Peter is making green paint by mixing blue and yellow paint in a cuboid container, shown below. The container has width of 30cm
1 answer:
Answer: height = 17.5cm
Step-by-step explanation: Peter mixes blue and yellow paint in the ratio 2:3, which means:
x = 12.6L
The container is full with the two paints, so total volume:
V = 12.6 + 8.4
V = 21L
Knowing that 1L = 1dm³ and sides of cuboid is measure in cm:
V = 21dm³ = 21000cm³
Volume of a cuboid is calculated as:
V = width*length*height
Height of the container is
height =
height =
height = 17.5cm
The height of the container is 17.5cm.
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Answer:
segment YZ ≈ 19.4 in
angle X ≈ 85.3°
angle Z ≈ 26.7°
Explanation:
1) Given two side lenghts and one angle you can use sine law:
2) Using the sides with length 43 in and 40in, and the corresponding opposite angles, Z and 68°, that leads to:
From which you can clear sinZ and get:
sinZ = 43 × sin(68) / 40 = 0.9967
⇒ Z = arcsine(0.9967) ≈ 85.36°
3) The third angle can be determined using 85.36° + 68° + X = 180°
⇒ X = 180° - 85.36° - 68° = 26.64°.
4) Finally, you can apply the law of sine to obtain the last missing length:
From which: x = 40 × sin(26.64°) / sin(68°) = 19.34 in
The answer, then is:
segment YZ ≈ 19.4 in
angle X ≈ 85.3°
angle Z ≈ 26.7°
segment YZ ≈ 19.4 in
angle X ≈ 85.3°
angle Z ≈ 26.7°
Explanation:
1) Given two side lenghts and one angle you can use sine law:
2) Using the sides with length 43 in and 40in, and the corresponding opposite angles, Z and 68°, that leads to:
From which you can clear sinZ and get:
sinZ = 43 × sin(68) / 40 = 0.9967
⇒ Z = arcsine(0.9967) ≈ 85.36°
3) The third angle can be determined using 85.36° + 68° + X = 180°
⇒ X = 180° - 85.36° - 68° = 26.64°.
4) Finally, you can apply the law of sine to obtain the last missing length:
From which: x = 40 × sin(26.64°) / sin(68°) = 19.34 in
The answer, then is:
segment YZ ≈ 19.4 in
angle X ≈ 85.3°
angle Z ≈ 26.7°
Answer:
(x, y) = (0, 1/2) or (1, 3)
Step-by-step explanation:
The first equation factors as ...
x(3x -y) = 0
This has solutions x=0 and y=3x.
__
<u>x = 0</u>
Using this in the second equation gives ...
2y -0 = 1
y = 1/2
(x, y) = (0, 1/2) is a solution
__
<u>y = 3x</u>
Using the expression for y in the second equation, we get ...
2(3x) -5x = 1
x = 1 . . . . . . . . . simplify
y = 3x = 3 . . . . using x=1 in the first equation
(x, y) = (1, 3) is a solution
_____
Interestingly, the (red line) graph of 3x^2 -xy = 0 produced by this graphing calculator has a "hole" at x=0, It says that point is (0, undefined). In a sense, y is undefined, in that it can be <em>anything</em>. A more appropriate graph would graph that equation as the two lines x=0 and y=3x.
