I am a number greater than 40,000 and less than 60,000:
40,000 < n < 60,000
This means that:
n = 10,000n₁ + 1,000n₂ + 100n₃ + 11n₄
And also:
4 ≤ n₁ < 6
0 ≤ n₂ ≤ 9
0 ≤ n₃ ≤ 9
0 ≤ n₄ ≤ 9
My ten thousands digit is 1 less than 3 times the sum of my ones digit and tens digit:
n₁ = 3*2n₄ - 1
n₁ = 6n₄ - 1
This means that:
n = 10,000*(6n₄-1) + 1,000n₂ + 100n₃ + 11n₄
n = 60,000n₄ - 10,000 + 1,000n₂ + 100n₃ + 11n₄
n = 60,011n₄ - 10,000 + 1,000n₂ + 100n₃
<span>My thousands digit is half my hundreds digit, and the sum of those two digits is 9:
n</span>₂ = 1/2 * n₃
<span>
n</span>₂ + n₃ = 9
<span>
Therefore:
n</span>₂ = 9 - n₃
<span>
Therefore:
9 - n</span>₃ = 1/2 * n₃
<span>
9 = 1/2 * n</span>₃ + n₃
<span>
9 = 1.5 * n</span>₃
<span>
Therefore:
n</span>₃ = 6
<span>
If n</span>₃=6, n₂=3.
<span>
This means that:
</span>n = 60,011n₄ - 10,000 + 1,000*3 + 100*6
n = 60,011n₄ - 10,000 + 3,000 + 600
n = 60,011n₄ - 6,400
Therefore:
0<n₄<2, so n₄=1.
If n₄=1:
n = 60,011 - 6,400
n = 53,611
Answer:
53,611
Answer:
18.7
Step-by-step explanation:
The Law of Cosines is 
, where c is the unknown side length of a triangle, a and b are the remaining two side lengths, and C is the angle opposite to side c. To answer this question just plug in the known values:
Simplify:
m≈18.665...
When rounded to the nearest tenth, m=18.7
Answer:
The distance is 5.20m
Step-by-step explanation:
Here, we want to get the height of the ladder
To get this, we need to understand that we have a right triangle, with the base of the triangle as 3 m, the angle at the downward part is 60, and we want to get the height of the triangle
The angle here faces the height we want to calculate
This height is known as the opposite
What we have is the adjacent
Now, the trigonometric identity that relates the opposite and the adjacent is the tan
The tangent of an angle is the ratio of the opposite to the adjacent
Mathematically;
tan 60 = h/3
h = 3 tan 60
h = 5.20 m
The ladder is at a height of 5.20 m above the ground
Answer:
>
Step-by-step explanation:
-3+7= 4
-10-2= -12
4> -12
