Answer:
The central angle is within the range π to 3π/2
Step-by-step explanation:
To convert from degrees to radians, we multiply the angle in degrees by 180/π.
To convert from radians to degree, we multiply the angle in radians by 180°/π.
π/2 = π/2 X 180°/π= 90°
π rad = π X 180°/π= 180°
3π/2 = 3π/2 X 180°/π= 270°
2π = 2π X 180°/π= 360°
Therefore the angle 250 which is between 180 and 270 is within the range :
π to 3π/2
Assuming that the topping order is not important, you need to use the combination to solve this question. The number of toppings is 12 and then added 2, so the number will become: 12+2= 14 toppings
From 14 toppings, ian need to choose 3. The possible ways would be:
14C3= 14!/(14-3)!3!= 14*13*12/ 3*2= 364 possible ways
We can use Law of Cosines to solve for the angle of Z. The solution is shown below:
cos C=(a²+b²-c²)/2ab
cos Z = (yz² + xz² - xy² )/2*yz*xz
cos Z = (20² + 25 - 13²)/2*20*25
cos Z = 856 / 1000
Z=31.13°
The answer is angle 31.13°.
Given:
4log1/2^w (2log1/2^u-3log1/2^v)
Req'd:
Single logarithm = ?
Sol'n:
First remove the parenthesis,
4 log 1/2 (w) + 2 log 1/2 (u) - 3 log 1/2 (v)
Simplify each term,
Simplify the 4 log 1/2 (w) by moving the constant 4 inside the logarithm;
Simplify the 2 log 1/2 (u) by moving the constant 2 inside the logarithm;
Simplify the -3 log 1/2 (v) by moving the constant -3 inside the logarithm:
log 1/2 (w^4) + 2 log 1/2 (u) - 3 log 1/2 (v)
log 1/2 (w^4) + log 1/2 (u^2) - log 1/2 (v^3)
We have to use the product property of logarithms which is log of b (x) + log of b (y) = log of b (xy):
Thus,
Log of 1/2 (w^4 u^2) - log of 1/2 (v^3)
then use the quotient property of logarithms which is log of b (x) - log of b (y) = log of b (x/y)
Therefore,
log of 1/2 (w^4 u^2 / v^3)
and for the final step and answer, reorder or rearrange w^4 and u^2:
log of 1/2 (u^2 w^4 / v^3)
Answer:
t(d) = 0.01cos(5π(d-0.3)/3)
Step-by-step explanation:
Since we are given the location of a maximum, it is convenient to use a cosine function to model the torque. The horizontal offset of the function will be 0.3 m, and the horizontal scaling will be such that one period is 1.2 m. The amplitude is given as 0.01 Nm.
The general form is ...
torque = amplitude × cos(2π(d -horizontal offset)/(horizontal scale factor))
We note that 2π/1.2 = 5π/3. Filling in the given values, we have ...
t(d) = 0.01·cos(5(d -0.3)/3)