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Vlada [557]
4 years ago
14

Heather works in a circular showroom for wallpaper and tiles. Aisles divide the showroom like the spikes of a wheel. Each spoke

aisle is 25 feet long. A spoke aisle goes from the center to the outer corridor that circles the entire showroom. In one eight-hour workday, Heather estimates that she walks around the outer corridor at least 17 times, and walks the length of 6 spoke aisles. What is the approximate distance that she walks in one day?

Mathematics
1 answer:
harina [27]4 years ago
4 0

Answer:

2820.36 feet

Step-by-step explanation:

First we need to find the length of the outer corridor, and we do that by finding the length of the circunference with a radius of 25 feet:

C = 2 * pi * r = 2 * pi * 25 = 157.08 feet

Now, as Heather walks the outer corridor 17 times and the length of 6 spoke aisles (the radius of the circunference), we have that the total distance she walks is:

Distance = 17 * 157.08 + 6 * 25 = 2820.36 feet

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The diameter of the circle is 361 units
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Trig: Solve Quadratic Equations by Factoring help with 3c and 3d
MissTica

Answer:

3c) x = 1/4, x = 6

3d) t = 0, t = 4

Step-by-step explanation:

3c).....................................

  • 6x² - 15x + 2 = 2x² + 10x - 4
  • 4x² -25x + 6 = 0
  • 4x² - 24x - (x - 6) = 0
  • 4x(x -6) - (x - 6) = 0
  • (4x - 1)(x - 6) =0
  • 4x - 1 = 0 ⇒ 4x = 1 ⇒ x = 1/4
  • x - 6 = 0 ⇒ x = 6

==============================

3d).....................................

  • - 16t² + 76t + 5 = 12t + 5
  • -16t² + 64t = 0
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  • t = 0
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8 0
3 years ago
Identify the parent function that can be used to graph the function f(x)= -9(x+5)2
olga nikolaevna [1]

Answer:

The parent function that can be used to graph f(x)=-9(x+5)^2 is:

f(x)=x^2

Step-by-step explanation:

We are asked to find the parent function that can be used to graph the function f(x) which is given as:

f(x)=-9(x+5)^2

We know that from the given options the parent function that best represents the relationship or that can be used to graph the function f(x) is:

f(x)=x^2

since the function f(x)=-9(x+5)^2 is just a transformation of the parent function the transformation that is applied is a combination of a dilation with a scale factor '-9' and a translation '-5' units to the left and a reflection along 'x' axis.

Hence, the parent function is:

f(x)=x^2

5 0
3 years ago
The corners of a square are cut off two centimeters from each corner to form an octagon. If the octagon is 10 centimeters wide,
zvonat [6]

Answer:

  • <u>92 cm²</u>

Explanation:

The area of the <em>octagon</em> may be calculated as the difference of the area of the original square and the area of the four corners cut off.

1) <u>Area of the square</u>.

The original square's side length is the same wide of the formed octagon: 10 cm.

So, the area of such square is: (10 cm)² = 100 cm².

2) <u>Area of the four corners cut off</u>.

Since, the corners were cut off two centimeters from each corner, the form of each piece is an isosceles right triangle with legs of 2 cm.

The area of each right triangle is half the product of the legs (because one leg is the base and the other leg is the height of the triangle).

Then, area of one right triangle: (1/2) × 2cm × 2cm = 2 cm².

Since, they are four pieces, the total cut off area is: 4 × 2 cm² = 8 cm².

3) <u>Area of the octagon</u>:

  • Area of the square - area of the cut off triangles = 100 cm² - 8cm² = 92 cm².

And that is the answer: 92 cm².

4 0
3 years ago
Air containing 0.04% carbon dioxide is pumped into a room whose volume is 6000 ft3. The air is pumped in at a rate of 2000 ft3/m
borishaifa [10]

Answer:

the concentration at 10 minutes= 0.4+0.0133= 0.4133%

Step-by-step explanation:

Air containing 0.04% carbon dioxide

V, volume of room is 6000 ft3.

Q, rate of air 2000 ft3/min,

initial concentration of 0.4% carbon dioxide,

determine the subsequent amount in the room at any time.

What is the concentration at 10 minutes?

firstly, we find the time taken for air to completely filled the room

Q = V/t

t = V/Q = 6000/2000 = 3min

so, its take 3mins for air to be completely filled in the room and for exhaust air to move out.

there is  an initial concentration of 0.4% carbon dioxide, and the air pump in is 0.04%.

therefore,

3mins = 0.04% of CO2

3*60 =180sec = 0.04%

1sec = 0.04/180 = 0.00022%/sec

so at any time the concentration of CO2 is 0.4 + 0.00022 =0.40022%/sec

What is the concentration at 10 minute

the concentration at 10minutes = the concentration for 1minute because at every minutes, the concentration moves in is moves out. = concentration for 2000ft3.

for 0.04% = 6000ft3

   ?          = 2000ft3

              = 2000* 0.04)/6000 =0.0133%

the concentration at 10 minutes= 0.4+0.0133= 0.4133%

4 0
3 years ago
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