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2 years ago

Find the sum of the first 30 terms in this geometric series -5 -4 -16/5

Mathematics

1 answer:

Maslowich2 years ago

6 0

Answer:

-24.97 to the nearest hundredth.

Step-by-step explanation:

First term a1 = -5.

Common ratio r = -4/-5 = 4/5.

Sum of n terms = a1 * [1 - (4/5)^n] / (1 - 4/5)

Sum of 30 terms = -5 * ( 1 - (4/5)^30) / 1/5

= -25 * ( 1 - (4/5)^30)

= -24.97

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A glass paperweight has a composite shape: a square pyramid fitting exacty on top of an 8 centimeter cube. The pyramid has a hei

ArbitrLikvidat [17]

Answer:

Part 1) The volume of the paperweight is $576\ cm^{3}$

Part 2) The total surface area of the paperweight is $400\ cm^{2}$

Step-by-step explanation:

Part 1) what is the volume of the paperweight?

we know that

The volume of the paperweight is equal to the volume of the square pyramid plus the volume of the cube

step 1

Find the volume of the pyramid

The volume of the pyramid is equal to

$V=\frac{1}{3}BH$

where

B is the area of the square base

H is the height of the pyramid

$B=8^{2}=64\ cm^{2}$

$H=3\ cm$

substitute

$V=\frac{1}{3}(64)(3)=64\ cm^{3}$

step 2

Find the volume of the cube

The volume of the cube is equal to

$V=b^{3}$

$V=8^{3}=512\ cm^{3}$

step 3

Find the volume of the paperweight

$64\ cm^{3}+512\ cm^{3}=576\ cm^{3}$

Part 2) what is the total surface area of the paperweight?

we know that

The total surface area of the paperweight is equal to the surface area of 5 faces of the cube plus the lateral area of the pyramid

step 1

Find the surface area of 5 faces of the cube

$SA=5b^{2}$

$SA=5(8^{2})=320\ cm^{2}$

step 2

Find the lateral area of the pyramid

$LA=4[\frac{1}{2}bh]$

$LA=4[\frac{1}{2}(8)(5)]=80\ cm^{2}$

step 3

Find the total surface area of the paperweight

$320\ cm^{2}+80\ cm^{2}=400\ cm^{2}$

8 0

2 years ago

Find each quotient using long division 676 ÷ 13 (need the full thing fast lol)

ra1l [238]

Answer:

Step-by-step explanation:

Ok then "cracks knuckles" heres an image of the division! hope it helps.

3 0

1 year ago

Pls help me guys!<br> Thanks =P

Tema [17]

(4*7/2)+(15*7)+(7*6/2) = 140

6 0

2 years ago

write the standard form of the line that passes through the given point. include your work in your final answer. (6,1)and (5,4)

bezimeni [28]

We are given two points on a line. First we need to find the slope of the line using these two points.

The given points are (6, 1) and (5, 4). The slope (m) of the line will be:

$m= \frac{4-1}{5-6} =-3$

Using the slope and the point (6,1) we can write the equation in point slope form as:

y - 1 = -3(x -6)

y = -3x + 18 + 1

y = -3x + 19

In standard form, the equation will be:

3x + y = 19

7 0

2 years ago

Read 2 more answers

Subtract what she has now from the total she needs. She needs ten. She has one 2 1/3 and 3 1/3 added is 5 2/3

tatiyna

Answer:

4 ⅓

Step-by-step explanation:

10 - 5 ⅔

10 - 5 × 3 + 2/3

10 - 17/3

3 × 10 - 17/3

30 - 17/3

13/3 = 4 ⅓

<u>-TheUnknownScientist</u>

6 0

2 years ago