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2 years ago

A chord is 10cm from the centre of a circle of radius 15cm. Find the length of the chord.

Mathematics

1 answer:

almond37 [142]2 years ago

5 0

Answer: 21.44 cm

Step-by-step explanation:

Given

Radius r=15 cm

distance of chord from the center is 10 cm

From the figure, the length of the chord is AC

Applying Pythagoras

$\Rightarrow AO^2=OB^2+AB^2\\\Rightarrow AB^2=15^2-10^2\\\Rightarrow AB^2=225-100=115\\\Rightarrow AB=\sqrt{115}=10.72\ cm$

The length of the chord is $AC=2AB=21.44\ cm$

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2 years ago

the ratio of the number of apples to the number of oranges is 4:6. The ratio of the number of oranges to the number of pears is

Maksim231197 [3]

The answer is <span>64 apples, 96 oranges, and 12 pears.</span>

Let's represent the fruit as following:
a - the number of apples,
o - the number of oranges,
p - the number of pears.

$a:o=4:6$
⇒ $\frac{a}{o}= \frac{4}{6}$
⇒ $a= \frac{4}{6}o$

$o:p=8:1$
⇒ $\frac{o}{p}= \frac{8}{1}$
<span>⇒ $o= 8p$
</span>
Therefore:
$a= \frac{4}{6}*8p =16/3p$

Now, if $a+o+p=172$ , then:
$\frac{16}{3}p +8p+p=172$
$\frac{16}{3}p +9p172$

Since $9= \frac{9}{1} = \frac{27}{3}$ , 9p can be expressed as 27/3p:
$\frac{16}{3}p+ \frac{27}{3}p=172$
$\frac{43}{3}p =172$
⇒ $p =172* \frac{3}{43}$
⇒ p = 12
There are 12 pears.

Since o = 8p, o = 96:
o = 8 × 12 = 96
There are 96 oranges.

Since $a= \frac{16}{3}p$ , a = 64:
$a= \frac{16}{3} *12=16*4=64$
There are 64 apples.

Therefore, there are 64 apples, 96 oranges, and 12 pears.

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