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3 years ago

4

Mathematics

1 answer:

Sloan [31]3 years ago

6 0

Answer:

The new version of a new one of the most popular connection for the next few weeks ago, I I later glamorousn for harmony and 3beautiful those the and era the

Step-by-step explanation:

yes but the fact is that the new one is going to be a big help the first half of an NCAA college old NCAA this to

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the area of a rectangle city park is 25/54 sqaure miles. the length of the park is 5/9 mile. what is the width in miles of the p

andreyandreev [35.5K]

A = lw

Plug in what we know:

25/54 = (5/9)w

Divide 5/9 to both sides or multiply by its reciprocal, 9/5:

25/54 * 9/5 = w

Multiply the numerators and denominators together:

225/270 = w

Simplify:

<span>w = 5/6</span>

6 0

3 years ago

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

Evaluate the expression:

FinnZ [79.3K]

Answer:

vw= 22

Step-by-step explanation:

To find the dot product of vw, multiply the corresponding numbers and add them.

v= <3, -8, -3> w= <-4, -2, -6>

vw= (3*-4)+(-8*-2)+(-3*-6)

vw= -12+16+18

vw= 4+18

vw= 22

6 0

3 years ago

the line of symmetry of a parabola whose equation is y = ax ^ 2 - 4x + 3 is =-2 what is the value of "a"

77julia77 [94]

Y= ax² -4x +3

-b/2a is x - coordinate of the vertex,
line of symmetry x=-2, x=-2 is a coordinate of the vertex also, because the line symmetry has vertex.

x= -b/2a
x= -2, b= -4
-2=-(-4)/2a
-2=4/2a
-2=2/a
a=2/(-2)=-1
a= - 1

5 0

3 years ago

What is the radius and diameter of the following circle?

prisoha [69]

Answer:

Radius = 6.5cm

Diameter = 13cm (given)

Step-by-step explanation:

The diameter is the length of one side of a circle to the other. It's already given in the diagram as 13cm.

The radius is half of the diameter. 13 divided by 2 is 6.5cm.

5 0

3 years ago

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