Answer:
2, 2, 3, 5, 7 that is the farthest you can go
Step-by-step explanation:
2,2,3,5,7 prime factorization of 420 but impossible to get 9 factors
Answer: The answer is 43.
Step-by-step explanation: Given that there is a quart, in which there are 946 millilitres and 22 pints. We are to find how many millilitres are there in a pint.
For that, we just need to divide number of milliliters by the number of pints in the quart.
Let us start as follows -
In 22 pints of the quart = 946 millilitres.
Therefore, in 1 pint of the quart = 946/22 = 43 millilitres.
Answer:
x=6
Step-by-step explanation:
81^x = 27 ^(x+2)
81 = 3^4 and 27 =3^3 so replace 81 and 27 in the equation
3^4^x = 3^3^(x+2)
When we have a power to a power we can multiply the exponents
a ^b^c = a^(b*c)
3^(4x) = 3^(3*(x+2))
Since the bases are the same, the exponents have to be the same
a^b = a^c means b=c
4x = 3(x+2)
Now we can solve for x
Distribute
4x = 3x+6
Subtract 3x from each side
4x-3x = 3x-3x+6
x = 6
Split up the integration interval into 4 subintervals:
![\left[0,\dfrac\pi8\right],\left[\dfrac\pi8,\dfrac\pi4\right],\left[\dfrac\pi4,\dfrac{3\pi}8\right],\left[\dfrac{3\pi}8,\dfrac\pi2\right]](https://tex.z-dn.net/?f=%5Cleft%5B0%2C%5Cdfrac%5Cpi8%5Cright%5D%2C%5Cleft%5B%5Cdfrac%5Cpi8%2C%5Cdfrac%5Cpi4%5Cright%5D%2C%5Cleft%5B%5Cdfrac%5Cpi4%2C%5Cdfrac%7B3%5Cpi%7D8%5Cright%5D%2C%5Cleft%5B%5Cdfrac%7B3%5Cpi%7D8%2C%5Cdfrac%5Cpi2%5Cright%5D)
The left and right endpoints of the 
-th subinterval, respectively, are
for 
, and the respective midpoints are
We approximate the (signed) area under the curve over each subinterval by
so that
We approximate the area for each subinterval by
so that
We first interpolate the integrand over each subinterval by a quadratic polynomial 
, where
so that
It so happens that the integral of reduces nicely to the form you're probably more familiar with,
Then the integral is approximately
Compare these to the actual value of the integral, 3. I've included plots of the approximations below.
