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3 years ago

Solve for x: |2x 6| − 4 = 20

1 answer:

7 0

| 2x + 6| - 4 = 20 has two absolute values
solution 1
2x + 6 - 4 = 20 --> 2x + 2 = 20 --> 2x = 18 --> x = 9
2 (9) + 6 - 4 = 24- 4 = 20 ✔
solution 2
2x - 6 - 4 = 20 --> 2x - 10 = 20 --> 2x = 10 --> x = 5
2 (5) - 6 - 4 = 10- 10 = 0

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Consider the volume of the region shown below, which shows a right circular cone with top radius 3 cm and height 10 cm. We have

koban [17]

I have the same problem here with a slight change in the given values:

radius is 2 & height of 6 indicates the bounding line is y = 3 x---> x = y / 3....

<span>thus the [ π radius ² thickness ] yields π (y² / 9 ) <span>dy ,</span> y in [ 0 , 6 ] for the volume... </span>

a Riemann sum is then : y_i = 0 + i [ 6 / n ] = 6 i / n , i = 1,2,3...n and do a right side sum

<span>π Σ { i = 1,2,3..n } [ 36 i² / 9 n² ] [ 6 / n ]
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I hope my guide has come to your help. God bless and have a nice day ahead!

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3 years ago

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>:

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

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

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3 years ago

Identify and circle all of the factors of<br> 3x2 - 9x + 6

aleksandr82 [10.1K]

I hope it helps you get it right

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3 years ago

Index notation simplify 4^9 x 4^3

LenKa [72]

Answer:

$4^{12}$

Step-by-step explanation:

Using the rule of exponents

$a^{m}$ × $a^{n}$ = $a^{(m+n)}$ , then

$4^{9}$ × $4^{3}$ = $4^{(9+3)}$ = $4^{12}$

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3 years ago

∠QPS is a right angle and m∠QPR = 71°, what is m∠RPS?

natta225 [31]

Answer: <RPS = 161

Step-by-step explanation:

P is the common vertex in all of these angles. From this we know that these have to be adjacent angles (<QPR and <QPS) that equal the whole angle (<RPS)

<QPR+<QPS= <RPS

71+90= 161

(<QPS is a right angle. Right angles are equal to 90 degrees.)

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3 years ago