Answer:
Step-by-step explanation:
The square of a complex number is a complex number. Here, we have:
We then have this system of equations:
Solving this system:
Answer:
Step-by-step explanation:
You are to assume in both problems that the two triangles are similar. That is a very dangerous assumption -- especially in later math classes. But in this case, there is no other way to do the problem. The two sets of triangles look like they are proportional. So set up two ratios that are = to each other
On the left
long side small triange / long side large triangle = base small triangle / base large triangle
On the right
hypotenuse/longest leg = hypotenuse / longest leg.
Problem A
Set up the similar Proportion
5/40 = x/20 Cross Multiply
40x = 20*5
40x = 100 Divide by 40
x = 100/40
x = 2.5
Problem B
Again set up the similar triangle proportion
15/10 = x/2 Multiply by 2
15*2/10 = x
3 = x
R^2+2r-33=0 move constant to other side by adding 33 to both sides
r^2+2r=33 halve the linear coefficient, square it and add to both sides, in this case it is just one
r^2+2r+1=34 now the left side is a perfect square...
(r+1)^2=34 take the square root of both sides...
r+1=34^(1/2) subtract 1 from both sides
r=-1+34^(1/2) and -1-34^(1/2)
Answer:
The slant height of a regular pyramid is 
Step-by-step explanation:
we know that
The lateral area of a regular pyramid is equal to
where
LA is the lateral area
P is the perimeter of the base
l is the slant height
we have
substitute in the formula and solve for l
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