Which points are the vertices of the eclipse

Mathematics

1 answer:

Advocard [28]2 years ago

7 0

Answer:

"points G and H"

Step-by-step explanation:

The vertices of the ellipse is the major axis.

From bottom to top edge of the curve and also from left to right edge of the curve can be vertices. Which ever's distance is greatest is the vertices.

Looking at J and K (top & bottom edge), we see that the length is 12 units.

Looking at G and H (left & right edge), we see that the length is 16 units.

Hence, G & H are the longer one and it is the vertices.

first answer choice is right, "points G and H"

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How old am i if 200 reduced by 2 times my age equals 16?

Anna [14]

Ok, so since it doesn't give a value for "my age", we'll call it x. So the sentence translates into an equation...

200 reduced means... 200 -
by 2 times my age means... 2x
equals 16 means... = 16

200 - 2x = 16

Now let's solve for x to find "my age"

First subtract 200 from each side to begin to isolate x

-2x = -184

Divide each side by -2 to isolate x

x = -184/-2
x = 92

I'm 92 years old!

3 0

2 years ago

Given:

diamong [38]

Answer:

10-5 $\sqrt{2}$

Step-by-step explanation:

As per the attached figure, right angled $\triangle MDL$ has an inscribed circle whose center is $I$ .

We have joined the incenter $I$ to the vertices of the $\triangle MDL$ .

Sides MD and DL are equal because we are given that $\angle M = \angle L = 45 ^\circ.$

Formula for area of a $\triangle = \dfrac{1}{2} \times base \times height$

As per the figure attached, we are given that side a = 10.

Using pythagoras theorem, we can easily calculate that side ML = 10 $\sqrt{2}$

Points P,Q and R are at $90 ^\circ$ on the sides ML, MD and DL respectively so IQ, IR and IP are heights of $\triangle$ MIL, $\triangle$ MID and $\triangle$ DIL.

Also,

$\text {Area of } \triangle MDL = \text {Area of } \triangle MIL +\text {Area of } \triangle MID+ \text {Area of } \triangle DIL$

$\dfrac{1}{2} \times 10 \times 10 = \dfrac{1}{2} \times r \times 10 + \dfrac{1}{2} \times r \times 10 + \dfrac{1}{2} \times r \times 10\sqrt2\\\Rightarrow r = \dfrac {10}{2+\sqrt2} \\\Rightarrow r = \dfrac{5\sqrt2}{\sqrt2+1}\\\text{Multiplying and divinding by }(\sqrt2 +1)\\\Rightarrow r = 10-5\sqrt2$