Step-by-step explanation:
Consider two points on a curve, (xᵢ, yᵢ) and (xᵢ₊₁, yᵢ₊₁). The distance between them can be found with distance formula:
d = √((xᵢ₊₁ − xᵢ)² + (yᵢ₊₁ − yᵢ)²)
d = √((Δx)² + (Δy)²)
Factor out Δx:
d = √(1 + (Δy/Δx)²) Δx
Adding up the distances from i=1 to i=n, the total arc length can be approximated as:
s ≈ ∑ᵢ₌₁ⁿ √(1 + (Δy/Δx)²) Δx
Taking the limit as n approaches infinity, we get the exact value of s:
s = lim(n→∞) ∑ᵢ₌₁ⁿ √(1 + (Δy/Δx)²) Δx
Which can be written as a definite integral:
s = ∫ₐᵇ √(1 + (dy/dx)²) dx
There are 35 students in art class and 57 students in dance class. Find the number of students who are either in art class or in dance class. Find
When two classes meet at different hours and 12 students are enrolled in both activities. ( 2marks)
When two classes meet at the same hour. ( 2 marks)
Answer:
a. 80 students
b. 92 students
Step-by-step explanation:
Represent arts students with A and Dance students with D.
So, we have,
n(A) = 35
n(D) = 57
Required
Determine n(A or D)
Solving (a):
Here, we have:
n(A and D) = 12
n(A or D) is calculated as thus:
n(A or D) = n(A) + n(D) - n(A and D)
n(A or D) = 35 + 57 - 12
n(A or D) = 80
b. From the given details
n(A and D) = 0 because both students are not mixed up as in (a) above
Using the same formula as (a).
n(A or D) = n(A) + n(D) - n(A and D)
n(A or D) = 35 + 57 - 0
n(A or D) = 92
The norman h.s. math club has twice as many male members as female members twenty percent of the male members and 30 female members participated in a math contest. What fraction of those members participating in the math contest were female? express your answer as a common fraction
Answer:
[tex]\frac{3}{7}[/tex]
Step-by-step explanation:
20% male and 30% female. 20% + 30%= 50% It is asking us what members participating was female. *50% out of 100%
> [tex]\frac{30}{70}[/tex] reduce or divide by 10 we get our fraction and answer, [tex]\frac{3}{7}[/tex].
Which of the following list contains exactly 2 composite numbers and 2 prime numbers?
Stonebridge neighborhood garage sale have the cash receipts for 5 days:
$136.97
$256.21
$366.10
$176.04
$72.49
Answer:
$1,007.81
Step-by-step explanation:
I need help with 20 please thank you.
Answer:
IM BACK!!!!
The answer is *DRUMROLLLLLLLL* B
jk
its 1 lol
Step-by-step explanation:
Plug in -8 to x and you end up multiplying -8 by 1/2 which is pretty simple but the Muhammad ibn Musa al-Khwarizmi guy invented Algebra, Gottfried Wilhelm Leibniz invented functions, and Brahmagupta of India invented addition, so thanks to them, you can solve this question. -8 times 1/2 is -4 and -4 plus 5 equals 1.
Hope this helps
What is the equation for a line with slope = 3 that passes through point (2, 5)?
a. y = 3x - 13
b. y = 3x - 1
C. y = 3x - 5
Need help on this pleaseeeeee
Answer:
I think it's C
Step-by-step explanation:
I just rotated point K 180 degrees and C was the only one with the coordinate points I got for K'
Corey earned
$3,200 working over the summer. If he
made $400 each week, how many weeks
did he work? How many weeks would he
need to work to earn $6,400? $8,800?
Answer:
He would need to work 8 weeks for 2300, 16 for 6400, and 22 for 8800
Step-by-step explanation:
You have to divide 3,200 by 400 since thats how much he makes in a week
that gives you 8
and you do the same for the rest
equation:
money wanted/400=weeks
Answer:)
he work for 8 weeks to earn 3,200
he needs to work 8 more weeks to earn 6,400
he needs to work 14 more weeks to earn 8,800
Step-by-step explanation:
Someone plz help me
Answer:
The first order.
