A circle is a curve sketched out by a point moving in a plane. The circumference of the ring of fire is 6.2831 meters.
<h3>What is a circle?</h3>
A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
The circumference of the ring if the radius is 1 meter is,
Circumference of the ring = 2πr = 2 × π × 1 = 6.2831 meters
Hence, the circumference of the ring of fire is 6.2831 meters.
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Answer: m∠ TUW = 38°
m∠WUV = 12°
m∠TUV = 103°
Step-by-step explanation:
Given: m∠ TUW = (5x + 3)°, m∠WUV=(10x-5)°, and m∠TUV=(17x-16)°
Since, m∠TUV = m∠ TUW + m∠WUV
So, 17X-16 = (5x + 3) + (10x-5)
⇒ 17X-16 = 5x + 3 + 10x-5 [open parenthesis]
⇒ 17X-16 =5x + 10x +3 -5 [combine like trems]
⇒ 17X-16 =15x -2
⇒ 17X -15x = -2+16 [subtract 15x and add 16 on both sides]
⇒ 2x = 14
⇒ x= 7 [divide both sides by 2]
Now, m∠ TUW = (5(7) + 3)°= 38°
m∠WUV=(10(7)-5)° = 12°
m∠TUV=(17(7)-16)° = 103°
Hence, m∠ TUW = 38°
m∠WUV = 12°
m∠TUV = 103°
To solve this problem, let us first assign variables. Let
us say that:
x = volume of 67% herbicide solution
y = volume of 46% herbicide solution
The total volume should be 42 liters therefore:
x + y = 42
x = 42 – y --> 1
The component mass balance on the pure herbicide would
be:
0.67 x + 0.46 y = 0.55 (42) --> 2
Substituting equation 1 to 2:
0.67 (42 – y) + 0.46 y = 23.1
28.14 – 0.67 y + 0.46 y = 23.1
- 0.21 y = - 5.04
y = 24 L
Calculating for x using equation 1:
x = 42 – 24
x = 18 L
Therefore we only need 18 L of the 67% herbicide
solution.
Answer:
A. 18 L
