THIS IS NOT A TEST OR ASSESSMENT!! NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! PLEASE EXPLAIN!! Chapter 13
1. What is a conic ? How would you be able to model different conic sections at home(how would you slice a 3D shape to create the conic sections)?
2. How does the equation for the ellipse compare to the equation for a hyperbola? How can you determine the difference?
3. What is the difference between a vertex, a focus, and a directrix?
Answers
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Explanation:
1.A cone is a 3-dimensional object created by revolving a line about an axis that intersects that line. This figure is a "double-napped" cone. The point where the revolved line and the axis meet is the a.pex, or vertex, of the cone. Typically, we're concerned with a finite portion of the cone, from the vertex to a base that is a circle in a plane perpendicular to the axis.
A "conic" is a 2-dimensional figure that results from the intersection of a plane and a cone. There are four general categories, named according to the angle the plane makes with the axis and/or the side of the cone. These are illustrated in the attachment.
a circle - the plane of intersection is perpendicular to the axisan ellipse - the plane of intersection is at an angle between 90° and the angle of the side relative to the axis. Both an ellipse and a circle are closed figures.a parabola - the plane of intersection is at the same angle as the side of the cone. A parabola is a one-sided open figure.a hyperbola - The plane of intersection is at an angle between that of the side of the cone and the axis of the cone. The plane will intersect both parts of a double-napped cone producing a double-sided open figure.Producing these at home can be an interesting project. A circle can be made using a compass.
An ellipse can be drawn using a pair of pins and a loop of string. The pins would be placed at the foci of the ellipse, and the string would constrain the drawing instrument (pen or pencil) to have a constant total distance to the two foci.
A parabola can be drawn on graph paper using coordinates derived from an equation for it. It can also be drawn using a compass and a set square by plotting points that are equidistant from the focus and a line that is called the directrix. If you have a physical cone-shaped object, you can cut it at an angle that will produce a parabola.
A hyperbola can be drawn on graph paper from an equation. It can also be drawn using a compass by plotting points that have a constant difference in their distance to the two foci, or by plotting points whose ratio of distance to focus and directrix is a constant. A physical cone-shaped object can be cut to produce a hyperbola.
__
2.The general form equation for a conic is ...
Ax² +Bxy +Cy² +Dx +Ey +F = 0
Usually, we're concerned with conics that have axes parallel to the coordinate axes, so B=0. The equation of an ellipse has A and C with the same sign. The equation of a hyperbola has A and C with opposite signs,
In standard form, the equations for figures centered at the origin are ...
ellipse: x²/a +y²/b = 1hyperbola: x²/a -y²/b = 1 (opens horizontally)hyperbola: y²/a -x²/b = 1 (opens vertically)__
3.The vertex of a conic is an extreme point on the (major) axis of the conic. The focus is a point used in the definition of the conic. The focus is "inside" the curve, on the axis of symmetry. The directrix is a line used in the definition of the conic. The directrix is "outside" the curve, perpendicular to the axis. The second attachment shows these for a parabola.
Related Questions
The surface areas of two similar solids are 16m2 and 100 m2. The volume of the larger one is 750m3. What is the volume of the smaller one?
Answers
Answer:
48 m^3
Step-by-step explanation:
If the scale factor of linear dimensions between two solids is k, then the scale factor for areas is k^2, and the scale factor of volumes is k^3.
Let's call the solid with 16 m^2 of area solid A, and the other one solid B.
The scale factor of areas from, A to B is (100 m^2)/(16 m^2) = 25/4
In other words, multiply the area of the solid A by 25/4 to get the area of solid B.
Let's check: 16 m^2 * 25/4 = 16 * 25/4 m^2 = 4 * 25 m^2 = 100 m^2
We do get 100 m^2 for solid B, so the area scale factor of 25/4 is correct.
The area scale factor is k^2, so we have:
k^2 = 25/4
We solve for k:
k = 5/2
Now we cube both sides to get k^3, the scale factor of volumes.
k^3 = 5^3/2^3
k^3 = 125/8
Let V = volume of smaller solid, solid A.
V * 125/8 = 750 m^3
V = 750 * 8/125 m^3
V = 48 m^3
Which equation is correct?
