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
Lapatulllka [165]
2 years ago
7

A stereo system is being installed in a room with a rectangular floor measuring 16 feet by 12 feet and an 8​-foot ceiling. The s

tereo amplifier is on the floor in one corner of the room. A speaker is at the ceiling in the opposite corner of the room. You must run a wire from the amplifier to the​ speaker, and the wire must run along the floor or walls​ (not through the​ air). What is the shortest length of wire you can use for the​ connection?

Mathematics
1 answer:
Snezhnost [94]2 years ago
8 0

Answer:

  4√41 ≈ 25.61 feet

Step-by-step explanation:

The shortest route is the one that crosses the longest edge between room surfaces. In this case, that is the 16-foot edge between the floor and wall opposite the amplifier, or the 16-foot edge between the ceiling and the wall adjacent to the amplifier.

The length of the required wire is ...

  √((8+12)² +16²) = √656 = 4√41 ≈ 25.61 . . . feet

You might be interested in
12,000 g____1.2 kg A greater than B less than C equal to
serious [3.7K]
12000 g would be equal to 12 kg not 1.2 kg so the answer has to be A) greater than.

Answer: A) GREATER THAN
7 0
3 years ago
A rectangle has its base on the x axis and its upper two vertices on the parabola y = 9 − x2. (a) Draw a graph of this problem.
gtnhenbr [62]

Answer:

  • (a) see attached
  • (b) width: 2x; height: y = 9-x²
  • (c) A=2x(9-x²) . . . 0 ≤ x ≤ 3
  • (d) dA/dx = -6x² +18; x=±√3
  • (e) 12√3 units²

Step-by-step explanation:

(a) The attachment shows the graph of the parabola in blue. It also shows an inscribed rectangle in black.

(b) The upper right point of the rectangle is shown in the attachment as (x, y). The dimension y is the height of the rectangle. The x-dimension is half the width of the rectangle, which is symmetrical about the y-axis. Hence the width is 2x.

(c) As with any rectangle, the area is the product of length and width:

... A = (2x)(9 -x²) . . . . . the attachment shows a graph of this

... A = -2x³ +18x . . . . . expanded form suitable for differentiation

A suitable domain for A is where both x and A are non-negative: 0 ≤ x ≤ 3.

(d) The derivative of A with respect to x is ...

... A' = -6x² +18

This is defined everywhere, so the critical values will be where A' = 0.

... 0 = -6x² +18

... 3 = x² . . . . . . . divide by -6, add 3

... √3 = x . . . . . . . -√3 is also a solution, but is not in the domain of A

(e) The rectangle will have its largest area where x=√3. That area is ...

... A = 2x(9 -x²) = 2√3(9 -(√3)²) = 2√3(6)

... A = 12√3 . . . . square units . . . . ≈ 20.785 units²

7 0
3 years ago
Give the equation of the circle centered at the origin and passing through the point (0,5)
Julli [10]

Answer:

x^{2} +y^{2}=25

Step-by-step explanation

The standard equation of a circle centered at origin is  x^{2} +y^{2} =r^{2}

r = radius of the circle

The circle is passing through the point (0,5)

∴ radius  r=\sqrt{(0-0)^{2}+(5-0)^{2} }

               r=\sqrt{0+25}

               r=\sqrt{25}

               r^{2}=25

∴ The equation of the circle is

     x^{2} +y^{2} = 25

5 0
2 years ago
What is 5\18 equal to
Evgesh-ka [11]
The answer is 3.3 hope this helps you  .Skateboards
6 0
3 years ago
A 51-foot ladder is leaning up against a building . The top of the ladder reaches the wall at a height of 50 feet . How far is t
alexandr402 [8]
If 50^2 +b^2=51^2 then
     2500+b^2=2601
           b^2=100
              b=10
4 0
3 years ago
Read 2 more answers
Other questions:
  • Chanel‌ ‌has‌ ‌two‌ ‌dogs,‌ ‌Mimi‌ ‌and‌ ‌Honey.‌ ‌
    8·1 answer
  • 0 is less than or equal to 2 - 2x less than 4
    13·1 answer
  • Evaluate the expression<br> 1. b ÷ 2.4; b = 16.8
    13·1 answer
  • The amount of a radioactive substance decreases by 10% every
    13·1 answer
  • 1/2 x 2 1/2 as a fraction in simplest form plz help fast
    5·1 answer
  • 2. Apply the laws of indices and simplify. h) <br><img src="https://tex.z-dn.net/?f=3%20%5Csqrt%7Bx%20%7B%3F%7D%5E%7B2%7D%20%20%
    6·2 answers
  • Translate the sentence into an equation.
    13·1 answer
  • Question 9 (3 points)
    8·1 answer
  • Solve -4/5x =12<br><br> please help
    5·2 answers
  • Work out the sum of 1/3, 1/5 and 3/10<br> Give your answer in its simplest form.
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!