<span>(x-3)(x^2+9)
or
x^3 -3x^2 + 9x - 27
First, let's see about factoring x^4 - 81. Cursory examination indicates that it's the difference of two squares and so it initially factors into
(x^2 - 9)(x^2 + 9)
And the (x^2 - 9) term is also the difference of 2 squares so it too factors into:
(x - 3)(x + 3)
So a partial factorization of x^4 - 81 is:
(x - 3)(x + 3)(x^2 + 9)
The (x^2 + 9) term could be factored as well, but that's not needed for this problem, and so I won't do it.
Now we can divide (x-3)(x+3)(x^2+9) by (x+3). The (x+3) terms will cancel and we get as the result
(x-3)(x+3)(x^2+9) / (x+3) = (x-3)(x^2+9)
We can leave the answer as (x-3)(x^2+9), or we can multiply it out, getting:
x^3 -3x^2 + 9x - 27</span>
Surface area = 4 pi r^2
where
pi : 3.14 a constant
r : raduis
surface area is the change of volume with respect to raduis
volume = 4/3 pi r^3
dvolume/dr = 4 pi r^2
you can prove the identity with double integration in spherical coordinates or volumes of revolutions and polar coordinates
Answer:
Area= 45 units squared
perimeter= 28 units
Step-by-step explanation:
Area: multiply 5 times 9 to get the number of squares inside (length times width)
Perimeter: add all the side lengths together; 9+9+5+5 ( becuase this is a rectangle, the top 2 lengths are the same and the 2 lengths on the side are equal, so you can also just do 2 times (9+5) and that will work fine too)
Answer:
1. UW // TX
2. VX // UY
3. UW ≅ TY ≅ YX
4. YW = 
TV
5. TX = 2 UW
6. ∠TXV ≅∠WUY
Step-by-step explanation:
The line segment joining the midpoint of two sides of a triangle is parallel to the third side and equal to half its length
In Δ XVT
∵ U is the midpoint of VT
∵ W is the midpoint of VX
∵ XT is the 3rd side of the triangle
→ By using the rule above
∴ UW // TX ⇒ (1)
∴ UW = TX
→ Multiply both sides by 2
∴ 2 UW = TX
∴ TX = 2 UW ⇒ (5)
∵ Y is the midpoint of TX
∴ TY = YX = TX
∵ UW = TX
∴ UW ≅ TY ≅ YX ⇒ (3)
∵ U is the midpoint of VT
∵ Y is the midpoint of XT
∵ VX is the 3rd side of the triangle
→ By using the rule above
∴ UY // VX
∴ VX // UY ⇒ (2)
∴ UY = VX
∵ W is the midpoint of VX
∵ Y is the midpoint of XT
∵ TV is the 3rd side of the triangle
→ By using the rule above
∴ YW // TV
∴ YW = TV ⇒ (4)
∵ 2 Δs UYW and XVT
∵ UY = XV
∵ YW = VT
∵ WU = TX
∴ 
= 
= 
=
→ By using the SSS postulate of similarity
∴ ∠TXV ≅∠WUY ⇒ (6)
Answer:
189
Step-by-step explanation:
If mark uses 19 gallons to travel 399 miles, that means he was able to travel 21 miles per gallon.
We get this by taking 399 divided by 19.
So if mark travels on 9 gallons of gas and goes 21 miles per gallon, he will have traveled 189 miles.
We get this by taking 21 times 9
