Good morning ☕️
Answer:
<h3>i¹ + i² + i³ +. . .+ i⁹⁹ + i¹⁰⁰ =
0</h3>
Step-by-step explanation:
Consider the sum S = i¹ + i² + i³ +. . .+ i⁹⁹ + i¹⁰⁰
S = i¹ + i² + i³ + . . . + i⁹⁹ + i¹⁰⁰
S = a₁ + a₂ + a₃ +. . . + a₉₉ + a₁₀₀
then, S is the sum of 100 consecutive terms of a geometric sequence (an)
where the first term a1 = i¹ = i and the common ratio = i
FORMULA:______________________
_______________________________
then
or i¹⁰⁰ = (i⁴)²⁵ = 1²⁵ = 1 (we know that i⁴ = 1)
Hence
S = 0
Answer:
A
Step-by-step explanation:
Note that
and
Then
Since you have that
<h3>
Answer: 4</h3>
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Rule:
If A+B = 90, then tan(A) = 1/( tan(B) ) and tan(B) = 1/( tan(A) )
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Since C = 90, this must mean the other two angles A and B are acute and complementary. So A+B = 90 must be the case. This allows us to use that rule above.
So,
tan(B) = 1/( tan(A) )
tan(B) = 1/( 0.25 )
tan(B) = 4
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Here's another way to think about it.
If tan(A) = 0.25, then we could have BC = 1 and AC = 4 as the opposite and adjacent sides respectively. That leads to tan(A) = opposite/adjacent = BC/AC = 1/4 = 0.25
When computing tan(B), the BC and AC sides swap roles in terms of opposite and adjacent,
tan(B) = opposite/adjacent = AC/BC = 4/1 = 4.
For any of these cases, we don't involve the hypotenuse AB.
We have an equation with parentheses. To make our lives easier, first get rid of the parentheses. We do this by using the distributive property.
It is used like this: a(b + c) = ab + ac.
Use the distributive property on the left-hand side.
3(x - 1) = 6
3x - 3 = 6
Now we have an equation that is easier.
The x variable is being multiplied by 3 and added to -3.
Reverse all of these operations with their inverse operation.
3x - 3 = 6
3x = 9 <--- I got rid of the -3 term by using the inverse of subtraction. Addition.
And I did the same for both sides to keep the equation true.
x = 3 <--- The inverse of multiplication is division.
So, I divided both sides by 3.
So, x is equal to 3.
8²+9(12÷3×2)-7
well we are going to start in the parentheses and do order of operations
so 12÷3=4
then 4×2=8
so you have 8² +9(8)-7
well we still need to get rid of the parentheses 9×8=72
so then we are left with 8²=72-7
so now we have to get rid of the exponents so8²=64
64+72-7
136-7=129
so 129 is your answer to the first one.
the second one is easy. its a single step equation.
you are trying to get x by itself. so you have 7x=42. you want to get rid of the seven so you have to do the opposite of what it is doing to x. the 7 is multiplying by the x. So whats the opposite of multiplication... division. so you have to divide both sides by 7. so you have 7÷7x=42÷7
now simplify and you have x=6