3 years ago

You measure a rectangle that the length is 3 inches and the width is

Mathematics

1 answer:

Kisachek [45]3 years ago

5 0

Answer:

Step-by-step explanation:

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Find all values of the angle θ (in radians, with 0 ≤ θ < 2π) for which the matrix a = cos θ −sin θ sin θ cos θ has real eigen

harina [27]

The matrix

$A=\begin{bmatrix}\cos\theta&-\sin\theta\\\sin\theta&\cos\theta\end{bmatrix}$

has eigenvalues $\lambda$ such that

$\det(A-\lambda I)=\begin{vmatrix}\cos\theta-\lambda&-\sin\theta\\\sin\theta&\cos\theta-\lambda\end{vmatrix}=0$

$(\cos\theta-\lambda)^2+\sin^2\theta=0$

$(\cos\theta-\lambda)^2=-\sin^2\theta$

$\cos\theta-\lambda=\pm\sqrt{-\sin^2\theta}$

$\lambda=\cos\theta\pm\sqrt{-\sin^2\theta}$

$\sin^2\theta\ge0$ for all values of $\theta$ , so we need to have $\sin\theta=0$ in order for $\lambda$ to be real-valued. This happens for

$\sin\theta=0\implies\theta=n\pi$

where $n$ is any integer, and over the given interval we have $\theta=0$ and $\theta=\pi$ .

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3 years ago

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lakkis [162]

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What solid can be folded from the net?

Novosadov [1.4K]

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I think it is triangular prisim

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3 years ago

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Luna is selling balloon animals at the park. She began with 35 balloons, and she has sold

MakcuM [25]

Answer:

$24.50

Step-by-step explanation:

So first we have to find what 2/5 of 35 is. So 35*2/5=14. So she has sold 14 balloon animals so far. So now we multiply 14 by 1.75 and we get 24.5.

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3 years ago

What is the base of the triangle if the height is 7.5 cm and the area is 17.25 cm

AleksandrR [38]

Answer:

B= 4.6cm

Step-by-step explanation:

A= $\frac{H_{b} B}{2}$

$B= 2\frac{A}{H_{b} } = 2 * \frac{17.25}{7.5}$

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3 years ago