You can make a solar hot-dog cooker by shaping foil-lined cardboard into a parabolic trough and passing a wire through the focus of each end piece. How far from the bottom should the wire be placed?
Answers
Answer:
The wire should be placed at a height of 2.25 inches from the bottom
Step-by-step explanation:
With the assumption that the shape of the solar hot-dog cooker is a parabola. we have the equation for the shape given as y = a·x² + b·x + c
Whereby the coordinates of the vertex is taken as (h, k) = (0, 0), we have;
c = 0
∴ y = a·x² + b·x
From the diagram, we have;
When x = 6, y = 4
When x = -6, y = 4
Which gives;
4 = a·(-6)² + b·(-6) = 36·a - 6·b
4 = 36·a - 6·b.........................................(1)
4 = a·(6)² + b·(6) = 36·a + 6·b
4 = 36·a + 6·b........................................(2)
Subtracting equation (1) from equation (2) gives;
4 - 4 = 36·a - 6·b - (36·a + 6·b) = -12·b
0 = -12·b
b = 0
Therefore;
4 = 36·a - 6×0
a = 4/36 = 1/9
The focus = F(h, k + p)
p = 1/(4·a) = 1/(4 × 1/9) = 1/(4/9) = 9/4 in = 2.25 inches
The coordinates of the focus, F = (h, k + p) = (0, 9/4) = (0, 2.25)
Therefore, the wire should pass through the focus and placed at 2.25 inches above the bottom.
Related Questions
help me it's due in less than an hour
Answers
Answer:
y = 5 and 1/4 + 1/5x, I think
Step-by-step explanation:
hope this helps
Select the three expressions that are equivalent to 9^4
Choose 3 answers
A. 9•4
B.9•9•9•9
C.9^8/9^2
D.(9^2•9^2)^1
E.(9^10/9^8)^2
Answers
Answer:
B and D
Step-by-step explanation:
the answer is B and D
The equivalent expression are [tex]9^4[/tex] = 9 x 9 x 9 x 9, 9² x 9² and
[tex](9^{10}/9^8)^2[/tex]
What is Expression?Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.
Given:
[tex]9^4[/tex]
So, if we expand the above expression using exponents and power
[tex]9^4[/tex] = 9 x 9 x 9 x 9
and, 9² x 9² = [tex]9^{2+2[/tex] = [tex]9^4[/tex]
Also, [tex](9^{10}/9^8)^2[/tex]
= (9²)²
= [tex]9^4[/tex]
Hence, the equivalent expression are [tex]9^4[/tex] = 9 x 9 x 9 x 9, 9² x 9² and
[tex](9^{10}/9^8)^2[/tex]
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what is an expression equivalent to m^238/m^-79 in the form m^v, where v is an integer?
Answers
Answer:
[tex]m^{317}[/tex]
Step-by-step explanation:
In indices, the division postulate is true:
[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]
Apply this to the question:
[tex]\frac{m^{238}}{m^{-79}} \\= m^{238-(-79)}\\= m ^{238+79}\\= m^{317}[/tex]
Hence the expression expressed in the form [tex]m^v \ is \ m^{317}[/tex]
Average movie in the Uruled States gerveral . Cost tickets in Japan plus two tickets in Switzerlandtickets in Switzerland plus two tickets in Japan would cost \$/5.27 . How much does an average movie ticket cost in each of these countries in Japan the average costis Switzerland the average cost is $
Answers
Answer:
The average cost of a movie ticket in Japan is $17.86 and the average cost of a movie ticket in Switzerland is $13.75
Step-by-step explanation:
The question seems to be incomplete. Here is a similar question and the solution:
Average movie prices in the United States are, in general, lower than in other countries. It would cost $81.08 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $76.97. How much does an average movie ticket cost in each of these countries?
Step-by-step explanation:
Let the cost of tickets in Japan be $x and the cost of tickets in Switzerland be $y.
