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2 years ago

What is x+(x+70)+28=180

Mathematics

1 answer:

vazorg [7]2 years ago

8 0

Answer:

Step-by-step explanation:

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A circle has its center at the origin, and (5, -12) is a point on the circle. How long is the radius of the circle?

aivan3 [116]

Hello here is a solution :
 the radius of the circle is OA A(5;-12) and O (0;0)
OA= square root ((5-0)² + (-12-0)²)
 = square root (25+144)
 = square root(169)
 OA = 13

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2 years ago

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Sin(60-theta)sin(60+theta)

ehidna [41]

Step-by-step explanation:

$\sin(60 - \theta) \sin(60 + \theta) \\ = \{ \sin(60) \cos( \theta) - \sin( \theta) \cos(60) \} \{ \sin(60) \cos( \theta) + \cos(60) \sin( \theta) \} \\ = \{ \frac{ \sqrt{3} }{2} \cos( \theta) - \frac{1}{2} \sin( \theta) \} \{ \frac{ \sqrt{3} }{2} \cos( \theta) + \frac{1}{2} \sin( \theta) \} \\ \\$

from difference of two squares:

${ \boxed{(a - b)(a + b) = ( {a}^{2} - {b}^{2} ) }}$

therefore:

$= \{ {( \frac{ \sqrt{3} }{2}) }^{2} { \cos }^{2} \theta \} - \{ {( \frac{ \sqrt{3} }{2} )}^{2} { \sin }^{2} \theta \} \\ \\ = \frac{3}{4} { \cos }^{2} \theta - \frac{3}{4} { \sin}^{2} \theta$

factorise out ¾ :

$= \frac{3}{4} ( { \cos }^{2} \theta - { \sin}^{2} \theta) \\ \\ = { \boxed{ \frac{3}{4} \cos(2 \theta) }}$

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2 years ago

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Please help fast.

podryga [215]

$\huge{\underline{\boxed{\tt{Answer:}}}}$

Let AB be a chord of the given circle with centre and radius 13 cm.

Then, OA = 13 cm and ab = 10 cm

From O, draw OL⊥ AB

We know that the perpendicular from the centre of a circle to a chord bisects the chord.

∴ AL = ½AB = (½ × 10)cm = 5 cm

From the right △OLA, we have

OA² = OL² + AL²

==> OL² = OA² – AL²

==> [(13)² – (5)²] cm² = 144cm²

==> OL = √144cm = 12 cm

Hence, the distance of the chord from the centre is 12 cm.

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