Step-by-step explanation:
1 km = 1000 m
(hence the term "kilo" which means 1000).
so. he runs 1000 m at the rate of 3 minutes per km, that means 3 minutes per 1000 m.
now, we can see the solution already with our eyes.
but let's do it formally :
the rate or ratio between time and distance must be the same for the same speed.
so,
3 min / 1000 m = x min / 500 m
500 m × 3 min / 1000 m = x min
1/2 × 3 min = x min
3/2 = 1.5 min = x min
so, it takes him 1.5 minutes (90 seconds) to run 500 m.
<h3>
Answer: 41</h3>
Work Shown:
f(x) = 6x^2 - 13
f(x) = 6(x)^2 - 13
f(-3) = 6(-3)^2 - 13 ... replace every x with -3; use PEMDAS to simplify
f(-3) = 6(9) - 13
f(-3) = 54 - 13
f(-3) = 41
Answer:
x = ±2
Step-by-step explanation:
3x ^2 -4 = 8
Add 4 to each side
3x ^2 -4+4 = 8+4
3x^2 =12
Divide each side by 3
3x^2 =12
3x^2/3 = 12/3
x^2 = 4
Take the square root of each side
sqrt(x^2) = ±sqrt(4)
x = ±2
The local minimum of function is an argument x for which the first derivative of function g(x) is equal to zero, so:
g'(x)=0
g'(x)=(x^4-5x^2+4)'=4x^3-10x=0
x(4x^2-10)=0
x=0 or 4x^2-10=0
4x^2-10=0 /4
x^2-10/4=0
x^2-5/2=0
[x-sqrt(5/2)][x+sqrt(5/2)]=0
Now we have to check wchich argument gives the minimum value from x=0, x=sqrt(5/2) and x=-sqrt(5/2).
g(0)=4
g(sqrt(5/2))=25/4-5*5/2+4=4-25/4=-9/4
g(-sqrt(5/2))=-9/4
The answer is sqrt(5/2) and -sqrt(5/2).
Answer:A number decreased by 40
Step-by-step explanation: I really don't feel like explaining this lol...