All categories

3 years ago

Using the figure below, find the value of x. Enter your answer as a simplified radical or improper fraction (if necessary)

Mathematics

1 answer:

julsineya [31]3 years ago

7 0

Answer:

x = 5 $\sqrt{3}$

Step-by-step explanation:

Using the tangent ratio in the outer right triangle

and tan30° = $\frac{1}{\sqrt{3} }$ = $\frac{\sqrt{3} }{3}$

tan30° = $\frac{opposite}{adjacent}$ = $\frac{x}{15}$

Multiply both sides by 15

15 × tan30° = x

x = 15 × $\frac{\sqrt{3} }{3}$ = 5 $\sqrt{3}$

You might be interested in

What is cubes in a mathematical term

victus00 [196]

When you cube something you times that number by itself 3 times.

4 0

3 years ago

In science class the students were asked to create a container to hold an egg. They would then drop the container from a window

belka [17]

Answer:

It will take 1.25 seconds to reach the ground.

Step-by-step explanation:

The equation of the containers pathway can be modeled by the equation given below :

$h=-16t^2+25$

t is time in seconds

It is required to find the time taken by the container to reach the ground. When it reached ground, its height is equal to 0 such that,

$h=0\\\\-16t^2+25=0$

$-16t^2=25\\\\t=\sqrt{\dfrac{25}{16}} \\\\t=1.25\ s$

So, it will take 1.25 seconds to reach the ground.

5 0

2 years ago

Use the graphing calculator to

Leviafan [203]

Answer:

Step-by-step explanation:

Answer is C: x-min = 0, x-max= 30, y-min = 0, y-max = 30

5 0

2 years ago

Read 2 more answers

The complement of 10 percent is 90 percent or in decimal .90.

jonny [76]

What is the question?

5 0

3 years ago

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

1 year ago