All categories

3 years ago

Triangle ABC is similar to triangle DBE.

Mathematics

1 answer:

allsm [11]3 years ago

3 0

Answer:

Step-by-step explanation:

You might be interested in

Find cos y and tan y if csc y = -√6/2 and cot y >0.

fomenos

Answer:

$\cos y = -\dfrac{\sqrt{3} }{3}$

$\tan y = \sqrt{2}$

Step-by-step explanation:

Recall that

$\boxed{\csc y := \dfrac{1}{\sin y}}$

$\boxed{\cot y := \dfrac{\cos y}{\sin y}}$

We know that

$\csc y = \dfrac{-\sqrt{6} }{2}$

Note that according to the definition of $\csc y$ it is true that both sine and cosine are negative, once $\csc y = \dfrac{-\sqrt{6} }{2}$ . Because $\cot y > 0$ , this conclusion is true. We basically have

$\boxed{(-a)(1/-b)=a/b \text{ such that } a,b\in\mathbb{R}_{\geq 0}}$

Sure it is true $\forall y\in\mathbb{R}$ but perhaps this way is better to understand.

In order to find sine, we can use the definition and manipulate the rational expression.

$\csc y = \dfrac{-\sqrt{6} }{2} = \dfrac{-\sqrt{6} / -\sqrt{6} }{2/-\sqrt{6} } = \dfrac{1 }{-\dfrac{2}{\sqrt{6} } }$

Therefore,

$\sin y =-\dfrac{2}{\sqrt{6} }$

Here I just divided numerator and denominator by $-\sqrt{6}$ .

Now, to find cosine we can use the identity

$\boxed{\sin^2y +\cos ^2y =1}$

Thus,

$\left(-\dfrac{2}{\sqrt{6} }\right)^2 + \cos ^2y =1 \implies \dfrac{4}{6 } +\cos ^2y =1$

$\implies \cos ^2y =1 - \dfrac{4}{6 } \implies \cos ^2y =\dfrac{1}{3 } \implies \cos y = \pm \dfrac{\sqrt{1} }{\sqrt{3} } = \pm \dfrac{\sqrt{1} \sqrt{3} }{3} = \pm \dfrac{\sqrt{3} }{3}$

$\cos y = \pm\dfrac{\sqrt{3} }{3}$

Once we have $\cot y > 0$ , we just consider

$\cos y = -\dfrac{\sqrt{3} }{3}$

FInally, for tangent, just consider

$\boxed{\tan y := \dfrac{\sin y}{\cos y}}$

thus,

$\tan y = \dfrac{\sin y}{\cos y} = \dfrac{-\frac{2}{\sqrt{6} }}{-\frac{\sqrt{3} }{3}} = \dfrac{6}{\sqrt{18} } =\dfrac{6}{3\sqrt{2} } =\dfrac{2}{\sqrt{2} } = \sqrt{2}$

5 0

3 years ago

A horse had 4 1/5 scoops of oats in his bucket. He ate 2 1/2 scoops of oats. How many scoops of oats were left in his bucket ?

Sergeu [11.5K]

He has 1 7/10 scoops of oats left in his bucket.

5 0

3 years ago

Factor -1(x^(2)-3x-4) and pls show steps

soldi70 [24.7K]

Answer:(-x-1)(x-4)

Step-by-step explanation:

$-1(x^{2} -3x-4)$

factor the equation (multiples of 4 are 1 and 4 and 2 and 2) 4-1=1 so the factor you want to use are 1 and 4

-1(x +1)(x-4) -- -4+1=3

distribute the -1 into the first factor

(-x-1)(x-4)

8 0

3 years ago

Read 2 more answers

Cuál era la causa que lograba que el Imperio Romano mantuviera su unidad

andrew11 [14]

Answer:

Causas de la decadencia del Imperio Romano

Otros factores que contribuyeron a la decadencia de Roma incluyen: -Inestabilidad política debida al tamaño del imperio. -Los intereses propios de las dos mitades del imperio. -La invasión de las tribus bárbaras.

Step-by-step explanation:

6 0

3 years ago

Solve for x. *<br> Round to nearest hundredths (0.00) and include unit labels.

Airida [17]

X=surd(19^2-11^2)
=15.5ft

7 0

3 years ago