Answer:
Step-by-step explanation:
Water is being pumped into an inflated rubber sphere at a constant rate of 0.03 cubic meters per second.
So, dV/dt = 0.03.
We want to show that dS/dt is directly proportional to 1/r.
In other words, we want to establish the relationship that dS/dt = k(1/r), where k is some constant.
First, the volume of a sphere V is given by:
Therefore:
Next, the surface area of a sphere S is given by:
Therefore:
We can divide both sides by 2:
We can substitute this into dV/dt. Rewriting:
So:
Since dV/dt = 0.03 or 3/100:
Therefore:
Where k = 3/50.
And we have shown that dS/dt is directly proportional to 1/r.
Answer: Rewrite equations:
5x+y=−13;6x+6y=−6
Step: Solve5x+y=−13for y:
5x+y=−13
5x+y+−5x=−13+−5x(Add -5x to both sides)
y=−5x−13
Step: Substitute−5x−13foryin6x+6y=−6:
6x+6y=−6
6x+6(−5x−13)=−6
−24x−78=−6(Simplify both sides of the equation)
−24x−78+78=−6+78(Add 78 to both sides)
−24x=72
−24x
−24
=
72
−24
(Divide both sides by -24)
x=−3
Step: Substitute−3forxiny=−5x−13:
y=−5x−13
y=(−5)(−3)−13
y=2(Simplify both sides of the equation)
Answer:
x=−3 and y=2
Step-by-step explanation:
Answer:
Solution given:
sin 47=opposite/hypotenuse
Sin 47=x/18
x=sin47*18
<u>x=13.16ft</u>
Answer:
if f(x)= -4x+3
f(-5)= 23
Step-by-step explanation:
first you substitute x for -5
f(-5)= -4(-5)+3
then you multiply
-4(-5)
f(-5)=20+3
you get the positive 20 because negative times negative equals positive
then you just add the rest (20+3) which will give you your answer
f(-5)= 23
Answer:
It's not that hard so lets get a divorce bro
Step-by-step explanation:
