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svetoff [14.1K]
3 years ago
9

The radius of a circle is 4 feet. What is the area of a sector bounded by a 45 degree arc

Mathematics
2 answers:
Kipish [7]3 years ago
6 0
45/360 * 4^2 pi = 6.283
ANSWER IS 6.283 (3 decimal places)
alexgriva [62]3 years ago
3 0

Answer:

2π ft²

Step-by-step explanation:

Circle Area:

A = πr²

A = π × (4 ft)²

A = 16π ft²

Sector Area:

A = (45°)/(360°) × 16π ft²

A = 2π ft²

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After heating up in a teapot, a cup of hot water is poured at a temperature of 204°F.
laila [671]

Answer:

  • Question 1: 0.081 min⁻¹
  • Question 2: 168ºF

Explanation:

The missing equation is:

             T=T_a+(T_0-T_a)e^{-kt}

You are given:

  • Ta = the temperature surrounding the object = 73ºF
  • T₀ = the initial temperature of the object = 204ºF
  • t = 2.5 min
  • T after 2.5 min = 180ºF

Question 1: Find the the value of k.

Substitute the data into the equation and solve for k:

          180\º=73\º+(204\º-73\º)e^{-k\cdot 2.5min}\\ \\ 107\º=131\ºe^{-k\cdot 2.5min}\\\\-k\cdot 2.5min=\ln (107/131)\\\\k=0.081min^{-1}

Question 2: Find the Fahrenheit temperature of the cup of water, to the nearest degree, after 4 minutes.

Subsititute into the formula and compute:

            T=73\ºF+(204\ºF-73\ºF)e^{-0.081min^{-1}\times 4min}\\ \\ T=73\ºF+(131\ºF)(0.72325024)\\\\T=168\ºF

4 0
3 years ago
In a box of 180 oranges, 15% are not ripe. How many oranges are not ripe?
mixas84 [53]
27 is the correct answer.
7 0
3 years ago
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Which is a possible turning point for the continuous function f(x)?
babymother [125]

Answer:

We are given coordinates of a continuous function f(x)

(–2, 0)

(0, –2)

(2, –1)

(4, 0).

We need to find the possible turning point for the continuous function.

Note: Turning point is a point on the graph where slope of the curve changes from negative to positive or positive to negative.

A turning point is always lowest or highest point of the curve (where bump of the graph seen).

For the given coordinates we can see that  (–2, 0) and (4, 0) coordinates are in a same line, that is on the x-axis.

But the coordinate  (0, –2) is the lowest point on the graph.

Therefore, (0, –2) is the turning point for the continuous function given.

hoped this was helpful!

5 0
3 years ago
Ms.Omar runs the school tennis club. She has a bin of tennis balls and rackets. For every 5 tennis balls in the bin, there are 3
stepan [7]

Answer:

see the explanation

Step-by-step explanation:

Let

x ----> number of tennis balls

y ----> number of tennis rackets

we know that

To find out the ratio of tennis balls to tennis rackets, divide the number of tennis ball by the number of tennis rackets

In this problem we have

\frac{x}{y}=\frac{5}{3}

so

x=\frac{5}{3}y

That means

The number of tennis balls is three-fifths times the number of tennis rackets

see the attached figure to better understand the problem

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3 years ago
Whole Lot If there are 7 bears in a room and they each hug each other once and only once, how many total bear hugs were there al
Dvinal [7]
1.They basically all did one big bug,not separate hugs with different bears.
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