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3 years ago

Which of the two solids below are similar ?

Mathematics

1 answer:

Pachacha [2.7K]3 years ago

3 0

Answer: I and II.

Step-by-step explanation:

By definition, two solids are similar if their corresponding sides are in the same ratio.

Knowing this, let's find which solids are similar:

Corresponding sides ratio of solids I and II:

$\frac{3}{2}=\frac{2}{\frac{4}{3}}=\frac{5}{\frac{10}{3}}$

$\frac{3}{2}=\frac{3}{2}=\frac{3}{2}$

Corresponding sides ratio of solids I and III:

$\frac{3}{\frac{9}{2}}=\frac{2}{3}=\frac{5}{8}$

$\frac{2}{3}=\frac{2}{3}=\frac{5}{8}$

Corresponding sides ratio of solids II and III:

$\frac{2}{\frac{9}{2}}=\frac{\frac{4}{3}}{3}}=\frac{\frac{10}{3}}{8}}$

$\frac{4}{9}=\frac{4}{9}=\frac{5}{12}$

You can observe that the solids I and II are similar.

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Show that the equation x^4/2021 − 2021x^2 − x − 3 = 0 has at least two real roots.

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See attachment for the graph of $\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}$

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brainly.com/question/12912962

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3 years ago

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Which statements about the hyperbola are true? Check all that apply. A. There is a focus at (0,−10). B. There is a focus at (0,

hichkok12 [17]

Answer:

A. There is a focus at (0,−10).

Step-by-step explanation:

Assume the hyperbola is like the one below.

The hyperbola is vertical and centred on the y-axis, so its general equation is

$\dfrac{y^{2}}{a^{2}} - \dfrac{x^{2}}{b^{2}} = 1$

The vertices of your parabola are (0,±8) so a = 8.

The covertices are (±6,0), so b = 6.

Calculate c

$\begin{array}{rcl}a^{2} + b^{2} & = & c^{2}\\8^{2} + 6^{2} & = & c^{2}\\64 + 36 & = & c^{2}\\100 & = & c^{2}\\c & = & \mathbf{10}\\\end{array}$

A. Foci

The foci are at (0, ±c) = (0, ±10)

TRUE. There is a focus at (0,-10).

B. Foci

The foci are at (0,±10).

False. There is no focus at (0,12)

C. and D. Asymptotes

The equations for the asymptotes are

$y = \pm\dfrac{a}{b}x = \pm\dfrac{8}{6}x = \pm\dfrac{4}{3}x$

So, y = ±x are not asymptotes.

False.

E. and F. Directrices

The equations of the directrices are

y = ±a²/c = ±64/10 = ±6.4

y = 6.4 is a directrix.

E is false. x = cannot be a directrix

F is uncertain. Your equation for the directrix is incomplete.

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3 years ago