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Ksivusya [100]
3 years ago
11

"tis greater than zero and less than or equal to 5" Complete the following steps to receive full credit for this question: . The

inequality translated in numerical form • The solution graphed on a number line • The solution in interval notation​
Mathematics
1 answer:
Shalnov [3]3 years ago
8 0

Answer:

A) 0 ≤ x ≥ 5

B) Number line is attached

C) Interval notation is; (0,5)

Step-by-step explanation:

We are told that the number is greater than zero and less than or equal to 5. If the number is x, then we can write the inequality as;

i) 0 ≤ x ≥ 5

ii) The solution graphed on a number line is attached.

iii) Since 0 ≤ x or x ≥ 5, then the interval notation is; (0,5)

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A lighthouse is built on an exposed reef, 4.5 miles off-shore. The shoreline is perfectly straight, and a town is located 6 mile
Alisiya [41]

Answer: 3.94 hours

Step-by-step explanation:

From the question, the following parameters are given:

Distance offshore = 4.5 miles

Distance downshore = 6 miles

Speed when running = 3.4 mph

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distance of boat rowing = sqrt(4.5^2 + x^2)

Where

Speed = distance/time

Time = distance/speed

Time = distance of boat rowing/1.8

distance of running = 6 - x

Time = (6-x)/3.4

total travel time

t = sqrt(4.5^2 + x^2)/1.8 + (6 - x)/3.4

dt/dx = x/(1.8×sqrt(4.5^2 + x^2) - 1/3.4

d^2t/dx^2 = +ve at any x

x is at its minimum when dt/dx=0

x/(1.8×sqrt(4.5^2 + x^2) = 1/3.4

x = 6/sqrt(253) × 4.5 = 1.697 miles

Substitute x in

t = sqrt(4.5^2 + x^2)/1.8 + (6 - x)/3.4

We obtaine

t = sqrt(4.5^2 + 1.697^2)/1.8 + (6 - 1.69)/3.4

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3 years ago
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