Answer:
The amount of acid in third container is =42%
Step-by-step explanation:
Given , one container is filled with a mixture that is 30% acid a second container filled with a mixture that is 50% acid and the second container 50% larger than the first .
Let, the volume of first container is = x
Then , the volume of second container = (x+ x of 50%)
= x + 0.5 x
= 1.5 x
Therefore the amount of acid in first container 
= 0.3 x
The amount of acid in second container 
= 0.75x
Total amount of acid= 0.3x + 0.75x = 1.05 x
Total amount of solution = x+1.5x = 2.5x
The amount of acid in third container is = 
%
= 42%
Find <span>tan<span>(<span><span>5π</span>12</span>)</span></span> and sin ((5pi)/12)
Answer: <span>±<span>(2±<span>√3</span>)</span>and±<span><span>√<span>2+<span>√3</span></span></span>2</span></span>
Explanation:
Call tan ((5pi/12) = t.
Use trig identity: <span><span>tan2</span>a=<span><span>2<span>tana</span></span><span>1−<span><span>tan2</span>a</span></span></span></span>
<span><span>tan<span>(<span><span>10π</span>12</span>)</span></span>=<span>tan<span>(<span><span>5π</span>6</span>)</span></span>=−<span>1<span>√3</span></span>=<span><span>2t</span><span>1−<span>t2</span></span></span></span>
<span><span>t2</span>−2<span>√3</span>t−1=0</span>
<span>D=<span>d2</span>=<span>b2</span>−4ac=12+4=16</span>--> <span>d=±4</span>
<span>t=<span>tan<span>(<span><span>5π</span>12</span>)</span></span>=<span><span>2<span>√3</span></span>2</span>±<span>42</span>=2±<span>√3</span></span>
Call <span><span>sin<span>(<span><span>5π</span>12</span>)</span></span>=<span>siny</span></span>
Use trig identity: <span><span>cos2</span>a=1−2<span><span>sin2</span>a</span></span>
<span><span>cos<span>(<span><span>10π</span>12</span>)</span></span>=<span>cos<span>(<span><span>5π</span>6</span>)</span></span>=<span><span>−<span>√3</span></span>2</span>=1−2<span><span>sin2</span>y</span></span>
<span><span><span>sin2</span>y</span>=<span><span>2+<span>√3</span></span>4</span></span>
<span><span>siny</span>=<span>sin<span>(<span><span>5π</span>12</span>)</span></span>=±<span><span><span>√<span>2+<span>√3</span></span></span>2</span></span></span>
Arc length of the quarter circle is 1.57 units.
Solution:
Radius of the quarter circle = 1
Center angle (θ) = 90•
Arc length = 1.57 units
Arc length of the quarter circle is 1.57 units.
Answer:
-20x-2
Step-by-step explanation:
Answer:
256 m and 3840 m²
Step-by-step explanation:
The 3 part of the ratio represents 48 m , then
48m ÷ 3 = 16 m ← value of 1 part of the ratio, so
5 parts = 5 × 16 m = 80 m
Then breadth = 48 m and length = 80 m
perimeter = 2l + 2b = 2(80) + 2(48) = 160 + 96 = 256 m
area = lb = 80 × 48 = 3840 m²
