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3 years ago

Please solve with explanation

Mathematics

2 answers:

Juliette [100K]3 years ago

8 0

Step-by-step explanation:

$4\frac{9}{20} - 1\frac{2}{6} =\\\frac{89}{20} - \frac{8}{6} = \frac{89 - 26.7}{20} = \frac{62.3}{20} \\$

$4\frac{6}{9} - 3\frac{3}{6} =\\\frac{42}{9} - \frac{21}{6} = \frac{252 - 189}{54} = \frac{63}{54} = 1\frac{9}{54}$

$2\frac{2}{4} - 1\frac{1}{3} =\\\frac{10}{4} - \frac{4}{3} = \frac{30 - 16}{12} = \frac{14}{12} = 1\frac{2}{12}$

harkovskaia [24]3 years ago

6 0

Answer:

4 9/20 - 1 2/6 =

Exact form : 187/60

Decimal form : 3.116 (place a line over the six to show that six is repeating itself many times. It will look like this... 3.116666666...)

Mixed Number form : 3 7/60

4 6/9 - 3 3/6 =

Exact form : 7/6

Decimal form : 1.16 (place a line over the six to show that six is repeating itself many times. It will look like this...1.166666666...)

Mixed Number form : 1 1/6

Step-by-step explanation: (For both answers...) Convert the mixed numbers to improper fractions, then find the LCD (Least Common Denominator) and combine.

Hope this helps you out! ☺

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Change the fraction 1/5 to a percent.

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3 years ago

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The angle of elevation from me to the top of a hill is 51 degrees. The angle of elevation from me to the top of a tree is 57 deg

julia-pushkina [17]

Answer:

Approximately $101\; \rm ft$ (assuming that the height of the base of the hill is the same as that of the observer.)

Step-by-step explanation:

Refer to the diagram attached.

Let $\rm O$ denote the observer.
Let $\rm A$ denote the top of the tree.
Let $\rm R$ denote the base of the tree.
Let $\rm B$ denote the point where line $\rm AR$ (a vertical line) and the horizontal line going through $\rm O$ meets. $\angle \rm B\hat{A}R = 90^\circ$ .

Angles:

Angle of elevation of the base of the tree as it appears to the observer: $\angle \rm B\hat{O}R = 51^\circ$ .
Angle of elevation of the top of the tree as it appears to the observer: $\angle \rm B\hat{O}A = 57^\circ$ .

Let the length of segment $\rm BR$ (vertical distance between the base of the tree and the base of the hill) be $x\; \rm ft$ .

The question is asking for the length of segment $\rm AB$ . Notice that the length of this segment is $\mathrm{AB} = (x + 20)\; \rm ft$ .

The length of segment $\rm OB$ could be represented in two ways:

In right triangle $\rm \triangle OBR$ as the side adjacent to $\angle \rm B\hat{O}R = 51^\circ$ .
In right triangle $\rm \triangle OBA$ as the side adjacent to $\angle \rm B\hat{O}A = 57^\circ$ .

For example, in right triangle $\rm \triangle OBR$ , the length of the side opposite to $\angle \rm B\hat{O}R = 51^\circ$ is segment $\rm BR$ . The length of that segment is $x\; \rm ft$ .

$\begin{aligned}\tan{\left(\angle\mathrm{B\hat{O}R}\right)} = \frac{\,\rm {BR}\,}{\,\rm {OB}\,} \; \genfrac{}{}{0em}{}{\leftarrow \text{opposite}}{\leftarrow \text{adjacent}}\end{aligned}$ .

Rearrange to find an expression for the length of $\rm OB$ (in $\rm ft$ ) in terms of $x$ :

$\begin{aligned}\mathrm{OB} &= \frac{\mathrm{BR}}{\tan{\left(\angle\mathrm{B\hat{O}R}\right)}} \\ &= \frac{x}{\tan\left(51^\circ\right)}\approx 0.810\, x\end{aligned}$ .

Similarly, in right triangle $\rm \triangle OBA$ :

$\begin{aligned}\mathrm{OB} &= \frac{\mathrm{AB}}{\tan{\left(\angle\mathrm{B\hat{O}A}\right)}} \\ &= \frac{x + 20}{\tan\left(57^\circ\right)}\approx 0.649\, (x + 20)\end{aligned}$ .