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3 years ago

Help I need this done soon!!! Thank you!!

Mathematics

1 answer:

jenyasd209 [6]3 years ago

4 0

D is the midpoint of segment AC, Given
Segment AD is congruent to segment CD, Definition of Midpoint
Angle BDC is congruent to angle BDA, Given
Segment BD is congrent to angle BD, Reflexive property of congruence
Triangle ABD is congruent to triangle CBD, SAS

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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.

4 0

3 years ago

Hello Pls help and thanks

Anna11 [10]

Answer:

c.) in the correct answer

6 0

3 years ago

Determine a rational number that is located between -2 1/4 and -2.8

Kipish [7]

Answer:

Step-by-step explanation:

3 0

3 years ago

Which function is the inverse of ſx) - 2x+ 3?

Sonbull [250]

If $f^{-1}(x)$ is the inverse of $f(x)$ , then

$f\left(f^{-1}(x)\right) = x$

which means

$2f^{-1}(x)+3 = x$

Solve for $f^{-1}(x)$ :

$2f^{-1}(x) + 3 = x \\\\ 2f^{-1}(x) = x - 3 \\\\ f^{-1}(x) = \dfrac{x-3}2 = \boxed{\dfrac12x-\dfrac32}$

5 0

3 years ago

Graphs of Function,

andrew-mc [135]

Answer:

A function is increasing when the gradient is positive

A function is decreasing when the gradient is negative

Question 7

If you draw a tangent to the curve in the interval x < -2 then the tangent will have a positive gradient, and so the function is increasing in this interval.

If you draw a tangent to the curve in the interval x > -2 then the tangent will have a negative gradient, and so the function is decreasing in this interval.

If you draw a tangent to the curve at the vertex of the parabola, it will be a horizontal line, and so the gradient at x = -2 will be zero.

The function is increasing when x < -2

$(- \infty,-2)$

The function is decreasing when x > -2

$(-2, \infty)$

Additional information

We can actually determine the intervals where the function is increasing and decreasing by differentiating the function.

The equation of this graph is:

$f(x)=-2x^2-8x-8$

$\implies f'(x)=-4x-8$

The function is increasing when $f'(x) > 0$

$\implies -4x-8 > 0$

$\implies -4x > 8$

$\implies x < -2$

The function is decreasing when $f'(x) < 0$

$\implies -4x-8 < 0$

$\implies -4x < 8$

$\implies x > -2$

This concurs with the observations made from the graph.

Question 8

This is a straight line graph. The gradient is negative, so:

The function is decreasing for all real values of x

$(- \infty,+ \infty)$

But if they want the interval for the grid only, it would be -4 ≤ x ≤ 1

$[-4,1]$

Question 9

If you draw a tangent to the curve in the interval x < -1 then the tangent will have a negative gradient, and so the function is decreasing in this interval.

If you draw a tangent to the curve in the interval x > -1 then the tangent will have a positive gradient, and so the function is increasing in this interval.

If you draw a tangent to the curve at the vertex of the parabola, it will be a horizontal line, and so the gradient at x = -1 will be zero.

The function is decreasing when x < -1

$(- \infty,-1)$

The function is increasing when x > -1

$(-1, \infty)$

5 0

2 years ago