Given:
To find:
The exact value of cos(u-v) if both angles are in quadrant 3.
Solution:
In 3rd quadrant, cos and sin both trigonometric ratios are negative.
We have,
Now,
On further simplification, we get
Similarly,
Now,
Therefore, the value of cos (u-v) is 0.1872.
Answer:
(1) The sum of the lengths of the edges of the cube is 36.
A cube has 12 equal edges. Sum = 36. Length of each edge = 36/12 = 3
Volume = 3*3*3 = 27
(2) The surface area of the cube is 54.
A cube has 6 identical faces. Area of each face = s^2 (s is the length of the side)
6s^2 = 54
s = 3
Volume = 3*3*3 = 27
Step-by-step explanation:
All you need to uniquely define a cube is any one measurement - length of a side/edge, area of a surface, volume etc. If you have any one of them, you can uniquely determine the others. So each statement alone is sufficient here.
To show how,
(1) The sum of the lengths of the edges of the cube is 36.
A cube has 12 equal edges. Sum = 36. Length of each edge = 36/12 = 3
Volume = 3*3*3 = 27
(2) The surface area of the cube is 54.
A cube has 6 identical faces. Area of each face = s^2 (s is the length of the side)
6s^2 = 54
s = 3
Volume = 3*3*3 = 27
Step-by-step explanation:
y is easy.
it is the Hypotenuse (baseline) of the small right-angled triangle created by the height (8) of the main triangle, the segment 6 of the main Hypotenuse and y.
so, Pythagoras :
y² = 8² + 6² = 64 + 36 = 100
y = 10
x is a bit more complex.
I think the easiest way to get it is to know that the height of a right-angled triangle to the Hypotenuse is the square root of the product of both segments of the Hypotenuse.
so, if we call the segments of the Hypotenuse a and b with a = 6, we have
x = a + b = 6 + b
height (8) = sqrt(a×b) = sqrt(6b)
therefore,
6b = height² = 8² = 64
b = 64/6 = 32/3 = 10 2/3 = 10.66666666...
so,
x = 6 + 10.66666... = 16.666666666...
round it to what is needed. e.g. 2 positions after the decimal point (hundredths) ? then it would be 10.67
Answer:
3y^4/5x^6
Step-by-step explanation:
