Answer:
(a + b + 2c)(a² + 2ab + b² - 2ac - 2bc + 4c²)
Step-by-step explanation:
Given
(a + b)³ + 8c³ ← this is a sum of cubes and factors in general as
a³ + b³ = (a + b)(a² - ab + b²)
Thus
(a + b)³ + 8c³
= (a + b)³ + (2c)³
= (a + b + 2c)( (a + b)² - 2c(a + b) + (2c)² )
= (a + b + 2c)(a² + 2ab + b² - 2ac - 2bc + 4c²)
The area of the given figure is equal to the area of a rectangle with sides 5 feets by 6 feets less the area of four square cut-outs of side 1 feet.
Area of the rectangle = 5 x 6 = 30 square feets.
Area of the four square cut-outs = 4(1 x 1) = 4 x 1 = 4 square feet
Area of the given figure = 30 - 4 = 26 square feet.
Area of a triangle = 1/2 x base x height
i.e. 1/2 bh = 26
bh = 26 x 2 = 52
possible values of base and height = (1 and 52), (2 and 26), (4 and 13)
Step-by-step explanation:
The upstream speed is S / t₁, and the downstream speed is S / t₂.
If we say f is the speed of the fish in calm water, and r is the speed of the river, then:
f − r = S / t₁
f + r = S / t₂
If we say T is the time it takes to cross the river, then the speed perpendicular to the river is ℓ/T, the speed parallel to the river is r, and the overall speed is f.
Using Pythagorean theorem:
f² = (ℓ/T)² + r²
f² − r² = (ℓ/T)²
(f − r) (f + r) = (ℓ/T)²
(S / t₁) (S / t₂) = (ℓ/T)²
S² / (t₁ t₂) = (ℓ/T)²
(t₁ t₂) / S² = (T/ℓ)²
√(t₁ t₂) / S = T/ℓ
T = ℓ√(t₁ t₂) / S
Answer:
Wait
Step-by-step explanation:
I solve first
