Answer:
(a) LM=12 units, LN=35 units, MN=37 units
(b)8 84 units
(c) 210 square units
Step-by-step explanation:
(a)
Since points L and M have same x coordinates, it means they are in the same plane. Also, since the Y coordinates of L and N are same, they also lie in the same plane
Length 
Length 
Length
Alternatively, since this is a right angle triangle, length MN is found using Pythagoras theorem where
Therefore, the lengths LM=12 units, LN=35 units and MN=37 units
(b)
Perimeter is the distance all round the figure
P=LM+LN+MN=12 units+35 units+37 units=84 units
(c)
Area of a triangle is given by 0.5bh where b is base and h is height, in this case, b is LN=35 units and h=LM which is 12 units
Therefore, A=0.5*12*35= 210 square units
1. Write the equation:
d(-3 + x) = kx + 9
2. "Open" the parenthesizes:
-3d + dx = kx + 9
3. Take kx to the left side, -3d to the right, everything with different sign (+ replace with - when transferring, - replace with +):
dx - kx = 9 + 3d
4. Factor x in the left side:
x(d - k) = 9 + 3d
5. Finally, divide the whole equation by (d - k):
x = (9 + 3d)/(d - k)
That's the final answer. Good luck!
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:
The probability of a successful event is the ratio of the number of successful events to the total number of events. In this case, a successful event is selecting a red marble from the box. The total number of events is the total number of marbles in the box:
Red marbles/Total number of marbles
4/12 divide
=1/3
