(Modeling) Grade Resistance Solve each problem. See Example 3....

Question

(Modeling) Grade Resistance Solve each problem. See Example 3. A car traveling on a -3° downhill grade has a grade resistance of -145 lb. Determine the weight of the car to the nearest hundred pounds.

Accepted Answer

Welcome back. Everyone in this problem. We want to find the weight of a bus to the nearest integer if it is traveling on a negative four degree downhill grade and has a great resistance of negative 281 kg. For our answer choices A is kg. B is 4028 kg. C is 2048 kg and D is 4820 kg. Now let's first draw a diagram to make sense of our problem. So we have a bus that's traveling downhill. Ok. So here's my little bus. I think it looks nice. Gotta put in my windows too, right? And we have this bus that's going downhill at a great angle of negative four degrees. We also know that it has a great resistance of negative 281 degrees. So our grade resistance F equals negative kg. My apologies not degrees kilograms. And we want to find the weight of the bus to the nearest integer that is that force that's labeled W now what do we know about grade resistance? Well, recall that grade resistance F equals W multiplied by the sign of theta where W is the weight of the object. In this case, the weight of the boss and theta is the grade angle. Now, if you look at it, we already have a great angle which is negative four degrees and the great resistance negative 281 kg. So we can substitute those values to solve for the weight of our bus to the nearest integer. So substituting substituting fe equals negative 281 kg. And our great angle equals negative four degrees to solve for the weight of the bus. This means our formula now becomes negative 281 kg equals dobi multiplied by the sign of negative four degrees. Therefore, to solve for W we can divide both sides by the sign of negative four degrees, which means that W equals negative kg divided by the sign of negative four degrees. Now, if you put that expression into your calculator, negative 281 divided by the sign of negative four, you should get 4028. and it continues on and on. But we're not interested in all those digits because we want our weight to the nearest integer. So if we round to our nearest integer, we'll find that the weight equals 4028 kg. So the weight of our bus is 4028 kg. And when we look on our answer choices that would have been answer choice. B thanks a lot for watching everyone. I hope this video helped.

(Modeling) Grade Resistance Solve each problem. See Example 3. A car traveling on a -3° downhill grade has a grade resistance of -145 lb. Determine the weight of the car to the nearest hundred pounds.

Key Concepts

Grade Resistance

Trigonometric Relationship in Inclined Planes

Solving for Unknowns Using Algebra and Trigonometry

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