ?
What is the imaginary part of z?
Answers
Answer:
real: -32imaginary: 73Step-by-step explanation:
The real part is everything that does not multiply i. The imaginary part is everything that does multiply i.
Conventionally, the real part is written first:
z = -32 +73i
Re(z) = -32
Im(z) = 73
4+3(15-2^(3)) Simplify the equation....
Answers
Answer:
25Step-by-step explanation:
[tex]4+3\left(15-2^3\right)\\\\3\left(15-2^3\right)=21\\\\=4+21\\\\=25[/tex]
Answer:
25
Step-by-step explanation:
4+3(15-2^(3)
4+3(15-(2*2*2)
4+3(15-8)
4+3(7)
4+21=25
Jason's monthly practice time on the piano is 35 hours. This month, he has practiced 8.5 hours in week 1, 12 hours in week 2, and 5.5 hours in week 3. How many more hours of practice time does Jason need to complete?
Answers
Given :
Monthly practice time , T=35 hours .
This month, he has practiced 8.5 hours in week 1, 12 hours in week 2, and 5.5 hours in week 3.
To Find :
Many more hours of practice time does Jason need to complete .
Solution :
Number of hours he practice in week 1 , [tex]t_1=8.5\ hours[/tex] .
Number of hours he practice in week 2 , [tex]t_2=12\ hours[/tex] .
Number of hours he practice in week 3 , [tex]t_3=5.5\ hours[/tex] .
Now , number of hours left is :
[tex]t=T-t_1-t_2-t_3\\\\t=35-(8.5+12+5.5)\ hours\\\\t=8\ hours[/tex]
Hence , this is the required solution .
- 2(w+6) +9< - 15
I'm make you brainliest
Answers
-2(w+6)+9<-15
-2w-12+9<-15
-2w-3<-15
-2w<-15+3
-2w<-12
-2w/-2 < -12/-2
Because they’re being divided by a negative number the sign changes and you get w>6
please help me solve this problem!!!
Answers
Answer:
w = 9
Step-by-step explanation:
We can use ratios to solve
2 3
---- = ------
6 w
Using cross products
2w = 3*6
2w = 18
Divide by 2
w = 9
A Blue Viper can travel 18 2/5 miles on 4/5
tank of gas. A Red Rocket can travel 17 2/5 miles on 3/4 tank of gas. Which car can travel
further on one tank of gas?
Answers
Answer:
A Blue Viper
Step-by-step explanation:
A Blue Viper can travel 18 2/5 miles on 4/5 tank of gas.
It can travel on full tank:
(18 2/5)*1/5 + 18 2/5 = 92/5*1/5 + 92/5 = 92/5*6/5 = 552/25 = 22.08 milesA Red Rocket can travel 17 2/5 miles on 3/4 tank of gas.
It can travel on full tank:
(17 2/5)*1/4 + 17 2/5 = 87/5*1/4 + 87/5 = 87/5*5/4 = 87/4 = 21.75 milesA Blue Viper can travel further as:
22.08 > 21.75after paying income 5% a man has Rs 7600 left. what is his income?
Answers
Answer:
His income was 8000 rupees
Step-by-step explanation:
We must find his income so let that be x
We take 100%-5% = 95%
Turn this 95% into a decimal which is 0.95
So:
x * 0.95 = 7600
Rearrange this to give x:
x = 7600/0.95
x = 8000 rupees
The man's income is Rs. 8000. He has been left with 95 percent of his income = Rs. 7600.
What are percentages?Percentages are fractional values where the total amount is taken as 100.
25% of a quantity means 25/100 of that quantity.
How to solve the given question?In the question, we are informed that after paying 5% of income, a man is left with Rs. 7600.
We are asked to find his income.
We are given that a man pays 5% of his income, so he will be left with (100-5)% = 95% of his income as percentages are taken over a total of 100.
We assume the man's total income to be Rs. Y.
∴ We can say that the man is left with 95% of Y.
We know the man is left with Rs. 7600. So we can write this case as:
95% of Y = 7600
or, 95/100 of Y = 7600
or, (95/100)*Y = 7600
or, Y = (7600*100)/95 = 760000/95 = 40000/5 = 8000.
∴ The man's income is Rs. 8000. He has been left with 95 percent of his income = Rs. 7600.
Learn more about percentages at
https://brainly.com/question/843074
#SPJ2
4x2 + 3x - 6
Label the terms in the expression as constant, linear, and quadratic.
A) constant: -6; linear: 3x; quadratic: 4x2
B) constant: 3x; linear: -6; quadratic: 4x2
C) constant: 4x2 ; linear: 3x; quadratic: -6
D) constant: -6; linear: 4x2 ; quadratic: 3x
Answers
Find m∠XYZ in the figure if ∠XYZ and ∠PQR are supplementary angles. please explain your answer Question 1 options: A) 83° B) 7° C) 173° D) 97°
Answers
Answer:
It's D) 97°
Step-by-step explanation:
Just stick this in ya brain
Supplementary angles => sum => 180
Answer:
D
Step-by-step explanation:
So, we know that ∠XYZ and ∠PQR are supplementary angles. This means that their total sum is 180 degrees. In an equation, this is:
[tex]\angle PQR+\angle XYZ=180[/tex]
Since we already know the measure of PQR, substitute 83 for PQR:
[tex]83+\angle XYZ=180[/tex]
Subtract 83 from both sides:
[tex](83+\angle XYZ)-83=(180)-83\\\angle XYZ=97\textdegree[/tex]
The answer is D
Solve the equation below for x.
