<span>Since: v =sqrt(3)/2 s^2h
6779 liters x 0.0353cu ft/1 liter= 239.299 cu ft
but by proportion s/h = 10/25
s = 10/25 h
and v = sqrt(3)/2 (10/25 h)^2 h
239.299 = 0.139 h^3
h = (239.299/0.139)^(1/3) = 11.985 ft</span>
Answer:
a*b = 1/2
a/ b = 8/9
Step-by-step explanation:
a = 0.66666 and b = 0.75
To multiply it we write the decimal numbers in fraction form
a= 0.666666...
Multiply by 10 on both sides
10 a = 6.66666...
a = 0.66666...
Subtract the second equation
9a = 6
divide by 9 on both sides
so 0.6666 = 2/3
Now we convert 0.75 into fraction form
Multiply top and bottom by 100 to remove decimal
so 0.75 is 3/4
a= 2/3 and b = 3/4
Answer:
Step-by-step explanation:
Given:
Scale
2 inches : 5 feet
Actual dimensions
Let x be the dimension of the scale drawing (in inches) and y, the corresponding dimension of the actual field (in feet).
Scaled dimension = scale × actual dimension
Actual dimension, x = y × 5 ft/2 in
2 × x = 5 × y
Equation:
2x = 5y
Compatible numbers are numbers which are easy to do mental calculation.
For example is when doing division like 25 and 5, 100 and 10, and 36 and 6.
First, we know that: 7 pounds=5 pounds + 2 pounds
or 7=5+2
In mathematics, the word “of” means to multiply. So:
grapes
given away = 7 * (2/5)
Replacing 7 with 5 and 2:
=
(5+2)*(2/5)
Using the distribution principle:
=5*(2/5)
+ 2*(2/5)
=2+
4/5
=2
4/5
So grapes given away is 2 4/5 pounds.
Answer:
x^2/12 - y^2/4 = 1
Step-by-step explanation:
As the diretrices have simetrical values of x and have y = 0, the center is located at (0,0)
The formula for the diretrices is:
x1 = -a/e and x2 = a/e
And the foci is located at (a*e, 0) and (-a*e, 0)
So we have that:
a/e = 3
a*e = 4
From the first equation, we have a = 3e. Using this in the second equation, we have:
3e*e = 4
e^2 = 4/3
e = 1.1547
Now finding the value of a, we have:
a = 3*1.1547 = 3.4641
Now, as we have that b^2 = a^2*(e^2 - 1), we can find the value of b:
b^2 = 3.4641^2 * (1.1547^2 - 1) = 4
b = 2
So the equation of the hyperbola (with vertical diretrices and center in (0,0)) is:
x^2/a^2 - y^2/b^2 = 1
x^2/12 - y^2/4 = 1
