Log base b=logb
4 log₂ 2x+ 2logb x=4
log₂(2x)⁴+logb x²=log₂16
log₂ 16x⁴+ logb x²=log₂ 16
logb x²=log₂ 16 - log₂ 16x⁴
logb x²=log₂ (16/16x⁴)
logb x²= log₂ x⁻⁴
logb x²=log₂ x² / log₂ b
log₂ x² / log₂ b=-log x⁴
log₂ b=log₂ x² /- log₂ x⁴
log₂ b=2 log x / -4 log₂ x
log₂ b=-1/2 ⇔ b=2⁻¹/² =1/√2=(√2)/2≈ 0.707106781....
Answer: b=(√2)/2
To chek
if x=10
log base √2/2= log√2/2
4 log₂ 20 + 2log√2/2 10=4(4.321928095...)+2 (-6.64385619=
= 17.28771238-13.28771238=4
Pythagorean Theorem: a^2 + b^2 = c^2
-A and B are legs of the triangle
-C is the hypotenuse
#1.
6^2 + 8^2 = c^2
36 + 64 = c^2
100 = c^2
c = 10
#2.
5^2 + 12^2 = c^2
25 + 144 = c^2
169 = c^2
c = 13
#4.
10^2 + 4^2 = c^2
100 + 16 = c^2
116 = c^2
c =
#5.
15^2 + 9^2 = c^2
225 + 81 = c^2
306 = c^2
c =
#6.
120^2 + b^2 = 150^2
14400 + b^2 = 22500
b^2 = 8100
b = 90
#7.
144^2 + b^2 = 194^2
20736 + b^2 = 37636
b^2 = 16900
b = 130
Hope this helps!! :)
Answer:
Jogging = 10 hours
Swimming = 7 hours
Cycling = 3 hours
Step-by-step explanation:
J = Hours jogging
S = Hours swimming
C = Hours cycling
Since jogging is the activity that burns the most calories, we should maximize the number of hours jogging:
Therefore, the man should jog for 10 hours.
Since swimming is the activity that burns the second most calories, we should maximize swimming hours:
In order to maximize the number of calories burn, the man should go jogging for 10 hours, swimming for 7 hours and cycling for 3 hours.
The sum of angles in the triangle = 180
1,0 should be the vertex for this parabola