Can someone please help me with math.

How the heck do you solve these type of problems?

Trava [24]

21) 3(2j-k)=108 It is asking you to set the equation equal to j
distribute the 3
6j-3k=108
move k to the other side by adding on both sides
6j=108+3k
divide everything by 6
j=18+0.5k

7 0

3 years ago

Sam's parents gave him a map to reach to

irina1246 [14]

2.5 km because 1.5 is half of 3 and half of 5 is 2.5

5 0

3 years ago

Read 2 more answers

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 $\rm \triangle OBA$ :

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

Equate the right-hand side of these two equations:

$0.810\, x \approx 0.649\, (x + 20)$ .

Solve for $x$ :

$x \approx 81\; \rm ft$ .

Hence, the height of the top of this tree relative to the base of the hill would be $(x + 20)\; {\rm ft}\approx 101\; \rm ft$ .

6 0

3 years ago

Which length measurement is the most precise.

vampirchik [111]

B: 6.03 The more numbers to the right of the decimal the more precise and accurate the number will be

5 0

3 years ago

Sam is at the top of a tower and will ride down a zip line to a lower tower. The total vertical drop of the zip line is 40 ft. T

jek_recluse [69]

Answer:

149.30ft

Step-by-step explanation:

Since the vertical distance between the two tower = 40ft

The angle of elevation from the lower tower to te higher tower = 15°

The horizontal distance between the two towers = x

Assuming the angle of elevation and the distance between the two towers makes a right angle triangle, we can use SOHCAHTOA and determine which one would be suitable to find x.

Check attached document for better illustration of the triangle.

Tanθ = opposite / adjacent

Opposite = 40

θ = 15°

Adjacent = x

Tan15 = 40 / x

0.2679 = 40 / x

X = 40 / 0.2679

X = 149.30ft

The horizontal distance between the two towers is 149.30ft

7 0

3 years ago