Possible number combinations are 1,1 2,1 3,1 4,1 5,1 6,1 1,2 2,2 3,2 4,2 5,2 6,2 1,3 2,3 3,3 4,3 5,3 6,3 1,4 2,4 3,4 4,4 5,4 6,4 1,5 2,5 3,5 4,5 5,5 6,5 1,6 2,6 3,6 4,6 5,6 and 6,6. of those 36 number combinations the ones that add up to more than 10 include: 4,6 5,5 5,6 6,4 6,5 6,6. thats 6 number combinations. 6/36 of the possible sums of the top faces equal out to 10 or more. 6/36=1/6=0.166666666666666666666666(repeating) and to put that in a percentage, 16.7%
the probability is 16.7%
Hope this helps.
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
Answer:
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The answer would be 7.5, since 6/9=2/3 and 5/7.5=2/3, then the sides are equal ratios.
31x^2 + 53x - 8
Use the FOIL method to find the area of the large rectangle. (7x - 2)(9 + 5x)
First term in each binomial: 7x * 9 = 63x
Outside terms: 7x * 5x = 35x^2
Inside terms: -2 * 9 = -18
Last term in each binomial: -2 * 5x = -10x
Now, just add them all up.
63x + 35x^2 - 8 - 10x
35x^2 + 53x - 8
Now find the area of the square.
2x * 2x = 4x^2
Now, subtract the areas.
31x^2 + 53x - 8
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