-3x-3 is the correct answer
We know that
volume of a sphere=(4/3)*pi*r³----> (r/3)*(4*pi*r²)
and
surface area of sphere=4*pi*r²
so
the volume of a sphere=(r/3)*surface area of sphere
therefore
if r=3
volume of a sphere=(3/3)*surface area of sphere
volume of a sphere=surface area of sphere
if r> 3
the term (r/3) is > 0
so
volume of a sphere > surface area of sphere
if r<3
the term (r/3) is < 0
so
volume of a sphere < surface area of sphere
examples
1) for radius r=3 units
volume of a sphere=(4/3)*pi*3³----> 113.04 unit³
surface area=4*pi*3²----> 113.04 units²
volume is equal to surface area
2) for radius r=10 units
volume of a sphere=(4/3)*pi*10³----> 4186.67 unit³
surface area=4*pi*10²----> 1256 units²
volume is > surface area
3) for radius r=2 units
volume of a sphere=(4/3)*pi*2³----> 33.49 unit³
surface area=4*pi*2²----> 50.24 units²
volume is < surface area
Answer:
x = -2/ 3
Step-by-step explanation:
in order to cancel out the logs they should have common bases
we can write 25 as 5²
we know that the reciprocal of the exponents of the bases are multiplied to the log
and now since the logs have common bases
we're left with
<u>x = -2/ 3</u>
Answer:
10 inches
Step-by-step explanation:
The formula for the triangle area is the following:
A = b * h / 2
Where b is the length of the base side and h is the height.
So, as the height is 4 less than the base, we have that:
h = b - 4
Using this value in the area equation, we have that:
A = b * (b - 4) / 2
30 = (b^2 - 4b) / 2
b^2 - 4b = 60
b^2 - 4b - 60 = 0
Using Bhaskara's formula to solve the quadratic equation, we have:
Delta = 4^2 + 4*60 = 256
sqrt(Delta) = 16
b1 = (4 + 16)/2 = 10
b2 = (4 - 16)/2 = -6 (negative value does not fit for this problem)
So the length of the base is 10 inches.
The slope of the line that passes through the points is y=8/5x