1
A. cos x =
sin a
1
B. tan x=
CSC 2
C. sec =
COS
1
D. cot 2 =
sec
SUBMIT
Answers
It’s a reciprocal identity
The requried secant function is the reciprocal of the cosine function, i.e., sec x = 1/cos x. Option C is correct.
What are trig ratios?If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.
Here,
The correct equation is option C: sec x = 1/cos x.
This is because the secant function is the reciprocal of the cosine function, i.e., sec x = 1/cos x.
Learn more about trig ratios here:
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a cookie recipe calls 3 1/4 cups of flour. the recipe makes 3 dozen cookies. how much flour us needed to make 144 cookies
Answers
1 dozen = 12
144 / 12 = 12 dozen
12 dozen/ 3 = 4
They need 4 times the amount of flour:
3 1/4 x 4 = 13
They need 13 cups of flour
How do you Find the acute Angle A when sinA=0.616?
Answers
Answer:
arcsin0.616
Step-by-step explanation:
arcsino.616
1 poir
Question 1. Jessica has $1,625.00 to purchase a five-year Certificate of
Deposit (CD). In the chart, there are CD rates frombankrate.com. What
would the account ending balance be at Synchrony Bank if it is
compounded quarterly? *
Use the Compound Interest Formula to calculate the ending balance. A = P(1 + 5)nt
Nationwide
Bank
Nationwide
2.01%
No
Synchrony Bank
all synchrony
1.95%
Answers
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Answer:
$1790.99
Step-by-step explanation:
Given:
$1625 is invested at an annual rate of 1.95% compounded quarterly for 5 years
Find:
the ending balance
Solution:
The compound interest formula applies.
FV = P(1 +r/n)^(nt) . . . Principal P at rate r for t years, compounded n per year
FV = $1625(1 +0.0195/4)^(4·5) = $1625(1.004875^20) ≈ $1790.99
The account ending balance would be $1790.99.
Can someone help me solve this problem ?
Answers
Answer:
B
Step-by-step explanation:
Since x= 3/4
To take the fraction on left hand side, inverse 4/3
Take π as denominator
Then cube root the entire equation on the left hand side.
Answer:
Step-by-step explanation:
SOMEONE PLS HELP ME!!!
Answers
Answer:
No
Step-by-step explanation: Bye
There is a pile of 55 coins consisting of nickels and dimes worth $3.90. Find the number of each if you say that the nickels are x.
Answers
Answer:
There are 32 nickels and 23 dimes.
Step-by-step explanation:
Lets say x is nickels and y is dimes
The first equation would be 55 = x + y
The second equation would be .05x + .10y = 3.90
The Solving Part:
Move y to the other side: x = 55 - y
Substitute x in the second equation: .05(55-y) + .10y = 3.90
Distribute, rearrange, and combine like terms: .05y = 1.15
Solve for y: Y = 23
Plug in 23 for y and solve: 55 - y = x ; 55 - 23 = x ; 55 - 23 = 32
x = 32
y = 23
32 nickels and 23 dimes
Answer:
There are 32 nickels and 23 dimes.
Step-by-step explanation:
Yay :) we solved the problem together :)))))
A local church holds an annual raffle to raise money for a new roof. They sell only 500 tickets at $50 each. This year's prizes include: $3,000 in cash, four $100 Amazon gift cards, and two $75 Visa gift cards. You buy one ticket. What is your mathematical expectation for this game
Answers
Answer:
The expectation for an event with outcomes:
{x₁, x₂, ..., xₙ}
Each one with probability:
{p₁, p₂, ..., pₙ}
Is:
Ev = x₁*p₁ + ... + xₙ*pₙ
There are 500 tickets sold.
1 of these, wins $3,000 (this is the event x₁)
4 of these, wins $100 (this is the event x₂)
2 of these, wins $75 (this is the event x₃)
The others do not have a prize.