Step-by-step explanation:
What do these symbols mean?
The funny shaped line is a square root, meaning what times itself (so for example, 3 x 3) gets that number. So the square root of 9=3.
The small 2 in the top right of the big numbers means square. The opposite. This means multiply that big number by itself twice. If the small number was say, 7, you would multiply the big number by itself 7 times. A common mistake is propel multiply the big number by the small number. The square used in these is 2 to the power of 3, the small number. This means you do 2x2x2, as the small 3 determines how many time you multiply the big number, 2. The result of 2x2x2=8.
The fraction is 11/9. The 9 means how many parts are in a whole number. The 11 means how many of those parts you actually have. Like a pizza-if you had a pizza (the whole) split into 7 parts, 7 would be your bottom number (as the 9 is here). If you are 4 parts and were left with 3 parts, 3 would be your top number (as the 11 is here). Seeing as 11 is bigger than 9, you have to imagine 2 pizzas. Each is split into 9, and you have 11 parts altogether. Thsi is 1 whole pizza and 2 extra parts, making the fraction 1 and 2/9. This is jaut another way to write 11/9 but I find it easier to look at.
The answer?
So. We have established that 11/9 = 1 & 2/9
And that 2 cubed (with the small 3 on it) = 8.
Amd the square roots of 5, 11 and 20 are approximately (Not exactly, but close enough) the following:
5. 2.2
11. 3.3
20. 4.4
So this leaves us a bunch of numbers to put in order from smallest to largest. This is fairly easy. It's not the second one. 8>3.3. It's not the third one. 8>2.2. It's not the fourth one. 1 & 2/9 may be smaller than 8, but 2.2 isn't. So this leaves the first order.
*Note that the symbol > means greater than or bigger than. So 8>2 means 8,is bigger than 2.
A farmer notes that in a field full of horses and chickens there are 35 heads and 98 feet. How many of each animal are there?
Answer:
There are 14 horses and 21 chickens.
Step-by-step explanation:
First, you have to make expression for horse and chicken. So we can let x be the number of horses and y will be the number of chickens. Next, given that the total number of feet for both animals is 98 so you have to make simultaneous equation :
[tex]4x + 2y = 98[/tex]
( horse has 4 feet and chicken has 2 feet )
There are a total of 35 heads so the other equation will be :
[tex]x + y = 35[/tex]
Lastly, you have to solve it :
[tex]4x + 2y = 98[/tex]
[tex]2(2x + y) = 98[/tex]
[tex]2x + y = 49 - - - (1)[/tex]
[tex]x + y = 35 - - - (2)[/tex]
[tex](1) - (2)[/tex]
[tex]2x + y - x - y = 49 - 35[/tex]
[tex]x = 14[/tex]
[tex]substitute \: x = 14 \: into \: (2)[/tex]
[tex]14 + y = 35[/tex]
[tex]y = 35 - 14[/tex]
[tex]y = 21[/tex]
Given m || n, find the value of x and y.
(3x-4)
(6x-5)
Answer:
X=21 and Y=121
Step-by-step explanation:
With these types of problems, we need to know our vertical angles and that lines are 180° when two angles on a line are next to each other.
To solve this problem algebraically we want to add (3x-4) and (6x-5) together so that they equal 180. The reason we do this is that they lie on the same line which is 180°. The equation would look like [tex]3x+6x-5-4=180[/tex]. We then want to add like terms which will leave us with [tex]9x-9=180[/tex]. Now we want to get 9x by itself by adding 9 on each side which leaves us with [tex]9x=189[/tex]. To isolate x we need to divide on each side by 9 which finally leaves us with [tex]x=21[/tex]
Now that we have the value of x (21) we can now utilize our knowledge of vertical angles (angles that are completely across and equal to one another.) We can find y by doing this equation: [tex]y=6x-5[/tex] and with the value of x found we can plug in the value to get [tex]y=6(21)-5[/tex] which simplifies to [tex]y=126-5[/tex] then to [tex]y=121[/tex].
The metal day fair has a recycling center that will a pay 10% early fee on the amount collected plus $2.75 for each metal collected to be recycled .If Isa brings 12.5 kilograms of metal to be recycled which is the closet amount of money she will receive.
