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
Find the value of a for which the solution of the inequality is all real numbers
a(x + 3) < 5x + 15 - X
Answers
Answer:
x = 3
Step-by-step explanation:
(3 • (5x - 15)) - 15 • (x - 3) = 0
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
5x - 15 = 5 • (x - 3)
Equation at the end of step
3
:
15 • (x - 3) - 15 • (x - 3) = 0
STEP
4
:
Pulling out like terms
4.1 Pull out 15
Pulling out like terms :
4.2 Pull out x-3
After pulling out, we are left with :
15 • x-3 • ( 1 * 1 +( (-1) * (-1) ))
Equation at the end of step
4
:
30 • (x - 3) = 0
STEP
5
:
Equations which are never true
5.1 Solve : 30 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
5.2 Solve : x-3 = 0
Add 3 to both sides of the equation :
x = 3
One solution was found :
x = 3
The required value of a for which the solution of the inequality is all real numbers is a > 4.
What is inequality?
A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.
Now the given inequality is,
a(x + 3) < 5x + 15 - x
or, a(x + 3) < 4x + 15
Now let us solve for x first,
⇒ ax + 3a < 4x + 15
Subtract 3a from both sides we get,
ax < 4x + 15 - 3a
Subtract 4x from both sides we get,
ax - 4x < 15 - 3a
or, (a - 4)x < 15 - 3a
Dividing both the side by (a - 4) we get,
x < (15 - 3a) / (a - 4)
Now for solutions to be real numbers,
a - 4 > 0
subtracting 4 both the side we get,
⇒ a > 4
this is the required value of a for which the solution of the inequality is all real numbers
Thus, the required value of a for which the solution of the inequality is all real numbers is a > 4.
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Write an expression to represent the submarine’s elevation after its final dive. Then simplify the expression to find its elevation
Answers
Answer:
-502.5 − 115 = -617.5
The submarine’s elevation after its final dive is -617.5 feet, or 617.5 feet below sea level.
Step-by-step explanation:
Plato answer
Answer:
63 1/4
Step-by-step explanation:
I did the edmentum
How much cents are in 12 quarterS answer fast!!!!
Answers
Answer: 300 cents or 3 dollars
Step-by-step explanation: 12x25=300.
Answer:
300 CENTS
Step-by-step explanation:
hope this helps
5% of 59 is what number?
Answers
Answer:
2.95
Step-by-step explanation:
Answer:
Hello!!! erz here ^^
Step-by-step explanation:
2.95
5 x 59
-----------
100
= 2.95
HELP PLEASE!!! - Uranus is about 1.784109 miles from the Sun. About how far is Uranus from Mercury?
Answers
Answer:
About 1,749,638,696 miles.
Step-by-step explanation:
It might be incorrect so don't fully trust me.
What is 4÷3/5 Options:6 6 2/5 6 2/3 8
Answers
Answer:
[tex]6\frac{2}{3}[/tex]
Step-by-step explanation:
Reduce the expression, if possible, by cancelling the common factors.
is 1,2 a function?
If it’s correct I will cashapp you :))
Answers
Answer:
yes
Step-by-step explanation:
Since there is one value of y for every value of x, this relation is a function.
The relation is a function.
Question 4(Multiple Choice Worth 3 points)
(03.01)
Which of the sums below can be expressed as 8(2 + 7)?
O2 +56
O 10 + 15
O 16 + 7
O 16 + 56
Answers
Answer:
16+56
Step-by-step explanation:
8(2 + 7)
=8*2+8*7
16+56
8(9)=
72
the only answer that equals the same as 72 in the choices is the last one..
16+56=
72
What is the value of x in the equation 8+4 = 2(x-1)?
5
11
2
13
2.
7
Answers
Answer:
x = 7
Step-by-step explanation:
HELP ME PLS OMG -LS PLS PLS PLS ASAP ASAP PLS pls
Answers
Answer:
No, Yes, Yes
Step-by-step explanation:
no yes yes
(gl on your test or whatever)
Suppose it was –5 degrees Celsius at 6:00 a.m. By noon, the temperature had Increased by 11 degrees. What was the temperature at noon?
Answers
Answer:
6
Step-by-step explanation:
11 - -5 = 6
The temperature at noon is 6 degrees Celsius.
GivenSuppose it was -5 degrees Celsius at 6:00 a.m.
By noon, the temperature had increased by 11 degrees.
What is temperature?Temperature declines as altitude increases.
The temperature at noon is calculated by adding the morning temperature and temperature in the afternoon.
The temperature in noon = temperature at 6;00 a.m. + increase in temperature in afternoon.
The temperature in noon = -5 + 11
The temperature in noon = 6 degrees.
Hence, the temperature at noon is 6 degrees Celsius.
