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gulaghasi [49]
3 years ago
9

Part B if the height of each prism is 10 Cm what is the surface area prism

Mathematics
1 answer:
Evgen [1.6K]3 years ago
7 0

Answer:

Prism A:

Area = 288cm^2

Prism B:

Area =250cm^2

Step-by-step explanation:

Given

See attachment for prisms

Height(h) = 10cm

Required

Determine the surface area of both prisms

Prism A is triangular and as such, the surface area is:

Area = 2 * A_b + (a + b + c) * h

Where

A_b = \sqrt{s * (s - a) * (s -b) * (s - c)}

and

s = \frac{a + b + c}{2}

Such that a, b and c are the lengths of the triangular sides of the prism.

From the attachment;

a = 8; b =6; c =10

So, we have:

s = \frac{a + b + c}{2}

s = \frac{8 + 6 + 10}{2}

s = \frac{24}{2}

s = 12

Also:

A_b = \sqrt{s * (s - a) * (s -b) * (s - c)}

A_b = \sqrt{12 * (12 - 8) * (12 - 6) * (12 - 10)}

A_b = \sqrt{576}

A_b = 24

So:

Area = 2 * A_b + (a + b + c) * h

Area = 2 * 24 + (8 + 6 + 10) * 10

Area = 288cm^2

Prism B is a rectangular prism. So, the area is calculated as:

Area = 2 * (ab + bh + ah)

From the attachment

a = b = 5

h =10

So:

Area =2 * (5 * 5 + 5 * 10 + 5 * 10)

Area =250cm^2

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Part A

Answer: The common ratio is -2

-----------------------------------

Explanation: 

To get the common ratio r, we divide any term by the previous one

One example:
r = common ratio
r = (second term)/(first term)
r = (-2)/(1)
r = -2

Another example:
r = common ratio
r = (third term)/(second term)
r = (4)/(-2)
r = -2
and we get the same common ratio every time

Side Note: each term is multiplied by -2 to get the next term

============================================================
Part B

Answer:
The rule for the sequence is 
a(n) = (-2)^(n-1)
where n starts at n = 1

-----------------------------------

Explanation:

Recall that any geometric sequence has the nth term
a(n) = a*(r)^(n-1)
where the 'a' on the right side is the first term and r is the common ratio

The first term given to use is a = 1 and the common ratio found in part A above was r = -2
So,
a(n) = a*(r)^(n-1)
a(n) = 1*(-2)^(n-1)
a(n) = (-2)^(n-1)

============================================================
Part C

Answer: The next three terms are 16, -32, 64

-----------------------------------

Explanation:

We can simply multiply each previous term by -2 to get the next term. Do this three times to generate the next three terms

-8*(-2) = 16
16*(-2) = -32
-32*(-2) = 64

showing that the next three terms are 16, -32, and 64

An alternative is to use the formula found in part B

Plug in n = 5 to find the fifth term
a(n) = (-2)^(n-1)
a(5) = (-2)^(5-1)
a(5) = (-2)^(4)
a(5) = 16 .... which matches with what we got earlier

Then plug in n = 6
a(n) = (-2)^(n-1)
a(6) = (-2)^(6-1)
a(6) = (-2)^(5)
a(6) = -32 .... which matches with what we got earlier

Then plug in n = 7
a(n) = (-2)^(n-1)
a(7) = (-2)^(7-1)
a(7) = (-2)^(6)
a(7) = 64 .... which matches with what we got earlier

while the second method takes a bit more work, its handy for when you want to find terms beyond the given sequence (eg: the 28th term)
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