Let's start by visualising this concept.
Number of grains on square:
1 2 4 8 16 ...
We can see that it starts to form a geometric sequence, with the common ratio being 2.
For the first question, we simply want the fifteenth term, so we just use the nth term geometric form:


Thus, there are 16, 384 grains on the fifteenth square.
The second question begs the same process, only this time, it's a summation. Using our sum to n terms of geometric sequence, we get:



Thus, there are 32, 767 total grains on the first 15 squares, and you should be able to work the rest from here.
Answer:
10x^2-11x-6
Step-by-step explanation:
To expand, we use the FOIL method. You do this by multiplying each number inside the parenthesis by the other numbers in the other set of the parenthesis. For example, on this problem, you would multiply 5x by 2x, and then 5x by -3.
Step by step, you would:
5x * 2x = 10x^2
5x * -3 = -15x
2 * 2x = 4x
2 * -3 = -6
In an equation, it would expand to 10x^2-15x+4x-6
To simplify, you add like terms (constants and those with the same variable). In this case, you would add together all the terms ending in x.
-15x+4x=-11x
Now, you have added like terms together, so your simplified answer is 10x^2-11x-6.
The slope is 10. For every 1 increase in x, y increases by 10.
19.18 / 2.8 = 6.85
So answer is D.6.850 h
Answer:
36 °
Step-by-step explanation:
In this case a rectangular triangle is formed so we can use the trigonometric functions to calculate the angle, they give us the value of the two legs, therefore we can apply the tangent function.
Tan A ° = opposite / adjacent
replacing:
Tan A ° = 50/68
Tan A ° = 0.735
A ° = arc tan (0.735)
A ° = 36.32
Which means that the angle of inclination is 36°