The equation of the ellipsoid is[tex]\frac{x^{2} }{a^{2} } + \frac{y^{2} }{b^{2} } +\frac{z^{2} }{c^{2} } =1[/tex]
The equation of an ellipsoid is represented as:
[tex]\frac{x^{2} }{a^{2} } +\frac{y^{2} }{b^{2} } +\frac{z^{2} }{c^{2} } =1[/tex]
Given that the ellipsoid passes through the points (±6,0,0),(0,±7,0) and (0,0,±5)
It means that:
(±a,0,0) = (±6,0,0)
(0,±b,0) = (0,±7,0)
(0,0,±c) = (0,0,±5)
By comparison, we have:
±a=±5
±b=±6
±c=±7
So, the equation of the ellipsoid becomes:
[tex]\frac{x^{2} }{a^{2} } +\frac{y^{2} }{b^{2} } +\frac{z^{2} }{c^{2} } =1[/tex]
By substituting the values, the equation of the ellipsoid becomes is
[tex]\frac{x^{2} }{36}+\frac{y^{2} }{49} +\frac{z^{2} }{25} =1[/tex]
.An ellipse is the set of all points on a plane whose distance from two fixed points F and G add up to a constant. In an ellipse, there are two radius measures, one horizontally along the x-axis, the other vertically along the y-axis.For a circle both these have the same value.
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Use polynomial identities to factor 1 – 125n3. Choose the correct factors.
Answer:
(1-5n)(25m^2+5n+1
Step-by-step explanation:
How do you find the lower quartile range?
Answer:
q1= n/4
is the formulato fine lower quartile
Hello can you help with this please
Answer:
133
Step-by-step explanation:
All 3 angles of a triangle must equal 180, so let's make these equal to that
[tex](x + 13) + (10x + 13) + (2x - 2) = 180[/tex]
Now let's combine the X's and the regular numbers together.
[tex]13x + 24 = 180[/tex]
Next, subtract 24 to get all the numbers on the right side.
[tex]13x = 156[/tex]
And lastly, we divide by 13 to get X alone
[tex]x = 12[/tex]
Since Q is (10x + 13), we plug that 12 in
[tex]10(12) + 13 = 133[/tex]
The median and the height of an isosceles trapezoid are equal in length. One diagonal of the trapezoid has length $12$. What is the area of the trapezoid?
The area of the isosceles trapezoid is 72 square units.
What is isosceles trapezoid ?A quadrilateral having at least one set of parallel sides and equal length non-parallel sides is called an isosceles trapezium. To put it another way, it is a trapezium whose two non-parallel sides are congruent. The trapezoid's parallel sides are referred to as the bases, and the segments that link the bases are referred to as the legs. The angle between the bases of an isosceles trapezoid determines its height.
Given:
[tex]\[d = 12 \quad \text{(length of one diagonal)}\][/tex]
Let;
[tex]\[h = \text{height of the trapezoid}\][/tex]
[tex]\[a = \text{smaller base of the trapezoid}\][/tex]
[tex]\[b = \text{larger base of the trapezoid}\][/tex]
Using the given information that the height and median are equal, we have:
[tex]Median(m)=\frac{1}{2} {(a+b)}\\\\Height(h)=\frac{1}{2} {(a+b)}\\\\2h=a+b ........(1)[/tex]
[tex]\[\text{Area} = \frac{1}{2} \cdot (a + b) \cdot h\][/tex]
[tex]\[\text{Area} = m \cdot h\] = h^2 ............(2)[/tex] (∵ [tex]Median(m)=\frac{1}{2} {(a+b)}[/tex] and m=h)
Now,
[tex]\[ d = \sqrt{h^2 + \frac{(a+b)^2}{4}} \][/tex] for isosceles trapezoid,
[tex]\[ 12^2 = h^2 + \frac{(a+b)^2}{4}}[/tex]
[tex]\[ 12^2 = h^2 + \frac{(2h)^2}{4}}[/tex] (∵from eq (1))
[tex]\[ 12^2 = h^2 + {(h)^2}}\\ \\144= 2h^2\\\\h^2=72 ..........(2)[/tex]
Lastly, we may change the values of "a," "b," and "h" in the following formula to find the area as;
[tex]\[\text{Area} = \frac{1}{2} \cdot (a + b) \cdot h\][/tex]
[tex]\[\text{Area} = \frac{1}{2} \cdot (2h) \cdot h\][/tex]
[tex]\[\text{Area} = h \cdot h\] = h^2 = 72 sq units[/tex]
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Pablo received $200 dollars for his high school graduation. He wants to save his money to buy a new laptop that cost $700 for when he attends
college. Each month, he adds $125 to his laptop savings. Write an equation in slope intercept form for m, the number of months that it will take Pablo to save $700.