So the probability of winning the $3000 is equal to the quotient between the number of tickets with that prize (1) and the total number of tickets (500)
p₁ = 1/500
Similarly, the probability of winning $100 will be:
p₂ = 4/500
And for the $75 prize:
p₃ = 2/500
Then the probability of not winning is:
p₄ = 493/500
Then the expected value for a single ticket is:
Ev = $0*493/500 + $75*2/500 + $100*4/500 + $3000*1/500
Ev = $7.1
If you take in account that you pay $50 for the ticket, the actual expectation should be:
E = $7.10 - $50 = -$42.90
A basic cellular package costs $30/month for 60 minutes of calling with an additional charge of $0.40/minute beyond that time. The cost function C (2) for using x minutes would be • If you used 60 minutes or less, i.e. if if x < 60, then C (x) = 30 (the base charge). If you used more than 60 minutes, i.e. (x – 60 minutes more than the plan came with, you would pay an additional $0.40 for each of those (x – 60 minutes. Your total bill would be C (x) = 30 + 0.40 (x – 60). If you want to keep your bill at $50 or lower for the month, what is the maximum number of calling minutes you can use? minutes. The maximum calling minutes you can use is ? Number
Answers
Answer:
The maximum number of minutes to keep the cost at $50 or less is 110 minutes
Step-by-step explanation:
Given
[tex]C(x) = 30[/tex] ---- [tex]x < 60[/tex]
[tex]C(x) = 30 + 0.40(x - 60)[/tex] --- [tex]x \ge 60[/tex]
Required
[tex]C(x) = 50[/tex] ---- find x
We have:
[tex]C(x) = 30 + 0.40(x - 60)[/tex]
Substitute 50 for C(x)
[tex]50 = 30 + 0.40(x - 60)[/tex]
Subtract 30 from both sides
[tex]20 = 0.40(x - 60)[/tex]
Divide both sides by 0.40
[tex]50 = x - 60[/tex]
Add 60 to both sides
[tex]110 = x[/tex]
[tex]x =110[/tex]
Question 10 of 25
If a regular polygon has exterior angles that measure 60° each, how many
sides does the polygon have?
A. 4
th
B. 6
O оо
C. 8
D. 3
SUBMIT
I need help ASAP
Answers
Answer:
I think the answer is 3
hope it will help you
the quotient of (x^4 - 3x^2 + 4x - 3) and a polynomial is (x^2 + x - 3) what is the polynormial
Answers
Answer:
Hello,
polynomial is x²-x+1
Step-by-step explanation:
if a=b*c+r then a=c*b+r
Using a long division, see the picture.
PLEASE HELP, IGNORE ALL ANWSERS FILLED IN CURRENTLY I WILL GOVE BRAINLIST
Answers
Answer:
32.64°
Step-by-step explanation:
From triangle Given :
The sides of the missing angle given are the Adjacent and hypotenus.
Since the triangle is right angled, we can apply trigonometry :
cosθ = adjacent / hypotenus
Cosθ = 16 / 19
θ = Cos^-1(16/19)
θ = 32.6368
θ = 32.64°
Days before a presidential election, a nationwide random sample of registered voters was taken. Based on this random sample, it was reported that "52% of registered voters plan on voting for Robert Smith with a margin of error of ±3%." The margin of error was based on a 95% confidence level. Fill in the blanks to obtain a correct interpretation of this confidence interval. We are ___________ confident that the ___________ of registered voters ___________ planning on voting for Robert Smith is between ___________ and ___________.
Answers
Answer:
We are 95% confident that the percentage of registered voters in the nation planning on voting for Robert Smith is between 49% and 55%.
Step-by-step explanation:
Given that :
Margin of Error = ±3%
Sample Proportion = 52%
Confidence level = 95%
The 95% confidence interval is :
Sample proportion ± margin of error
52% ± 3%
Lower boundary = 52% - 3% = 49%
Upper boundary = 52% + 3% = 55%
The interpretation is that at a given confidence level ; the popukation proportion based on the sample proportion and margin of error is in the confidence interval.
write your answer in simplest radical form
Answers
Answer:
a = 3√6 in
Step-by-step explanation:
From the question given above, the following data were obtained:
Angle θ = 60°
Adjacent = 3√2 in
Opposite = a =?
