If you add the lengths of the focal radii of an ellipse, what other value will you produce?
2a
2b
2c
The eccentricity
Answers
Equation of an ellipse
→having center (0,0) , vertex ([tex](\pm a ,0)[/tex] and covertex [tex](\pm b ,0)[/tex] and focus [tex](\pm c ,0)[/tex] is given by:
[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2}=1[/tex]
As definition of an ellipse is that locus of all the points in a plane such that it's distance from two fixed points called focii remains constant.
Consider two points (a,0) and (-a,0) on Horizontal axis of an ellipse:
Distance from (a,0) to (c,0) is = a-c = [tex]F_{1}[/tex]
Distance from (-a,0) to (c,0) is = a + c = [tex]F_{2}[/tex]
[tex]F_{1} + F_{2} =[/tex] a -c + a +c
= a + a
= 2 a →(Option A )
Related Questions
The U-Drive Rent-A-Truck company plans to spend $15 million on 310 new vehicles. Each commercial van will cost $35 comma 000 , each small truck $70 comma 000 , and each large truck
$60 comma 000 . Past experience shows that they need twice as many vans as small trucks. How many of each type of vehicle can they buy?
Answers
x+y+z = 310 ----- (1)
But, the company will spend $15 million. Then,
35000x+ 70000y +60000z = 15,000,000
35x + 70y + 60z = 15000 ---- (2)
Additionally, twice as many van as small trucks will be required. Then,
x = 2y ---- (3).
Substituting for x in (1) and (2);
2y +y +z = 310 => 3y +z =310 ---- (4)
35(2y) + 70y + 60z = 15000 => 70y+70y+60z = 15000 => 140y + 60z = 15000 ---- (5)
Solving (4) and (5)
From (4), z = 310 -3y
Then, using (5)
140y +60(310-3y) = 15000
140y + 18600 - 180y = 15000
-40y = -3600
y = 3600/40= 90
Then, z= 310 -3y = 310 -3(90) = 310 -270 = 40
And, x = 2y = 2(90) = 180
Therefore, the number will be:
Vans (x) = 180
Small trucks (y) = 90
Large trucks (z) = 40
Set the situation up as a system of linear equations based on the information provided in the problem. Then, solve the system to get the number of each type of vehicle that the company can buy.
Explanation:To solve this problem, let's set it up as a system of linear equations. This is a mathematics problem involving problem-solving and linear equations.
Let's denote v as the number of vans, s as the number of small trucks, and l as the number of large trucks.
We know that the total money spent should equal $15 million, and we can express this as:
(35,000v) + (70,000s) + (60,000l) = 15,000,000
We also know that the number of vans is twice the number of small trucks, so we can express this as:
v = 2s
We know also that the total number of vehicles is 310, so we have:
"v + s + l = 310"
Solving these three equations will give us the number of vans, small trucks, and large trucks that the company can buy.
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PLEASE HELP URGENT!!!
The price of the land is $2300 per acre ( 1 acre = 4840) how much does the land cost?
Answers
a^2 = b^2 + c^2 - 2ac*cosA
Here, a^2 = 500^2 + 750^2 - 2(500)(750)cos 100 deg, or
a^2 = 250000 + 572500 - 750000(-0.1736), or
= 692264
Then a = +sqrt(692264) = 832 yds
Use Heron's Formula to find the area of the land.
First, calculate s=(a+b+c)/2: (500+750+832)/2 = 1041=s
According to Heron's Formula, A = sqrt( s(s-a)(s-b)(s-c) )
Here, A = sqrt( 1041*(1041-500)*(1041-750)*(1041-832) )
I will leave this calculation to you to complete.
Suppose the area of the land is A square yards. Convert this to acres, using the fact that 1 acre = 4840 yd^2.
In acres, the area is
1 acre
A* ---------------- = (A/4840) acres
4840 yd^2
How much will this cost? Recall that the unit cost of the land is $2300/acre.
Then the total cost will be:
$2300
(A/4840) acres * ------------- = 0.475*A dollars. (Substitute your value for A)
1 acre
Two of the three side lengths are given. To find the area of the triangular piece of land, we'll need to calculate the length of the third side, the side opposite the 100 degree angle. Use the Law of Cosines for this task.
a^2 = b^2 + c^2 - 2ac*cosA
Here, a^2 = 500^2 + 750^2 - 2(500)(750)cos 100 deg, or
a^2 = 250000 + 572500 - 750000(-0.1736), or
= 692264
Then a = +sqrt(692264) = 832 yds
Use Heron's Formula to find the area of the land.
