You can model the ellipse with the equation
(x/6)² + (y/5)² = 1
If you're comfortable with calculus, read on.
Let x = 6 cos(t ) and y = 5 sin(t ), with 0 ≤ t ≤ π/2. Then the curve C parameterized by (x(t), y(t)) traces out one quarter of the ellipse. The arc length of this curve is given by the integral,
[tex]\displaystyle\int_C\mathrm ds = \int_0^{\pi/2}\sqrt{x'(t)^2+y'(t)^2}\,\mathrm dt \\\\ = \int_0^{\pi/2}\sqrt{36\sin^2(t)+25\cos^2(t)}\,\mathrm dt \\\\ = \int_0^{\pi/2}\sqrt{25+11\sin^2(t)}\,\mathrm dt \\\\ = 5\int_0^{\pi/2}\sqrt{1+\frac{11}{25}\sin^2(t)}\,\mathrm dt[/tex]
Unfortunately, you cannot find the exact value of this integral. (Well, you can, but it involves introducing a special kind of function; I'll link it in a comment.)
But you can approximate it, and the integral above comes out to about 8.657.
I'm not sure if there's a simpler, purely geometric way to estimate the arc length. But since the semiaxes (5 ft and 6 ft) are fairly close, you could try a circle with a radius somewhere in between. The arc length would range between 7.854 ft and 9.425 ft. If the material isn't too expensive, you can always overshoot and trim off the excess or repurpose it.
Write an equation of a line perpendicular to y = -1/5x + 5
that passes through the point (-1,-3)
Select one:
a. y = 5x + 2
b.y = 2x - 5
c.y = -5x - 5
d. y = -5x + 2
Please help me out . Find x please
Answer:
on my screen I cant see anything sorry!
Step-by-step explanation:
There are 8.54 grams of sugar in 7 servings of grapes. How many grams of sugar are in a single serving of grapes?
Answer:
1.22
Step-by-step explanation:
divide 8.54 by 7 to get one serving
The perimeter of a rectangle is 16 inches. The equation that represents the perimeter of the rectangle is , where l represents the length of the rectangle and w represents the width of the rectangle. Which value is possible for the length of the rectangle? 7 in. 8 in. 9 in. q 10 in.
Answer:
B) 8in
Step-by-step explanation:
Two traffic lights both turn green at 1:20 pm. One light is on a 72-second 0cycle from green back to green while the other light is on a 1-minute cycle. After how many minutes will they again turn green together?
Answer:
32
Step-by-step explanation:
Answer:
6 minutes
Step-by-step explanation:
1 minute = 60 seconds
LCM of 60 and 72 = 360
360 seconds = 6 minutes
The ratio between the distances of two cities from a third city is 7:8. If the total distance is 150 km, what are the distances of the two cities from the third one?
Answer:
70km and 80km
The option you chose is correct
Answer:
70 km and 80 km.
First city:
[tex]{ \tt{ = \frac{7}{15} \times 150 }} \\ = 70 \: km[/tex]
Second city:
[tex]{ \tt{ = \frac{8}{15} \times 150}} \\ = 80 \: km[/tex]
Solve the system of equations below by graphing both equations with a
pencil and paper. What is the solution?
y=-x-1
y= x+3
A. (0,3)
B. (-2,1)
C. (-1,2)
O D. (0, -1)
The table below shows some inputs and outputs of the invertible function f with domain all real numbers.
PLEASE HELP ME!!!!! ( photo given )
Answer:
-6, 0
Step-by-step explanation:
since the first question is a inverse function, the -15 isn't an x value anymore so it is a y.
the second question is the same thing for the 4 because it is an inverse function. so that would be -11, and the function of 9 you would look at the x value of 9 and find the corresponding y, which 11. so -11+11 =0
SOMEONE HELP ME PLEASE
Decide if the following scenario involves a permutation or combination. Then find the number of possibilities.
You are setting the combination on a five-digit lock. You want to use the numbers 12345 but you don't care what order they are in.
Answer:
It's a combination, BUT...
Step-by-step explanation:
Definition: A combination is a grouping of outcomes in which the order does not matter. That's the difference between combination and permutation.
Combination Formula: nCr = (n!)/[r!(n-r)!)] where n stands for number of things and r the pair chosen
Applied to this case: We have n=5 (12345) and r=5 for the 5-digit lock combination.
