All Questions ⁺⁰237767 Questions

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140

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ellipse

The equation of an ellipse is
\[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1,\]
A circle is drawn so that it is contained in the ellipse, its center lies on the $x$-axis, and it touches the ellipse only at the point $(a,0).$ If a = b = 5, find read more ..

Guest Jun 28, 2023

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81

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Counting Problem (Urgent Help!)

You are given the 4x4 grid below. Find the number of ways of placing 8 counters in the squares (at most one counter per square), so that each row contains exactly two counters, and each column contains exactly two counters.
I read more ..

Guest Jun 28, 2023

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132

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ellipse

The foci of an ellipse are at $F_1 = (0,2)$ and $F_2 = (2,0).$ The ellipse passes through the origin, and intersects the $x$-axis at one other point. What is this point of intersection?

Guest Jun 28, 2023

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143

1

ellipse

An ellipse has the following properties:
It is tangent to the $x$-axis at $(4,0).$
It is tangent to the $y$-axis at $(0,4).$
Its axes are parallel to the coordinate axes.
Find the distance between the foci of the ellipse. read more ..

Guest Jun 28, 2023

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129

1

ellipse

The equation of an ellipse is
\[\frac{x^2}{3} + \frac{y^2}{3} = 1.\]
All four vertices of a square lie on the ellipse, and its sides are parallel to the coordinate axes. Find the area of the square.

Guest Jun 28, 2023

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135

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ellipse

The foci of an ellipse are at $F_1$ and $F_2.$ The circle with diameter $\overline{F_1 F_2}$ intersects the ellipse at four points, one of which is $P.$ If the major axis of the ellipse is $16$ and the area of triangle $PF_1 F_2$ is $10,$ compute read more ..

Guest Jun 28, 2023

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128

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ellipse

The foci of an ellipse are at $(3,7)$ and $(d,1).$ The ellipse is tangent to both the $x$-axis and the $y$-axis. Compute $d.$

Guest Jun 28, 2023

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130

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ellipse

An ellipse is tangent to both the $x$-axis and the $y$-axis, and its foci are at $(2, -3)$ and $(2, -8).$ Find the length of the major axis.

Guest Jun 28, 2023

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139

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ellipse

The equation of an ellipse is
\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1.
Point $Q$ is at $(0,b).$ Points $P$ and $R$ lie on the ellipse so that $\overline{PR}$ is parallel to the $x$-axis, and sides $\overline{QR}$ and $\overline{PQ}$ contain read more ..

Guest Jun 28, 2023

Jun 27, 2023

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142

3

Help for stat and binom theorem

1 what is the coefficient of x^3 in (1+x+x^2+x^3)^12?
2 For what value of n<24 are the coefficients of x14 and x24 equal in the expansion of (1+x)^n?

Guest Jun 27, 2023

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114

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solve

If I give my brother 5 dollars, then we will have the same amount of money. If instead he gives me 25 dollars, then I'll have twice as much money as he will have. How much money does my brother currently have (in dollars)?

Guest Jun 27, 2023

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147

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Please help

Consider the given functions: \begin{align*} f(x) & = 5x^2 - \frac{1}{x}+ 3\\ g(x) & = x^2-k \end{align*}If $f(2) - g(2) = 2$, what is the value of $k$?

Guest Jun 27, 2023

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104

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help me

Let AB be a diameter of a circle, and let C be a point on the circle such that AC = 8 and BC = 8. The angle bisector of angle ACB intersects the circle at point M. Find CM.

Guest Jun 27, 2023

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134

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I have been working on this for hours. Can someone please try to help me get it right

Alice and Bob each have a certain amount of money. If Alice receives n dollars from Bob, then she will have 7 times as much money as Bob. If, on the other hand, she gives n dollars to Bob, then she will have 3 times as much money as read more ..

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Guest Jun 27, 2023

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134

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Need help

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Guest Jun 27, 2023

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135

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need help quick

In how many ways can the numbers 1 through 5 be entered once each into the five boxes below so that all the given inequalities are true?

Guest Jun 27, 2023

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84

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please help ive asked 5 people and the answers are all wrong

Alice and Bob each have a certain amount of money. If Alice receives n dollars from Bob, then she will have 7 times as much money as Bob. If, on the other hand, she gives n dollars to Bob, then she will have 3 times as much money read more ..

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Guest Jun 27, 2023

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124

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help plz

Catherine rolls a standard 6-sided die six times. If the product of her rolls is then how many different sequences of rolls could there have been? (The order of the rolls matters.)

Guest Jun 27, 2023

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142

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system

Find the ordered quintuplet (a,b,c,d,e) that satisfies the system of equations
a + 2b + 3c + 4d + 5e = 41
2a + 3b + 4c + 5d + e = 15
3a + 4b + 5c + 1d + 2e = 34 read more ..

Guest Jun 27, 2023

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126

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solve

A candy bar and a piece of bubble gum together cost 1.50. The candy bar costs a dollar more than the bubble gum. How much does the piece of bubble gum cost, in cents?

Guest Jun 27, 2023

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129

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algebra

At a cafeteria, Mary orders two pieces of toast and a bagel, which comes out to $3.15. Gary orders a bagel and a muffin, which comes out to $3.50. Larry orders a piece of toast, two bagels, and three muffins, which comes out to $8.15. How read more ..

Guest Jun 27, 2023

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