Answer:
D
Step-by-step explanation:
Using the Sine rule in Δ QRS , that is
= 
, that is
= 
( cross- multiply )
12× sinQ = 15 × sin50.1° ( divide both sides by 12 )
sinQ = 
, thus
Q = 
( ) ≈ 73.5° ( to the nearest tenth )
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: 529 students
Step-by-step explanation:
To solve this, we will be using the formula for finding averages:
> (total sum of student weights) ÷ (total sum of students) = (average of student weights)
Plugging in the values that are given in the problem, you get:
> 16,293.2 ÷ x = 30.8
Where x is equal to the total sum of students. From here, it's a simple equation to isolate x, and find out what numerical value x is equal to. In case you are unsure how to do this, I've created a clear step by step process for how to do this (NOTE: The slash represents division, while the asterisk represents multiplication.):
> 16,293.2 / x = 30.8
> (16,293.2 / x) * x = (30.8) * x
> 16,293.2 = 30.8 * x
> (16,293.2) / 30.8 = (30.8 * x) / 30.8
> 529 = x
In total, there are 529 students in the school.
Answer:
5) 140.8m^2 6) 360in^2
Step-by-step explanation:
5.
6.4 x 6.4 = 40.96
(7.8 x 6.4) ÷ 2 = 24.96
24.96 x 4 = 99.84
99.84 + 40.96 = 140.8m^2
6.
12 x 10 = 120in
13 x 10 = 130in
5 x 10 = 50in
(12 x 5) ÷ 2 = 30in
30 x 2 = 60in
60 + 50 + 130 + 120 = 360in^2
53.65 gallons → B
Since the tanks are equal in size then to find the volume of 1 tank
divide the total by 12
one tank = 
= 53.65
