Answer:
Father's age is 50, Son's age is 10
Step-by-step explanation:
X+Y=60
X-Y= 40
Let X represent the Father's age while Y represents the Son's age;
therefore, from the two equations, the value of X is
X= 60-Y
X= 40+Y then putting in the value of x
(40+Y) + Y= 60,
40+2Y=60
2Y=60-40 =20
Y= 10,
Now that we know the value of Y, we can get the value of x
If X+Y=60, then
X+10=60,
X=60-10,
X= 50
Answer:
The vector joining the ship to the rock is t= 7 i + 5 j
The direction is 0.9505 radians east of north.
Step-by-step explanation:
The position vector of the ship:
r= 1 i + 0 j
The position vector of the ship:
s= 6 i + 5 j
The vector joining the ship to the rock is:
t = r + s
t = (1 i + 0 j) + (6 i + 5 j)
t = 7 i + 5 j
The bearing of the rock to the ship is:
Θ= 
= 0.9505 radians
Well this is simple a calculator type problem...but if you are curious as the the algorithm used by simple calculators and such...
They use a Newtonian approximation until it surpasses the precision level of the calculator or computer program..
A newtonian approximation is an interative process that gets closer and closer to the actual answer to any mathematical problem...it is of the form:
x-(f(x)/(df/dx))
In a square root problem you wish to know:
x=√n where x is the root and n is the number
x^2=n
x^2-n=0
So f(x)=x^2-n and df/dx=2x so using the definition of the newton approximation you have:
x-((x^2-n)/(2x)) which simplifies further to:
(2x^2-x^2+n)/(2x)
(x^2+n)/(2x), where you can choose any starting value of x that you desire (though convergence to an exact (if possible) solution will be swifter the closer xi is to the actual value x)
In this case the number, n=95.54, so a decent starting value for x would be 10.
Using this initial x in (x^2+95.54)/(2x) will result in the following iterative sequence of x.
10, 9.777, 9.774457, 9.7744565, 9.7744565066299210578124802523397
The calculator result for my calc is: 9.7744565066299210578124802523381
So you see how accurate the newton method is in just a few iterations. :P
Answer: A right triangle.
Step-by-step explanation:
This is because an acute triangle would have all of its three sides acute while an obtuse one would have two acute angles as well, but also an obtuse one. If the question is specifically asking for a triangle with exactly two acute angles, a right triangle would be the answer.
