Trigonometry
cos(a) = sin(a)
a = п/4 + 2пk; 5п/4 +2пk;
If $3,000 is loaned for 4 months at a 4.5% annual rate, how much interest is earned?
45$
You see a boat filled with people. It has not sunk, but when you look again you don’t see a single person on the boat. Why?
All the people on the boat are married.
This type of function, commonly used in economics and biology, describes a process where the rate of change of the function is proportional to the function itself
Exponential Function
Whose quote it is?
"I am GROOT"
Groot from "Guardians of the Galaxy"
3cos(2x) + 3 = 0 0<x<3п
п/2; 3п/2; 5п/2
What is the next number?
1,3,10,51,358,....
3939
This sequence is generated by multiplying each number by the next prime number and then adding 1.
So, 1 * 2 + 1 = 3
3 * 3 + 1 = 10
10 * 5 + 1 = 51
51 * 7 + 1 = 358
358 * 11 + 1 = 3939
What comes once in a minute, twice in a moment, but never in a thousand years?
The letter M
This type of function is defined as a function where each element of the domain is paired with exactly one element of the range, and no element of the domain is paired with more than one element of the range.
one-to-one
Whose quote it is?
"Why so serious?"
The Joker from Dark Knight
A triangular playground has sides of length 475 m, 595 m, and 401 m. What are the measures of the angles between the sides to the nearest tenth of a degree?
42.2
When a ball dropped is dropped, it rebouds 75% of its height after each bounce. If the ball travels a total distance of 490 cm, from what height was the ball dropped?
70
When the two met, one was half the others age plus seven years. Ten years later, when they married, the bride was thirty but this time one was nine tenths the age of the other. How old was the groom?
The bride was 30 years old so the groom was 27
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Whose quotes it is?
Hakuna Matata. It means no worries for the rest of your days.
Timon from The Lion King
2sin^2(x) - sin(x) - 3 = 0 for 0<x<360
270
In an arithmetic sequence the difference between the sum of the first nine terms and the sum of the first seven terms is 20. Find the of the first sixteen terms.
160
You are presented with three closed boxes: one contains a treasure, and the other two are empty. Each box has a label on it, but you know that all the labels are incorrect. The labels read as follows:
Using the information provided, can you determine which box contains the treasure?
If the treasure were in Box 1, then the label on Box 1 would be true, but it contradicts the fact that all labels are incorrect. Therefore, the treasure cannot be in Box 1.
If the treasure were in Box 2, then the label on Box 2 would also be true, which contradicts the fact that all labels are incorrect. Therefore, the treasure cannot be in Box 2.
If the treasure were in Box 3, then the label on Box 3 would be false, which is consistent with the fact that all labels are incorrect. Therefore, the treasure must be in Box 3.
So, the answer is: The treasure is in Box 3.
Find x and y intercepts for the function
y = x^3-6x^2+11x-6=0
x intercepts 1,2,3
y intercept -6
To infinity and beyond!
Buzz Lightyear from "Toy Story"
3sin^2(x) + 4cos(x) - 4 = 0; 0<x<90
x = arccos(1/3)
(x-1)/x^2 - (x-2)/x^2 + (x-3)/x^2 - (x-4)/x^2.......(x-576)/x^2 = 1/2
+24; -24
If exactly one of these statements is false, which statement is false?
A. Statement D is true.
B. Statement A is false.
C. Statement B is false.
D. Statement C is true.
Since one of the statements is false, it suffices to consider 4 cases, each case assuming one of statements to be false and then checking if this assumption is consistent with other statements or not.
Case 1: Statement A is false. This implies Statement D is false. Since no more than one statements can be false, this assumption is wrong.
Case 2: Statement B is false. This leads to conclusion that A is true, D is true, and C is true. (Looks good)
Case 3: Statement C is false. This results in conclusion of truthfulness of B, and thus fallacy of A, which is not possible.
Case 4: Statement D is false. It signifies that C is false, which is invalid.
So the statement which is wrong is Statement B.
An open square-based container is made by cutting 4 cm square pieces out of a piece of tinplate. If the volume of the container is 120 cm^2, find the size of the original piece of tinplate
13.5 cm by 13.5 cm
You're a wizard, Harry.
Hagrid from "Harry Potter and the Sorcerer's Stone"