The value of 'a' can be obtained by using the tan ratio as illustrated below:
Tan θ = Opposite / Adjacent
Tan 60 = a / 3√2
√3 = a / 3√2
Cross multiply
a = √3 × 3√2
Recall:
c√d × n√m = (c×n) √(d×m)
Thus,
√3 × 3√2 = (1×3)√(3×2)
√3 × 3√2 = 3√6
a = 3√6 in
If there are g girls and b-boys in a room, write an expression for the total number of children in the room.
Answers
Answer:
g+b
number of girls+number of boys
if i am incorrect forgive me plz
The expression for the total number of children in a room is g+ b.
What is an expression?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
What is addition?Addition is the process of finding the total, or sum, by combining two or more numbers or variables.
According to the given question
We have
Number of girls = g
And, number of boys = b
Therefore, the expression for the total number of children in room is given by
Total number of children = g + b
Hence, the expression for the total number of children in a room is g+ b.
Learn more about expression and addition here:
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Find the length of AC
Answers
Answer:
377.19 (rounded off to 2dp)
Step-by-step explanation:
since its a right angled triangle, we can use tangent
tan(x) =opp/adj
tan(5) =33/AC
AC =33/tan(5)
Use the given information to determine which of the following relationships
can be proved and why.
L= 20
ME ZP
ML = PO
A. ALMN - A OPQ, because of AAS.
B. ALMNE A OPQ, because of ASA.
C. We cannot prove any relationship based on these data.
D. ALMN=A OPQ, because of SAS,
Answers
Answer:
B. ∆LMN ≅ ∆OPQ because of ASA
Step-by-step explanation:
Two triangles are congruent if two angles and an included side of one triangle are congruent to two corresponding angles and a corresponding included side of the other.
From the information given, we have:
Two angles (<L and <M) in ∆LMN that are congruent to two corresponding angles (<O and <P) in ∆OPQ.
Also, included side in both triangles are congruent (ML ≅ PO).
Therefore, ∆LMN ≅ ∆OPQ by the ASA Theorem.
7. Solve for x: x/6 - y/3 = 1
Please give steps!
Answers
<=> x/6 = 1+ y/3
<=> x/6 = (3+y)/3
<=> x = (3+y)/3 x 6
<=> x = 2(3+y)
So the answer is x = 2(3+y)
which of the following is the formula in solving for the area of a circle?
A.A=2πr
B.A=πr²
C.A=πd
D.A=2πr²
Answers
The area of circle is πr²
Answer:
πr²
Step-by-step explanation:
The answer is πr² where,
π = pi, 3.14...
r = radius
This is the most common way of solving for the area of the circle.
A truck rental is $25 plus $ 0.40/mi find out how many miles ken traveled if his bill is $59.40
Answers
Answer:
Step-by-step explanation:
C = 59.4
Fixed Cost (F) = 25
C = 25 + 0.4*x Solve for x
59.40 = 25 + 0.4x Subtract 25
34.4 = 0.4x Divide by .4
34.4/0.4 = x
x = 86 miles
Which statement best applies to the slope of the line below?
A.
the slope is negative
B.
the slope is zero
C.
the slope is positive
D.
the line has no slope
Answers
Answer:
D
Step-by-step explanation:
fro the diagram below there line has no slope
Answer: B) The slope is zero
============================================================
Explanation:
Any horizontal line will always have a slope of 0. This is because there is no change in y (aka the rise is 0).
So we could say something like
slope = rise/run = 0/1 = 0
The run can be anything we want, and we'd still get 0 every time.
------------
Another way to see this is to pick two points from this line. Whichever points are selected, they are plugged into the slope formula
m = (y2-y1)/(x2-x1)
You'll find that the y2-y1 expression turns into 0. Why? Because y1 and y2 are the same, so they subtract to 0. It doesn't matter what x2-x1 turns into.
w^2+2w-42=0
what is the width and the length
Answers
Answer:
answers in the explanation cz I'm too lazy to type :(
not entirely sure tho
Step-by-step explanation:
w²+2w-42=0
*quadratic formula*
w= -1+ square root 43 m
or w= -1- square root 43 m
then since the length is 2m more than w
add 2 to both answers
l= 1+ square root 43 m
l=1- square root 43 m
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Answer:
width: 5.557 mlength: 7.557 mStep-by-step explanation:
Given:
a rectangular patio of width w meters, length w+2 meters, and area 42 m²
Find:
width and length
Solution:
The area is ...
