Answer:
[tex]b = \sqrt{\frac{C^{2} }{2(\pi )^{2} } - a^{2}}[/tex]
Step-by-step explanation:
Given - The circumference of the ellipse approximated by [tex]C = 2\pi \sqrt{\frac{a^{2} + b^{2} }{2} }[/tex]where 2a and 2b are the lengths of 2 the axes of the ellipse.
To find - Which equation is the result of solving the formula of the circumference for b ?
Solution -
[tex]C = 2\pi \sqrt{\frac{a^{2} + b^{2} }{2} }\\\frac{C}{2\pi } = \sqrt{\frac{a^{2} + b^{2} }{2} }[/tex]
Squaring Both sides, we get
[tex][\frac{C}{2\pi }]^{2} = [\sqrt{\frac{a^{2} + b^{2} }{2} }]^{2} \\\frac{C^{2} }{(2\pi)^{2} } = {\frac{a^{2} + b^{2} }{2} }\\2\frac{C^{2} }{4(\pi)^{2} } = {{a^{2} + b^{2} }[/tex]
[tex]\frac{C^{2} }{2(\pi )^{2} } = a^{2} + b^{2} \\\frac{C^{2} }{2(\pi )^{2} } - a^{2} = b^{2} \\\sqrt{\frac{C^{2} }{2(\pi )^{2} } - a^{2}} = b[/tex]
∴ we get
[tex]b = \sqrt{\frac{C^{2} }{2(\pi )^{2} } - a^{2}}[/tex]
Chloe divides an hour of revision up between maths and english in the ratio 3:2. how much does she spend revising maths?
Answer:
Step-by-step explanation:
let chloe revise maths for x minutes
3/2=x/30
do cross multiplication
2x=30*3
x=90/2
x=45
therefore chloe takes 45 minute to revise maths.
Which inequality is true when s = -4 and t = 2?
1. s > t
2. s < -t
3. -s < t
4. -s < -t
What is the surface area of the ice cream
cone? (Hint: The top of the cone is open and
not included in the surface area.)
mm
Cone Surface Area =
Answer:
[tex]13194.7\ mm^2[/tex]
Step-by-step explanation:
The total surface area of a cone is given by:
Surface area = [tex]\pi r(r+\sqrt{h^2+r^2} )[/tex]
where r is the radius of the cone, h is the height of the cone, l is the length of the cone = [tex]\sqrt{h^2+r^2}[/tex]
Given that h = 136 mm, r = 60 mm /2 = 30 mm, l = 140 mm. Also the top of the cone is not included in the surface area, hence the surface area becomes:
[tex]Surface \ area=\pi r(\sqrt{h^2+r^2} )=\pi rl\\\\Surface \ area=\pi (30\ mm)(140\ mm)=13194.7\ mm^2[/tex]
What is the volume of the composite figure? Explain your work. A complete answer should include how you broke up the figure, which numbers you multiplied to find the volume. You may want to use the formula for volume to find the solution.
Answer:
[tex]15,000\:\mathrm{mm^3}[/tex]
Step-by-step explanation:
The composite figure consists of a square prism and a trapezoidal prism. By adding the volume of each, we obtain the volume of the composite figure.
The volume of the square prism is given by [tex]V=s^2\cdot h[/tex], where [tex]s[/tex] is the base length and [tex]h[/tex] is the height. Substituting given values, we have: [tex]V=14^2\cdot 30=196\cdot 30=5,880\:\mathrm{mm^3}[/tex]
The volume of a trapezoidal prism is given by [tex]V=\frac{b_1+b_2}{2}\cdot l\cdot h[/tex], where [tex]b_1[/tex] and [tex]b_2[/tex] are bases of the trapezoid, [tex]l[/tex] is the length of the height of the trapezoid and [tex]h[/tex] is the height. This may look very confusing, but to break it down, we're finding the area of the trapezoid (base) and multiplying it by the height. The area of a trapezoid is given by the average of the bases ([tex]\frac{b_1+b_2}{2}[/tex]) multiplied by the trapezoid's height ([tex]l[/tex]).
Substituting given values, we get:
[tex]V=\frac{14+24}{2}\cdot (30-14)\cdot 30,\\V=19\cdot 16\cdot 30=9,120\:\mathrm{mm^3}}[/tex]
Therefore, the total volume of the composite figure is [tex]5,880+9,120=\boxed{15,000\:\mathrm{mm^3}}[/tex] (ah, perfect)
Alternatively, we can break the figure into a larger square prism and a triangular prism to verify the same answer:
[tex]V=30^2\cdot 14+\frac{1}{2}\cdot10\cdot 16\cdot 30=\boxed{15,000\:\mathrm{mm^3}}\checkmark[/tex]
A) Angela has more than 8 cats in her studio apartment. (Too bad she's allergic.) Write an inequality that represents the number of cats in Angela's apartment.
