Answer:
16) r = C/(2·π)
17) [tex]r^2 = \dfrac{3 \ \cdot V}{\pi \cdot h}[/tex]
18) x = (9 - 3·y)/2
19) Please find attached the required graph of the inequality x ≤ 4 created with MS Excel
20) z ≥ 1
Solve each inequality and graph the solution
21) n ≤ 1
22) p > -5
23) -3 ≤ q ≤ 2/5
24) x > 1/5
25) x < -11
26) 7
Step-by-step explanation:
Solving for the indicated variable
16) C = 2·π·r for r
Dividing both sides by 2·π gives;
C/(2·π) = 2·π·r/(2·π) = r
∴ r = C/(2·π)
17) [tex]V = \dfrac{1}{3} \cdot \pi \cdot r^2 \cdot h \ for \ r^2[/tex]
Dividing both sides by [tex]\left( \dfrac{1}{3} \cdot \pi \cdot h \right)[/tex] gives;
[tex]\dfrac{V}{\left( \dfrac{1}{3} \cdot \pi \cdot h \right)} = \dfrac{ \dfrac{1}{3} \cdot \pi \cdot r^2 \cdot h}{\left( \dfrac{1}{3} \cdot \pi \cdot h \right)}[/tex]
[tex]\therefore r^2 = \dfrac{V}{\left( \dfrac{1}{3} \cdot \pi \cdot h \right)} = \dfrac{3 \ \cdot V}{\pi \cdot h}[/tex]
[tex]r^2 = \dfrac{3 \ \cdot V}{\pi \cdot h}[/tex]
18) 2·x + 3·y = 9 for x, gives;
x = (9 - 3·y)/2
19) Please find attached the required graph of the inequality x ��� 4 created with MS Excel
20) Solve each inequality
z - 3 ≥ -2
z ≥ -2 + 3 = 1
∴ z ≥ 1
Solve each inequality and graph the solution
21) 3·n + 5 ≤ 2·n + 6
n ≤ 1
22) 10·p + 20 - p > p + 3 - 23
9·p + 20 > p - 20
8·p > -40
p > -5
23) -1 ≤ 1 - 5·q ≤ 16
∴ 2/5 ≥ q ≥ -3
-3 ≤ q ≤ 2/5
Solve each word problem
24) Let x represent the number, we have;
2·x + 3·(x + 2) > 17
5·x + 6 > 7
∴ x > 1/5
The numbers are numbers larger than (1/5)
Solve each inequality
25) 2·(x - 5) + 3·x < 4·(x - 6) + 3
2·x - 10 + 3·x < 4·x - 24 + 3
x < -11
26) -2 - [-4 - (3 - 2)] = -2 + 4 + 3 - 2 = 7
