Answer:
(x + 10 and (x + 12)
Step-by-step explanation:
x^2 + 22x + 120 = ( ? )( ? )
We need to find two constants whose product is 120 and whose sum is 22.
Let the two constants be a and b. Then:
a*b = 120 and a + b = 22.
It's a bit easier to find a and b such that a + b = 22: 2 and 20, 4 and 18, 6 and 16, and so on. Note that 6 + 16 = 22 (correct) but that 6*16 = 96 (not correct). Try 8 and 14, 10 and 12. Note that 10 + 12 = 22 and that 10*12 = 120. So the desired roots are {10, 12} and the desired factors are (x + 10 and (x + 12).
Check: Does (x + 10)(x + 12) work out to x^2 + 22x + 120?
x^2 + 12x + 10x + 120 = x^2 + 22x + 120? YES
The factors are (x + 10 and (x + 12).
Answer:
![\bf cos(x)\approx1-\displaystyle\frac{x^2}{2}+\displaystyle\frac{x^4}{4!}=\\\\=1-\displaystyle\frac{x^2}{2}+\displaystyle\frac{x^4}{24}](https://tex.z-dn.net/?f=%5Cbf%20cos%28x%29%5Capprox1-%5Cdisplaystyle%5Cfrac%7Bx%5E2%7D%7B2%7D%2B%5Cdisplaystyle%5Cfrac%7Bx%5E4%7D%7B4%21%7D%3D%5C%5C%5C%5C%3D1-%5Cdisplaystyle%5Cfrac%7Bx%5E2%7D%7B2%7D%2B%5Cdisplaystyle%5Cfrac%7Bx%5E4%7D%7B24%7D)
The polynomial is an approximation with an error less than or equals to <em>0.002652</em> for x in the interval
[-1.113826815, 1.113826815]
Step-by-step explanation:
According to Taylor's theorem
with
for some c in the interval (-x, x)
In the particular case f
<em>f(x)=cos(x)
</em>
<em>
</em>
we have
therefore
and the polynomial approximation of T5(x) of cos(x) would be
In order to find all the values of x for which this approximation is within 0.002652 of the right answer, we notice that
for some c in (-x,x). So
and we must find the values of x for which
Working this inequality out, we find
Therefore the polynomial is an approximation with an error less than or equals to 0.002652 for x in the interval
[-1.113826815, 1.113826815]
Answer:
63 Inches.
Step-by-step explanation:
2 yards - 9 inches is equal to 1.75 yards and when converted to inches, equals 63 inches.
This is the commutative property because you have 3*x*2*y and you turn the x and the 2 around. The commutative property states that a * b = b * a and therefore x*2 = 2*x.
Answer:
35 grams
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Step-by-step explanation:
350/10=35