<u>Given</u>:
Given that the triangular prism with height 10 inches.
The side lengths of the base of the triangle are 12 inches, 13 inches and 5 inches.
We need to determine the surface area of the prism.
<u>Surface area of the prism:</u>
The surface area of the prism can be determined using the formula,
where b is the base and h is the height of the triangle.
s₁, s₂, s₃ are the side lengths of the triangle and
H is the height of the prism.
Substituting b = 12, h = 5, s₁ = 12, s₂ = 5, s₃ = 13 and H = 10 in the above formula, we get;
Thus, the surface area of the triangular prism is 360 square inches.
Hence, Option b is the correct answer.
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Let
be any integer. Then
In other words:
(1) If
is a multiple of 4, then
.
(2) If dividing
by 4 leaves a remainder of 1, then
, since
for some integer
, and from (1) we know that
(because, obviously,
is a multiple of 4).
(3) If instead you get a remainder of 2, then
. This follows from (1) as well.
.
(4) Finally, if you get a remainder of 3, then
.
Answer:
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Step-by-step explanation:
Given:
f(x) is an exponential function.
To find:
The value of f(6.5).
Solution:
Let the exponential function is
...(i)
Where, a is the initial value and b is the growth factor.
We have, 
. So, put x=-3.5 and f(x)=25 in (i).
...(ii)
We have, 
. So, put x=6 and f(x)=33 in (i).
...(iii)
On dividing (iii) by (ii), we get
Putting b=1.03 in (iii), we get
Putting a=27.63 and b=1.03 in (i), we get
Therefore, the required exponential function is .
