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4 years ago

Prove that a cyclic parallelogram is a rectangle.

Mathematics

1 answer:

ZanzabumX [31]4 years ago

4 0

Answer:

Step-by-step explanation:

let ABCD be cyclic parallelogram.

Then ∠A=∠C

as it is cyclic so ∠A+∠C=180

∠C+∠C=180

2∠ C=180

∠C=90

So ∠A=90

similarly ∠B=∠D=90

so it is a rectangle.

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Solve the following equation for 0° ≤ θ < 360°. Use the "^" key on the keyboard to indicate an exponent. For example, sin2x w

never [62]

Answer-

$\boxed{\boxed{x=90^{\circ},270^{\circ}}}$

Solution-

The given equation-

$\Rightarrow 2\sin^2 x-\cos^2 x-2=0$

$\sin^2 x+\cos^2 x=1\ \ \Rightarrow \cos^2 x=1-\sin^2 x$

Putting this,

$\Rightarrow 2\sin^2 x-(1-\sin^2 x)-2=0$

$\Rightarrow 2\sin^2 x-1+\sin^2 x-2=0$

$\Rightarrow 3\sin^2 x-3=0$

$\Rightarrow 3\sin^2 x=3$

$\Rightarrow \sin^2 x=1$

$\Rightarrow \sin x=\sqrt1$

$\Rightarrow \sin x=\pm 1$

$\Rightarrow \sin x=1,\ \sin x=-1$

$\Rightarrow x=\sin^{-1}(1),\ x=\sin^{-1}(-1)$

$\Rightarrow x=90^{\circ}+n360^{\circ},\ x=270^{\circ}+n360^{\circ}$

Where n=0, 1, 2, ......

As given 0° ≤ x < 360°, so putting n = 0

$\Rightarrow x=90^{\circ},\ x=270^{\circ}$

3 0

4 years ago

Which equation in point-slope form contains the point (2, 3) and has slope 2?

sergiy2304 [10]

------------------------------------------------------
Option A
------------------------------------------------------

------------------------------------------------------
Check if slope = 2
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y + 2 = 2(x + 3)
y + 1 = 2x + 6
y = 2x + 6 - 1
y = 2x + 5

Slope = 2

Answer: Yes, Slope is 2

------------------------------------------------------
Check if it passed through (2, 3)
------------------------------------------------------
When x = 2
y = 2(2) + 5
y = 9

Answer: No, it does not passed through (2, 3)

------------------------------------------------------
Option B
------------------------------------------------------

------------------------------------------------------
Check if Slope is 2
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y - 3 = 2(x - 2)
y - 3 = 2x - 4
y = 2x - 4 + 3
y = 2x - 1
Slope = 2

Ans : Yes, slope is 2.

------------------------------------------------------
Check if it passed through (2, 3)
------------------------------------------------------
when x = 2
y = 2(2) - 1
y = 4 - 1
y = 3

Answer : Yes, it passed through (2, 3)

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Answer: (B) y – 3 = 2(x – 2)
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3 years ago

If the item regularly cost d dollars and is discounted 12percent which of the following represents discount price dollar

FromTheMoon [43]

Answer:

-12

Step-by-step explanation:

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3 years ago

What is 4xy + x + 2xy

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