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I really need the answer to this plzzzzzz
Answers
Answer:
it may be c but im not usre
Step-by-step explanation:
5 tomatoes divided into $3.10
Answers
Answer:
0.62
Step-by-step explanation:
3.1 divided by 5
.............................
Question 4
Which of the following statements is true (read each carefully!):
.
The square root of 30 is between 6 and 7.
• The square root of 41 is between 5 and 6.
The square root of 14 is between 3 and 4.
• The square root of 27 is between 14 and 15.
Answers
√14= 3.74
Answer:
The square root of 14 is between 3 and 4.
Step-by-step explanation:
The answer would be that because the square root of 14 is 3.74165738677. HOPE THIS HELPS! CAN I HAVE BRAINLIEST?!
Use the side lengths of triangle DEF and the fact that the triangles are similar to find the measure of angle E and type your answer below. (Note: Do NOT include a unit label in your answer.)
Answers
Answer:
Angle E = 65 degrees
Step-by-step explanation:
Since triangle DEF is similar to triangle BAC, angle E = angle A = 180 degrees - angle B - angle C = 180 degrees - 90 degrees - 25 degrees = 65 degrees
:((((((((((((((((((
Answers
Answer:
132°
Step-by-step explanation:
Find the supplementary angle of 48°
To do this, subtract 48° from 180°
180 - 48 = 132°
Step-by-step explanation:
ABD = 180
[tex]180 - 48 = 132[/tex]
A function goes through the point (-5,2). What point is the inverse of this function guaranteed to go through ?
Answers
the inverse function just changes the coordinates
if f goes through (a,b), then f^-1 must goes through (b,a)
Which expression is equivalent?
- 5(2x -3y +4)
Answers
Answer:
A
Step-by-step explanation:
HELP ASAP!!!!! I’ll give u brainlest
Answers
Answer:
first one (382,000)
Step-by-step explanation:
just multiply by 10^5
Answer:
382000
Step-by-step explanation:
3.82*100*1000=382*1000=382000
6x + 1 = 6x - 8 what is the value of x
Answers
Answer:
No solution
Step-by-step explanation:
6x + 1 = 6x - 8
-6x -6x
1 ≠ -8
How long is 75% of a 24-hour day?
Answers
Answer:
18 hrs
Step-by-step explanation:
6hrs is 25%, so 6 times 3 is 18, Hope This Helps!
75% of a 24-hour day is 18 hour.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
75% of a 24-hour day
let 75% of 24 hour day be x.
So, 75% of 24 = x
x= 75/100 x 24
x= 3/ 4 x 24
x= 18 hours
Hence, 75% of a 24-hour day is 18 hour.
Learn more about algebra here:
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What is the sum of zeros in this equation (m-10)(8m-1)=0? Enter your ancwer as a fraction. PLSSS I RLLYYY NEEDD HELPP
Answers
Answer:
Step-by-step explanation:
m-10=0
m = 10
8m-1=0
8m=1
m=1/8
x3 = 0.008 what does the x equal
Answers
HELP ME I NEED HELP EASY 10 POINTS
Answers
Answer:
X = 14
give me brainliest please
Step-by-step explanation:
3x + 29 = 7x - 27
3x + 56 = 7x
56 = 4x
x = 14
Simplify√16 r6
A) 4r2
B) 4r3
C) 8r2
D) 8r3
Answers
Answer:
B) [tex]4r^{3}[/tex]
Step-by-step explanation:
[tex]\sqrt{16r^{6}}=\sqrt{4*4* r^{(3*2)}\\[/tex]
[tex]=\sqrt{4^{2}*(r^{3})^{2}}\\\\=4*r^{3}\\\\=4r^{3}[/tex]
Answer:
B) 4r3
Step-by-step explanation:
Hope this helps.
Find all points on the y-axis that are 5 units from the point
(4,4).
Answers
Answer:
-4,9 , -4,-1 , 4,-1 , 4,9
Step-by-step explanation:
The y-axis is straight up and if you move down on the and moving up 5 is 9 and moving down 5 is -1 and depending if it's on the right of left (negative or positive) the x-axis is (the 4) is postive or negative.
13 candy bars weigh 39 ounces.what is the weight of 25 candy bars
Answers
Answer:
75 ounces
Step-by-step explanation:
39/13=3 so each candy bar weighs 3 ounces each so 25*3=75
Answer:
75 ounces
Step-by-step explanation:
39 divided by the amount of candy bars (13) is 3. Which means each candy bar weighs 3 ounces. So 3 times 25 is 75.
Write the explicit formula for the arithmetic sequence 6, 8, 10, 12, . . . What is term number 46 in this sequence?
Answer:
Answers
Answer:
102
Step-by-step explanation:
For 0.00001 what would the exponent be? 10^?
Answers
Answer:
would be 1
Step-by-step explanation:
you take 0.00001 and keep multiplying that by your answer
Complete the statement relating solutions and roote