Answer:
The height above sea level at <em>B</em> is approximately 1,604.25 m
Step-by-step explanation:
The given length of the mountain railway, AB = 864 m
The angle at which the railway rises to the horizontal, θ = 120°
The elevation of the train above sea level at <em>A</em>, h₁ = 856 m
The height above sea level of the train when it reaches <em>B</em>, h₂, is found as follows;
Change in height across the railway, Δh = AB × sin(θ)
∴ Δh = 864 m × sin(120°) ≈ 748.25 m
Δh = h₂ - h₁
h₂ = Δh + h₁
∴ h₂ ≈ 856 m + 748.25 m = 1,604.25 m
The height above sea level of the train when it reaches <em>B</em> ≈ 1,604.25 m
So the recipe calls for 96 grams of sugar, and one cup is 128 grams of sugar.
She added a half of a cup, and as they said before one cup was 128 grams of sugar. So half of 128 is 64. So she added 64 grams of sugar. The recipe needs 96 grams so 64 grams is not enough sugar.
So 96 grams minus 64 equals 32 grams. So she still needs 32 grams of sugar.
So since the answers are all in cups, we must convert our answer from grams to cups.
So we have 32 grams of sugar left and to convert it we must put the 32 grams out of one cup. Once again one cup is 128 grams of sugar. So the amount of cups we need is 32/128 (fraction).
Also we need to simplify our fraction to completely answer the question. So we divide the numerator and denominator by 32.
So the final answer is 1/4. So the answer is D or the last answer out of the multiple choice.
Answer:
(2,16)
Step-by-step explanation:
y=8x-----------(i)
y= 10x-4---------(ii)
Substituting the value of y=8x in equation (ii)
8x=10x-4
8x-10x=-4
-2x= -4
x=2
Now, substituting the value of x= 2 in equation (i)
y=8x=8(2)=16
Solution of the system is (2,16)
48 and 6/8 that is the answer
<em>z</em> = 3<em>i</em> / (-1 - <em>i</em> )
<em>z</em> = 3<em>i</em> / (-1 - <em>i</em> ) × (-1 + <em>i</em> ) / (-1 + <em>i</em> )
<em>z</em> = (3<em>i</em> × (-1 + <em>i</em> )) / ((-1)² - <em>i</em> ²)
<em>z</em> = (-3<em>i</em> + 3<em>i</em> ²) / ((-1)² - <em>i</em> ²)
<em>z</em> = (-3 - 3<em>i </em>) / (1 - (-1))
<em>z</em> = (-3 - 3<em>i </em>) / 2
Note that this number lies in the third quadrant of the complex plane, where both Re(<em>z</em>) and Im(<em>z</em>) are negative. But arctan only returns angles between -<em>π</em>/2 and <em>π</em>/2. So we have
arg(<em>z</em>) = arctan((-3/2)/(-3/2)) - <em>π</em>
arg(<em>z</em>) = arctan(1) - <em>π</em>
arg(<em>z</em>) = <em>π</em>/4 - <em>π</em>
arg(<em>z</em>) = -3<em>π</em>/4
where I'm taking arg(<em>z</em>) to have a range of -<em>π</em> < arg(<em>z</em>) ≤ <em>π</em>.