Let's call the number of months that it takes Pablo to save $700 as "m". The amount of money Pablo has saved after "m" months can be represented by the equation:
y = 200 + 125m
where y is the total amount of money saved after "m" months.
To find the number of months it will take Pablo to save $700, we can set y equal to $700 and solve for m:
700 = 200 + 125m
500 = 125m
m = 500 / 125 = 4
So it will take Pablo 4 months to save $700.
The equation in slope-intercept form is:
y = 125m + 200
where m is the number of months and y is the total amount of money saved. The slope of the line is 125, which represents the amount added to the savings each month, and the y-intercept is 200, which represents the initial amount of money Pablo received for graduation.
If the length of minor arc ab is 12 feet and the radius of the circle is 10 feet, find the measure of the central angle subtended by minor arc ab, to the nearest degree.
The measure of the central angle subtended by minor arc ab, to the nearest degree is 67.
A minor arc is a part of a circle that is created by two points on the circumference of the circle.
To find the measure of the central angle subtended by the minor arc ab, we need to use the formula for the circumference of a circle, which is C = 2πr. The length of the minor arc ab is 12 feet, which is a part of the circumference of the circle. So, we can write an equation:
12 = C * (arc ab / C)
where C is the circumference of the circle and arc ab is the length of minor arc ab. We know that the radius of the circle is 10 feet, so we can find the circumference of the circle using the formula for circumference:
C = 2πr = 2π * 10 = 20π
Substituting the value of C in the equation above, we get:
12 = 20π * (arc ab / 20π)
Dividing both sides of the equation by 20π, we get:
12 / 20π = (arc ab / 20π)
We can now find the central angle subtended by the minor arc ab by using the formula:
Central angle = 2 * arctan(arc ab / 2r)
Substituting the values, we get:
Central angle = 2 * arctan(12 / (2 * 10)) = 2 * arctan(0.6)
Using a calculator, we can find that the value of arctan(0.6) is about 33.7 degrees. Hence, the central angle subtended by minor arc ab is:
Central angle = 2 * 33.7 = 67.4 degrees
Rounding off to the nearest degree, we get that the central angle subtended by minor arc ab is 67 degrees.
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Is the union of countably infinite sets countable?
The answer is that it depends on the specific countable sets being considered and how they are being combined.
The union of countably infinite sets can be countable, as in the case of the union of all positive integers and all negative integers, which is also countable.
However, the union of countably infinite sets can also be uncountable. For example, consider the union of all the intervals [n, n+1) for n = 1, 2, 3, .... Each of these intervals is countable (since it contains all the real numbers between two integers, which is a countable set), but the union of these intervals is the uncountable set of all real numbers greater than or equal to 1. Therefore, the union of these countably infinite sets is uncountable.
So the answer is that it depends on the specific countable sets being considered and how they are being combined.
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PLEASE ANSWER IMMEDITLY I NEED TO FILL OUT MY TEST STAT !!!!!!! WILL GIVE 100 POINTS!
Cujo is making pies. Each pie must contain 14 strawberries and 22 slices of banana.
Drag numbers to complete the table to show how many of each fruit are in each pie. Numbers may be used once, more than once, or not at all.
options to choose from ( 4 drop down)
18 22 56 88 66 32 42 70
Number of Pies Strawberries Slices of Banana
1 14 _____
__ 44
2 28 ____
3 56 ____
4 _____ 110
5
Answer: Can you help me with the questions that I asked today.
Step-by-step explanation: Please.
Answer:
(To shawnrg
ask me the questions. I'm not promising I'll be able to help
Step-by-step explanation:
Compare 5/8 and 1/3 please hurry!
Answer:5/8
Step-by-step explanation:
Lowest common denominator is 24
15/24 > 8/24
5/8>1/3
Please answer with the work shown
The area and the perimeter of the various given figures above are listed below:
1.) area=70 cm²
perimeter = 29cm
2. area= 80mm²
perimeter = 36mm
3.) area=108m²
perimeter = 42m
4.) area=72cm²
perimeter = 34cm
How to calculate the area and perimeter of the given figures above?For figure 1;
The area of the given figure = length×width.
Where;
Length = 7cm, width = 10
area = 7×10 = 70 cm²
The perimeter = summation of the whole sides.
