All Questions ⁺⁰237313 Questions

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Trigonometry

Let x be an acute angle such that \tan x + \sec x = \cos x. Find \cos x.

bader Jan 1, 2024

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38

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+1782

Trig question

Let \theta be an acute angle. If \cos \theta = \frac{1}{3}, then what is \sin \theta?

blackpanther Jan 1, 2024

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55

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+1782

Radians

Degrees are not the only units we use to measure angles. We also use radians. Just as there are $360^\circ$ in a circle, there are $2\pi$ radians in a circle. Compute $\tan \pi,$ where the angle is in radians.

blackpanther Jan 1, 2024

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41

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Trig question

A tall pole is constructed in a flat parking lot; the pole stands straight up and forms a right angle with the ground. The pole casts a shadow, as shown below. Find the height of the pole, to the nearest foot. You may use a calculator. read more ..

blackpanther Jan 1, 2024

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66

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Equation of line

Write the equation of the line below in the form $Ax + By = C,$ where $A$, $B$, and $C$ are integers with greatest common divisor $1,$ and $A$ is positive. read more ..

blackpanther Jan 1, 2024

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73

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Algebra

Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to $\frac{28}{9}$ times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

blackpanther Jan 1, 2024

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29

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Factoring

Factor $9a^4 +3a^3- 21a + 6a^3 + 21a$ as far as you can.

blackpanther Jan 1, 2024

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43

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+199

Solutions

Find the number of solutions to
x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + x_7 \le 10
in nonnegative integers, where x_2 is even and x_5 is odd.

Boseo Jan 1, 2024

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54

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+199

plz help

In how many ways can you distribute $8$ indistinguishable balls among $5$ distinguishable boxes, if at least three of the boxes must be empty?

Boseo Jan 1, 2024

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60

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+199

help how do you do this

Miyu is giving out $8$ identical chocolates to her $5$ friends, including Dhruv. All possible distributions are equally likely. What is the probability that Dhruv gets at least $6$ chocolates?

Boseo Jan 1, 2024

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59

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+199

i need help

Find the number of paths from $A$ to $B,$ if each step must go towards the right. One example path is shown below.

Boseo Jan 1, 2024

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63

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+199

plz help

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?

Boseo Jan 1, 2024

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79

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+199

need help with this

Find the number of ways of choosing three circles below, so that no two circles are next to each other.

Boseo Jan 1, 2024

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35

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+199

help me

Starting with the A moving one letter at a time vertically, horizontally, or diagonally, how many different paths spell ARCH?
A
RRR
CCCCC read more ..

Boseo Jan 1, 2024

Dec 31, 2023

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49

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+1776

Prism

Let $ABCDEFGH$ be right rectangular prism. The total surface area of the prism $1.$ Also, the sum of all the edges of the prism is $2.$ Find the length of the diagonal joining one corner of the prism to the opposite corner.

bader Dec 31, 2023

+1

25

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tetrahedron

Let $ABCD$ be a regular tetrahedron. Let $E$, $F$, $G$, $H$ be the centers of faces $BCD$, $ACD$, $ABD$, $ABC$, respectively. The volume of pyramid $ABCD$ is $18.$ Find the volume of pyramid $DEFG$.

bader Dec 31, 2023

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62

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+1776

Solid geometry

Donatello starts with a marble cube. He then slices a pyramid off each corner, so that in the resulting polyhedron, all the edges have the same side length. If the side length of the original cube is $6$, then find the volume of the resulting read more ..

bader Dec 31, 2023

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