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The right hand side is equal to



Since , and the right hand side is equal to

, same as the left hand side.

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Actually you have to multiply first before dividing:

35(41 - 33) ÷ 8 - 11 + 17
35(8) ÷ 8 - 11 + 17
35 - 11 + 17
= 41

Multiplying and dividing typically take equal precedence over each other, and in such a case you would simply go from left to right

(I checked WolframAlpha for its answer, it seemed as if it divided first, but both WolframAlpha and I got 41. This is mainly because the order of these operations usually doesn't matter, i.e. ).

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The inverse of taking a quantity to the nth power is taking the nth root of that quantity.

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Two perpendicular lines simply mean that one line is perpendicular to the other.

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It is 625. But i to an even power is not always positive, and i to an odd number is always imaginary. Basically,






and so on.

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A U B = {3, 4, 5, 6, 7, 8, 9} (simply take all elements in either A or B)

C ∩ (A U B) = {4, 6, 8} (these are the elements in both C and A U B)

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Apparently it seems like the other tutor taught you this...:)

From Euler's formula, . By substituting you will obtain , . Euler's formula itself is derived using the Maclaurin series for , namely (you will learn this sometime in calculus).

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"how do you solve this help show me please so i can understand"

What is "this?"

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The absolute value is the positive distance between that number and zero.

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You can compute the number of ways to make change for $1 using a bijection. We let n, d, q be the number of nickels, dimes, and quarters, and , which implies . Hence, this is equivalent to finding the number of ways to make 20 "cents" using one-, two-, and five-cent pieces.

Suppose we want to find the number of ways to make 20 cents *without* using a five cent piece.

Case 0: We wish to make 0 cents --> 1 way (just use no coins)
Case 1: We wish to make 1 cent --> 1 way 2*0 + 1*1
Case 2: We wish to make 2 cents --> 2 ways 2*1 + 1*0; 2*0 + 1*2
Case 3: We wish to make 3 cents --> 2 ways 2*1 + 1*1; 2*0 + 1*3
Case 4: We wish to make 4 cents --> 3 ways 2*2 + 1*0; 2*1 + 1*2, 2*0 + 1*4
Case 5: We wish to make 5 cents --> 3 ways 2*2 + 1*1, 2*1 + 1*3, 2*0 + 1*5

We can prove using either induction or modular arithmetic that the number of ways to make n cents in this way is , where denotes the floor value of x. We can evaluate this at n = 20 to get , or 11.

Similarly, we can count the number of ways to obtain 20 cents using one five-cent piece. However, we can subtract off the five-cent piece and say that this is analogous to computing the number of ways to obtain 15 cents. Hence, this is equal to .

For 10, 5, and 0 cents, we have , and . Therefore the total number of ways is 11 + 8 + 6 + 3 + 1 = 29 ways.


Note: the other tutor counted 293 ways, however this included pennies and half dollars, which was not stated in the question. To count the number of ways using pennies, nickels, dimes, and quarters, you can also use a bijection, but instead of counting the number of ways to obtain 20 cents, you evaluate at 20, 19, 18, ..., 0 since this will uniquely determine the number of pennies. We do the same with 15, 10, 5, and 0 to obtain sums:



Then, if you want half dollars involved, it is equal to where is the number of ways to make a dollar using i half dollars, equivalently, the number of ways to make 50 cents and 0 cents without half dollars (here you should get 293!).

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It can hold six cubic inches of something, say water. One cubic inch is the volume of water in a 1" x 1" x 1" container.

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Replacing x with u/2,

(however you must be careful what quadrant u and u/2 are in, because it could be positive or negative).

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If you're given an equation or inequality such as , it helps to clear the fraction or decimal since we are trying to find the value of , not .

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Suppose , and . From we obtain . We can subtract from both sides to get --> --> . Finally, we can scale both sides by the same positive number to get .

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6g + f

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Out of the days {21, 22, ..., 31} there are 11 days (inclusive). Therefore the probability is 11/31.

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The quadratic will have and as factors. Hence, the quadratic is equal to (applying the difference of two squares)

Expanding and simplifying, this is equal to .

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multiply

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Factor out the largest square divisor of 98. Since , .

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Simply apply the basic rules of differentiation, as well as the derivatives of various trigonometric functions:

1.

2.

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I would suppose you would get 1 mole, since the other 999,999 moles of chlorine would not react.

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If -2 and 5 are roots, then x-(-2) and x-5 are factors of the polynomial. We can write the equation in the form

C(x+2)(x-5) = 0, where C is some nonzero constant.

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is not a polynomial, because this the exponent of x is negative.

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Arccosine and cosine are inverses of each other, so would be equal to . However, since the arccosine function restricts the range (since an infinite number of values are obtained), we say that this . Depending on the context of the problem, either answer could be correct, or even some general answer in the form .

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Use the quadratic formula. The quadratic formula says that the roots of any quadratic equation in the form (with a,b,c real) are . From here, it's just simply identifying what a,b,c are and then substitution.

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We have where A =
| -3 -7.5 1 |
| -1.5 6.5 1 |
| 1.5 -5.5 1 | (3x3 matrix)

Here,

,

Therefore, the area is equal to 1/2 of 60, or 30.

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You could go to WolframAlpha (www.wolframalpha.com) and provide your graphs there.

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The restaurant is open up to 12 hours after the opening, so it is reasonable to say . Also, between 0 and 80 people are allowed, so .

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Using the addition formula for cosine:

Since and ,



= .

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No, because a triangle with sides 6,8,11 is not a valid counterexample (it is not a right triangle).