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3 years ago

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Mathematics

1 answer:

SashulF [63]3 years ago

4 0

Answer:

Option D: 2 . cos(90 + x) = -2a

Step-by-step explanation:

Given that:

sin x = a --------- eq1

As we know that trignometry says:

cos(90 + x) = -sinx-------- eq2

In option two we are given that:

cos(90 + x) = -2a ---------- eq3

So by equating both sides of eq2 and eq3:

-2a = -2sinx

By cancelling -2 from both sides we get:

sinx = a

That is given in eq1

hence proved

i hope it will help you!

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3 years ago

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3 years ago

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Pani-rosa [81]

Answer:

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Step-by-step explanation:

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3 years ago

a square has a side length of x. A rectangle has a length that is 4 inches longer than the square and a width that is 2 inches s

vodomira [7]

Answer:

Length of the rectangle is = 8 inches.

Step-by-step explanation:

Given :

Area of square = Area of the rectangle

According to the question:

Length of the square be 'x'.

Its area = (Side)*(Side) = $x^2$ ...equation (i)

Length of the rectangle = $(x+4)$

Width of the rectangle = $(x-2)$

Area of the rectangle =Length * Width

⇒ $(x+4)(x-2)=x^2-2x+4x-8$

⇒ $x^2+2x-8$ ...equation (ii)

Equating both the equation as area of both the figure are equal.

⇒ $x^2+2x-8=x^2$

⇒ $2x-8=0$ ...subtracting $x^2$ both sides

⇒ $2x=8$ ...dividing both sides with 2

⇒ $x=\frac{8}{2}=4$ inches

Plugging the value of x=4 in the length of the rectangle.

We have,

⇒ $(x+4)=(4+4)=8$

So the length of the rectangle = 8 inches.

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3 years ago

Prove algebraically that r = 10/2+2sinTheta is a parabola

Xelga [282]

Answer:

$y = - \frac{ 1 }{10} {x}^{2} + \frac{5}{2}$

Step-by-step explanation:

We want to prove algebraically that:

$r = \frac{10}{2 + 2 \sin \theta}$

is a parabola.

We use the relations

${r}^{2} = {x}^{2} + {y}^{2}$

and

$y = r \sin \theta$

Before we substitute, let us rewrite the equation to get:

$r(2 + 2 \sin \theta) = 10$

$r(1+ \sin \theta) = 5$

Expand :

$r+ r\sin \theta= 5$

We now substitute to get:

$\sqrt{ {x}^{2} + {y}^{2} } + y = 5$

This means that:

$\sqrt{ {x}^{2} + {y}^{2} }=5 - y$

Square:

${x}^{2} + {y}^{2} =(5 - y)^{2}$

Expand:

${x}^{2} + {y}^{2} =25 - 10y + {y}^{2}$

${x}^{2} =25 - 10y$

${x}^{2} - 25 = - 10y$

$y = - \frac{ {x}^{2} }{10} + \frac{5}{2}$

This is a parabola (0,2.5) and turns upside down.

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3 years ago

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