We use the given data above to calculate the volume of gasoline that is being burned per minute by commercial airplanes.
Amount burned of 1 commercial airplane = <span>3.9 × 10³ ml of gasoline per second
Number of airplanes = </span><span>5.1 × 10³ airplanes
We calculate as follows:
</span> 3.9 × 10³ ml of gasoline per second / 1 airplane (5.1 × 10³ airplanes)(60 second / 1 min ) = <span>1.2 x 10^9 mL / min</span>
Answer:
dy/dx = -1/√(1 - x²)
For 0 < y < π
Step-by-step explanation:
Given the function cos y = x
-siny dy = dx
-siny dy/dx = 1
dy/dx = -1/siny (equation 1)
But cos²y + sin²y = 1
=> sin²y = 1 - cos²y
=> siny = √(1 - cos²y) (equation 2)
Again, we know that
cosy = x
=> cos²y = x² (equation 3)
Using (equation 3) in (equation 2), we have
siny = √(1 - x²) (equation 4)
Finally, using (equation 4) in (equation 1), we have
dy/dx = -1/√(1 - x²)
The largest interval is when
√(1 - x²) = 0
=> 1 - x² = 0
=> x² = 1
=> x = ±1
So, the interval is
-1 < x < 1
arccos(1) < y < arxcos(-1)
= 0 < y < π
Answer:
16.40
Step-by-step explanation:
3 min-> 180 s
180÷16≈11
11+1=12
12x1.20=14.40
14.40 + 2 = 16.40
Answer:
She subtracted the GCF from the second term in the expression instead of dividing.
Step-by-step explanation:
Given the expression 32ab-8b, to find the common greatest factor, we will bring out a function that us common to both terms 32ab and 8b. To do that, we need to first find their individual factors as shown:
32ab = (2×2×2)×2×2×a×(b)
8b = (2×2×2×b)
From both factors, the common terms are the values in parenthesis i.e 2×2×2×b = 8b
Hence the GCF of the expression 32ab - 8b is 8b. On factoring out 8b from the expression we will have;
= 32ab - 8b
= 8b(32ab/8b - 8b/8b)
= 8b(4a-1)
Comparing the gotten equation with Venita's own, 8b(4a-0), we can say that she correctly factored out the GCF but her error was that she subtracted 8b from the second term of the expression instead of dividing by 8b. 8b-8b is what gives her 0 making her expression wrong. She should have divided her second term also by 8b to have 8b/8b which results in 1 instead of 0 that venita got.
The sum of arithmetic series is given by:
Sn=n/2(a1+an)
where:
n=number of terms
a1=first term
an=nth term
but
n=18, an=275, Sn=4185
plugging the values in the formula we get:
4185=18/2(a1+275)
simplifying this we get:
4185=9(a1+275)
dividing through by 9 we get:
465=a1+275
thus
a1=465-275
a1=190
Answer: first number is 190
