The answer is D because in an Equilateral triangle all the angles are 60 degrees which is acute
1/2 = cos(2*t)sqrt(3) /2 = sin(-2*t)find tfind the time derivative of x(t), y(t)(-2sin(2*t) , -2cos(2*t) )plug in the t you found to find the velocity vector.
Answer:
Step-by-step explanation:
w / h = u / HG
w = 8
h = 48
u = 5
lets use h / w = HG / u this is the same relationship but looks easier to me
48/8 = HG / 5
6 = HG / 5
6 * 5 = HG
30 = HG
not too tuff... when you set the relationship so it's easiest :)
and yes.. we cold have swapped the fractions and done it the other way and gotten the same answer.. but maybe with a bit more algebra.. and... avoid extra algebra ... that's where the mistakes can be made :P
In the second one I'm pretty sure you just measure the length of the points.
18 kg of 15% copper and 72 kg of 60% copper should be combined by the metalworker to create 90 kg of 51% copper alloy.
<u>Step-by-step explanation:</u>
Let x = kg of 15% copper alloy
Let y = kg of 60% copper alloy
Since we need to create 90 kg of alloy we know:
x + y = 90
51% of 90 kg = 45.9 kg of copper
So we're interested in creating 45.9 kg of copper
We need some amount of 15% copper and some amount of 60% copper to create 45.9 kg of copper:
0.15x + 0.60y = 45.9
but
x + y = 90
x= 90 - y
substituting that value in for x
0.15(90 - y) + 0.60y = 45.9
13.5 - 0.15y + 0.60y = 45.9
0.45y = 32.4
y = 72
Substituting this y value to solve for x gives:
x + y = 90
x= 90-72
x=18
Therefore, in order to create 90kg of 51% alloy, we'd need 18 kg of 15% copper and 72 kg of 60% copper.
