Answer:
D.
Step-by-step explanation:
The problem is clearly addition, so we can rule out B and C. Associative property is the movement of the parentheses, whereas commutative property is the movement or reorganization of the numbers. The parentheses moved in this problem, so it is associative. I suggest reviewing these properites, they come in handy later and are good to know :)
5
you use the formula a^2+b^2=c^2
a=3, b=4
3*3=9 and 4*4=16
16+9=25
square root of 25 is 5.
5 is the answer
Answer:
negative 5. or -5
Step-by-step explanation:
f(-1)= (-1)2-3
2 times -1= -2
-2-3= -5
f= -5
1 gallon = 128 ounces
Divide total ounces by ounces per cup:
128 / 4 = 32
She had 32 servings
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