From the question,
It would cost $81.08 to buy three tickets in Japan plus two tickets in Switzerland. That is
3x + 2y = 81.08 ...... (1)
Also from the question,
Three tickets in Switzerland plus two tickets in Japan would cost $76.97. That is
2x + 3y = 76.97 ...... (2)
Multiply equation (1) by 2, so that we get
6x + 4y = 162.16 ...... (3)
and multiply equation (2) by 3, so that we get
6x + 9y = 230.91 ...... (4)
Now, Subtract equation (3) from equation (4), we get
5y = 68.75
y = 68.75/5
y = 13.75
Put the value of y into equation (1) to determine x
3x + 2y = 81.08
3x + 2(13.75) = 81.08
3x + 27.5 = 81.08
3x = 81.08 - 27.5
3x = 53.58
x = 53.58/3
x = 17.86
∴ x = 17.86 and y =13.75
Hence, the average cost of a movie ticket in Japan is $17.86 and the average cost of a movie ticket in Switzerland is $13.75.
Make a conjecture: What happens to
M AJK, m_BKJ, and m_CLJ as you
change the line of reflection?
The angles change.
The angles do not change.
The angles are always right
angles.
Answers
Answer:
the angles change
Step-by-step explanation:
The price of a sweater was reduced from $20-$12 by the percentage was the price of the sweater reduced ?
Answers
What is the distance between the point (4, 7) and its reflection over the x-axis, as shown on the graph below?
0 units
7 units
8 units
14 units
Answers
Answer:
14
Step-by-step explanation:
the x formate times xn
Answer:The answer is 14 units i got this right on my school and the person up there is right as well
Step-by-step explanation: have a great day.=D
5/8 - 5/24
I am doing some homework my brain isnt working right now can someone help me out?
Answers
Answer:
5/12
Step-by-step explanation:
i just looked it up...
====================================================
Explanation:
Multiply top and bottom of 5/8 by 3 to get 15/24
This means 5/8-5/24 is the same as 15/24-5/24
The denominators are the same, so we can subtract the numerators to have them placed over the common denominator
15/24 - 5/24 = (15-5)/24 = 10/24
Then we reduce by dividing each part of the fraction by the GCF 2
10/2 = 5
24/2 = 12
Meaning that 10/24 = 5/12
Note how multiplying top and bottom of 5/12 by 2 leads to 10/24 again.
So overall,
5/8 - 5/24 = 5/12
how can I measure the length of letters
Answers
Answer:
With a really small ruler.
Step-by-step explanation:
What do you mean?
Add the polynomials 5x - 2 + y and -3y + 5x + 2
Answers
Sjjssjsjskmsksx
Each of the four shapes represents a positive whole number. The sum of the
shapes in each row and column is displayed at the end of each row and
column. Using this information, determine the numerical value of each shape.
{
23
16
24
15
19
20
23
16
Answers
Answer:
The pentagon shape = 8
The star shape = 6
The curl shape = 3
The wave pattern shape = 5
Step-by-step explanation:
Let the pentagon shape = w, the star shape = x, the curl shape = y, and the wave pattern shape = z
Horizontally, we have;
w + 2·x + y = 23.....(1)
2·y + 2·z = 16...........(2)
2·z + w + x = 24.. ..(3)
3·y + x = 15..............(4)
Vertically, we have;
2·x + z + y = 20.......(5)
2·y + w+ z = 19........(6)
From the above equations, we have;
From equation (4), we have x = 15 - 3·y
From equation (2), we have z = 8 - y
From equation (1), we have w = 23 - (2·(15 - 3·y) + y)
∴ w = 23 - 30 + 6·y - y = 5·y - 7
w = 5·y - 7
Substituting the above values for x, and z i equation (5) gives;
2·x + z + y = 2·(15 - 3·y) + 8 - y + y = 20
30 - 6·y + 8 - y + y = 20
6·y = 30 + 8 - 20 = 18
y = 18/6 = 3
y = 3
w = 5·y - 7 = 5×3 - 7 = 8
w = 8
z = 8 - y = 8 - 3 = 5
z = 5
x = 15 - 3·y = 15 - 3×3 = 15 - 9 = 6
x = 6
Therefore, we have;
w = The pentagon shape =8
x = The star shape =6
