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ludmilkaskok [199]
3 years ago
7

Help me find the solution set for 8x-3=2(x-1/2)

Mathematics
1 answer:
daser333 [38]3 years ago
6 0
8x -3 = 2(x-1/2)
⇒ 8x -3= 2x -2*(1/2)
⇒ 8x -3 = 2x -1
⇒ 8x -2x= -1+ 3
⇒ 6x = 2
⇒ x= 2/6
⇒ x= 1/3

The final answer is x= 1/3~
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Suppose that 5 J of work is needed to stretch a spring from its natural length of 30 cm to a length of 39 cm.
vesna_86 [32]

Answer

given,

work = 5 J

spring stretch form 30 cm to 39 cm

W = \dfrac{1}{2}kx^2

x = 0.39 - 0.30 = 0.09 m

5 = \dfrac{1}{2}k\times 0.09^2

k = \dfrac{5\times 2}{0.09^2}

k = 1234.568 N/m

a) work when spring is stretched from  32 cm to 34 cm

x₂= 0.34 -0.30 = 0.04 m

x₁ = 0.32 - 0.30 = 0.02

W = \dfrac{1}{2}k(x_2^2-x_1^2)^2

W = \dfrac{1}{2}\times 1234.568 \times (0.04^2-0.02^2)^2

W = 0.741 J

b) F = k x

  25 = 1234.568 × x

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3 0
3 years ago
During a test period, an experimental group of 10 vehicles using an 85 percent ethanol-gasoline mixture showed mean CO2 emission
Zinaida [17]

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-1.683

Step-by-step explanation:

Given :

Group 1 :

x1 = 667 ; n1 = 10 ; s1 = 20

Group 2 :

x2 = 679 ; n2 = 14 ; s2 = 15

The test statistic assuming equal variance :

x1 - x2 / √[Sp² * (1/n1 + 1/n2)]

sp² = [(n1 - 1)*s1² + (n2 - 1)*s2²] ÷ (n1 + n2 - 2)

Sp² = [(10 - 1)*20² + (14 - 1)*15²] = 296.59

Test statistic =

(667 - 679)/ √[296.59 * (1/10 + 1/14)]

-12 / 7.1304978

Test statistic = - 1.682

8 0
2 years ago
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