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3 years ago

11

Another sigma notation question. Please check. Hopefully I did this one correctly!

1 answer:

Neko [114]3 years ago

8 0

Answer:

Your answer is correct. The series is a geometric series with common ratio -1/4 and first term 40. So each term is:

an = 40 (-1/4)^(n−1)

So the sum of the first 10 terms is:

∑(n=1 to 10) [ 40 (-1/4)^(n−1) ]

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A lampshade has a height of 12cm and upper and lower diameters of 10cm and 20cm A)what area of material is required to cover tha

netineya [11]

Answer:

$(a)\ Area = 195\pi$

$(b)\ Volume = 700\pi$

Step-by-step explanation:

Given

$h = 12$

$d_1 = 10$ --- lower diameter

$d_2 = 20$ --- upper diameter

Solving (a): The curved surface area

This is calculated as:

$Area = \pi l(r_1 + r_2)$

Where

$r_1 = 0.5 * d_1 = 0.5 * 10 = 5$ --- lower radius

$r_2 = 0.5 * d_2 = 0.5 * 20 = 10$ --- upper radius

And

$l = \sqrt{h^2 + (r_1 - r_2)^2$ ---- l represents the slant height of the frustrum

$l = \sqrt{12^2 + (5 - 10)^2$

$l = \sqrt{12^2 + (-5)^2$

$l = \sqrt{144 + 25$

$l = \sqrt{169$

$l = 13$

So, we have:

$Area = \pi l(r_1 + r_2)$

$Area = \pi * 13(5 + 10)$

$Area = \pi * 13(15)$

$Area = 195\pi$

Solving (b): The volume

This is calculated as:

$Volume = \frac{1}{3}\pi * h * (r_1^2 + r_2^2 + (r_1 * r_2))$

This gives:

$Volume = \frac{1}{3}\pi * 12 * (5^2 + 10^2 + (5 * 10))$

$Volume = \frac{1}{3}\pi * 12 * (25 + 100 + (50))$

$Volume = \frac{1}{3}\pi * 12 * (175)$

$Volume = \pi *4 * 175$

$Volume = 700\pi$

6 0

3 years ago

Hi, Could anyone help me with my homework

tatiyna

Answer:

$\hookrightarrow \sf x^6+24x^5+240x^4+1280x^3+3840x^2+6144x+4096$

solving steps:

$\rightarrow \sf (x + 4)^6$

$\bold{rewrite \ the \ following}$

$\rightarrow \sf (x + 4)^2 (x + 4)^2 (x + 4)^2$

$\bold {formula \ used : \sf (x+a)^2 = (x^2 + 2xa + a^2)}$

$\rightarrow \sf (x^2 + 8x+16) (x^2 + 8x+16) (x^2 + 8x+16)$

$\bold{simplify \ by \ removing \ parenthesis}$

$\rightarrow \sf (x^4 +8x^3 + 16x^2 + 8x^3 +64x^2 + 128x+16x^2+128x+256 ) (x^2 + 8x+16)$

$\bold{basic \ addition \ of \ integers }$

$\rightarrow \sf (x^4+16x^3+96x^2+256x+256) (x^2 + 8x+16)$

$\bold{remove \ parenthesis}$

$\rightarrow \sf (x^6 + 16x^5 + 96x^4 + 256x^3 + 256x^2 + 8x^6 + 128x^4 + 768x^3 + 2048x^2 + 2048 + 16x^4 + 256x^3 + 1536x^2 + 4096x + 4096)$

$\bold {final \ answer:}$

$\rightarrow \sf x^6+24x^5+240x^4+1280x^3+3840x^2+6144x+4096$

8 0

2 years ago

Yay! tysm guys for helping me on this test! i got a 85! :)

irakobra [83]

Answer:

Proud of you!! <3 :)

Step-by-step explanation:

8 0

2 years ago

Which equation could be solved using the graph above?

Oduvanchick [21]

Answer:

Option b is the correct answer

Step-by-step explanation:

The graph in the picture is the graph of a quadratic equation and it takes the shape of a parabola.

The points on the x axis through which the parabola cuts across is used to determine the solution of the quadratic equation.

Looking at the parabola formed from the plotted points, it cuts the x axis at

x = -1 and x= -2

These are the factors of the equation. To get the equation, we multiply the factors.

x= -1, x +1 = 0

x =-2 , x + 2= 0

The equation is (x+1)(x+2)

Expanding the brackets,

x×x + x×2 +1×x + 1×2

= x^2 + 2x + x +2

= x^2 + 3x +2 = 0

Option b is the correct answer

6 0

3 years ago

A company's board of directors wants to form a committee of

NeTakaya

1∪ 2/3.....................

8 0

3 years ago