Write a system of equations and solve.
x + y = 10
5x + 10y = 90
Multiply and combine equations
-5x - 5y = -50
5x + 10y = 90
------------------
5y = 40
y = 8
x = 2
There are 2 nickels and 8 dimes in the jar. Hope this helps! :)
Answer:
2.29 ft of side length and 1.14 height
Step-by-step explanation:
a) Volume V = x2h, where x is side of square base and h is hite.
Then surface area S = x2 + 4xh because box is open.
b) From V = x2h = 6 we have h = 6/x2.
Substitude in formula for surface area: S = x2 + 4x·6/x2, S = x2 + 24/x.
We get S as function of one variable x. To get minimum we have to find derivative S' = 2x - 24/x2 = 0, from here 2x3 - 24 = 0, x3 = 12, x = (12)1/3 ≅ 2.29 ft.
Then h = 6/(12)2/3 = (12)1/3/2 ≅ 1.14 ft.
To prove that we have minimum let get second derivative: S'' = 2 + 48/x3, S''(121/3) = 2 + 48/12 = 6 > 0.
And because by second derivative test we have minimum: Smin = (12)2/3 + 4(12)1/3(12)1/3/2 = 3(12)2/3 ≅ 15.72 ft2
3 to the power of 4:
=34
x
n
=
3
4
=3⋅3⋅3⋅3
=
3
⋅
3
⋅
3
⋅
3
=81
=
81
For example, 3 to the power of -4:
=3−4
x
n
=
3
−
4
=134
=
1
3
4
=13⋅3⋅3⋅3
=
1
3
⋅
3
⋅
3
⋅
3
=181
=
1
81
=0.012346
The measure of the third angle is 50 because a triangle has a sum of 180 degrees by angle.
so... 46+84=130 and to get to 180, the last angle has to be worth 50.
Answer:
X = 45
Step-by-step explanation:
