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2 years ago

Which is a feature of a ROTH IRA

Mathematics

1 answer:

expeople1 [14]2 years ago

4 0

C) you can withdraw your earnings once you are 59.5 years old without paying a penalty

You might be interested in

If (8, 12) and (3, 4.5) belong to a proportional relationship, what is the constant of

Musya8 [376]

Answer:

1.5

Step-by-step explanation:

k= y/x

y= 12-4.5 =7.5

x= 8-3 = 5

k = 7.5/5 = 1.5

7 0

2 years ago

Ples help me find slant assemtotes

FrozenT [24]

A polynomial asymptote is a function $p(x)$ such that

$\displaystyle\lim_{x\to\pm\infty}(f(x)-p(x))=0$

$(y+1)^2=4xy\implies y(x)=2x-1\pm2\sqrt{x^2-x}$

Since this equation defines a hyperbola, we expect the asymptotes to be lines of the form $p(x)=ax+b$ .

Ignore the negative root (we don't need it). If $y=2x-1+2\sqrt{x^2-x}$ , then we want to find constants $a,b$ such that

$\displaystyle\lim_{x\to\infty}(2x-1+2\sqrt{x^2-x}-ax-b)=0$

We have

$\sqrt{x^2-x}=\sqrt{x^2}\sqrt{1-\dfrac1x}$
$\sqrt{x^2-x}=|x|\sqrt{1-\dfrac1x}$
$\sqrt{x^2-x}=x\sqrt{1-\dfrac1x}$

since $x\to\infty$ forces us to have $x>0$ . And as $x\to\infty$ , the $\dfrac1x$ term is "negligible", so really $\sqrt{x^2-x}\approx x$ . We can then treat the limand like

$2x-1+2x-ax-b=(4-a)x-(b+1)$

which tells us that we would choose $a=4$ . You might be tempted to think $b=-1$ , but that won't be right, and that has to do with how we wrote off the "negligible" term. To find the actual value of $b$ , we have to solve for it in the following limit.

$\displaystyle\lim_{x\to\infty}(2x-1+2\sqrt{x^2-x}-4x-b)=0$

$\displaystyle\lim_{x\to\infty}(\sqrt{x^2-x}-x)=\frac{b+1}2$

We write

$(\sqrt{x^2-x}-x)\cdot\dfrac{\sqrt{x^2-x}+x}{\sqrt{x^2-x}+x}=\dfrac{(x^2-x)-x^2}{\sqrt{x^2-x}+x}=-\dfrac x{x\sqrt{1-\frac1x}+x}=-\dfrac1{\sqrt{1-\frac1x}+1}$

Now as $x\to\infty$ , we see this expression approaching $-\dfrac12$ , so that

$-\dfrac12=\dfrac{b+1}2\implies b=-2$

So one asymptote of the hyperbola is the line $y=4x-2$ .

The other asymptote is obtained similarly by examining the limit as $x\to-\infty$ .

$\displaystyle\lim_{x\to-\infty}(2x-1+2\sqrt{x^2-x}-ax-b)=0$

$\displaystyle\lim_{x\to-\infty}(2x-2x\sqrt{1-\frac1x}-ax-(b+1))=0$

Reduce the "negligible" term to get

$\displaystyle\lim_{x\to-\infty}(-ax-(b+1))=0$

Now we take $a=0$ , and again we're careful to not pick $b=-1$ .

$\displaystyle\lim_{x\to-\infty}(2x-1+2\sqrt{x^2-x}-b)=0$

$\displaystyle\lim_{x\to-\infty}(x+\sqrt{x^2-x})=\frac{b+1}2$

$(x+\sqrt{x^2-x})\cdot\dfrac{x-\sqrt{x^2-x}}{x-\sqrt{x^2-x}}=\dfrac{x^2-(x^2-x)}{x-\sqrt{x^2-x}}=\dfrac
 x{x-(-x)\sqrt{1-\frac1x}}=\dfrac1{1+\sqrt{1-\frac1x}}$

This time the limit is $\dfrac12$ , so

$\dfrac12=\dfrac{b+1}2\implies b=0$

which means the other asymptote is the line $y=0$ .

4 0

3 years ago

A circular running track is 1/4 mile long. Elena runs on this track completing each lap in 1/4 of an hour. What is Elena's runni

daser333 [38]

Answer:

She is going 1mph

Step-by-step explanation:

each lap is 1/4 of a mile and 1/4 of an hour so 4 laps = 1 mile and in 1 hour

7 0

2 years ago

1. If one side of the square is 12in, what is the perimeter and area of the parallelogram?

gayaneshka [121]

Answer:

Not sure for 1. Area might be 144. Perimeter might be 50. I got perimeter by finding slant height of the parallelogram and then substituting it to the perimeter formula (P=2(a+b) where a is a side and b is a base). I found area by just multiplying 12*12 since to find area of parallelogram, it is base x height.

2. 45, 135, 135

Step-by-step explanation:

2. We know that an isosceles trapezoid has congruent base angles and congruent upper angles, so if one base angle measures 45 degrees, the other base angle will also be 45 degrees.

For the upper angles, we know that diagonal angles are supplementary, so 180- base angle 1 (45 degrees)= upper angle 1

180-45=upper angle 1

upper angle 1 = 135 degrees

Mentioned above, upper angles are congruent, so upper angles 1 and 2 will be 135 degrees.

Check: The sum of angles in a quadrilateral is equal to 360 degrees. We can use this to check if our answer is correct.

135+135=270 degrees (sum of upper angles)

45+45= 90 degrees (sum of base angles)

270+90=360

So the angle measures of the other three angles are 135, 135, and 45.

Hope this helps!

7 0

2 years ago

Alicia has 3 vases. She wants 9 flowers in each vase. She buys enough flowers for 2 vases. For the third vase, she cuts 9 flower

Citrus2011 [14]

she can use all of the flowers. she cut down 9 and bought 18.

6 0

3 years ago