6+5X<21
******(THE < IS SUPPOSE TO HAVE A LINE UNDER IT)
Answer:
68.30200
Step-by-step explanation:
Answer:
B. 
Step-by-step explanation:
The sides forming the right angle are called the legs. Since the two angles shown are congruent, the legs are congruent.
We can use the Pythagorean theorem.
Solve for v(t)=0 over the interval [0,2]
<span>sin(pi)<0, try t=pi/2, </span>
<span>3e^(-pi/4)sin(pi)= 0, so the interval 0 to pi/2 the particle travels forward [0,pi/2), then it goes negative for the rest of the interval (pi/2,2) and travels backward. </span>
<span>total distance = |integral 0 to pi/2 v(t) dt| + |integral pi/2 to 2 v(t) dt|
</span>∫[0 to π/2] v(t) dt = ∫[0 to π/2] (3 e^(−t/2) sin(2t)) dt
<span>. . . . . . . . . . . . . = ∫[0 to π/2] (3 e^(−t/2) sin(2t)) dt </span>
<span>. . . . . . . . . . . . . = −6/17 e^(−t/2) (sin(2t) + 4cos(2t)) |[0 to π/2] </span>
<span>. . . . . . . . . . . . . = −6/17 (e^(−π/4) (sin(π) + 4cos(π)) − e^(0) (sin(0) + 4cos(0))) </span>
<span>. . . . . . . . . . . . . = −6/17 (e^(−π/4) (0 − 4) − (0 + 4)) </span>
<span>. . . . . . . . . . . . . = −6/17 (−4e^(−π/4) − 4) </span>
<span>. . . . . . . . . . . . . = 24/17 (e^(−π/4) + 1) </span>
<span>. . . . . . . . . . . . . = 2.05544
</span>
∫[π/2 to 2] v(t) dt = ∫[π/2 to 2] (3 e^(−t/2) sin(2t)) dt
<span>. . . . . . . . . . . . . = ∫[π/2 to 2] (3 e^(−t/2) sin(2t)) dt </span>
<span>. . . . . . . . . . . . . = −6/17 e^(−t/2) (sin(2t) + 4cos(2t)) |[π/2 to 2] </span>
<span>. . . . . . . . . . . . . = −6/17 (e^(−1) (sin(4) + 4cos(4)) − e^(−π/4) (sin(π) + 4cos(π))) </span>
<span>. . . . . . . . . . . . . = −6/17 ( (sin(4)+4cos(4))/e − e^(−π/4) (0 − 4)) </span>
<span>. . . . . . . . . . . . . = −6/17 ( (sin(4)+4cos(4))/e + 4e^(−π/4)) </span>
<span>. . . . . . . . . . . . . = −0.205938 </span><span> </span>
<span>when you add absolute values of area you get actual distance traveled: </span>
<span>∫[0 to π/2] v(t) dt − ∫[π/2 to 2] v(t) dt </span>
<span>= 2.05544 − (−0.205938) </span>
<span>= 2.05544 + 0.205938 </span>
<span>= 2.261378 </span>
Answer:
1 2/5 = 1 1/2
7/9 = 1
4/9 = 1/2
3 5/7 = 4
Step-by-step explanation:
1. we must round 1 2/5
based on the answer choices we can determine that 1 1/2 is the most rational answer. This is because it is not only the only answer with the whole number, 1 but also 2/5 would round to 1/2.
2. We must round 7/9
This would round up to 1. This is because it is closest to the whole number, not 0 and not 1/2.
7 * 2 = 14
9 * 2 = 18
14/18 is only 4/18 away from being 1. This means that it would round up to 1.
3. we must round 4/9
This rounds to 1/2. If you multiply both side by 2:
4 * 2 = 8
9 * 2 = 18
8/18 for that to be 1/2 it would need 1/18. Thus this rounds up to 1/2.
4. We must round 3 5/7
5/7 would round up to a whole number.
3 + 1 = 4
Thus 3 5/7 = 4 when rounded to the nearest whole number.
