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 1

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

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

Which expression is equivalent?

- 5(2x -3y +4)

Answers

Answer:

Step-by-step explanation:

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.

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

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.

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

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

:((((((((((((((((((

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]

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

x3 = 0.008 what does the x equal

Answers

.2 because 2^3 is equal to 8. Which is 2*2*2=8.

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

The answer is : square root of 14 is between 3 and 4
√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?!

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)

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)

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

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:

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

Complete the statement relating solutions and roote

Answers

There as no problems to solve srry

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

Pulling out like terms

3.1 Pull out like factors :

5x - 15 = 5 • (x - 3)

Equation at the end of step

15 • (x - 3) - 15 • (x - 3) = 0

STEP

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

30 • (x - 3) = 0

STEP

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.

To learn more about inequality :

https://brainly.com/question/13363104

#SPJ2

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.

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:

https://brainly.com/question/24875240

#SPJ2

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(2+7)=
8(9)=
72

the only answer that equals the same as 72 in the choices is the last one..

16+56=
72

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:

Step-by-step explanation:

11 - -5 = 6

The temperature at noon is 6 degrees Celsius.

Given

Suppose 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.

To know more about Temperature click the link given below.

https://brainly.com/question/22618350

5 tomatoes divided into $3.10

Answers

It would be .62 for one

Answer:

0.62

Step-by-step explanation:

3.1 divided by 5

.............................

I really need the answer to this plzzzzzz

Answers

Answer:

it may be c but im not usre

Step-by-step explanation:

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:

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.

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

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.

Other Questions

rewrite the expression using rational exponents If the interest rate this year is 8.8% and the interest rate next year will be 10.8%, what is the future value of $1 after 2 years? What is the present value of a payment of $1 to be received in 2 years? Which of the following is true of prokaryotic cells? 2. Great Britain developed a huge debt from fighting which war? write me a horror story (short) Rewrite the expression by factoring out (w+3).7w2(w+3)-3(w+3) Help please!! Thank you! what is another name for I will give brainliest! 2(6x+3) 2) Caculate the unit rate. Paying $28 for 8 pounds of pears. What is the cost per pound of pears? 12. An object is fired from the top of a 200 ft. tower with an initial velocity of 80 ft/sec. and ismodeled by the equation h(t) = -16t^2+80t + 200.a) How long after firing does it reach its maximum height?b) What is the maximum height? The new lotion smells amazing. Identify the noun You and a partner are considering the purchase of a convenience store.? The store has annual sales of $500,000 and is paying annual payroll of $100,000. The cost of goods sold every year is $150,000. The firm has miscellaneous expenses (taxes, insurance, garbage, electricity, natural gas, security, maintenance, property taxes, training, advertising, accounting fees, bank charges, etc.) of roughly $68,000 per year. If depreciation is equal to $15,000 per year and the tax rate is equal to 38% then what is the net income? The sum of three consecutive odd integers is 18 less than five times the middle number fimd the three integers In the poem Ellis Island By Joseph Bruchac:1) how do the words used to describe the Statue of Liberty contribute to the tone of the poem? (Tone = authors attitude)2) How does the poem explore Americas unique history of offering hope and opportunity to some people, while subjugating others3)The speaker of this poem references one component of American history that is complicated. Can you think of others? What makes them complicated?4) In the poem, the speaker feels a sense of connection to his ancestors who immigrated to America and to the Native Americans who lived on the land before them. What might cause the speaker to feel connected to both groups of people? How can both parts of the history the speaker describes be part of their identity? Describe the term "semi-permeable" (or "selectively-permeable) membrane. Why is it important? PLEASE HELP Select the correct answer from each drop-down menu. Options are (equal to, not equal to) what is the medium of the sound waves the student hears What is the maximum number of solutions each of the following systems could have? The Jackson-Timberlake Wardrobe Co. just paid a dividend of $1.55 per share on its stock. The dividends are expected to grow at a constant rate of 6 percent per year indefinitely. Investors require a return of 14 percent on the company's stock. a. What is the current stock price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. What will the stock price be in 3 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c. What will the stock price be in 7 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)