y = The curl shape = 3, and
z = The wave pattern shape =5
The number of each of the four given shapes filled in the rows and columns are;
8 inscribed pentagon shape
6 star shapes
3 spiral shapes
5 Waves inside rectangle shape
From the diagram, we see four shapes and so let us identify them with letters;
Inscribed pentagon shape = a
Star shape = b
Spiral shape = c
Waves inside rectangle shape = d
For the first row, we see 2 stars, one inscribed pentagon and one spiral shape. Thus;
a + 2b + c = 23 .....(eq 1)
For the second row, we see 2 spiral shapes and 2 Waves inside rectangle shape. Thus;
2c + 2d = 16 ......( eq 2)
For the third row, we see 1 star, one inscribed pentagon and 2 Waves inside rectangle shape. Thus;
a + b + 2d = 24 ....(eq 3)
For the fourth row, we see 3 spiral shapes and one star shape. Thus;
b + 3c = 15 ....(eq 4)
Looking at the columns, we see that;
First column;
2c + a + d = 19 ....(eq 5)
Second column, we have;
2b + c + d = 20 .....(eq 6)
From eq 4; b = 15 - 3c
From eq 2, we have; d = 8 - c
Putting them in eq 1 gives;
a + 2(15 - 3c) + c = 23
a + 30 - 6c + c = 23
a = 5c - 7
Putting d = 8 - c and a = 5c - 7 into eq 5 gives;
2c + 5c - 7 + 8 - c = 19
6c + 1 = 19
6c = 18
c = 3
Put 3 for c in a = 5c - 7
a = 5(3) - 7
a = 8
Put 3 for c in b = 15 - 3c
b = 15 - 3(3)
b = 6
Put 3 for c in d = 8 - c
d = 8 - 3
d = 5
Thus, we have;
8 inscribed pentagon shape
6 star shapes
3 spiral shapes
5 Waves inside rectangle shape
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9m-4/=6+3m find the value of m
if anybody answer i will give 20 points and brainlist
Answers
Answer:
The value of m is 5/3 .
Step-by-step explanation:
=> 9m -4 = 6 + 3m.
=> 9m - 3m = 6 + 4.
=> 6m = 10.
=> m = 10/6.
=> m = 5/3 .
Anthony borrows $6.50 from a friend to pay for a sandwich and a drink at lunch. Then he borrows $3.75 from his sister to pay for a library fine. Choose an equation to express Anthony’s total debt that day.
Answers
please help due in 5 min
Answers
Answer:
True
Step-by-step explanation:
Value of the function increases as x increaes
Which graph represents the solution set of the system of inequalities?
−3x+y>1
{
y≥x−1
Answers
I think is A
10.6 + 6x2 - 4
Factor the negative greatest common factor
Answers
Write an equation in slope-intercept form of the line with slope −1 that contains the point (5,−2).
Answers
Answer:
y=-x+3
Step-by-step explanation:
[tex]y-y_{1}=m(x-x_{1})\\ y-(-2)=-(x-5)\\y+2=-(x-5)\\y+2=-x+5\\y+2-2=-x+5-2\\y=-x+3[/tex]
A cookie recipe called for 3 3.5 cups of sugar for every 246
cups
of
flour. If you made a batch of cookies using 4 cup of flour, how many
cups
of sugar would you need?
O 54/35 cups of sugar for 4 cups of flour
O 1 19/35 cups of sugar for 4 cups of flour
O 6 6/35 cups of sugar for 4 cups of flour
O 5 2/5 cups of sugar for 4 cups of flour
Answers
Answer:
D=5 2/5 cups of sugar for 4 cups of flour
Step-by-step explanation:
I cross multiplied and man was that a lot of fractions
The earth's crust is:
1.broken into several plates
2.floating on top of the mantle
3.made of granite and basalt
4.all of the above
Answers
Answer:
Well ummmmm 1
Step-by-step explanation:
Answer:
All of the above because we know that the earths crust is above the mantle AND that there are several plates, and I read in an article that the earth is made of basalt and granite
I also got this right on a test in odsseyware:-)
Step-by-step explanation:
Write the number in standard form: 9.82 × 10 ³
Answers
Answer:
that would be 9820
Step-by-step explanation: 9.82, count 3 to the right beginning at the decimal and boom
Which is greater 60% or ⅝
Answers
60% is greater than 5/8
Compare the ratios 4:5 and 16:20.
