Break up chain with AND statement:
(2/3)t - 1 < t + 7 AND <span>t + 7 ≤ -2t + 15
left side, we solve for t
</span>
<span>(2/3)t - 1 < t + 7
(2/3)t - t < 7 + 1
(-1/3)t < 8
t > -24
right side, we solve for t</span>
<span>t + 7 ≤ -2t + 15
t + 2t </span><span>≤ 15 - 7
3t </span><span>≤ 8
t </span><span>≤ 8/3
So our answer would be </span>
t > -24 AND t <span>≤ 8/3
as an interval, this is
</span>-24 < t <span>≤ 8/3
or in interval notation
(-24, 8/3]</span>
<span>The canyon starts at an elevation of (-14.5). After each year, the elevation drops by (-1.5). The equation that could be written for this, then, would be (-14.5 - 1.5x = -31). First, we could add 14.5 to both sides of the equation to isolate the unknown. This would leave -1.5x = -16.5. Next, we can remove the negative signs so both sides of the equation are positive and easier to work with. This leaves 1.5x = 16.5. Finally, dividing both sides by 1.5 gives us "x = 11", which means that after 11 years, the canyon floor will be at -31 feet.</span>
Answer:
Step-by-step explanation:
cot²(3x)=y
y²-3y+2=0
y²-y-2y+2=0
y(y-1)-2(y-1)=0
(y-1)(y-2)=0
y=1,y=2
cot3x=1
tan 3x=1=tan (π/4)=tan (nπ+π/4)
3x=nπ+π/4=(4nπ+π)/4=(4n+1)π/4
x=(4nπ+1)π/12,n is an integer.
cot 3x=2
tan 3x=1/2
3x=tan^{-1}(1/2)≈26.57°+360n
x≈8.86°+120n
Perform the indicated multiplication first: -15 + 5q + 4 = 5q - 11
Note that 5q appears on both sides of this equation. Cancelling, we get :
-11 = -11. This is always true. Thus, -5(3-q) +4=5q-11 is true for all q.
