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3 years ago

A square is inscribed in a circle with an area of 10 pi square inches. what is the area of the square

1 answer:

8 0

We need to determine the radius and diameter of the circle. If the area of the circle is 10 pi in^2, then, according to the formula for the area of a circle,

A = 10 pi in^2 = pi*r^2. Thus, 10 in^2 = r^2, and r = radius of circle = sqrt(10) in.

Thus, the diam. of the circle is 2sqrt(10) in. This diam. has the same length as does the hypotenuse of one of the triangles making up the square.

Thus, [ 2*sqrt(10) ]^2 = x^2 + x^2, where x represents the length of one side of the square. So, 4(10) in^2 = 2x^2. Then:
40 in^2 = 2x^2, or 20 in^2 = x^2, and so the length x of one side of the square is sqrt(20). The area of the square is the square of this result:

Area of the square = x^2 = [ sqrt(20) ]^2 = 20 in^2 (answer). Compare that to the 10 pi sq in area of the circle (31.42 in^2).

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The height of a plant, y, in centimeters, is measured x weeks after planting a seed. The height can be modeled by the regression

Gnoma [55]

Answer:

D. The limiting value for the height of the plant is 6.88 cm.

Step-by-step explanation:

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3 years ago

Because of variability in the manufacturing process, the actual yielding point of a sample of mild steel subjected to increasing

photoshop1234 [79]

Answer:

P-value ≈ 0.3463

Step-by-step explanation:

Hypothesis test would be

$H_{0}$ :p=0.20

$H_{a}$ :p>0.20

We need to calculate the z-score of sample proportion and then the corresponding P-value.

z-score can be calculated as:

z= $\frac{p(s)-p}{\sqrt{\frac{p*(1-p)}{N} } }$ where

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N is the sample size (40)

Using the numbers

z= $\frac{0.225-0.2}{\sqrt{\frac{0.2*0.8}{40} } }$ =0.3953

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4 0

3 years ago

Helpppppp please please

GenaCL600 [577]

3/10=4/x
3x=10(4)
3x=40
x=13.33

8 0

3 years ago

A contractor is building the base of a circular fountain. On the blueprint, the base of the fountain has a diameter of 18 centim

Daniel [21]

The answer is 1808.64 ft²

To calculate area of square we need to find radius r. Radius is a half of a diameter:
r = d/2

The blueprint:
d = 18 cm
r = 18/2 = 9 cm

<span>The blueprint has a scale of three centimeters to four feet. Actual radius r1 is:
</span>3 cm : 4 ft = 18 cm : r1
After crossing the products:
r1 = 4 ft * 18 cm : 3 cm
r1 = 24 ft

The area of the circular base of the fountain is:
A = r1² * π
π = 3.14
r1 = 24 ft

A = 24² * 3.14
A = 1808.64 ft²

3 0

3 years ago

Find the inverse of f(x)=4x+3

zhuklara [117]

$f(x) = 4x+3\\\\\text{Write f(x) as y = 4x+3}\\\\\text{Replace x with y,}\\\\x =4y +3\\\\\text{Solve for y:}\\\\ \implies x =4y+3\\\\\implies 4y = x-3 \\\\\implies y =\dfrac{x-3}4\\\\\implies f^{-1} (x) = \dfrac{x-3}4\\\\\text{This is the inverse of f(x)}$

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2 years ago