= 10+7+5+4+3
= 29cm
For figure 2;
The area of the given figure = length×width.
Where;
Length = 8 mm; width = 10mm
area = 8×10 = 80mm²
The perimeter = 6+8+6+10+(8-6)+(10-6)
= 6+8+6+10+2+4
= 36mm
For figure 3;
The area of the given figure = length×width.
Where;
Length= 6+3 = 9m
width ,= 8+5 = 12m
area = 9×12 = 108m²
The perimeter: 2( 9+12) = 42m
For figure 4;
The area of the given figure = length×width.
Where;
Length= 8cm
width = 4+5 = 9cm
area = 8×9 = 72cm²
The perimeter = 6+4+5+8+(5+4)+(8-6)
= 6+4+5+8+9+2
= 34cm.
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Round 1.587 to the hundredths
place.
Answer:
1.59
Step-by-step explanation:
Rounding to the hundredths has the same meaning as rounding to the second decimal place. Since the third decimal place is 7, we have to round up the decimal. Therefore the rounded value would be 1.59
I hope this makes sense to you. I am generally good with following up with additional questions. Feel free to leave a comment if you have any questions or you can also message me as well!
HELP ! A phone company offers two monthly plans. Plan A costs $30 plus an additional $0.03 for each minute of calls. Plan B has no initial fee but costs $0.18 for each minute of calls. What is the cost when the two plans cost the same for a set number of minutes?
Group of answer choices
$100
$200
$36
$30
The cost when the two plans cost the same for a set number of minutes is $36. Option C is correct.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Plan A costs $30 plus an additional $0.03 for each minute of calls.
This can be expressed in equation as
y=30+0.03x
Plan B has no initial fee but costs $0.18 for each minute of calls.
y=0.17x
Now we have to find the cost when the two plans cost the same for a set number of minutes
30+0.03x=0.18x
30=0.18x-0.03x
30=0.15x
Divide both sides by 0.15
x=200
when the number of minutes of calls is 200, the two plans cost the same.
To find the cost when the two plans cost the same,
we can substitute x = 200 into either expression for Cost_A or Cost_B:
Cost_A = 30 + 0.03(200) = $36
Cost_B = 0.18(200) = $36
Therefore, the cost when the two plans cost the same for a set number of minutes is $36. Option C is correct.
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2.5b +5r = 80
The given equation describes the relationship
between the number of birds, b, and the number of
reptiles, r, that can be cared for at a pet care business
on a given day. If the business cares for 16 reptiles on
a given day, how many birds can it care for on this
day?
The number of birds they can take care on that day is zero.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, An expression 2.5b + 5r = 80.
Where, b represents the number of birds and r represents the number of reptiles.
On a given day. If the business cares for 16 reptiles, Therefore,
2.5b + 5(16) = 80.
2.5b + 80 = 80.
2.5b = 0.
So, They can not take care of any birds during the day.
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Reese wants the find the equation of the line that passes through the point (-4, 8) and has a slope of 3. Help her complete the work below.
Reese will first need to use _______ Formula to plug in ________ for x1
, ________ for y1, and ________ for the m
. Reese's final answer will be _________, which is written in _________ Form.
Answers:
A. Slope
B. 3
C. y=3x+20
D. Standard
E. -4
F. y=3x+12
G. Slope Intercept
H. Point Slope
I. 8
J. y=3x+4
Answer:
Reese will first need to use point slope Formula to plug in- 4 for x1, 8 for y1, and 3 for the m
Reese's final answer will be y = 3x + 20, which is written in slope intercept Form.
Step-by-step explanation:
The answers in terms of the choices and order in which the blanks appear are
H. Point Slope
E. -4
I. 8
B. 3
C. y=3x+20
G. Slope Intercept
The point slope form for a line
y - y1 = m(x - x1)
Pugging in x1 = -4, y1= 8 and m = 3 gives
y -8 = 3(x - (-4))
y - 8 = 3x + 12 Move -8 to right side
y = 3x +12 + 8
y = 3x + 20
What is 7 Roman numbers?
Answer:
VII
Step-by-step explanation:
Which proportion can you use to find the value of a?
The proportion used to find the value of a is a/18 = 16/a
What is proportion?Proportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.
Given are three similar triangles, (refer to attached figure to separately see the similar triangles)
We know that, similar triangle have corresponding sides in equal ratio,
Therefore,
a/18 = 16/a
Hence, the proportion used to find the value of a is a/18 = 16/a
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please help! it’s pretty easy I just am confused!