Answer:
$37.8125
Step-by-step explanation:
$2.75 x 12.5 = 34.375
34.375 x 10% = 3.4375
$34.375 + 3.4375 = 37.8125
Write an equation for the description.
Tanmayi wants to raise $150 for a school fundraiser. She has raised $100 so far. How much more does she
need to reach her goal? Let m be how much more is needed.
Plzzzzzz helppppp
Answer: 50
Step-by-step explanation: All you need to do is subtract $100 from $150, and you'll get 50 as your answer. Hope this helps!
Once cup of instant rice makes 1.5 cups of cooked rice. How many cups of cooked rice will 3 cups of instant rice make?
Answer:
2
Step-by-step explanation:
If 1 = 1.5
2 = 3
That is the answer
Answer: 3 cups will make 4.5 cups of cooked rice.
Step-by-step explanation: 3 * 1.5
true or false? y=x^2 - 1 defines y as a function of x
Answer:
true
Step-by-step explanation:
it equals to
x1= -1
and
x2= 1
Answer:
Step-by-step explanation:
y=x²-1 is not a function for every value of y , x has more than one value
ex: if x=-1 , y=(-1)²-1 then y=0
if x=1 then y=0
Which lists all the multiples of 6 that are less than 20?
O 6,9,12,15,18
O 6.12
O 6.12.18
O 6, 12, 18, 24
Answer:
6 , 12 ,18
Step-by-step explanation:
6 time 2 = 12
6 times 3 = 18
not more that 20 so that is it
How much is 2/3 - 1/6 =
Answer:
1/2
Step-by-step explanation:
First create like dominators
2/3 -1/6 = 4/6 - 1/6
simplify using subtraction
4/6 - 1/6 = 3/6
Simplify the answer
3/6 = 1/2
Answer:
1/2
Step-by-step explanation:
2/3 - 1/6
Subtract the two fractions:
2/3 - 1/6 = 1/2
The answer we get is:
1/2
Divide the numerator by the denominator for the decimal form:
1 ÷ 2 = 0.5
0.5 is our decimal form.
1/2 and 0.5 are our answers.
Hope you learned from this answer!
Which of the following is the equation of the line that is parallel to
y= 3/5x+ 8 and goes through point (-10,4)?
Select one:
a. y = 5/3x + 20 2/3
b. y=-5/3x – 12 2/3
c.y= 3/5x + 10
d. y = -3/5x-2
Answer:
C
Step-by-step explanation:
We want to write the equation of a line that is parallel to:
[tex]y=\frac{3}{5}x+8[/tex]
And also passes through (-10, 4).
Remember that parallel lines have the same slope.
The slope of our old line is 3/5.
Therefore, the slope of our new line is also 3/5.
We know that it passes through (-10, 4). So, we can use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope and (x₁, y₁) is a point.
So, let's substitute 3/5 for m and let (-10, 4) be our (x₁, y₁). This yields:
[tex]y-(4)=\frac{3}{5}(x-(-10))[/tex]
Simplify:
[tex]y-(4)=\frac{3}{5}(x+10)[/tex]
Distribute on the right:
[tex]y-4=\frac{3}{5}x+6[/tex]
Add 4 to both sides:
[tex]y=\frac{3}{5}x+10[/tex]
So, our answer is C.
And we're done!
Step-by-step explanation:
Hey there!
The equation of a st.line passing through point (-10,4) is ;
(y-y1)= m1(x-x1) [one point formula]
Put all values.
(y - 4) = m1( x + 10)..........(i)
Another equation is; y = 3/5 + 8.............(ii)
From equation (ii)
Slope (m2) = 3/5 [ By comparing equation with y = mx+c].
As per the condition of parallel lines,
Slope of equation (i) = slope of equation (ii)
(i.e m1 = m2 )
Therefore, the value of m1 is 3/5.
Putting value of slope in equation (i).
