A weather forecaster predicts that the temperature in Antarctica will decrease 8∘F each hour for the next 6 hours. Write and solve an inequality to determine how many hours it will take for the temperature to drop at least 36∘F

Question

SkladanH · Accepted Answer

Given information:  Since, the temperature in Antarctica decreases by 8∘F each hour for every 6 hours, using h as the number of hours it will take to drop at least 36∘F, then we can use the inequality 8h≥36:  Calculation:  Given,  8h≥36  Divide both sides of the inequality by 8  8h8≥368  h≥4.5  Hence, the minimum hours it will take at least 4.5 hours before the temperature drops to 36∘F.

Jeffrey Jordon · Accepted Answer

Given: m = -8 degrees/hour, the rate of change of temperature  Let x =  hours  Let y = temperature, ∘F Then y = -8x + b where b = constant  When x = 0, then y = b. Therefore b = initial temperature  If the temperature drops by at least 36 ∘F in the next x hours, then b−y(6)≥36 b−(−8x+b)≥36 8x≥36 x≥4.5 hours  Answer:  At least 4.5 hours

Mr Solver · Accepted Answer

Answer:x≥4.5Explanation:According to the given information, the temperature decreases 8 degrees Fahrenheit each hour for the next 6 hours. Therefore, the total temperature decrease can be calculated as 8x.We want the temperature to drop at least 36 degrees Fahrenheit, so we can write the following inequality:8x≥36To solve for x, we divide both sides of the inequality by 8:8x8≥368Simplifying further, we have:x≥4.5Therefore, it will take at least 4.5 hours for the temperature to drop at least 36 degrees Fahrenheit in Antarctica.

Eliza Beth13 · Accepted Answer

We know that the temperature decreases 8 degrees Fahrenheit each hour for the next 6 hours. Therefore, the total temperature decrease after h hours can be expressed as 8h.To determine how many hours it will take for the temperature to drop at least 36 degrees Fahrenheit, we can set up the following inequality:8h≥36Simplifying the inequality, we have:h≥368Simplifying further, we find:h≥4.5Since h represents the number of hours, it cannot be a fraction. Therefore, we round up the solution to the nearest whole number, giving us:h≥5Thus, it will take at least 5 hours for the temperature in Antarctica to drop by at least 36 degrees Fahrenheit.

Nick Camelot · Accepted Answer

Step 1:To solve the given problem, let&#039;s assume the initial temperature in Antarctica is denoted by T0 (in degrees Fahrenheit) and the number of hours is denoted by h. According to the weather forecaster&#039;s prediction, the temperature will decrease by 8 degrees Fahrenheit each hour. Therefore, we can represent the temperature at any given hour h as T(h).Since we are interested in determining how many hours it will take for the temperature to drop at least 36 degrees Fahrenheit, we need to find the value of h that satisfies this condition.The inequality can be expressed as:T0−8h≤T0−36Simplifying the inequality, we get:−8h≤−36To solve for h, we need to isolate it on one side of the inequality. To do this, we can multiply both sides of the inequality by −1 and reverse the inequality sign:8h≥36Step 2:Finally, dividing both sides of the inequality by 8, we find:h≥368Therefore, the temperature will drop at least 36 degrees Fahrenheit in h hours, where h is greater than or equal to 368.The solution can be written as:h≥368

A weather forecaster predicts that the temperature in Antarctica will decrease 8^{circ}F each hour for the next 6 hours. Write and solve an inequality to determine how many hours it will take for the temperature to drop at least 36^{circ}F

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