All Questions ⁺⁰236352 Questions

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In how many ways can the numbers 1 through 9 be placed once each in the squares below, if the numbers 1 and 2 cannot be placed in adjacent squares (either horizontally, vertically, or diagonally), and rotations and reflections of the grid are considered read more ..

kachow Feb 25, 2024

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32

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+823

Cosine

Let \theta be an acute angle. If $\cos \theta = \frac{1}{4},$ then what is $\sin \theta?$

booboo44 Feb 25, 2024

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36

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+823

Trigonometry

Let x be an acute angle such that \tan x + \sec x = 0. Find $\cos x$.

booboo44 Feb 25, 2024

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Cone

The cone below has a lateral surface area of $16 \sqrt{11} \cdot \pi$. Find the volume of the cone.

Also, the read more ..

kittykat Feb 25, 2024

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+1520

Solid

Triangle $ABC$ below is rotated completely around side $\overline{BC}$, sweeping out a solid in space. Find the volume of the solid. read more ..

kittykat Feb 25, 2024

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Sphere

A plane and a sphere intersect in a circle. The circle has an area of $25 \pi$. The distance between the plane and the center of the sphere is $5$ units. Find the surface area of the sphere.

kittykat Feb 25, 2024

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Frustum

Find the total surface area and the volume of the conical frustum below.

kittykat Feb 25, 2024

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+70

help

The letters A, B, C, and D represent four distinct integers from 0 through 9. When A is added to B the result is C. When B is subtracted from A the result is D. How many possible ways are there to assign values to A, B, C, and D?

Hamburger Feb 25, 2024

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3d geo question

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 $DEFG$ is $18.$ Find the volume of pyramid $EFGH$

Vxrtate Feb 25, 2024

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3d geo

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 ..

Vxrtate Feb 25, 2024

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Lines

Line $\ell_1$ represents the graph of $3x + 2y = -14 - 8x + 5y$. Line $\ell_2$ passes through the point $(5,-6)$, and is perpendicular to line $\ell_1$. Write the equation of line $\ell_2$ in the form $y=mx +b$.

Vxrtate Feb 25, 2024

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+400

Quadratic Equation

Fill in the blanks to make a quadratic whose roots are 5 and -5.
x^2 + ___x + ____

omgitsrne Feb 25, 2024

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+400

Algebra

Let $a$ and $b$ be the roots of the quadratic $x^2 - 5x + 3 = 2x^2 + 14x + 8.$ Find the quadratic whose roots are 1/(a + 1) and 1/(b + 1).

omgitsrne Feb 25, 2024

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+400

Algebra

Consider the two expressions $1$ and $\frac{2x+3}{2x+3}.$
a) Show that the two expressions represent equal numbers when $x=10.$
b) Explain why these two expressions do not represent equal numbers when $x=-\dfrac32.$
c) Show that these read more ..

omgitsrne Feb 25, 2024

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27

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+823

Minimum

Find the minimum value of \frac{x^2}{x - 1 + x^3} for x > 1

booboo44 Feb 25, 2024

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Floor Function

Let f(x) = \left \lfloor \frac{2 - 3x}{3x + 3} \right \rfloor.
Find f(1) + f(2) + f(3) + ... + f(999) + f(1000).

booboo44 Feb 25, 2024

Feb 24, 2024

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31

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limits question. dont know how to start

wmath Feb 24, 2024

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Floor Function

Find all values of t such that floor(t) = 3t + 4 - t^2. If you find more than one value, then list the values you find in increasing order, separated by commas.

booboo44 Feb 24, 2024

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Function

The function f(x) is defined for 1 \le x \le 5 as follows:
f(x) = 2x + 8 if 1 \le x \le 2
f(x) = 13 - 5x if 2 < x \le 3
f(x) = 20 - 14x if 3 < x \le 4 read more ..

booboo44 Feb 24, 2024

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+1560

Square

In the diagram, ABCD is a square. Find PR.

L, M, N, O, are midpoints of sides.
Side AB = 12

blackpanther Feb 24, 2024

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Hexagon

Let $IJKLMN$ be a hexagon with side lengths $IJ = LM = 3,$ $JK = MN = 3,$ and $KL = NI = 3$. Also, all the interior angles of the hexagon are equal. Find the area of hexagon $IJKLMN$.

blackpanther Feb 24, 2024

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+1560

Angles

The interior angles of a polygon form an arithmetic sequence. The difference between the largest angle and smallest angle is $56^\circ$. If the polygon has $3$ sides, then find the smallest angle, in degrees.

blackpanther Feb 24, 2024

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