Two geometrical objects are called similar if they both have the same shape, or one has the ... Due to this theorem, several authors simplify the definition of similar triangles<span> to only require that the corresponding three angles are congruent. I hope that helps you.</span>
The answer is 36
Hope it helps
Answer:
849.24 cm²
Step-by-step explanation:
we know it is a cube so to find the surface area of each square you do
12x12=144 and there are 5 sides so 144x5=720
We know sides of the squares are 12 cm so half of that (6) would be the bottom of the triangle
Now using pythagorus you would do a²+b²=c²
15²+6²=c²
225+36=c²
√261=√c²
16.15=c this only half of one of the sides of the pyramid so you would times 16.15 by 8 to equal 129.24
now add 720+129.24=849.24 cm²
Answer:
a solution is 1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) + π/4
Step-by-step explanation:
for the equation
(1 + x⁴) dy + x*(1 + 4y²) dx = 0
(1 + x⁴) dy = - x*(1 + 4y²) dx
[1/(1 + 4y²)] dy = [-x/(1 + x⁴)] dx
∫[1/(1 + 4y²)] dy = ∫[-x/(1 + x⁴)] dx
now to solve each integral
I₁= ∫[1/(1 + 4y²)] dy = 1/2 *tan⁻¹ (2*y) + C₁
I₂= ∫[-x/(1 + x⁴)] dx
for u= x² → du=x*dx
I₂= ∫[-x/(1 + x⁴)] dx = -∫[1/(1 + u² )] du = - tan⁻¹ (u) +C₂ = - tan⁻¹ (x²) +C₂
then
1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) +C
for y(x=1) = 0
1/2 *tan⁻¹ (2*0) = - tan⁻¹ (1²) +C
since tan⁻¹ (1²) for π/4+ π*N and tan⁻¹ (0) for π*N , we will choose for simplicity N=0 . hen an explicit solution would be
1/2 * 0 = - π/4 + C
C= π/4
therefore
1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) + π/4
