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2 years ago

Name two numbers that add to -16 and multiply to 63

Mathematics

1 answer:

aniked [119]2 years ago

3 0

Answer:

-7 × -9 and (-7)+(-9).......//

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What term is 1/1024 in the geometric sequence,-1,1/4,-1/6..?

Trava [24]

Answer:

$\large\boxed{\text{sixth term is equal to}\ \dfrac{1}{1024}}$

Step-by-step explanation:

The explicit formula for a geometric sequence:

$a_n=a_1r^{n-1}$

$a_n$ - n-th term

$a_1$ - first term

$r$ - common ratio

$r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}$

We have

$a_1=-1,\ a_2=\dfrac{1}{4},\ a_3=-\dfrac{1}{6},\ ...$

The common ratio:

$r=\dfrac{\frac{1}{4}}{-1}=-\dfrac{1}{4}\\\\r=\dfrac{-\frac{1}{6}}{\frac{1}{4}}=-\dfrac{1}{6}\cdot\dfrac{4}{1}=-\dfrac{2}{3}\neq-\dfrac{1}{4}$

<h2>It's not a geometric sequence.</h2>

If $a_3=-\dfrac{1}{16}$ then the common ratio is $r=\dfrac{-\frac{1}{16}}{\frac{1}{4}}=-\dfrac{1}{16}\cdot\dfrac{4}{1}=-\dfrac{1}{4}$

Put to the explicit formula:

$a_n=-1\left(-\dfrac{1}{4}\right)^{n-1}$

Put $a_n=\dfrac{1}{1024}$ and solve for <em>n </em>:

$-1\left(-\dfrac{1}{4}\right)^{n-1}=\dfrac{1}{1024}\qquad\text{use}\ a^n:a^m=a^{n-m}\\\\-\left(-\dfrac{1}{4}\right)^n:\left(-\dfrac{1}{4}\right)^1=\dfrac{1}{1024}\\\\-\left(-\dfrac{1}{4}\right)^n\cdot(-4)=\dfrac{1}{1024}\\\\(4)\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{1024}\qquad\text{divide both sides by 4}\ \text{/multiply both sides by}\ \dfrac{1}{4}/\\\\\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{4096}\\\\\dfrac{(-1)^n}{4^n}=\dfrac{1}{4^6}\qquad n\ \text{must be even number. Therefore}\ (-1)^n=1$

$\dfrac{1}{4^n}=\dfrac{1}{4^6}\iff n=6$

5 0

3 years ago

Sin^-1(1/2)<br> Please help I don't know how to do inverse or arcs<br> Thanks

Anit [1.1K]

Answer:

pi/6

Step-by-step explanation:

An inverse sin is asking which point on the unit circle has that value as its sin

Which in this case, is pi/6

$(\frac{\sqrt{3} }{2} ,\frac{1}{2})$

Hope this helps

6 0

2 years ago

Read 2 more answers

What is the area of the shaded region of the figure

Alborosie

So we're looking at two rectangles, one cut out of the other, so all you do is find the area of the big one, base times height equals area, minus the area of the small one, base times height equals area. So the equation you have to solve for is this,

Area=(12.6X14)-(3X8.4)

6 0

3 years ago

Read 2 more answers

Find the arc length of the

Agata [3.3K]

Answer:

Circle circumference = radius * 2 * PI

Arc Length = radius * 2 * PI * Central Angle / 360 degrees

Arc Length = 7 * 2 * PI * (1/4)

= 3.5 * PI

= 10.9955742876

Arc Length = 10.996 (rounded)