[tex](y - 4) = \frac{3}{5} (x + 10)[/tex]
[tex](y - 4) = \frac{3}{5} x + \frac{3}{5} \times 10[/tex]
[tex](y - 4) = \frac{3}{5} x + 6[/tex]
[tex]y = \frac{3}{5} x + 10[/tex]
Therefore the required equation is y = 3/5x + 10.
Hope it helps...
Please help me answer this question:
Answer:
Total area = 141,
the trapezoid = 117, the triangle=24
I’ll mark brainliest!!!! What is the length of BC in the right triangle below?
A. 63
В. 3
С. 21
D. -/63
E. 15
Е 225
Answer:
E. 15
Step-by-step explanation:
Use the Pythagorean theorem: a²+b²=c²
9²+ 12²= c² (This is the info we have so far.)81 + 144 = c² (Simplify. 9² = 81 ; 12² = 144)
225 = c² (Added 81 + 144 = 225)√225 = 15 (Square root of 225 is 15.)
Answer:
Step-by-step explanation:
15
. A triangle has one angle measuring 3x degrees. A second angle measures 2x+20 degrees and the third angle measures 4x-20 degrees. What is the value of x
Answer:
Step-by-step explanation:
You know that all of the angles of a triangle have to add to equal 180°.
Therefore, (3x)+(2x+20)+(4x-20)= 180°
If you combine like terms you get:
9x=180°
Divide both sides by 9 to get:
X=20
Sippose there is a 1.4 drop in temperature for every thousand feet that an airplane climbs into the sky if the temperature on the ground is 53.2 what will the temperature when the plane reaches a altitude of 8,000
Answer:
whats rhe question my g
Listed below are the heights from a sample of male students (in inches). 75 72 72 73 74 65 69 74 70 70 71 75 71 75 69 75 78 70. How many students are measured?
Answer:
18
Step-by-step explanation:
count
The number of students measured in this sample is 18.
The number of students measured is the number of heights that were acquired for the sample.
Looking at the question, the number of heights acquired were 18 which means that there were 18 students.
Knowing the number of students is important as it can help you calculate things such as mean:
Mean = Sum of heights / Number of students
= (75 + 72 + 72 + 73 + 74 + 65 + 69 + 74 + 70 + 70 + 71 + 75 + 71 + 75 + 69 + 75 + 78 + 70) / 18
= 72.11
In conclusion, the number of students measured is 18.
Find out more at https://brainly.com/question/20855935.
2. Find the distance between (-2,1) and (3,4).
Answer:
[tex]\sqrt{34}[/tex] or 5.83095
Step-by-step explanation:
Use the distance formula [tex]\sqrt{(x_{2}-x_{1} )^{2}+(y_{2}-y_{1} )^2 }[/tex]
Make sure to round the answer appropriately if not asked for in square root form!!
NEED HELP PLEASEE!!!!!
Answer:
x=1
Step-by-step explanation:
i believe its asking at which point is the output the same and when x=1 they both output 3
select the correct answer which equation has no solution
Answer:
C: 7(x+2)-3x = 2/3(6x+3)
Step-by-step explanation:
Graphing both lines shows that they are parallel to each other.
Answer:
There ya go love
Step-by-step explanation:
What is the answer to 6x + 7= -x + 70
Answer:
x = 9
Step-by-step explanation:
6x + 7 = -x + 70
~Subtract 7 to both sides
6x = -x + 63
~Add x to both sides
7x = 63
~Divide 7 to both sides
x = 9
Best of Luck!
f(x) = x^3 translate 3 units left translate 1 unit down
Answer:
the function would look like: f(x)=(x³+3)-1
the graph would literally look like the cubic parent graph, just shifted 3 left and 1 down
Simplify 3-8 divided by 3-2
Answer:
-5
Step-by-step explanation:
[tex] \frac{3 - 8}{3 - 2} [/tex]
[tex] \frac{ - 5}{1} [/tex]
[tex] - 5[/tex]
The biggest zucchini from Joe’s Farm is 2. 5/8 pounds,which is 1 1/12 pound more than the average weight from his farm.what is the average weight of zucchini’s from his farm?
Answer:
1 13/ 24
Step-by-step explanation:
2-1=1
5/8 - 1/12=26/48 =13/24