Answer:
since p is irrational it is not expressible as a ratio of two integers and has an infinite and nonrecurring expansion when expressed as a decimal
Step-by-step explanation:
so a
The Beach Shack rents boats for $60 the first hour and $30 each hour after that. The Surf
Shop rents boats for $40 an hour. At what number of hours are the rental fees for a boat
from each shop equal?
Answer:
After 3 hours.
Step-by-step explanation:
60 + 30x = y
40x = y
Beach Shack:
60, 90, 120, 150, 180, 210
Surf Shop:
40, 80, 120, 160, 200
The Spartan basketball team scored 108 points in the game last night. They scored 48 baskets in all, making a combination of two-point and three-point baskets. There were no points due to free throws.
Question 1
Part A
Which system of equations could be used to find the number of three-point baskets the Spartans made?
Answer:
(108 - (48 x 2)) / 3 = p
Step-by-step explanation:
;)
How to create the great paper outline templete?
First we need to select the subject to create the great paper outline template. Then follow the steps to create a paper.
Step 1: Choose the topic for the paper.
Step 2: Make a list of all the concepts you wish to discuss or incorporate.
Step 3: Separate similar concepts into smaller groupings.
Step 4: Put your concepts in order of importance: What ought the reader to discover first? What matters the most? Which conclusion will best suit your paper?
Step 5: Make good headers and subheadings for your documents.
Step 6: Format the outline in decimal, full-sentence, or alphanumeric form.
Step 7: State and review the paper by oneself first.
Follow all the steps to create the great paper outline template.
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Write using positive exponents
x^3 * x^5
Answer: easy, the answer is x^6 (look at the image for the solution and make sure to give me brainliest)
Step-by-step explanation:
21. CT
The flag of Scotland is a rectangle with white stripes as the diagonals.
In rectangle SCOT, SO = 92.4, and CO = 41. Find the indicated measure.
19. OL
S
20. ST
22. LT
+
T
120°
C
Determine whether the parallelogram with the given vertices is a rectangle,
rhombus, or square. Give all names that apply. Explain your reasoning.
23. A(-6, -2), B(-3, 3), C(2, 0), D(-1, -5)
The answers are a) OL = 46.2, CT = 92.4, ST = 41 and LT = 46.2
b) parallelogram ABCD is a rectangle.
What is a rectangle?A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.
a) Given that, the flag of Scotland is a rectangle with white stripes as the diagonals. In rectangle SCOT, SO = 92.4, and CO = 41.
We need to find the measure of CT, OL, ST and LT,
We know that, the diagonals of a rectangle bisects each other and are congruent, and its opposite sides are equal,
Therefore,
OL = SO/2 = 92.4/2 = 46.2
CT = SO = 92.4
ST = CO = 41
LT = OL = 46.2
b) Given are vertices of parallelogram, A(-6, -2), B(-3, 3), C(2, 0), D(-1, -5), we need to verify if this is a rectangle or not,
Since, the diagonals of a rectangle are congruent, so, we will find AC and BD and see if they equal or not if equal then it is a rectangle.
Distance between two points is =
D = [tex]\sqrt{(x_{2}-x_1)^2+(y_2-y_1)^2 }[/tex]
AC = √(2+6)²+(2)² = √68
BD = √(-1+3)²+(-5-3)² = √68
∵ AC = BD, therefore, parallelogram ABCD is a rectangle.
Hence, the answers are a) OL = 46.2, CT = 92.4, ST = 41 and LT = 46.2
b) parallelogram ABCD is a rectangle.
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The graph shows a scuba diver's ascent over time. Use the graph to write an equation in slope-intercept
form that represents the diver's depth over time.
The equation that represents this situation is
The equation that represents the situation is m= 1/8s-10
What is a Graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
When
s= 0, m= -10
When
s= 80, m= 0
[tex]\frac{0-(0-10)}{80-0} = \frac{10}{80} = \frac{1}{8}[/tex]
m-0 = 1/8(s-80)
m= 1/8s-10. The equation
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ILL GIVE BRAINLIEST PLS HELP The stem-and-leaf plot displays the distances that a heavy ball was thrown in feet.
2 0, 2, 5
3 1, 3, 4
4 1, 1, 5
5 0, 6
6 7
Key: 3|1 means 3.1
What is the mean, and what does it tell you in terms of the problem?
3.1 feet; The value means the furthest the ball went.
