2022-03-08
Answered

Sketch the graph of the inequality.(x + 2)2 + y2 > 1

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Answered 2022-03-23
Author has **162** answers

$(x+2{)}^{2}+{y}^{2}>1$

Subtract $(x+2)}^{2$ from both sides of the inequality.

$y}^{2}>1-{(x+2)}^{2$

Take the square root of both sides of the inequality to eliminate the exponent on the left side.

$\sqrt{{y}^{2}}>\sqrt{1-{(x+2)}^{2}}$

Simplify the equation.

$\left|y\right|>\sqrt{(x+3)(-x-1)}$

Write $\left|y\right|>\sqrt{(x+3)(-x-1)}$ as a piecewise.

$\{\begin{array}{ll}-y>\sqrt{(x+3)(-x-1)}& -3\le y\le -1\end{array}\phantom{\rule{em}{0ex}}$

Solve $-y>\sqrt{(x+3)(-x-1)}$ when $-3\le y\le -1$.

−3≤y≤No(Minimum)$-3\le y\le No\left(Minimum\right)$

Find the union of the solutions.

$-3\le y\le iNo\mathrm{Min}{m}^{2}u$

asked 2021-02-08

Let B be a 4x4 matrix to which we apply the following operations:

1. double column 1,

2. halve row 3,

3. add row 3 to row 1,

4. interchange columns 1 and 4,

5. subtract row 2 from each of the other rows,

6. replace column 4 by column 3,

7. delete column 1 (column dimension is reduced by 1).

(a) Write the result as a product of eight matrices.

(b) Write it again as a product of ABC (same B) of three matrices.

1. double column 1,

2. halve row 3,

3. add row 3 to row 1,

4. interchange columns 1 and 4,

5. subtract row 2 from each of the other rows,

6. replace column 4 by column 3,

7. delete column 1 (column dimension is reduced by 1).

(a) Write the result as a product of eight matrices.

(b) Write it again as a product of ABC (same B) of three matrices.

asked 2021-01-31

Find a basis for the space of $2\times 2$ diagonal matrices.

$\text{Basis}=\{\left[\begin{array}{cc}& \\ & \end{array}\right],\left[\begin{array}{cc}& \\ & \end{array}\right]\}$

asked 2021-01-19

These three points are on the same line: (1,2,3),(2,4,−6),(−3,−6,x). Find x. Explain your answer fully.

asked 2022-04-01

A polynomial *f*(*x*) with real coefficients and leading coefficient 1 has the given zero and degree. Express *f*(*x*) as a product of linear and/or quadratic polynomials with real coefficients that are irreducible over ℝ.

7 + 8*i*; degree 2

asked 2022-04-30

Proof of

$\sum _{n=1}^{\mathrm{\infty}}\frac{1}{{n}^{3}}\frac{\text{sinh}\pi n\sqrt{2}-\mathrm{sin}\pi n\sqrt{2}}{\text{cosh}\pi n\sqrt{2}-\mathrm{cos}\pi n\sqrt{2}}=\frac{{\pi}^{3}}{18\sqrt{2}}$

asked 2021-01-08

Write the simplest polynomial function with the given roots.
1, 1, 2.

asked 2022-07-15

Find ${c}_{1},{c}_{2},{c}_{3}\in \mathbb{Q}$ such that $(1+{\alpha}^{4}{)}^{-1}={c}_{1}+{c}_{2}\alpha +{c}_{3}{\alpha}^{2}$