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erastova [34]
3 years ago
11

Find the area of the circle. Use your calculator's value of π. Round your answer to the nearest tenth. A) 27.6 yd2 B) 283.5 yd2

C) 243.3 yd2 D) 289.5 yd2

Mathematics
1 answer:
yan [13]3 years ago
6 0
<h2>Answer:</h2>

s \approx 282.20ft^2

<h2>Step-by-step explanation:</h2>

A circle is a curve made up of all the points that are the same distance from the center. In this problem, we are asked to find the area of the sector. A sector is a region of a circle between two radii. Suppose you have a central angle \theta degrees, the sector can be found as:

s=\frac{\theta}{360}\times\pi r^{2}

We know:

r=14ft \\ \\ \theta=165^{\circ}

So:

s=\frac{165^{\circ}}{360^{\circ}}\times\pi (14^{2}) \\ \\ s=\frac{11}{24}\times (196\pi) \\ \\ s=\frac{539}{6}\pi \approx 282.20ft^2

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Over which interval is the graph of f(x) = one-halfx2 + 5x + 6 increasing?
kaheart [24]

Answer:

\large\boxed{x\in[-5,\ \infty)}

Step-by-step explanation:

f(x)=\dfrac{1}{2}x^2+5x+6\\\\\text{The coeficient of}\ x^2\ \text{is the positive number. Therefore the parabola is op}\text{en up}.\\\\\text{If a parabola op}\text{en up, then the graph increasing in interval}\ (h,\ \infty),\\\text{and decreasing in interval}\ (-\infty,\ h).\ \text{Where}\ h\ \text{is a first coordinate of a vertex.}\\\\\text{For}\ y=ax^2+bx+c,\ h=\dfrac{-b}{2a}.\\\\\text{We have}\ a=\dfrac{1}{2}\ \text{and}\ b=5.\ \text{Substitute:}\\\\h=\dfrac{-5}{2\left(\frac{1}{2}\right)}=-\cdot\dfrac{5}{1}=-5.

8 0
3 years ago
Read 2 more answers
The vendor of a coffee cart mixes coffee beans that cost $9 per pound with coffee beans that cost $5 per pound. How many pounds
lidiya [134]

Answer:

56.25 pound of the coffee that costs $5 per pound is needed

18.75 pound of the coffee that costs $9 per pound is needed

Step-by-step explanation:

Let the number of pounds be x and y respectively

The total pounds is 75;

So;

x + y. = 75 •••••••(i)

Total cost of first type

9 * x = $9x

Total cost of second type;

5 * y= $5y

75 pound at $6 per pound; total cost of this is;

6 * 75 = $450

Thus;

9x + 5y = 450 ••••••••(ii)

From i, x = 75-y

Put this into ii

9(75-y) + 5y = 450

675 -9y + 5y = 450

4y = 675-450

4y = 225

y = 225/4

y = 56.25

x = 75 - y from i

x = 75-56.25

x = $18.75

8 0
3 years ago
The wavelength of green lights is about 0.00000051 meter. What is the estimated wavelength as a single digit times a power of 10
kari74 [83]

<em><u>Answer:</u></em>

<h2>5.1 X 10^-7</h2>

<u><em>Reason:</em></u>

It is to the -7 because you would have to move the decimal left (-) 7 times to get the original 0.00000051.

Hope this helps! ;)

6 0
3 years ago
A 15 ft. telephone pole has a wire that extends from the top of the pole to the ground. The wire and the ground form a 42° angle
Lorico [155]

Answer:

Correct choice is A

Step-by-step explanation:

Consider right triangle ABC formed by the telephone pole (side AB) and ground (side BC). In this triangle AC is the length of the wire, BC is the distance from the base of the pole to the spot where the wire touches the ground and AB=15 ft, ∠ACB=42°.

Then

  • \sin 42^{\circ}=\dfrac{AB}{AC}\Rightarrow AC=\dfrac{AB}{\sin 42^{\circ}}=\dfrac{15}{\sin 42^{\circ}}\approx 22.4\ ft.
  • \tan 42^{\circ}=\dfrac{AB}{BC}\Rightarrow BC=\dfrac{AB}{\tan 42^{\circ}}=\dfrac{15}{\sin 42^{\circ}}\approx 16.7\ ft.

8 0
3 years ago
What is the surface area of a cone that has a radius of 8 feet and a slant height of 12 feet? (Use 3.14 for π.)
kodGreya [7K]

Answer:

Surface area of cone is 502.4\ ft^2

Step-by-step explanation:

Given:

radius of a cone (r) = 8 feet

slant height of cone (l) = 12 feet

We need to find the surface area of cone.

Total surface area of cone = Area of circle + Area of curved surface

Now we know that,

Area of circle = \pi r^2

Area of curved surface = \pi rl

Hence Total surface area of cone = \pi r^2+\pi rl=\pi r(r+l) = 3.14 \times 8 (8+12)=3.14\times8\times20= 502.4 \ ft^2

Surface area of cone is 502.4\ ft^2.

4 0
3 years ago
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