First, calculate s=(a+b+c)/2: (500+750+832)/2 = 1041=s
According to Heron's Formula, A = sqrt( s(s-a)(s-b)(s-c) )
Here, A = sqrt( 1041*(1041-500)*(1041-750)*(1041-832) )
I will leave this calculation to you to complete.
Suppose the area of the land is A square yards. Convert this to acres, using the fact that 1 acre = 4840 yd^2.
In acres, the area is
1 acre
A* ---------------- = (A/4840) acres
4840 yd^2
How much will this cost? Recall that the unit cost of the land is $2300/acre.
Then the total cost will be:
$2300
(A/4840) acres * ------------- = 0.475*A dollars. (Substitute your value for A)
1 acre
1
A lab worker monitors the growth of a bacteria colony starting at 9:00 a.m. At that time, there are 100 bacteria. According to the exponential function f(x) = 100(4)x, the bacteria quadruple every hour. Which equation could you use to determine the number of bacteria in the colony after 6 hours?
Answers
[tex]f(x)=100(4)^x[/tex]
[tex]f(6)=100(4)^6[/tex]
[tex]f(6)=409600[/tex]
We can conclude that the we should use the equation: [tex]f(6)=100(4)^6[/tex] to find the number of bacteria in the colony after 6 hours. Evaluating the function we get that the number is 409,600.
The equation to determine the number of bacteria in the colony after 6 hours is [tex]f(x) = 100(4)^x[/tex] and after 6 hours, there will be 409,600 bacteria in the colony.
To find the number of bacteria after 6 hours, one would substitute x with 6 in the exponential function [tex]f(x) = 100(4)^x[/tex].
This function models the growth of the bacteria colony, where the initial number of bacteria is 100 and they quadruple every hour.
The variable x represents the number of hours that have passed since the initial measurement at 9:00 a.m.
By substituting x = 6 into the function, we get:
[tex]f(6) = 100(4)^6[/tex]
Now, calculate the value of [tex](4)^6[/tex]:
[tex](4)^6 = 4 \times 4 \times 4 \times 4 \times 4 \times 4 = 4096[/tex]
Then, multiply this by the initial number of bacteria, which is 100:
f(6) = 100 [tex]\times[/tex] 4096
Finally, calculate the total number of bacteria after 6 hours:
f(6) = 409600
If a circle has a radius of 18 feet what's the closest approximation for circumference
Answers
Anyone know the answer to this geometry problem?
Answers
◯ ∠4 and ∠5 . . . . . . . . these are complementary angles whose sum is 90°
◯ ∠7 and ∠9 . . . . . . . . these are vertical angles, equal to each other
◯ ∠2 and ∠3 . . . . . . . . these are supplementary angles that together form a straight line. They are a linear pair.
◯ ∠1 and ∠2 . . . . . . . . these are "adjacent" angles in the quadrilateral that also includes ∠9 and ∠10.
The appropriate choice is ...
◉ ∠2 and ∠3
Length of side AB???
Answers
[tex]\cos(62) = \dfrac{AB}{12} [/tex]
[tex]AB = 12 \cos (62)[/tex]
[tex]AB = 5.6 \text { cm}[/tex]
Seven subtracted from the quotient of a number and 2 is -6
Answers
add 7 to both sides;
n/2 -7+7 = -6+7
n/2 = 1
multiply both sides by 2 ( or divide by 1/2 ) in order to get n by itself.
n/2 * 2/1 = 1 * 2/1
n = 2
18 / n - 7 = 2
18 / n =9
18 = 9n
2 = n
18 / 2 - 7 = 2
9 - 7 = 2
2 = 2
Find the product.
y 4 · y 6
Answers
Therefore the answer is y^10.
Hope this helps! :)
[tex]y^6 y*y*y*y*y*y y=10[/tex]
Answer is y=10
Hope it helped you.
