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Manvir K.

Top of the Class, UC Davis B.Sc Neurobiology, Physiology, and Behavior

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Pre-Algebra

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Question:

-67 + 25/5 - (16/4 - 3^2) = ?

Manvir K.

Answer:

This question involves various operations. When such a scenario comes up, think of order of operations or the acronym PEMDAS which stands for parenthesis, exponents, multiplication, division, addition, and lastly subtraction. Operations must be followed in the said order. In the above question, there are parenthesis, so we will tackle those first. Within the parenthesis, there are three operations: division (16 is divided by 4), subtraction, and exponents (3 is raised to the power of 2). Which one of these three comes first according to PEMDAS? exponents are first. so what is three raised to 2? It is 3 times 3 which equals is 9. we are left with the following: -67 + 25/5 - (16/4 - 9) now out of the other two left, division and subtraction, which operation should be solved first? PEMDAS says division should be done first. So 16 divided by 4 equals 4. Thus, -67 + 25/5 - (4 - 9) let's go ahead and finish the last operation inside the parenthesis as well: -67 +25/5 - (-5) Before removing the parenthesis completely, make sure you notice that the minus outside the parenthesis and the minus inside the parenthesis will make a plus, leaving us with: -67 +25/5 +5 now we are left with addition and division. so as PEMDAS says, we will divide 25 by 5 first. -67 +5 +5 addition and subtraction are the same level of operations. When these are the only two operations you are left with, you can simply solve the problem from left to right. In this case, starting with the left end of the problem, -67 + 5 which gives us -62 (opposite signs subtract, so we subtracted 5 from 67, and the sign of the greater number goes in front of the answer), leaving us with: -62 +5 using the same rules as above, -62 +5 = -57 which is our final answer.

Biology

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Question:

When you sit for a long period of times without moving your legs, and then suddenly get up and begin walking, why do you feel dizzy for a short period of time?

Manvir K.

Answer:

One of the ways in which blood is returned to the heart is via the skeletal muscle pumps that are found in the veins of highly muscular body parts such as legs. The skeletal muscle pumps work by contracting the muscles around the veins, constricting the veins, and forcing the blood up towards the heart. Veins are not elastic, and do not have a large recoil force. Therefore, this pump is essential in pumping the blood back to the heart. Now, when one sits for a long period of time, he/she is not engaging the muscles in the legs, which in turn means that the skeletal muscle pumps are not at work. The heart is continuously pumping blood away towards the legs, but the legs are not sending the same amount back efficiently. Thus, the blood pooling in the legs leads to a lower blood pressure in upper body parts such as head, and the person feels dizzy.

Algebra

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Question:

The length of a rectangular field is four times the width of the field. If the perimeter of the field is 250 feet, what are the dimensions of the given field.

Manvir K.

Answer:

Let us start by extracting the information given to us in the word problem. We are told that the length of four times the width. Let us assume that the width of the field is x ft. This means that the length of the field is 4 times x, or 4x. Now, draw a rectangle. Label the two shorter sides (width) of the rectangle as x. Label the two longer sides (lengths) of the rectangle as 4x. At this point, let us go back to the question which states that the perimeter is 250 ft. Remember, perimeter is sum of all sides of a figure. Therefore, x + x + 4x + 4x = 250 add like terms (like terms are the ones that have the same variable associated with them). in this case, all terms on the left hand side are alike (all have an x associated with them). So, we can add them, leaving us with 10x = 250 To solve for x, you must undo the multiplication going on between the 10 and the x on the left side. What reverses multiplication? Division. So, divide both sides by 10 10x/10 = 250/10 Tens cross out on the left side, leaving us with x = 25 We are almost done. Width is 25 ft. Length is four times the width, therefore 4 times 25 which gives a 100ft for the length. Do not forget to put units (ft. in this case) with the length and width.

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