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2 years ago

Find the volume of this sphere. Use 3 for TT. V ≈ [?]in³ V = πr³ 5in Entering

Mathematics

1 answer:

nydimaria [60]2 years ago

6 0

Answer:

500

Step-by-step explanation:

r = 5

r³ = 125

V = (4/3)pi(r³)

pi = 3

V = (4/3)3(125)

/3 and x3 cancel

V = 4 x 125

V = 500

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Considering only the values of β for which sinβtanβsecβcotβ is defined, which of the following expressions is equivalent to sinβ

-Dominant- [34]

Answer:

$\tan(\beta)$

Step-by-step explanation:

For many of these identities, it is helpful to convert everything to sine and cosine, see what cancels, and then work to build out to something. If you have options that you're building toward, aim toward one of them.

${\tan(\theta)}={\dfrac{\sin(\theta)}{\cos(\theta)}$ and ${\sec(\theta)}={\dfrac{1}{\cos(\theta)}$

Recall the following reciprocal identity:

$\cot(\theta)=\dfrac{1}{\tan(\theta)}=\dfrac{1}{ \left ( \dfrac{\sin(\theta)}{\cos(\theta)} \right )} =\dfrac{\cos(\theta)}{\sin(\theta)}$

So, the original expression can be written in terms of only sines and cosines:

$\sin(\beta)\tan(\beta)\sec(\beta)\cot(\beta)$

$\sin(\beta) * \dfrac{\sin(\beta) }{\cos(\beta) } * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) } {\sin(\beta) }$

$\sin(\beta) * \dfrac{\sin(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}}{\cos(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}} * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}} {\sin(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}}$

$\sin(\beta) *\dfrac{1 }{\cos(\beta) }$

$\dfrac{\sin(\beta)}{\cos(\beta) }$

Working toward one of the answers provided, this is the tangent function.

The one caveat is that the original expression also was undefined for values of beta that caused the sine function to be zero, whereas this simplified function is only undefined for values of beta where the cosine is equal to zero. However, the questions states that we are only considering values for which the original expression is defined, so, excluding those values of beta, the original expression is equivalent to $\tan(\beta)$ .

8 0

2 years ago

PLEASE HELP!!

alexandr1967 [171]

Answer:A

Step-by-step explanation:

Side lengths do not adhere to the triangle inequality theorem.

6 0

3 years ago

How do you simplify 875/1000

OverLord2011 [107]

$Find\ GCF(875;\ 1000)$

$875|5\\175|5\\.\ 35|5\\.\ \ 7|7\\.\ \ 1|\\875=\fbox5\times\fbox5\times\fbox5\times7\\\\1000|5\\.\ 200|5\\.\ \ 40|5\\.\ \ \ 8|2\\.\ \ \ 4|2\\.\ \ \ 2|2\\.\ \ \ 1|\\1000=\fbox5\times\fbox5\times\fbox5\times2\times2\times2$

$GCF(875;\ 1000)=\fbox5\times\fbox5\times\fbox5=125\\\\\frac{875}{1000}=\frac{875:125}{1000:125}=\frac{7}{2\times2\times2}=\boxed{\frac{7}{8}}$

8 0

3 years ago

Prove that if one solution for a quadratic equation of the form x 2 + bx + c = 0 is rational (where b and c are rational), then

erica [24]

$x^2+bx+c = (x-r)(x-s)\\
x^2+bx+c = x^2-(r+s)x+rs\\\\
b = -(r+s)\\ c = rs$

Say r is rational. Suppose for a second, that s is not. Then, r+s is irrational. But this contradicts the fact that b is rational.

So, if one root is rational, then the other root is also rational

7 0

3 years ago

What is 6.25% written as a fraction in lowest terms

Feliz [49]

= 6.25%

= 0.0625

= 625/10000

= 1/16

8 0

3 years ago