-Charlie
explain one of the theorems that you would use to find the zero of higher degree polynomial
Answers
Rational Root Theorem:
If the rational number [tex]x=\frac{b}{c}[/tex] is a zero of a higher degree polynomial:
[tex]P(x)=kx^{n}+...+m[/tex]
where all the coefficients are integers. Then [tex]b[/tex] will be a factor of [tex]m[/tex] and [tex]c[/tex] will be a factor of [tex]k[/tex]
1. Use the rational root theorem to enumerate all possible rational zeroes of the polynomial [tex]P(x)[/tex]
2. Evaluate the polynomial from the first step until you can find a zero. Let’s suppose the zero is [tex]x=r[/tex]. It will be a zero if [tex]P(r)=0[/tex]. Then if this is true, write the polynomial as:
[tex]P(x)=(x-r)Q(x)[/tex]
3. Repeat this process using [tex]Q(x)[/tex] this time rather than [tex]P(x)[/tex]. The process finishes until we reach a second degree polynomial, then solve as it is widely known for a quadratic equation.
Due tomorrow please help
Answers
The sum is 294903.
_____
This is the sum of 15 terms of a geometric sequence with first term 9 and common ratio 2. That sum is given by the formula
[tex]S_{n}=a\dfrac{r^{n}-1}{r-1}[/tex]
[tex]S_{15}=9\dfrac{2^{15}-1}{2-1}=9\cdot(32768-1)=294903[/tex]
Which number is irrational? A. square root of 64 B. square root of 256 C. square root of 100 D. square root of 80
Answers
What is the simplified form of the following expression? 10abc^2 sqrt 49a^2b^2c^2
Answers
Answer: [tex]70a^2b^2c^3[/tex] will be the answer.
Explanation:
Since Given expression is [tex]10abc^2\sqrt{49a^2b^2c^2}[/tex]
We can write, [tex]10abc^2\sqrt{49a^2b^2c^2}= 10abc^2\sqrt{7^2a^2b^2c^2}[/tex]
[tex]\Rightarrow 10abc^2\sqrt{49a^2b^2c^2}= 10abc^2\sqrt{(7abc)^2}[/tex]
[tex]\Rightarrow 10abc^2\sqrt{49a^2b^2c^2}= 10abc^27abc[/tex]
[tex]\Rightarrow 10abc^2\sqrt{49a^2b^2c^2}= 10\times7abc^2abc[/tex]
[tex]\Rightarrow 10abc^2\sqrt{49a^2b^2c^2}= 70abc^2abc[/tex]
[tex]\Rightarrow 10abc^2\sqrt{49a^2b^2c^2}= 70a^2b^2c^3[/tex]
1. The simplified form of the expression [tex]10abc^2[/tex] is simply [tex]10abc^2[/tex] itself.
2. The simplified form of the expression [tex]\sqrt{49a^2b^2c^2}[/tex] is 7abc.
1. Since there are no like terms to combine, and no operations to perform, the expression remains unchanged.
2. The expression [tex]\sqrt{49a^2b^2c^2}[/tex] represents the square root of [tex]49a^2b^2c^2[/tex]. To simplify this, we need to find the square root of each term under the radical.
[tex]\sqrt{49a^2b^2c^2} = \sqrt{49} * \sqrt{a^2} * \sqrt{b^2} * \sqrt{c^2}[/tex]
The square root of 49 is 7, and the square root of any variable raised to the power of 2 is simply the variable itself. So, we have: [tex]\sqrt{49a^2b^2c^2} = 7 * a * b * c[/tex]
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Solve the open sentence.
–2 ≤ n + 4 ≤ 7
A. n ≤ 2 and n ≤ 7
B. n ≥ –6 and n ≤ 3
C. n ≥ 6 and n ≤ –4
D. n ≤ –6 and n ≤ 4
Answers
–6 ≤ n ≤ 3
Answer: B. n ≥ –6 and n ≤ 3
When rounding to.the nearest hundred are you to add or subtract?
Answers
Answer:
When you round to the nearest hundred:
150 or higher turns into 200, so you'd do add.
But when it's 149 or lower, you simply subtract it by 49.
Step-by-step explanation:
The relationship between the monthly fee for Brandon’s phone and the price per minute for long distance is modeled by the linear function f (x) = 0.05x + 3, where x is the number of minutes used for long distance. What is the total bill if Brandon used 20 minutes of his long distance service in a month?
