Answer:
30,063 Brainest pls I really need it
Answer:
It will take 7 years ( approx )
Step-by-step explanation:
Given equation that shows the amount of the substance after t years,

Where,
= Initial amount of the substance,
If the half life of the substance is 19 years,
Then if t = 19, amount of the substance =
,
i.e.



Taking ln both sides,



Now, if the substance to decay to 78% of its original amount,
Then 


Again taking ln both sides,



Hence, approximately the substance would be 78% of its initial value after 7 years.
Answer:
Constructive Proof
Step-by-step explanation:
Let x be a positive integer
x must be equal to sum of all positive integers exceeding it
i.e.
x = x + (x - 1) + ( x - 2) + ......... + 2 + 1
Equivalently,
x = ∑i (where i = 1 to x)
The property finite sum;
∑i (i = 1 to x) = x(x + 1)/2
So,
x = x(x + 1)/2 ------- Multiply both sides by 2
2 * x = 2 * x(x + 1)/2
2x = x(x + 1)
2x = x² + x ------- subtract 2x from both sides
2x - 2x = x² + x - 2x
0 = x² + x - 2x ----- Rearrange
x² + x - 2x = 0
x² - x = 0 ------ Factorise
x(x - 1) = 0
So,
x = 0 or x - 1 = 0
x = 0 or x = 1 + 0
x = 0 or x = 1
But x ≠ 0
So, x = 1
The statement is only true for x = 1
This makes sense because 1 is the only positive integer not exceeding 1
1 = 1
It is a Constructive Proof
A proof is constructive when we find an element for which the statement is true.
Answer:
$600 - $40 = $560
$560/ $25 = 22.4
this means he can have up to a total of 22 people at his party
Let the smaller angle be x.
smaller = x
larger = 3x
known angle = 65°
All angles add up t10 180:
x + 3x + 65 = 180
4x + 65 = 180
4x = 115
x = 28.75
Smaller angle = 28.75
Larger angle = 86.25
Answer: The angles are 28.75° and 86.25°