Answer:
The dimension of the base of the Rectangle Pyramid is Length = 10 and Width = 8/3
Step-by-step explanation:
Given
Rectangle Pyramid
Base Length = 3x + 1
Base Width = x
Height = 12
Volume = 96
Required
Dimension of the base of the pyramid
Given that the volume of the pyramid is ⅓ of the base area * the height.
This is represented mathematical as
Volume = ⅓ * base area * height.
Where
Base area = width * length
Base area = (3x + 1) * x
Base area = 3x² + x.
So,
Volume becomes
Volume = ⅓ * (3x² + x) * 12.
Volume = (3x² + x) * 4
Substitute 96 for volume
96 = (3x² + x) * 4
Divide both sides by 4
96/4 = (3x² + x) * 4/4
24 = 3x² + x
Subtract 24 fr both sides
24 - 24 = 3x² + x - 24
0 = 3x² + x - 24
3x² + x - 24 = 0
Expand
3x² + 9x - 8x - 24 = 0
Factorize
3x(x + 3) - 8(x + 3) = 0
(3x - 8)(x + 3) = 0
3x - 8 = 0 or x + 3 = 0
3x = 8 or x = -3
x = 8/3 or x = -3
Recall that
Length = 3x + 1
Width = x
For any of the above expression, x can't be less than 0; so, x = -3 can't be considered.
Substitute x = 8/3
Length = 3x + 1
Length = 3(8/3) + 1
Length = 8 + 1
Length = 9
Width = x
Width = 8/3
Hence, the dimension of the base of the Rectangle Pyramid is Length = 10 and Width = 8/3
Answer:
A)
x= the number of ride tickets
y= the total cost of admission plus how many ride tickets a person purchases
B)
y= 1.25x + 9.5
C)
It is a$1.25 per ticket for the rides at the fair, so it would be 1.25 multiplied by the amount of tickets that are purchased (x). Spencer bought 17 tickets, so 17x1.25= 21.25 and it says that he spent a total of $30.75 at the fair, so 30.75-21.25=9.5, so that means the cost of admission is $9.50.
Step-by-step explanation:
I hope this helps!
HEYYYYYYYYYYYYYYYYY BAHSJJSIS
15 vg
18 vg
Just put a line in-between them to make a fraction.
<span>As the age of the U-235 sample is 2.631 billion years, and the half-life of U-235 is 713 million years, the sample has undergone 2.361 X 1,000,000,000 / 713 X 1,000,000 = 3.69 half lives. In each half-life the sample reduces to half its original weight according to the radioactive Half-Life Formula:
ln (Nt /N0) = -kt, where N0 = mass of the original weight of radioactive material, Nt = mass of radioactive material at time t, k = decay constant and t = time interval . We have to put Nt/N0 = 1/2 for time interval = half-life.</span>