Answers
the linear function f (x) = 0.05x + 3,
f(x) is the monthly fee and x is the price per minute
Brandon used 20 minutes of his long distance
So x is 20 minutes
We plug in 20 for x
f(x) = 0.05x + 3
f(20) = 0.05(20) + 3 = 4
So total bill is $4 if Brandon used 20 minutes of his long distance service in a month
A flagpole stands on a concrete region, as shown. What is the approximate perimeter of the concrete region? Use 3.14 for π.
Thanks!
Answers
The outer edges of the concrete region form semicircles. The perimeter of a circle is called the circumference, and is given by the formula
C=πd
Since these are semicircles, the circumference is given by C=1/2πd.
There are 4 of these semicircles, so the total would be
C=4(1/2)πd
The diameter of each one is 4 feet:
C=4(1/2)(3.14)(4) = 25.12
A ladder leans against a building. The angle of elevation of the ladder is 70°. The top of the ladder is 25 ft from the ground.
To the nearest tenth of a foot, how far from the building is the base of the ladder?
20.5 ft
30.5 ft
32.3 ft
39.5 ft
Answers
The distance from the building to the base of the ladder, when the ladder makes an angle of 70 degrees with the ground and the ladder is 25 feet long, can be calculated using the cosine function. The calculated distance is approximately 8.6 feet.
Explanation:To calculate the distance from the building to the base of the ladder, we have to use the trigonometric function cosine given the information in the problem. The cosine of an angle in a right triangle is defined as the adjacent (which is the distance we wish to find) over the hypotenuse (which is given as 25 feet).
Therefore, we write the equation as follows:
cos(70) = Adjacent/25
To find the 'Adjacent', we rearrange the equation:
Adjacent = 25*cos(70)
When you perform the calculation, you get Approximately 8.6 feet as the distance from the building to the base of the ladder.
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The base of the ladder is approximately 8.5 feet from the building. This is determined using trigonometry and the cosine of the ladder's angle of elevation.
Explanation:This is a trigonometry problem where we have to find the base of the triangle formed by the ladder, the ground, and the distance from the building. The question gives us the length of the ladder (hypotenuse in the right triangle) and the angle of elevation. We can thus use cosine of the angle (base/hypotenuse) to find the base.
We know that Cosine of 70° is equal to the (base / Hypotenuse). And in the present case, the hypotenuse is given to be 25 ft.
Therefore, calculation will be as follow:
Base = Cosine (70°) * Hypotenuse.
Base = Cosine (70°) * 25 ft.
After calculating, this gives a base length of approximately 8.5 feet. So, the base of the ladder is approximately 8.5 feet from the building.
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PLEASE HELP I NEED SOMEBODY TO PARAPHRASE THIS FOR ME! I'LL MARK BRAINLIEST!! 50 POINTS!!!
if the variables cancel out leaving u with an untrue statement, like 0 = 4 or 2 = 6, then u will have no solutions
if the variables cancel out leaving u with a true statement, like 2 = 2 or 4 = 4, then u will have infinite solutions
if u end up with a variable equaling a number, then u have 1 solution
Answers
3x - 2x = 2 - 4
x = -2
one solution
3x-2x=2x+2-2x
1x=2
The other person is wrong
Ginger wanna join a gym.she goes to the local gym and is told that there is a one-time fee of $100 to join and then a monthly fee of $30.if she belongs to the gym for one year then the 12th month is free.how much will a one year membership cost her?
Answers
100+30(11)
100+330
430 dollars, which is highway robbery..
The radius of the base of a cone is 4 inches. the slant height of the cone is 6 inches. which is closest to the surface area of the cone?
Answers
So you know two things, the radius and the slant height.
The formula you are going to use is SA=π•r^2+π•r•L
SA= Surface Area
r = Radius
L= Slant Height
So now you plug the variables into the formula.
[tex]\pi \times {4}^{2} + \pi \times 4 \times 6[/tex]
[tex]\pi \times 16 + \pi \times 24[/tex]
[tex]40 \times \pi = 125.66[/tex]
After just pick the answer closest to this one. And you should get the correct answer. :)
The volume of a cuboid is 1404cm3. The length is 9cm and the width is 130mm. Work out the height of the cuboid in cm.
Answers
130mm = 13cm
Formula:
Volume = Length x Width x Height
Substitute known values into the variables:
1404 = 9 x 13 x height
1404 = 117 x height
height = 1404 ÷ 117 = 12 cm
Answer : Height = 12 cm
To calculate the height of the cuboid, we convert the width to centimeters and use the volume formula. After conversion, we find the height by dividing the volume (1404cm³) by the product of the length (9cm) and width (13cm), resulting in a height of 12cm.
