Let x is the interest rate
$17,500 * 2 * x = <span>$2975
</span>$35,000x = $2,975
x = $2,975/$35,000
<span>x = 0.085
0.085 * 100 = 8.5%
Answer: annual interest rate was 8.5%
</span>
I'm guessing the sum is supposed to be
Split the summand into partial fractions:
If 
, then
If 
, then
This means
Consider the 
th partial sum of the series:
The sum telescopes so that
and as 
, the second term vanishes and leaves us with
Answer:
(x-5)^2+(y+4)^2=100
Step-by-step explanation:
As we know the given points
Center = (5, -4)
and
Point on circle = (-3,2)
The distance between point on circle and center will give us the radius of circle
So,
The formula for distance is:
The standard form of equation of circle is:
where h and k are the coordinates of the center. So putting in the value:
Answer:
See answer below
Step-by-step explanation:
The statement ‘x is an element of Y \X’ means, by definition of set difference, that "x is and element of Y and x is not an element of X", WIth the propositions given, we can rewrite this as "p∧¬q". Let us prove the identities given using the definitions of intersection, union, difference and complement. We will prove them by showing that the sets in both sides of the equation have the same elements.
i) x∈AnB if and only (if and only if means that both implications hold) x∈A and x∈B if and only if x∈A and x∉B^c (because B^c is the set of all elements that do not belong to X) if and only if x∈A\B^c. Then, if x∈AnB then x∈A\B^c, and if x∈A\B^c then x∈AnB. Thus both sets are equal.
ii) (I will abbreviate "if and only if" as "iff")
x∈A∪(B\A) iff x∈A or x∈B\A iff x∈A or x∈B and x∉A iff x∈A or x∈B (this is because if x∈B and x∈A then x∈A, so no elements are lost when we forget about the condition x∉A) iff x∈A∪B.
iii) x∈A\(B U C) iff x∈A and x∉B∪C iff x∈A and x∉B and x∉C (if x∈B or x∈C then x∈B∪C thus we cannot have any of those two options). iff x∈A and x∉B and x∈A and x∉C iff x∈(A\B) and x∈(A\B) iff x∈ (A\B) n (A\C).
iv) x∈A\(B ∩ C) iff x∈A and x∉B∩C iff x∈A and x∉B or x∉C (if x∈B and x∈C then x∈B∩C thus one of these two must be false) iff x∈A and x∉B or x∈A and x∉C iff x∈(A\B) or x∈(A\B) iff x∈ (A\B) ∪ (A\C).
H = 60 + 8x
h = Tree's height in inches
x = years of growth