Answer:
c > 8
where c = cats
Step-by-step explanation:
Note that
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
What is the value of X?
Answer:
x=20
Step-by-step explanation:
First, find LJ
Angle L = 60 (180 - 30 - 90)
The cosine of an angle is equal to the ratio of the adjacent side to the hypotenuse.
cos(L)=adj/hyp
cos(60)=LJ/40√2
LJ = cos(60)*40√2
LJ = 20√2
Now you can use LJ to find x. You also know the value of each angle, 45
x=20√2⋅cos(45)
x=20
find the sum of the first 10 terms 0.5,0.9,1.3,1.7,..
Answer:
0.5, 0.9, 1.3, 1.7, 2.1, 2.5, 2.9, 3.3, 3.7, 4.1
Now you can add them all
which is equal to 23
Step-by-step explanation:
who knows how to solve this problem
a = 3√3
a = 3 × 1.732
a = 5.196
a = 5.2 inches
Simplify:
2
(
5
+
3
x
)
+
(
x
+
10
)
2(5+3x)+(x+10)
Answer:
7x + 20
Step-by-step explanation:
I dont have a explanation, but this could be right. :)
What is the solution of-+-<?
1 1 1
X35
Answer:
A. [tex]-\frac{15}{2} < x< 0[/tex]
Step-by-step explanation:
Multiply to remove the fraction, then set equal to 0 and solve.
Goro just bought a new television for $610.00. He made a down payment of $64.00 and will pay monthly payments of $26.00 until it is paid off. How many months will Goro be paying?
Answer:
Step-by-step explanation:
Let the total Cost = y
Let the monthly payment number = x
Let the y intercept = 64
y = 26x + 64
610 = 26x + 64 Subtract 64 from each side
-64 - 64
546 = 26x
26x = 546 Divide by 26
x = 546/26
x = 21 months
A family on vacation records the time in hours) and the distance (in miles) that they travel. The data are shown in the scatter plot below.
Distance (miles)
YA
450
400
350
300
250
200
L
150
100
50
0
0 1 2 3 4 5 6 7 8 9
Time (hours)
Based on the scatter plot, the family travels miles in the first 3.5 hours.
If you answer with a link I will report you and get your account blocked
Answer:
In the first 3.5 hours, the family travelled 175 miles.
Step-by-step explanation:
We have the table:
time (hours) distance ( miles)
0 0
1 50
2 100
3 150
4 200
5 250
6 300
7 350
8 400
9 450
This seems like a linear relationship, let's write the general line:
y = a*x + b
That represents this situation, y is the distance in miles and x is the time in hours.
In the line equation, a represents the slope and b the y-intercept.
And if the line passes through the points (x₁, y₁) and (x₂, y₂), then the slope of the line is:
a = (y₂ - y₁)/(x₂ - x₁)
In this case we have a lot of points for the line, we can use any pair we want (we actually should use a few different pairs to see that the slope is always the same)
So if we use the first two (0, 0) and (1, 50)
the slope is:
a = (50 - 0)/(1 - 0) = 50
Now, if we use the third and fifth points (4, 200) and (5, 250) now the slope is:
a = (250 - 200)/(5 - 4) = 50/1 = 50
So we can conclude that the slope of the equation is a = 50
Then the equation is something like:
y = 50*x + b
To find the value of b, we can use any of the points of the line, for example (0, 0)
This means that when x = 0, y also must be 0, then:
0 = 50*0 + b
0 = b
Then the equation is:
y = 50*x
Now, to answer how many miles the family travelled in the first 3.5 hours, we just need to replace x by 3.5 in the equation:
y = 50*3.5 = 175
In the first 3.5 hours, the family travelled 175 miles.
mm mmm m m m n b gg mm m m m m m
Answer:
2x-2+2x-2+x+x=50
6x-4=50
6x=54
x=9
hope this helps
have a good day :)
Step-by-step explanation:
Austin correctly answered 92% of the questions on a geography quiz.
Liz answered 47 of the 50 questions correctly.
Use the drop-down menus to explain who earned the higher score.
Answer:
Liz scored more because she would score 94%, while Austin only scored 92%
What is the value of x in the equation -6 +x= -1?
0-5
0-7
07
05
Help please
Answer:
0-5
Step-by-step explanation:
ok y’all i need to know something.
today is the last day of school and my grades are all a’s and b’s but i have a few projects i didn’t do. will i still pass the school year?
