1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
grigory [225]
3 years ago
10

A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one-third of the sheet on each side through a

n angle θ. How should θ be chosen so that the gutter will carry the maximum amount of water?

Mathematics
1 answer:
sukhopar [10]3 years ago
5 0

Answer:

  θ = 60°

Step-by-step explanation:

The cross sectional area of the trapezoid shape will be that of a trapezoid with bases of 10 cm and (10 cm + 2·(10 cm)·cos(θ)) and height (10 cm)·sin(θ).

That area in cm² is ...

  A = (1/2)(b1 +b2)h = (1/2)(10 + (10 +20cos(θ))(10sin(θ)

  A = 100sin(θ)(1 +cos(θ))

A graphing calculator shows this area to be maximized when ...

  θ = π/3 radians = 60°

_____

<em>A</em> will be maximized when its derivative with respect to θ is zero. That derivative can be found to be 2cos(θ)² +cos(θ) -1, so the solution reduces to ...

  cos(θ) = 1/2

  θ = arccos(1/2) = π/3

You might be interested in
Name the remainder for the quotient and describe or show how you found the remainder.
horsena [70]

Answer:

Step-by-step explanation:

The expression x^3 - x^2 - 17x -15) ÷ (x-5) shows that x+5 is one of the factor if the polynomial function. According to factor theorem, we will equate the factor to zero and find x;

x+5 = 0

x = -5

Next is to generate the remainder.

Substitute x = -5 into the polynomial function

P(x) = x^3 - x^2 - 17x -15

P(-5) = (-5)^3 - (-5)^2 - 17(-5) -15

P(-5) = -125-25+85-15

P(-5) = -150+70

P(-5) = -80

Hence the remainder is -80

5 0
4 years ago
Sophia is saving money for a new bicycle. The bicycle will cost at least $623. Sophia makes $8.22 per hour.
Luda [366]
$8.22h greater than or equal to $623
3 0
3 years ago
Read 2 more answers
What is an equation of the line that passes through the point (-2,-8) and has the slope of 3
NeTakaya

Answer:

y = 3x - 2

Step-by-step explanation:

y +8 = 3 (x + 2)

y + 8 = 3x + 6

y = 3x - 2

3 0
3 years ago
Drag each label to the correct location on the table. Each label can be used more than once, but not all labels will be used.
Natalka [10]

Answer:

what lable i dont see nothing

Step-by-step explanation:

7 0
3 years ago
The quotient of six and one
Nastasia [14]

A quotient of a number and 6

Explanation: Quotient means that you divide something by another. Let's let n be the "number". Therefore, "a quotient of a number and 6" refers to n6 or n÷6 .

6 0
2 years ago
Read 2 more answers
Other questions:
  • 63.
    7·2 answers
  • What is the value of 5 in 2.195
    15·1 answer
  • Help with 12 please
    9·1 answer
  • Rewrite f(x) = x2 + 12x + 26 in general form. Because both sides of the equals sign will be manipulated, replace the f(x) with t
    8·1 answer
  • I need help with this problem
    6·2 answers
  • Which of the following subsets of vectors x y z are subspaces of R 3 ?
    15·1 answer
  • What is the slope of the line passing through the points (3,3) and (6,15)?
    7·1 answer
  • 3/8 to percentage pls answer​
    11·1 answer
  • Yoko has to carry 290 apples from a farm to the market. How many baskets will she need, given that each basket can hold 43 apple
    5·2 answers
  • According to Euclid's second postulate, how far can the line segment be extended in either direction?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!