Mathematics, 25.07.2019 19:30 IkarosSakurai

Asquare of area 32 cm2 is inscribed into a semi-circle. what is the area of the semi-circle?

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Answers

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Find Length of the square :
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Given that the area of the square is 32 cm²:

Area = Length²

$\text {Length =} \sqrt{32}$

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Find Radius :
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Using Pythagorus Theorem to find the radius of the circle:

a² + b² = c²

$( \sqrt{32})^2 + (\frac{ \sqrt{32} }{2} )^2 = ( \text {radius} )^2$

$(\text {radius} )^2 = 32 + \dfrac{32}{4}$

$(\text {radius} )^2 = 40$

$\text { Radius = } \sqrt{ 40 }$

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Find Area of the semi-circle :
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$\text {Area of the semi-circle = } \dfrac{1}{2} \pi r^2$

$\text {Area of the semi-circle = } \dfrac{1}{2} \pi ( \sqrt{40}) ^2$

$\text {Area of the semi-circle = } 20 \pi$

$\text {Area of the semi-circle = } 62.83 \ cm^2$

Answer from: lmolmlm5420

*incorect caculations do not read*
we have a formula for that
${r}^{2} = \frac{5 {a}^{2} }{4}$
r being the radius and a being the edge of our square

a is
$\sqrt{32}$
so lets find r
${r}^{2} = \frac{5 \times { \sqrt{32} }^{2} }{4}$
after solving we reach these two answers
$r = - 2 \sqrt{10} \\ r = 2 \sqrt{10}$
we are looking for a radius so negetive numbers are disregarded. now that we have the radius for our semi circle we can calculate the area of our semi circle. with this formula
$\frac{\pi \times {r}^{2} }{2}$
(just the formula for the area of a circle divided by half)
$area = \frac{\pi \times 2\sqrt{10} }{2} \\area = \pi \times 20$

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

Answer from: Quest

answer: the anser is 3

step-by-step explanation:

c- 2o is equal to 9

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How is the equation of this circle written in standard form? x2 + y2 - 6x + 14y = 142 a) (x - 3)2 + (y + 7)2 = 200 b) (x+ 3)2 + (y - 7)2 = 200 (x - 6)2 + (y + 14)2 = 142 d) (x+6)2 + (y- 14)2 = 142