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2 years ago

Combine these radicals. Help please unit test on Ed

Mathematics

1 answer:

Drupady [299]2 years ago

7 0

Answer: the answer is C

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Find the sum of the geometric series 512+256+ . . .+4

mario62 [17]

$\bf 512~~,~~\stackrel{512\cdot \frac{1}{2}}{256}~~,~~...4$

so, as you can see above, the common ratio r = 1/2, now, what term is +4 anyway?

$\bf n^{th}\textit{ term of a geometric sequence}\\\\a_n=a_1\cdot r^{n-1}\qquad \begin{cases}n=n^{th}\ term\\a_1=\textit{first term's value}\\r=\textit{common ratio}\\----------\\r=\frac{1}{2}\\a_1=512\\a_n=+4\end{cases}$

$\bf 4=512\left( \cfrac{1}{2} \right)^{n-1}\implies \cfrac{4}{512}=\left( \cfrac{1}{2} \right)^{n-1}\\\\\\\cfrac{1}{128}=\left( \cfrac{1}{2} \right)^{n-1}\implies \cfrac{1}{2^7}=\left( \cfrac{1}{2} \right)^{n-1}\implies 2^{-7}=\left( 2^{-1}\right)^{n-1}\\\\\\(2^{-1})^7=(2^{-1})^{n-1}\implies 7=n-1\implies \boxed{8=n}$

so is the 8th term, then, let's find the Sum of the first 8 terms.

$\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases}n=n^{th}\ term\\a_1=\textit{first term's value}\\r=\textit{common ratio}\\----------\\r=\frac{1}{2}\\a_1=512\\n=8\end{cases}$

$\bf S_8=512\left[ \cfrac{1-\left( \frac{1}{2} \right)^8}{1-\frac{1}{2}} \right]\implies S_8=512\left(\cfrac{1-\frac{1}{256}}{\frac{1}{2}} \right)\implies S_8=512\left(\cfrac{\frac{255}{256}}{\frac{1}{2}} \right)\\\\\\S_8=512\cdot \cfrac{255}{128}\implies S_8=1020$

7 0

3 years ago

(4x^3-12x^2-5)-(-8x^2+4x+3)

krok68 [10]

Answer:

Hey! Here is your answer simplified!

Step-by-step explanation:

4 x 3 − 4 x 2 − 4 x − 8

Hope this helps! ❤

8 0

2 years ago

PLEASE ITS MY LAST QUESTION

Serjik [45]

Answer:

$y = - \frac{1}{4} x - 10$

Step-by-step explanation:

The negative reciprocal of 4 is -1/4.

Let's substitute in our values, to find the y-intercept:

$y = - \frac{1}{4} x + c$

$- 11 = - 1 + c$

$c = - 10$

Finally, our full equation is:

$y = - \frac{1}{4} x - 10$

4 0

1 year ago

Kirsten is making lanyards for a conversation.

JulijaS [17]

If 1 lanyard = 1.75 ft, then 1000 lanyards = (1000 x 1.75) = 1750 ft

8 0

3 years ago

What is the value of x to the nearest tenth??

Stolb23 [73]

Answer:

$\displaystyle 12,3 ≈ x$

Step-by-step explanation:

We have to determine which trigonometric ratio to use, depending on what is displayed for us, and we will be using the <em>cotangent</em> [or <em>tangent</em>] ratio, this time with two angle measures:

$\displaystyle cot\:39° = \frac{x}{10} → 10cot\:39° ≈ 12,34897157 ≈ 12,3 \\ \\ tan\:39° = \frac{10}{x} → \frac{10}{tan\:39°} ≈ 12,34897157 ≈ 12,3 \\ \\ \\ OR \\ \\ \\ cot\:51° = \frac{10}{x} → \frac{10}{cot\:51°} ≈ 12,34897157 ≈ 12,3 \\ \\ tan\:51° = \frac{x}{10} → 10tan\:51° ≈ 12,34897157 ≈ 12,3$

Extended Information on Trigonometric Ratios

$\displaystyle \frac{OPPOSITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOSITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOSITE} = csc\:θ \\ \frac{ADJACENT}{OPPOSITE} = cot\:θ$

I am joyous to assist you anytime.

3 0

2 years ago