сх — 4 = 7
Answers
Answer:
x = 11/c
Step-by-step explanation:
To solve this equation for x, we simply need to apply equation operations and isolate the x variable.
cx - 4 = 7
cx - 4 + 4 = 7 + 4
cx = 7 + 4
cx = 11
cx * (1/c) = 11 * (1/c)
x = 11 * (1/c)
x = 11/c
Cheers.
Cx = 7 + 4
Cx = 11
X = 11/c
Hope it helps :)
In the diagram, 1 inch represents 20 feet
Which are the actual dimensions of the
family room?
Answers
Answer: 10 Feet by 15 Feet
Step-by-step explanation:
find the 40th term of an AP where 12th term is 45 and 17th term is 80.
Answers
Answer:
40th term = 241.
Step-by-step explanation:
17th term:
= a1 + 16d = 80
12th term
= a1 + 11d = 45 Subtracting the 2 equations:
5d = 80 - 45 = 35
d = 7
and a1 + 16(7) = 80
a1 = 80 -112 = -32.
Therefore the 40th term = -32 + 39*7
= 241.
In a poll, 1004 women in a country were asked whether they favor or oppose the use of "federal tax dollars to fund medical research using stem cells obtained from human embryos." Among the respondents, % said that they were in favor. Identify the population and the sample.
Answers
Answer:
Population: A) All woman in the country
Step-by-step explanation:
Sample: A) The 1004 woman selected
What is the solution set for 5x – 1 < 7x - 47
Answers
Answer:
x > 23
Step-by-step explanation:
5x – 1 < 7x - 47
Add 1 to -47, you get -46.
5x < 7x - 46
Subtract 7x from 5x.
-2x < -46
Multiply both sides to reverse the inequality.
2x > 46
Divide both sides by 2.
x > 23
-78 divided by (-1.3)
Answers
Answer:
60
Step-by-step explanation:
What is the value of x? Enter your answer in the box.
Answers
Answer:
I think the value of x might be 127°
Beverly Hibbs earns $683.00 a week. She is single and claims 2 allowances. What amount is withheld weekly for federal income tax
Answers
Answer:
$18 per week
Explanation:
The amount that is withheld weekly for federal income tax is $52.25
Federal Insurance Contribution Act is the legal organization used in the United States which contain the rules and regulations applied for calculating payroll taxes on the paychecks of the employee. The tax process is contributed by both the employees as well as the employers for funding the social security and Medicare programs.
The rate of federal tax withheld for the weekly paycheck is:
= 6.2% of social security + 1.45% for medicare
= 7.65% of the gross weekly pay.
If Beverly Hibbs earns $683.00 a week, the amount withheld weekly by the Federal income tax is:
= 0.0765 × 683
= $52.25
Learn more about federal income tax here:
https://brainly.com/question/17092810?referrer=searchResults
¿Por que 10/25 es equivalente a 2/5?
Answers
Answer:
because if u divide the top and bottom by 5, you'll get 2/5
Step-by-step explanation:
Answer: Porque dividir ambos por 5 y eso es lo más bajo que pueden ir
Step-by-step explanation:
10 / 5 = 2
25 / 5 = 5
write an equation for each line :
m = -4 and the y-intercept is 3
Answers
Answer:
y = -4x + 3
Step-by-step explanation:
m = slop
b = y-int
y = mx + b
Your teacher will give you a set of cards. On each card, Figure A is the original and Figure B is a scaled copy.
Sort the cards based on their scale factors. Be prepared to explain your reasoning.
Answers
Name a positive or negative number to represent a drop of 10°F in the temperature.
Answers
is 1,600 1 tenth of 16,000
Answers
Answer:
true
Step-by-step explanation:
16,000 / 10 = 1,600
One box of colored pencils has 9•10 to the power of 6 pencils . Another box has 10 to the power of 3 pencils. What is the total number of pencils in both boxes
Answers
here’s the step by step as well
(Colored Pencils)
9•10^6
10^6 = 60 • 9 = 540
(Pencils)
10^3 = 1,000
and if you’re getting the sum of both combined, it’s 1,540. hoped this helped!
An item is on sale for $100. If it was discounted by 20%, what was the original selling price?
Answers
Answer: The original price was $125
Step-by-step explanation:
If an item is on sale for $100 and it was discounted by 20% then we could set up an equation and solve for the original price.
Remember if there were 20% discount then 80% of the price will be left.
80% * x = 100
0.8x =100
x = 125
Step-by-step explanation:
We have :
• Selling Price = $100
• discount = 20%
As we know
• Selling Price = Cost - Discount
Now we have
• Discount = 20%
Let cost be x
→ Selling Price = x - 20% of x
→ selling price = 80% of x
→ 80% of x = 100
→ 80/100 x = 100
→ x = 100 × 100 / 80
→ x = $ 125
Is 9 a natural number?
Answers
Answer: yes
Step-by-step explanation:
Answer:
I think so
Step-by-step explanation:
I think all numbers are technically natural