Answer:
you will still pass
Step-by-step explanation:
your grades might drop a little
A box contains 12 balls of which 5 are red, and 7 are blue. If 4 balls are drawn from the box, in how many ways can this be done if 1 is red and 3 are blue?
Answer:
175 ways
Step-by-step explanation:
5 balls are red, and 7 balls are blue making a total of 12 balls.
4 balls are drawn from the box,
1 ball is red and 3 balls are blue out of the 4 drawn from the box.
We have to choose 1 ball from 5 red balls and 3 blue balls from 7 blue balls.
Since the order is not essential we use combinations to find out
5C1 * 7C3= 5*35 = 175 ways
please help!!!! due soon!!
It takes 0.750.75 cups of sugar to make a batch of lemon cookies. I have 5.55.5 cups of sugar. How many batches can I make?
84 is What percent of 70?
Answer:
120%
Step-by-step explanation:
It just is
If u know pls help me I have no clue
Answer:
7 ft3
Step-by-step explanation:
A teacher uses a stem-and-leaf plot to record the typing speeds of her students, in words per minute.
Drag values to the table to show the median and mode of the data she recorde
3 1/3 divided by 20 in simplest form
Answer:
1/6
Step-by-step explanation:
Hope it helps plz give brainliest! :D
[tex]3\frac{1}{3}[/tex] divided by 20 in simplest form we get 3/2.
Here we have to divide,
[tex]3\frac{1}{3}[/tex] by 20
Now the given mixed fraction,
[tex]3\frac{1}{3}[/tex] = 10/3
Now we have to evaluate,
10/3 ÷ 20
Since we know that,
To divide two fractions,
Follow the procedures below when splitting two mixed fractions. Transform the mixed fraction into the incorrect fraction. Now multiply the first and second fractions by the reciprocal of the second fraction (i.e., divisor).
Therefore,
10/3 x 1/20 = 3/2
Hence,
[tex]3\frac{1}{3}[/tex] by 20 = 3/2
To learn more about division visit:
https://brainly.com/question/2273245
#SPJ6
Carter wants to cover his bedroom window with a piece of plywood to prepare for an upcoming storm. The window measures 4 1/2 feet tall and 2 1/4 feet wide. Find the area of the window.
fast please
Answer:
Step-by-step explanation:
Basically you turn 1/2 into fourths, 1/2 = 2/4
After that you would multiply 4 2/4 x 2 1/4
Then you get 10.125 turned into a fraction is 81/8
The Smith family was one of the first to come to the U.S. They had 8 children. Assuming that the probability of a child being a girl is .5, find the probability that the Smith family had: (do not round your answers)
Answer: Hello some part of your question is missing below is the missing part
Missing question: Find the probability that the Smith family had at least 6 girls?
answer : 0.1406
Step-by-step explanation:
Number of children = 8
probability of a child being a girl ( success ) = 0.5 (
P( boy ) ( q ) = 1 - 0.5 = 0.5
P( at least 6 girls ) = p(k = 6 ) + p(k = 7 )
= 0.109375 + 0.03125 ≈ 0.1406
( using Binomial probability Calculator )
Can someone please check if this is correct?
Answer:
Just two corrections! See attached image.
Step-by-step explanation:
The product of 8 and b taken from 10 means begin with 10 and subtract 8b from it.
8 times the difference of 10 and b means find 10 - b first, then multiply by 8.
Find the shaded area of the circle below.
Answer:
area of the circle,
radius=10m
diameter=20m
πr²
3.14×100
314m²
area of the triangle=1/2×20×10
=100
area of the shaded area=314-100=214 m²
the answer is option H
You are a manager in one of the branches of a restaurant. The area manager assigned
you to analyze the statistical data of the ages of the customers who eat in your
restaurant. From the survey forms, the following are the summary of their evaluations:
Age - - - - - - - No. of Customers
16–20 - - - - - -32
21–25 - - - - - -40
26–30 - - - - - -15
31–35 - - - - - - 29
36–40 - - - - - - -11
Using the given data, determine how spread out the ages of the customers are using
measures of variability. Find out what ages fall within one standard deviation from the
mean. Knowing this, what range of ages or what age group should the restaurant give
more focus on, and what products do you think should the restaurant come up with to
generate higher sales? Submit a typewritten report detailing your answers, solutions, and
explanations to these questions.
Answer:
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A basket holds a set of balls. Each ball is red, green, or blue. How many balls must there be in the basket in order to guarantee that there are at least 5 balls of the same color
The rectangle is rotated 180 degrees about the orgin. What are the new coordinates of point D?
Answer:2,2
Step-by-step explanation:
Rotate and flip
Plz give me a branliest