5C5 = (5!)/[5!(5-5)] = 1
But!! As you can see, we cannot have 1 possible combinations so.. We have to assume that this is a permutation!!! Conceptually, this looks pretty much like a combination, but being the same range as number of items, we conclude that it's a permutation.
Permutation Formula: nPr = (n!)/(n-r)!
nPr = (5!)/(5-5)! = 120
Well, this looks way more accurate now, right?
Final Answer: The scenario involves a permutation, and there's 120 possible combinations of those 5 numbers in a 5-digit lock.
Please help urgent!!! Find the value of x in the triangle shown below!
Answer:
Step-by-step explanation:
so we know a few things about t his triangle, it's a special one :P , it's called isosceles because two of the legs are the same length, which also mean that the angle x is the same at the other unknown angle sooo there are 2 x's if that makes sense? and then we can solve this , b/c we also know that the interior angles of a triangle add up to 180°
180 = 32 + 2x
148 = 2x
74 =x
∠x = 74°
mathematics question
Answer:
it's option B the second one
Solve the following quadratic function
by utilizing the square root method.
y = 100 – x2
Answer:
x = ± 10
Step-by-step explanation:
To solve the equation let y = 0 , that is
0 = 100 - x²( add x² to both sides )
x² = 100 (I take the square root of both sides )
x = ± [tex]\sqrt{100}[/tex] = ± 10
Then solution is x = - 10, x = 10
Answer:
10
Step-by-step explanation:
the guy on top put -10 he's right but it's just 10
Simplify as far as possible;
x²+ 3x²-4x²+5x
Answer:
5x
Step-by-step explanation:
[tex] {x}^{2} + {3x}^{2} - {4x}^{2} + 5x \\= 4 {x}^{2} - 4 {x}^{2} + 5x \\ = 5x[/tex]
a bag contains 10 white balls and 14 red balls.a ball is taken out of the bag,what is the probability that it is a red ball
Answer:
7/12
Step-by-step explanation:
Total = 10W+14R
probability of red = R/total
10+14 = 24 so total = 24
R = 14
14/24
reduce (divide by two on the top and bottom)
14/2
-------
24/2
= 7/12
Guys Help me
Does (4, 7) make the equation y = 2x + 7 true?
Answer:
false
Step-by-step explanation:
x=4andy=7
2×4+7 isnot equal to 7
Answer:
Tue equation is
y=2x+7
So, the answer is
(2,7)
And (4,7) is wrong
!!Plz urgent help!!
this triangular prism can contain that holds beads that are spherical and each 0.525 cm. How many
beads can fit inside this container?
Will mark brainliest
Answer:
890 beads can be fitted in the triangular prism.
Step-by-step explanation:
If we can fill the spherical beads completely in the triangular prism,
Volume of the triangular prism = Volume of the spherical beads
Volume of triangular prism = Area of the triangular base × Height
From the picture attached,
Area of the triangular base = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(AB)(BC)[/tex]
By applying Pythagoras theorem in the given triangle,
AC² = AB² + BC²
(13)² = 5² + BC²
169 = 25 + BC²
BC² = 144
BC = 12
Area of the triangular base = [tex]\frac{1}{2}(5)(12)[/tex]
= 30 cm²
Height of the triangular prism = 18 cm
Volume of the triangular prism = 30 × 18
= 540 cm³
Volume of one spherical bead = [tex]\frac{4}{3}\pi r^{3}[/tex]
= [tex]\frac{4}{3}\pi (0.525)^{3}[/tex]
= 0.606 cm³
Let there are 'n' beads in the triangular prism,
Volume of 'n' beads = Volume of the prism
540 = 0.606n
n = 890.90
n ≈ 890
Therefore, 890 beads can be fitted in the triangular prism.
yes or no? please help
Answer:
yes
Step-by-step explanation:
....
James brought a dress & t-shirt for $85 and it is 5 times as much as t-shirt how much did James pay for the t-shirt.
