Ok so let's start with what we know- the shortest piece is 8 inches so there's one length... then the middle piece is 6 inches longer than the shortest (6+ 8) so the middle piece would be 14 inches long. To find the last piece we can add up the other two pieces we know (14+8) which would be 22 and subtract that from how long the whole sandwich is (59-22) which would be 37 inches long. So in the end he shortest piece would be 8 inches, the middle 14 inches and the longest 37 inches.
Answer:
7/6 or 1 1/6
Step-by-step explanation:
when you add or subtract fractions, you have to have a common denominator. in this case, your common denominator is 6
1/2=3/6
2/3=4/6
add the numerators and keep the denominator 6
4+3=7
7/6 or 1 1/6
To answer this item, we have 4 as the speed of the kayaker in still water and the speed of current be y.
When the karayaker moves upstream or against the current, his speed would be 4 - y. Further, if he moves downstream or with the current, the total speed would be 4 + y. The time utilized for the travel is equal to the ratio of the distance and the speed.
Total time = 9/(4 - y) + 9/(4 + y) = 6
We multiply the equation by (4-y)(4+y)
9(4-y) + 9(4 + y) = 6(4-y)(4+y)
Simplifying,
72 = 96 - 6y²
Transposing all the constants to only one side of the equation and rearranging,
6y² = 96 - 72
y² = 4
y = 2
Hence, the speed of the river's current is 2 miles/hr. <em>The answer is letter B.) 2 miles/hour.</em>
We can create two equations here:
(1) Volume = area of square * height of box
85.75 = s^2 h
(2) Cost = 3 * area of square + 1.5 * area of side box
C = 3 s^2 + 1.5 s h
From (1), we get:
h = 85.75 / s^2
Combining this with (2):
C = 3 s^2 + 1.5 s (85.75 / s^2)
C = 3 s^2 + 128.625 s-
Taking the 1st derivative and equating dC/ds =
0:
dC/ds = 6s – 128.625 / s^2 = 0
Multiply all by s^2:
6s^3 – 128.625 = 0
6s^3 = 128.625
s = 2.78 cm
So h is:
h = 85.75 / s^2 = 85.75 / (2.78)^2
h = 11.10 cm
So the dimensions are 2.78 cm x 2.78 cm x 11.10 cm
The total cost now is:
C = 3 (2.78)^2 + 1.5 (2.78) (11.10)
C = $69.47
Answer:
5 drahms.
Step-by-step explanation:
From the question given above, the following data were obtained:
120 grains = 6 scruples
6 scruples = 2 drahms
300 grains (in drahms) =..?
From the above data,
120 grains = 6 scruples
6 scruples = 2 drahms
Therefore,
120 grains = 2 drahms
Thus, we can obtain 300 grains in drahms as follow:
120 grains = 2 drahms
Therefore,
300 grains = 300 grains × 2 drahms /120 grains
300 grains = (300 × 2)/120 drahms
300 grains = 5 drahms
Therefore, 300 grains is equivalent to 5 drahms.