A = LW
42 = w(w +2)
43 = w² +2w +1 . . . . . . add 1 to complete the square
√43 = w+1
w = √43 -1 ≈ 5.557 . . . meters
l = w+2 = √43 +1 ≈ 7.557 . . . meters
The width and length of the patio are 5.557 m and 7.557 m, respectively.
If a point in quadrant IV is reflected in the y-axis, its image will lie in quadrant:
A. IV
B. II
C. I
D. III
Answers
Answer:
Option D is correct.
Step-by-step explanation:
A plane mirror shows that the image formed by it is of same size as that of object, same distance as that of object and same orientation and laterally inverted.
So, when a point is in IV quadrant and reflection is from Y axis, the image is in III quadrant.
A normal distribution has a mean of 15 and a standard deviation of 2. Find the value that corresponds to the 75th
percentile. Round your answer to two decimal places.
N
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.5
0.6915
0.6950
0.6985
0.7019
0.7054
0.7088
0.7123
0.7157
0.7190
0.7224
0.6 0.7257
0.7291
0.7324
0.7357
0.7389 0.7422
0.7454
0.7486
0.7517
0.7549
0.7 0.7580
0.7611
0.76420.7673
0.7704
0.7734
0.7764
0.7794
0.7823
0.7852
0.8
0.7881
0.7910
0.7939
0.7967
0.7995
0.8023
0.8051
0.8078
0.8106
0.8133
Answers
I wish I could help
The point (3,-4) is on the terminal side of an angle 0. What is cos 0?
А. 3/4
В. -3/4
C. 3/5
D. -3/5 E. 3
Answers
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Answer:
C. 3/5
Step-by-step explanation:
The distance from the origin to the given point is ...
d = √(3² +(-4)²) = √(9+16) = 5
The cosine of the angle is the ratio of the x-coordinate to this value:
cos(θ) = x/d
cos(θ) = 3/5
I Will Mark Brainliest
The figure shows a rectangue with its length and breadth as indicated,
Give that the perimeter of a rectangle is 120cm, find the area of rectangle .
Answers
Answer:
Length = 2x+y cm and since it's a rectangle,
2x+y=3x-y ---------------- (i)
width = 2x-3 cm
It's perimeter,
2(2x+y+2x-3)=120 ---------------- (ii)
Solving both equations,
x = 14 cm
y = 7 cm
so length is, 2×14+7 = 35 cm
and width is, 2×14-3 = 25 cm
so area will be, 35×25 = 875 cm²
Answered by GAUTHMATH
Answer:
len = 35
width = 25
Step-by-step explanation:
3x-y = 2x+y
1) x-2y = 0
9x -6= 120
x = 14
y = 7
Evaluate the functions
Answers
Answer:
Step-by-step explanation:
by selling a purse for rupees 250 Rajan loses one sixth of what cost should find the cost price of the first her loss percentage
Answers
Answer:
300, 16.67%
Step-by-step explanation:
Let x be the cost price. x-(1/6)x=250. 5x/6=250. x=300. Losss percentage is 16.67%
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 3 large boxes and 5 small boxes has a total weight of 88 kilograms. A delivery of 12 large boxes and 2 small boxes has a total weight of 235 kilograms. How much does each type of box weigh?
Answers
Answer:
Step-by-step explanation:
We need a system of equations here. The first equation is that 3L boxes + 5s boxes (L = large and s = small) = 88 kg so
3L + 5s = 88
12L + 2s = 235 according to the other information given.
Solve the first equation for either L or s. I'll solve for L, just because:
3L = 88 - 5s and
L = [tex]\frac{88}{3}-\frac{5}{3}s[/tex] and sub that into the second equation for L:
[tex]12(\frac{88}{3}-\frac{5}{3}s)+2s=235[/tex] and if you distribute the 12 into the parenthesis you'll simplify it down a bit to
352 - 20s + 2s = 235 and combine like terms:
-18s= -117 so
s = 6.5 kg and plug that in to solve for L:
L = [tex]\frac{88}{3}-\frac{5}{3}(6.5)[/tex] and
L = 18.5 kg