Answer:
$17
Step-by-step explanation:
You reverse the operation, and you do 85 divided by 5, which is 17. Have an amazing day!!
the verticies of the triangle OAB are the origin O, A(-15,0) and B(0,8)
What is the relationship between G and the triangle OAB
G(-7.5,4)
Answer:
G is the midpoint of the side [tex]\overline {AB}[/tex] of triangle ΔOAB
Step-by-step explanation:
The vertices of the triangle ΔOAB are A(-15, 0), B(0, 8), and C(0, 0)
The coordinates of the point G = (-7.5, 4)
The length from the point A to the point G, [tex]\overline {AG}[/tex] is given as follows;
[tex]\overline {AG} =\sqrt{(-7.5 - (-15))^2 + (4 - 0)^2} = \sqrt{7.5^2 + 4^2} = 8.5[/tex]
The length from the point A to the point B, [tex]\overline {AB}[/tex] is given as follows;
[tex]\overline {AB} =\sqrt{(-15 - 0)^2 + (8 - 0)^2} = \sqrt{15^2 + 8^2} = 17[/tex]
Therefore, the point G is the half way mark of [tex]\overline {AB}[/tex] = The midpoint of the side [tex]\overline {AB}[/tex]
What is the value of f ^-1 (0)? ( photo given )
PLEASE HELP ME, I would greatly appreciate it !!!
Answer:
[tex] {f}^{ - 1}(0) = 6[/tex]
Step-by-step explanation:
When trying to solve for inverses, we are given a y value in place of an x value. Thus we are solving for the x value which the given y value corresponds to.
4(x-3)+5x-x^2 for x=3
Answer:
6
Step-by-step explanation
Answer:
6
Step-by-step explanation:
plug in the 3
4(3-3)+5(3)-3^2
4(0)+15-9
0+15-9
15-9
6
How many different numbers are possible?
A personal identification number consists of 3 letters followed by 3 digits. The letters X, Y, and Z are not used and the last digit cannot be 0 or 9.
Each of the first 3 letters can be chosen from the 23 letters, {A, B, C, …, U, V, W}, so there are 23³ possible choices.
The first 2 digits can be any number from {0, 1, 2, …, 9}, so there are 10² choices.
The last digit cannot be 0 or 9, so you can select from {1, 2, 3, …, 8} which gives 8 choices.
Then the total number of PINs that you can make is
23³ × 10² × 8 = 9,733,600
PLEASE HELPP URGENT
20 points!!!
Please help ASAP!!!! What is the length of BC?
Answer:
x=24
Step-by-step explanation:
Answer:
BC = 24
Step-by-step explanation:
Since ∠ B and ∠ C are congruent the the triangle is isosceles with
AC = AB , that is
3x - 15 = x + 33 ( subtract x from both sides )
2x - 15 = 33 ( add 15 to both sides )
2x = 48 ( divide both sides by 2 )
x = 24
Then
BC = x = 24
How do I find the low value of a box plot
The far left of the chart is the minimum(low) value of the box plot.
Answered by Gauthmath must click thanks and mark brainliest
please help, it is associated with angles. thank u ;)
Answer:
angle c is 63
Step-by-step explanation:
Angles in a triangle add up to 180 therefore
70+47+x=180
x=180-117
=63°
I hope this helps
Mr. Matthew was testing the only popularity of us custom-made belts and wallets that are marked differently some items were sold prior to the online launch date
Complete question is;
Mr. Matthew is testing the online popularity of his custom made belts and wallets that were marketed differently. Some items were sold prior to the online launch date.
The equation below represents the number of belts sold, s, x days after its online launch. S = 3^(x)
The equation below represents the number of wallets sold, s, x days after its online launch. S = 4x + 15
Using graphing technology, complete the statements. After ___ days, the total number of belts sold will be the same as the total number of wallets sold. The number of belts and the number of wallets Mr. Matthew sold after this many days is ___
Answer:
Number of days = 3 days
Total belts and wallets after 3 days = 54
Step-by-step explanation:
We are told that the number of belts sold, s, x days after its online launch. S = 3^(x)
Also, we are told that the number of wallets sold, s, x days after its online launch. S = 4x + 15
Now, we want to find the Number of days that total number of belts sold will be the same as the total number of wallets sold using graphing technology.
The number of days will simply be the value of x where the two graphs meet.
I have drawn the graph of both equations.
From the attached graph, we can see that the x-value at where the both graph lines meet is approximately 3. I didn't take the negative solution because number of days cannot be negative.
