Answer:
D. 60°
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that the relationship of interest is ...
Sin = Opposite/Hypotenuse
sin(M) = ON/OM = 4(√3)/8 = (√3)/2
M = sin⁻¹((√3)/2) = 60°
Its an equilateral triangle so all sides are equal.
2x + 5 = 4x - 1
5 = 2x - 1
6 = 2x
3 = x
Do you get it?
Let's work on Sections. The top rectangle has an area of 54 (6x9) the base rectangle has an area of 360 ((9+6+9+5)×12) and the bottom rectangle has an area of 54 (9×6) now we add and we get 468. thus the answer is C.
Answer:
3.
Step-by-step explanation:
This is a geometric series so the sum is:
a1 * r^n - 1 / (r - 1)
= 1 * (2^101 -1) / (2-1)
= 2^101 - 1.
Find the remainder when 2^101 is divided by 7:
Note that 101 = 14*7 + 3 so
2^101 = 2^(7*14 + 3) = 2^3 * (2^14)^7 = 8 * (2^14)^7.
By Fermat's Little Theorem (2^14) ^ 7 = 2^14 mod 7 = 4^7 mod 7.
So 2^101 mod 7 = (8 * 4^7) mod 7
= (8 * 4) mod 7
= 32 mod 7
= 4 = the remainder when 2^101 is divided by 7.
So the remainder when 2^101- 1 is divided by 7 is 4 - 1 = 3..
We know the perimeter formula would be 1200=2x+2y. And the area will be A=x*y
We can to take the derivative of the area formula to find where it is a max but we must first substitute something in from the first formula so we only have one variable.
1200-2x=2y
600-x=y
A=(x)*(600-x)
A=600x-x^2
Now we take the derivative:
A'=600-2x (set equal to 0 and solve)
0=600-2x
2x=600
x=300
Then when we plug this into the perimeter formula, we can solve for y
1200=2x+2y
1200=2(300)+2y
1200=600+2y
600=2y
y=300
So both the length and width are 300 yards, and the area would be 90,000 square yards
Hope this helps
