Let
be the statement that
Check to see that
holds for
:
Now suppose that
is true, and use that assumption to show that
must also be true. When
, you have
and so
is also true, thus proving the statement is true for all
.
We need to find the interest rate in order to solve this problem:
.12/12 = (.01)
The number of years is unknown. T represents time in the following formula:
1000 (initial investment)
2000 (balance after t years from investment)
=$2000
In order to isolate the exponential term, both sides must be divided by 1000.
=2
By using natural logarithm:
By dividing both sides of the equation by 
Vertex form is
y=a(x-h)^2+k
vertex is (h,k)
axis of symmetry is x=4, therfor h=4
y=a(x-4)^2+k
we have some points
(3,-2) and (6,-26)
input and solve for a and k
(3,-2)
-2=a(3-4)^2+k
-2=a(-1)^2+k
-2=a(1)+k
-2=a+k
(6,-26)
-26=a(6-4)^2+k
-26=a(2)^2+k
-26=a(4)+k
-26=4a+k
we have
-2=a+k
-26=4a+k
multiply first equation by -1 and add to second
2=-a-k
<u>-26=4a+k +</u>
-24=3a+0k
-24=3a
divide both sides by 3
-8=a
-2=a+k
-2=-8+k
add 8 to both sides
6=k
the equation is
5+4❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤
Density = mass/volume
Plug in your Provided Values
v=volume
18g/cm^3 = 4.5g/v. Multiple both sides by v
v(18g/cm^3) = 4.5g Divide both sides by 18g/cm^3.
v = 4.5g/(18g/cm^3) Your grams cancel out leaving 4.5/18 cm^3 as your volume which is also. .25 cm^3.
Hope this helps!
