Hello!
To solve each expression, you need to substitute the given value for each given variable. If there is an <em>x</em> in the expression, then you substitute 5.07. If there's a <em>y</em>, then you substitute 1.5, and if there's a <em>z</em>, then you substitute 0.403.
7. 3.2x + y (substitute x = 5.07 and y = 1.5)
3.2(5.07) + (1.5)
16.224 + 1.5
17.724
8. yz + x (substitute y = 1.5, z = 0.403, and x = 5.07)
(1.5)(0.403) + (5.07)
0.6045 + 5.07
5.6745
9. z × 7.06 - y (substitute z = 0.403 and y = 1.5)
(0.403) × 7.06 - (1.5)
2.84519 - 1.5
1.34518
<u>Final answers</u>:
- Number 7: 17.724
- Number 8: 5.6745
- Number 9: 1.34518
Answer:
a = - 2, b = - 6
Step-by-step explanation:
Substitute the values of the zeros into the polynomial and equate to zero.
x² +(a + 1)x + b
x = - 2 → (- 2)² - 2(a + 1) + b = 0 , that is
4 - 2a - 2 + b = 0
2 - 2a + b = 0 ( subtract 2 from both sides )
- 2a + b = - 2 → (1)
x = 3 → 3² + 3(a + 1) + b = 0, that is
9 + 3a + 3 + b = 0
12 + 3a + b = 0 ( subtract 12 from both sides )
3a + b = - 12 → (2)
Subtract (1) from (2) term by term to eliminate b
5a = - 10 ( divide both sides by 5 )
a = - 2
Substitute a = - 2 into either of the 2 equations and evaluate for b
Substituting into (2)
3(- 2) + b = - 12
- 6 + b = - 12 ( add 6 to both sides )
b = - 6
Thus a = - 2 and b = - 6
Answer:
Step-by-step explanation:
given,
angular deceleration, α = -0.5 rad/s²
final angular velocity,ω_f = 0 rad/s
angular position, θ = 6.1 rad
angular position at 3.9 s = ?
now, Calculating the initial angular speed
now, angular position calculation at t=3.9 s
Hence, the angular position of the wheel after 3.9 s is equal to 5.83 rad.
<span>h<span>(t)</span>=<span>t<span>34</span></span>−3<span>t<span>14</span></span></span>
Note that the domain of h is <span>[0,∞]</span>.
By differentiating,
<span>h'<span>(t)</span>=<span>34</span><span>t<span>−<span>14</span></span></span>−<span>34</span><span>t<span>−<span>34</span></span></span></span>
by factoring out <span>34</span>,
<span>=<span>34</span><span>(<span>1<span>t<span>14</span></span></span>−<span>1<span>t<span>34</span></span></span>)</span></span>
by finding the common denominator,
<span>=<span>34</span><span><span><span>t<span>12</span></span>−1</span><span>t<span>34</span></span></span>=0</span>
<span>⇒<span>t<span>12</span></span>=1⇒t=1</span>
Since <span>h'<span>(0)</span></span> is undefined, <span>t=0</span> is also a critical number.
Hence, the critical numbers are <span>t=0,1</span>.
I hope that this was helpful.