I need this quick
Answers
The function f(t) = |98.6-x|, represents a persons's variance from normal body temperature, where x represents a person's current body temperature in degrees Fahrenheit. Medical professionals say healthy individuals should have a variance of no more than 0.5 degrees Fahrenheit.
Answers
Answer:
98.1°F ≤ x ≤ 99.1°F
Step-by-step explanation:
Given the function:
f(x) = |98.6 - x|
Variance = 0.5
98.6°F - x = ± 0.5
Lower bound :
98.6 - 0.5 ≤ x
98.1 ≤ x
Upper bound :
x ≤ 98.6 + 0.5
x ≤ 99.1
Hence,
98.1°F ≤ x ≤ 99.1°F
Anyone know how to do this???
Answers
Answer:
6
Step-by-step explanation:
Because 1 is either on top or on the bottom and 6 would be on the opposite side of 1 meanwhile the other numbers are on the sides
is (8,-44) a solution to y=-7x+6
Answers
................................
Please answer!!!
What is the instantaneous slope of y = eight over x at x = -3?
A. -8/3
B. 8/3
C. -8/9
D. 8/9
Answers
Answer:
C
Step-by-step explanation:
[tex]\frac{d}{dx} (8x^-1)\\-8x^{-2}\\[/tex]
using x = -3
[tex]-8(-3)^{-2}\\\frac{-8}{9}[/tex]
The instantaneous slope of the function y = 8/x at x = -3 is -8/9.
Option C is the correct answer.
We have,
To find the instantaneous slope of the function y = 8/x at x = -3, we can differentiate the function with respect to x.
Differentiating y = 8/x using the power rule, we get:
dy/dx = -8/x²
Now, we can evaluate the instantaneous slope at x = -3 by substituting the value into the derivative:
dy/dx = -8/(-3)²
= -8/9
Therefore,
The instantaneous slope of the function y = 8/x at x = -3 is -8/9.
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(14x – 13)
(4x + 13)
(6x + 2)
Answers
Answer:
x = 7.416666667
Step-by-step explanation:
Set everything equal to 180 (the total # of degrees in a triangle)
180 = 14x-13 + 4x+13 + 6x+2
Combine the variables
180 = 24x - 13 + 13 + 2
Do the math
180 = 24x +2
178 = 24x
x = 7.416666667
A variable is, to put it simply, a quantity that can be altered and is not fixed. If the variables be (14x – 13), (4x + 13) and (6x + 2) then the value of x exists 7.416666667.
What is meant by variables?An unknown numerical value in an equation or algebraic expression is represented by a symbol (typically a letter) in algebra. A variable is, to put it simply, a quantity that can be altered and is not fixed.
Let the variables be (14x – 13), (4x + 13) and (6x + 2).
Set all values to 180 (the sum of the triangle's degrees).
180 = (14x - 13) + (4x + 13) + (6x + 2)
180 = 14x - 13 + 4x + 13 + 6x + 2
simplifying the above equation, we get
180 = 24x - 13 + 13 + 2
180 = 24x +2
178 = 24x
Divide both sides of the equation by 24, we get
178/24 = 24x/24
x = 7.416666667
Therefore, the value of x = 7.416666667.
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simplify 3+5i/ 6-i!!! Pls help I’m taking a test!!
Answers
Answer:
3 - 0.166666667 i
Step-by-step explanation:
I think this is the answer
I Want a board of peoples Nick names Give me Max 10 Min 5
Answers
Answer:
ZZ Top
Step-by-step explanation:
I don't know why, but my brother is evil and calls me that. Don't ask.
Answer:
nike,jordan,fila,gucci,louey
Step-by-step explanation:
For which inequality would x= 2.7 not be a solution?
O X+ 14.9
O X-4<0
O 3x + 6 2 10
O 6- X21
Answers
Answer:
1st one
Step-by-step explanation:
The inequality that is not correct for x = 2.7 will be x + < 9. The correct option is A.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
Given that the value of x is 2.7. Check all the options for x = 2.7.
Option A:-
x + 14 < 9
x < 9 - 14
x < -5 False
Option B:-
x - 4 < 0
x < 4 True
Option C:-
3x + 6 ≥ 10
3x ≥ 4
x ≥ 4/3 True
Option D:-
6 - x ≥ 1
x ≤ 5 True
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