Find the slope of the line

To measure a stone face carved on the side of a mountain, two sightings 900 feet from the base of the mountain are taken. If th

olga nikolaevna [1]

Answer:

Height of the stone face = 66.29 feet

Step-by-step explanation:

Refer the given figure, here we need to find height of the stone face,

Height of the stone face = CD

CD = AD - AC

In ΔABC we have

$tan31=\frac{AC}{AB}\\\\tan31=\frac{AC}{900}\\\\AC=540.77feet$

In ΔABD we have

$tan34=\frac{AD}{AB}\\\\tan34=\frac{AD}{900}\\\\AD=607.06feet$

CD = AD - AC = 607.06 - 540.77 = 66.29 feet

Height of the stone face = CD = 66.29 feet

7 0

3 years ago

What is 04.151515... into a fraction

Sergio039 [100]

Answer:

$\displaystyle 4.\overline{15} = \frac{137}{33}$ .

Step-by-step explanation:

Start by separating this decimal number into its integer part and its fraction part:

$4.151515\cdots = 4 + 0.151515\cdots$

The most challenging task here is to express $0.151515\cdots$ as a proper fraction. Once that fraction is found, expressing the original number $4.151515\cdots$ will be as simple as rewriting a mixed number as an improper fraction.

Let $x = 0.151515\cdots$ . $(x + 4)$ would then represent the original number.

Note that the repeating digits appear in groups of two. Therefore, if the digits in $x$ are shifted to the left by two places, the repeating part will continue to match:

$\begin{aligned}x = 0.&151515\cdots && \\ 100\, x = 15.& 151515\cdots \end{aligned}$ .

Note, that this "shifting" is as simple as multiplying the initial number by $100$ (same as $10$ raised to the power of the number of digits that needs to be shifted.)