Answer:
x = 3
x = (-1)/2
x = 13/4
Step-by-step explanation:
Solve for x:
(2 x)/3 + 15 = 17
Put each term in (2 x)/3 + 15 over the common denominator 3: (2 x)/3 + 15 = (2 x)/3 + 45/3:
(2 x)/3 + 45/3 = 17
(2 x)/3 + 45/3 = (2 x + 45)/3:
1/3 (2 x + 45) = 17
Multiply both sides of (2 x + 45)/3 = 17 by 3:
(3 (2 x + 45))/3 = 3×17
(3 (2 x + 45))/3 = 3/3×(2 x + 45) = 2 x + 45:
2 x + 45 = 3×17
3×17 = 51:
2 x + 45 = 51
Subtract 45 from both sides:
2 x + (45 - 45) = 51 - 45
45 - 45 = 0:
2 x = 51 - 45
51 - 45 = 6:
2 x = 6
Divide both sides of 2 x = 6 by 2:
(2 x)/2 = 6/2
2/2 = 1:
x = 6/2
The gcd of 6 and 2 is 2, so 6/2 = (2×3)/(2×1) = 2/2×3 = 3:
Answer: x = 3
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Solve for x:
3 x - x + 8 = 7
Grouping like terms, 3 x - x + 8 = (3 x - x) + 8:
(3 x - x) + 8 = 7
3 x - x = 2 x:
2 x + 8 = 7
Subtract 8 from both sides:
2 x + (8 - 8) = 7 - 8
8 - 8 = 0:
2 x = 7 - 8
7 - 8 = -1:
2 x = -1
Divide both sides of 2 x = -1 by 2:
(2 x)/2 = (-1)/2
2/2 = 1:
Answer: x = (-1)/2
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Solve for x:
4 (2 x - 6) = 2
Divide both sides of 4 (2 x - 6) = 2 by 4:
(4 (2 x - 6))/4 = 2/4
4/4 = 1:
2 x - 6 = 2/4
The gcd of 2 and 4 is 2, so 2/4 = (2×1)/(2×2) = 2/2×1/2 = 1/2:
2 x - 6 = 1/2
Add 6 to both sides:
2 x + (6 - 6) = 1/2 + 6
6 - 6 = 0:
2 x = 1/2 + 6
Put 1/2 + 6 over the common denominator 2. 1/2 + 6 = 1/2 + (2×6)/2:
2 x = 1/2 + (2×6)/2
2×6 = 12:
2 x = 1/2 + 12/2
1/2 + 12/2 = (1 + 12)/2:
2 x = (1 + 12)/2
1 + 12 = 13:
2 x = 13/2
Divide both sides by 2:
x = (13/2)/2
2×2 = 4:
Answer: x = 13/4
Answer:
Cartesian
z₁= 3 +4*j
z₂= 2 +3*j
Polar
z₁=5 * e^ (0.927*j)
z₁=√13 * e^ (0.982*j)
Step-by-step explanation:
for the complex numbers z the cartesian form of is
z= x + y*j
then
1) z₁= 3 +4*j (cartesian form)
2) z₂= 2 +3*j (cartesian form)
the polar form is
z= r* e^jθ
where
r= √(x²+y²) → r₁ = √(3²+4²) = 5 , r₂ = √(2²+3²) = √13
and
θ = tan⁻¹ (y/x) → θ₁ = tan⁻¹ (4/3)= 0.927 rad , θ₂ = tan⁻¹ (3/2)= 0.982 rad
then
z₁=5 * e^ (0.927*j)
z₁=√13 * e^ (0.982*j)
Answer:
Part a) to find the maximum height of the snowball, you have to differentiate the function. Therefore you get ----> dh/dt= -32x-8 . Now equate this to zero and solve for x. x= (-1)/4 now sub this value in to find h(x) [note: i'm talking about the original function] . I got h max = h((-1)/4) = 9 which is the max height.
Step-by-step explanation:
I'm not too sure about the other questions. Sorry
Answer:
1.75
Step-by-step explanation:
h(t) = -16t² + 56t
h'(t) = -32t + 56
To find time at max height equate h' to 0
0 = -32t + 56
t = 56/32 = 1.75 s
It takes 1.75 s to reach max highest point
Answer:
Step-by-step explanation:
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