To find the height of the cuboid, we can use the formula for calculating volume, which is volume = length x width x height. The question gives us the volume of the cuboid as 1404cm³, the length as 9cm, and the width as 130mm. However, we need to ensure all units are the same, so let's convert the width from millimeters to centimeters: 130mm = 13cm (since 1cm = 10mm).
Now, using the formula for volume:
Volume = length x width x height1404cm³ = 9cm x 13cm x heightTo find the height, we divide the volume by the product of the length and width:
height = Volume / (length x width)height = 1404cm³ / (9cm x 13cm)height = 1404cm³ / 117cm²height = 12cmTherefore, the height of the cuboid is 12cm.
Which of these ordered pairs is a solution to the linear inequality?
Answers
There are 80 marbles in a bag. You randomly choose 20 marbles from the bag. The results are shown in the table. Predict the total number of yellow marbles.
Color
Blue 6
Red 9
Yellow 5
There are about ___ yellow marbles.
Answers
The experimental probability is 5/20, since 5 yellow marbles were drawn out of 20 in the sample.
5/20(80) = 400/20 = 20
which of these is an example of discrete data?
A) distance
B) temperature
C) area of a room
D) pages in a book
Answers
Discrete data is numerical but only has a limited number of values
With this the answer is D) pages in a book since you can't have 6.8 pages of a book
Hope this helps!
Anyone know the answer?
Answers
21x = 3x + 36 |substract 3x from both sides
18x = 36 |divide both sides by 18
x = 2
Susan has a rectangular garden that measures 20 feet by 10 feet. what is the least amount of fencing that she needs to buy in order to enclose the garden?
Answers
To find the perimeter you add the links of all sides.
20 feet + 10 feet + 20 feet + 10 feet= 60 feet
Susan will need a minimum of 60 feet of fencing.
Prove and show your work
cos t (sect -cos t)= sin^2 t
sin 0 cot 0= cos 0
Answers
cost · sect - cos²t (Note: sect= 1/cost, cos²t = 1-sin²t)
cost · (1/cost) - (1 - sin²t)
1 - 1 + sin²t
0 + sin²t
sin²t
2) Manipulating the Left side
sinФ · cotФ (Note: cotФ = cosФ/sinФ)
sinФ · (cosФ/sinФ)
(sinФ · cosФ)/sinФ
cosФ
What is the difference for this question?
Answers
5x^2 + 2x + 11 - 7 - 4x + 2x^2
= 7x^2 - 2x + 4
(5x2 + 2x + 11) - (7 + 4x - 2x2)
Rewriting we have:
5x2 + 2x + 11 - 7 - 4x + 2x2
By grouping terms of the same degree we have:
x2 (5 + 2) + x (2-4) + (11-7)
Rewriting:
7x2 - 2x + 4
Answer: the difference is
7x2 - 2x + 4
the right rectangular prism will be sliced perpendicular to its base along the dashed line. Select from the drop-down menus to correctly describe the cross section formed by the slice.
Answers
A rectangular prism is the shape of a box with 6 rectangular sides. If you slice down perpendicular to the base, you would still have another rectangle.
All at once, pandemonium broke loose. ______________ the marching band came around the corner, dogs began barking, and the horses pulling the mayor's carriage began to run!
Which word best completes the passage above? (5 points)
Anyway
Because
Following
Simultaneously
Answers
Answer:
The answer is word SIMULTANEOUSLY.
Step-by-step explanation:
The alternative that fits best is " d.Simultaneously"
All at once, pandemonium broke loose. Simultaneously, the marching band came around the corner, dogs began barking, the horses pulling the Mayors carriage began to run.
This word maintains the coherence and cohesion of the given text.
Answer:
The alternative that fits best is " d. Simultaneously"
Step-by-step explanation:
Thus, the complete sentence would read: "All at once, pandemonium broke loose. Simultaneously the marching band came around the corner, dogs began barking, and the horses pulling the mayor's carriage began to run!"
The explanation for this is that the word "Simultaneously" is the only one that fits the phrase, and maintains the coherence and cohesion of the text. The words "anyway", "because", and "following", when embedded in the phrase, change the meaning of what the author wanted to go through.