Thus, x = 3
Putting x = 3 in;
S = 3^(x)
S = 3^(3)
S = 27
Similarly, Putting x = 3 in;
S = 4x + 15
We have;
S = 4(3) + 15
S = 12 + 15
S = 27
Thus,total number of belts and wallets sold after 3 days = 27 + 27 = 54
A dealer spent a total amount of $5250 for importing some cosmetics. If the total cost of the cosmetics was $5000 without tax, what was the percentage of import tax?
Answer:
5%
Step-by-step explanation:
First, find the amount of tax:
5250 - 5000
= 250
Divide this by the original price of $5000 to find the percent of import tax:
250/5000
= 0.05
So, the percent of import tax is 5%
For each graph below, state whether it represents a function.
Graph exists as an illustration of any object or a physical format by dots, lines, etc.
What is graph function?The graph of a function f exists the set of all points in the plane of the form (x, f(x)). We could also describe the graph of f to be the graph of the equation y = f(x). So, the graph of a function exists in a particular case of the graph of an equation.
A function is defined as a connection between a set of inputs containing one output each. In simple words, a function exists as an association between inputs where each input is connected to exactly one output. Every function includes a domain and codomain or range. A function exists generally represented by f(x) where x is the input.
From the given figure,
Graph 1 exists a function.
Graph 2 exists a function.
Graph 3 doesn't exist as a function.
Graph 4 exists a function.
Graph 5 doesn't exist as a function.
Graph 6 doesn't exist as a function.
Hence, Graph exists as a representative of any object or a physical design by dots, lines, etc.
To learn more about graph refer to:
https://brainly.com/question/11803331
#SPJ2
What do I need to do to be able to solve this problem?
9514 1404 393
Answer:
(x, y, z) = (5, 11, 6)
Step-by-step explanation:
To solve this problem, you need to understand "row operations". The ones we're concerned with are multiplying a row by a scalar, and adding rows together.
You also need to understand what the solution looks like, and the usual way that is achieved. The solution will have the 3×3 matrix left of the vertical line be a diagonal of 1s (the identity matrix). Then the numbers to the right of the vertical line represent the solution.
__
In the following, we will use the notation [a]+b[c]⇒[d] to mean that row 'a' is added to the product of row 'c' and the scalar 'b' and that sum replaces row [d]. Multiplying a row by a scalar multiplies each element in the row by that scalar.
The first several operations look like this. Notice we have made the upper left 2×2 matrix an identity matrix. Steps will continue to take care of the 3rd column.
[tex]\left[\begin{array}{ccc|c}1&1&1&22\\6&1&8&89\\-6&4&4&38\end{array}\right] \qquad\text{given}\\\\\left[\begin{array}{ccc|c}1&1&1&22\\0&-5&2&-43\\0&5&12&127\end{array}\right]\qquad\text{[2]+[3]$\rightarrow$[3];\ 6[1]+[2]$\rightarrow$[2]}\\\\\left[\begin{array}{ccc|c}1&1&1&22\\0&1&-0.4&8.6\\0&0&14&84\end{array}\right]\qquad\text{[2]+[3]$\rightarrow$[3];\ $-\frac{1}{5}$[2]$\rightarrow$[2]}\\\\\left[\begin{array}{ccc|c}1&0&1.4&13.4\\0&1&-0.4&8.6\\0&0&14&84\end{array}\right]\qquad\text{[1]-[2]$\rightarrow$[1]}[/tex]
Now, we normalize the third column.
[tex]\left[\begin{array}{ccc|c}1&0&1.4&13.4\\0&1&-0.4&8.6\\0&0&1&6\end{array}\right] \qquad\text{$\frac{1}{14}$[3]$\rightarrow$[3]}\\\\\left[\begin{array}{ccc|c}1&0&0&5\\0&1&0&11\\0&0&1&6\end{array}\right] \qquad\text{$-\frac{7}{5}$[3]+1$\rightarrow$[1];\ $\frac{2}{5}$[3]+[2]$\rightarrow$[2]}[/tex]
This is the target of our row operations. It tells us the solution to the system of equations is ...
(x, y, z) = (5, 11, 6)
_____
A number of online calculators and phone or tablet apps are available for putting a coefficient matrix into this "reduced row-echelon form." Many graphing calculators will do this, too.
In the end, this is not terribly different from ad hoc solution using "elimination" methods. That is precisely what we did when we created the zeros in the first two columns of row 3.