3.875 feet; The value means that a typical throw of the ball results in 3.875 feet.
4.1 feet; The value means this measurement had the most occurrences.
4.65 feet; The value means that a typical throw of the ball results in 4.65 fe
The mean distance that the ball was thrown is approximately 38.92/12 = 3.24 feet.
Ball throwing distancesTo find the mean distance that the heavy ball was thrown, we need to calculate the sum of all the distances and then divide by the total number of throws:
(20+25+25+31+33+34+41+41+45+50+56+67)/12 = 467/12 ≈ 38.92
So, the mean distance that the ball was thrown is approximately 38.92/12 = 3.24 feet.
This means that on average, the ball was thrown a distance of 3.24 feet. However, it's important to note that the mean can be influenced by outliers, which in this case is the one throw of 6.7 feet.
So, while the mean is a useful measure of central tendency, it's important to also consider other measures such as the median and mode to get a complete picture of the data.
The mean is the sum of all the values in a dataset divided by the total number of values. It provides an estimate of the central location of the data and can be a useful summary statistic for describing a dataset. However, the mean can be influenced by outliers, which are values that are significantly different from the rest of the data.
In this case, the one throw of 6.7 feet is an outlier because it is much further than any other throw, and it will increase the mean value.
For this reason, it's important to consider other measures of central tendency such as the median and mode. The median is the middle value in a dataset, and it's not affected by outliers. The mode is the value that appears most frequently in a dataset and can provide useful information about the typical or most common value in the data.
By considering all three measures (mean, median, and mode), we can get a more complete picture of the data and make better inferences or conclusions about it.
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The length of a rectangle is represented by the function L(x) = 2x. The width of that same rectangle is represented by the function W(x) = 8x2 − 4x + 1. Which of the following shows the area of the rectangle in terms of x?
(L + W)(x) = 8x2 − 2x + 1
(L + W)(x) = 8x2 − 6x + 1
(L ⋅ W)(x) = 16x3 − 4x + 1
(L ⋅ W)(x) = 16x3 − 8x2 + 2x
Answer:
Step-by-step explanation:
The area of a rectangle is given by the product of its length and width. Therefore, the area of the rectangle is:
A(x) = L(x) ⋅ W(x) = 2x(8x^2 - 4x + 1)
Simplifying the expression, we get:
A(x) = 16x^3 - 8x^2 + 2x
Therefore, the answer is (D) (L ⋅ W)(x) = 16x3 − 8x2 + 2x.
Write a division problem with ¼
as the dividend and 3 as the divisor. Then, find the quotient.
Answer:
[tex]\dfrac{1}{12}[/tex]
See the explanation for more details
Step-by-step explanation:
Not sure if you want this as a word problem or not. So here goes anyway
3 friends decided to share 1/4 of a pizza equally. How much of the original pizza portion did each get
In equation form:
[tex]\dfrac{1}{4} \div 3[/tex]
When dividing, flip the divisor so it is the reciprocal of the original divisor
Then multiply both the dividend and the flipped value
[tex]\textrm{Reciprocal of 3 = }[/tex] [tex]\dfrac{1}{3}[/tex]
[tex]\dfrac{1}{4} \div 3 = \dfrac{1}{4} \times \dfrac{1}{3}[/tex]
[tex]= \dfrac{1 \times 1}{4 \times 3} \\\\= \dfrac{1}{12}[/tex]
This is the quotient
how many pounds is 65 kg
Compare / Contrast Exponential Equations
1.) 2 (1/5)x-5
2.) y=4x
The intersection point of the exponential and linear equation is at (3.748, 14.993).
What is the solution to the equation?An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.
The equations are given below.
[tex]\rm y = 2 \left ( \dfrac{1}{5} \right )^{x - 5}[/tex]
The graph of the exponential equation is drawn.
y = 4x
The graph of the linear equation is also drawn.
From the graph, the intersection point of the exponential and linear equation is at (3.748, 14.993).
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How do you find the square root of 22 using heron's formula method?
(No spam for the points plss"
Answer:
we can't find it by herons formula. but here is your answer.....
Step-by-step explanation:
[tex]\\\sqrt{22}\\\\we can do by long division method \\ the actual value of \sqrt{22} = 4.69041575982343.\\well \sqrt{22} itself is in the simplest form[/tex]
Find the side length of a square with diagonals 18 cm long.
Answer:
162cm²
Step-by-step explanation:
Formula of square with diagonals=1/2*d²
=1/2*(18)²
=1/2*324cm²
we get,
=162cm²