To solve this problem it is necessary to use the multiplication counting rule, that states that if there are two events a and b, the total number of outcomes will be a times b (a*b).
In this case, the total number of outcomes will be the product of the number of options for each event (cages, kinds of wood shavings and water bottles).
Baldwin's family can set up a home for their hamster in 20 different ways.
X^2 - xy + xy - Y^2
=
X^2 - Y^2
The formula for volume of cone is:
V = π
r^2 h / 3
or
π r^2
h / 3 = 36 cm^3
Simplfying in terms of r:
r^2 = 108 / π h
To find for the smallest amount of paper that can create
this cone, we call for the formula for the surface area of cone:
S = π
r sqrt (h^2 + r^2)
S = π
sqrt(108 / π h) * sqrt(h^2 + 108 / π h)
S = π sqrt(108 / π h) * sqrt[(π h^3 + 108) / π h]
Surface area = sqrt (108) * sqrt[(π h + 108
/ h^2)]
<span>Getting the 1st derivative dS / dh then
equating to 0 to get the maxima value:</span>
dS/dh = sqrt (108) ((π – 216
/ h^3) * [(π h + 108/h^2)^-1/2]
Let dS/dh = 0 so,
π – 216
/ h^3 = 0
h^3 = 216 / π
h = 4.10
cm
Calculating
for r:
r^2 = 108 / π (4.10)
r = 2.90 cm
Answers:
h = 4.10 cm
<span>r = 2.90 cm</span>
Answer:
1 speaker is $91.48
3 speakers = $91.48 × 3
= $274.44
1 tire is 9$2.55
5 tires = $92.55 × 5
= $462.75
8, 100 bills = $800
The cost for the 3 speakers and 5 tires = $274.44 + $462.75
= $737.19
Therefore, the change that Jason got was = $800 - $737.19
= $62.81
X² = 17
To simplify this, you need to find the square root of x², which is x, and the square root of 17.
x = √17
Also remember that when you are using square root, the answer can be either positive or negative.
x = +/-√17 ≈ +/- 4.12
