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3 years ago

Find the Solution of 2cos^2x + 3sin x =0

1 answer:

5 0

2cos^2 x + 3sin x = 0
2(1 - sin^2 x) + 3sin x = 0
2 - 2sin^2 x + 3sin x = 0
2sin^2 x - 3sin x - 2 = 0

Let sin x = m, then
2m^2 - 3m - 2 = 0
2m^2 + m - 4m - 2 = 0
m(2m + 1) - 2(2m + 1) = 0
(m - 2)(2m + 1) = 0
m = 2 or m = -1/2

Now, sin x = -1/2
Therefore, x = 1/6(12nπ - π) and 1/6(12nπ + 7π)

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Find the missing measure for a right circular cone given the following information.

xxTIMURxx [149]

<h2>Answer:</h2>

The radius of the cone is:

$r=\dfrac{2}{\sqrt{\pi}}$

<h2>Step-by-step explanation:</h2>

The total area of cone is given by:

$T.A.=\pi r(l+r)=\pi rl+\pi r^2=12---------(1)$

where r is the radius of the cone and l is the slant height of the cone.

and the lateral area of cone is given by:

$L.A.=\pi rl=8---------(2)$

Hence, from equation (1) and (2) we have:

$8+\pi r^2=12\\\\\\i.e.\\\\\\\pi r^2=4$

i.e.

$r^2=\dfrac{4}{\pi}$

i.e.

$r=\dfrac{2}{\sqrt{\pi}}$

6 0

3 years ago

Find the equation of the sphere passing through pleft parenthesis negative 4 comma 7 comma 6 right parenthesis(−4, 7, 6) and qle

Oksi-84 [34.3K]

The equation of a sphere is:

(x – h)^2 + (y – k)^2 + (z – l)^2 = r^2

where h, k and l are the coordinates of the center of the sphere

Using the midpoint formula, the coordinate of the center is:

h = (-4 + 6) / 2 = 1

k = (7 + -5) / 2 = 1

l = (6 + 7) / 2 = 6.5

so the equation becomes:

(x – 1)^2 + (y – 1)^2 + (z - 6.5)^2 = r^2

we plug in any point, in this case point P to solve for r:

(-4 -1)^2 + (7 – 1)^2 + (6 - 6.5)^2 = r^2

r^2 = 61.25

So the full equation is:

8 0

3 years ago

An empty bulldozer weighed 5 6/8 tons. If it scooped up 6 1/2 tons of dirt, what would be the

muminat

Answer:

12 1/4

Step-by-step explanation:

common denominator between 8 and 2 is 4, adding those up will be 12.25 in decimal form or 12 1/4

8 0

2 years ago

3(q-7)=273(q−7)=27 find q

skelet666 [1.2K]

Answer:

q = 16

Step-by-step explanation:

3(q - 7) = 27

3q - 21 = 27

3q = 27 + 21

3q = 48

q = 48/3

q = 16

5 0

3 years ago

Ayuda por favor

sergeinik [125]

A partir de la definición de razón y la teoría de semejanza entre triángulos, la razón del área del triángulo AMN y el área del cuadrilátero BMNC es equivalente a 1/3.

<h3>¿Cómo determinar la medida de un lado de un triángulo desconocido?</h3>

En este problema tenemos un sistema formado por dos triángulos <em>similares</em>, la semejanza entre los dos triángulos se debe a la colinealidad entre los segmentos de línea AP' (triángulo <em>pequeño</em>) y AP'' (triángulo <em>grande</em>), así como de los lados AM y AB, así como los lados AN y AC, así como los <em>mismos</em> ángulos en la <em>misma</em> distribución. (Semejanza Lado - Ángulo - Lado)

En consecuencia, obtenemos las siguientes proporciones:

AP'/AP'' = MN/BC = 1/2 (1)

Finalmente, la proporción entre el triángulo AMN y el cuadrilátero BMNC es:

$\frac{AMN}{ABC - AMN} = \frac{\frac{1}{2}\cdot a \cdot \left(\frac{1}{2}\cdot h \right)}{\frac{1}{2}\cdot (2\cdot a) \cdot h - \frac{1}{2}\cdot a \cdot \left(\frac{1}{2}\cdot h \right)} = \frac{\frac{1}{4}\cdot a\cdot h }{a\cdot h - \frac{1}{4}\cdot a \cdot h }$

$\frac{AMN}{ABC - AMN} = \frac{\frac{1}{4} }{\frac{3}{4} } = \frac{1}{3}$

Para aprender sobre triángulos semejantes: brainly.com/question/21730013

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3 0

2 years ago