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exis [7]
3 years ago
12

A guy-wire is attached to a pole for support. If the angle of elevation to the pole is 67° and the wire is attached to the groun

d at a point 137 feet from the base of the pole, what is the length of the guy wire (round to 2 decimal places)?
Mathematics
1 answer:
vovangra [49]3 years ago
4 0
You have to go at this in a round-about fashion...by finding the length of the leg across from the 67 degree angle.  This is found by using the tangent ratio...Tan(67)=x/137; x=137tan(67) = 322.8. Now you can use this in one of two ways: use Pythagorean's Theorem to find the length of the hypotenuse OR you could use the sin67=322.8/x.  Up to you. Either way, make sure you have your calculator in degree mode!
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What is the volume of the sphere that has a diameter of 3? use 3.14 for pie​
aev [14]

Hey ! there

Answer:

  • <u>1</u><u>1</u><u>3</u><u>.</u><u>0</u><u>4</u><u> </u><u>unit </u><u>cube</u>

Step-by-step explanation:

In this question we are provided with a sphere <u>having</u><u> </u><u>radius </u><u>3 </u><u>units </u>and <u>value </u><u>of </u><u>π </u><u>is </u><u>3.</u><u>1</u><u>4</u><u> </u><u>.</u><u> </u>And we're asked to find the<u> </u><u>volume</u><u> of</u><u> </u><u>sphere</u><u> </u><u>.</u>

For finding volume of sphere , we need to know its formula . So ,

\qquad \qquad \: \underline{\boxed{ \frak{Volume_{(Sphere)} =  \dfrac{4}{3} \pi r {}^{3} }}}

<u>Where</u><u> </u><u>,</u>

  • π refers to <u>3.</u><u>1</u><u>4</u>

  • r refers to <u>radius</u><u> of</u><u> sphere</u>

<u>Sol</u><u>u</u><u>tion </u><u>:</u><u> </u><u>-</u>

Now , we are substituting value of π and radius in the formula ,

\quad \longrightarrow \qquad \: \dfrac{4}{3}   \times 3.14 \times (3) {}^{3}

Simplifying it ,

\quad \longrightarrow \qquad \: \dfrac{4}{3}  \times 3.14 \times 3 \times 3 \times 3

Cancelling 3 with 3 :

\quad \longrightarrow \qquad \: \dfrac{4}{ \cancel{3}}  \times 3.14 \times 3 \times 3 \times  \cancel{3}

We get ,

\quad \longrightarrow \qquad \:4 \times 3.14 \times 9

Multiplying 4 and 3.14 :

\quad \longrightarrow \qquad \:12.56 \times 9

Multiplying 12.56 and 9 :

\quad \longrightarrow \qquad \:    \pink{\underline{\boxed{\frak{113.04  \: unit \: cube}}}} \quad \bigstar

  • <u>Henceforth</u><u> </u><u>,</u><u> </u><u>volume</u><u> </u><u>of</u><u> </u><u>sphere</u><u> </u><u>having </u><u>radius </u><u>3 </u><u>units </u><u>is </u><em><u>1</u></em><em><u>1</u></em><em><u>3</u></em><em><u> </u></em><em><u>.</u></em><em><u>0</u></em><em><u>4</u></em><em><u> </u></em><em><u>units </u></em><em><u>cube </u></em><em><u>.</u></em>

<h2><u>#</u><u>K</u><u>e</u><u>e</u><u>p</u><u> </u><u>Learning</u></h2>

5 0
1 year ago
Manny and Evan were flying paper airplanes. Manny’s airplane flew 36.5 centimeters and Evan’s airplane flew 18 centimeters. How
professor190 [17]
First subtract manny value 36.5 from Evan values 18 which will give u 18.5 cm which then u have to convert. Since 1 cm is about .4, we can multiply 18.5 by .4 to get the answer 7.4 inches
7 0
3 years ago
Read 2 more answers
Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are locat
zavuch27 [327]

Answer:

The equation contains exact roots at x = -4 and x = -1.

See attached image for the graph.

Step-by-step explanation:

We start by noticing that the expression on the left of the equal sign is a quadratic with leading term x^2, which means that its graph shows branches going up. Therefore:

1) if its vertex is ON the x axis, there would be one solution (root) to the equation.

2) if its vertex is below the x-axis, it is forced to cross it at two locations, giving then two real solutions (roots) to the equation.

3) if its vertex is above the x-axis, it will not have real solutions (roots) but only non-real ones.

So we proceed to examine the vertex's location, which is also a great way to decide on which set of points to use in order to plot its graph efficiently:

We recall that the x-position of the vertex for a quadratic function of the form f(x)=ax^2+bx+c is given by the expression: x_v=\frac{-b}{2a}

Since in our case a=1 and b=5, we get that the x-position of the vertex is: x_v=\frac{-b}{2a} \\x_v=\frac{-5}{2(1)}\\x_v=-\frac{5}{2}

Now we can find the y-value of the vertex by evaluating this quadratic expression for x = -5/2:

y_v=f(-\frac{5}{2})\\y_v=(-\frac{5}{2} )^2+5(-\frac{5}{2} )+4\\y_v=\frac{25}{4} -\frac{25}{2} +4\\\\y_v=\frac{25}{4} -\frac{50}{4}+\frac{16}{4} \\y_v=-\frac{9}{4}

This is a negative value, which points us to the case in which there must be two real solutions to the equation (two x-axis crossings of the parabola's branches).

We can now continue plotting different parabola's points, by selecting x-values to the right and to the left of the x_v=-\frac{5}{2}. Like for example x = -2 and x = -1 (moving towards the right) , and x = -3 and x = -4 (moving towards the left.

When evaluating the function at these points, we notice that two of them render zero (which indicates they are the actual roots of the equation):

f(-1) = (-1)^2+5(-1)+4= 1-5+4 = 0\\f(-4)=(-4)^2+5(-4)_4=16-20+4=0

The actual graph we can complete with this info is shown in the image attached, where the actual roots (x-axis crossings) are pictured in red.

Then, the two roots are: x = -1 and x = -4.

5 0
3 years ago
A cylinder has a base diameter of 12in and a height of 17in. What is its volume in cubic in, to the nearest tenths place?
Anna35 [415]

Answer:

1922.7 cubic inches

Step-by-step explanation:

The volume of a cylinder can be found with this formula:

V=πr^2h

The radius, r, is half the diameter.

So, 12/2=6

r=6 inches

Then, just plug the numbers in.

V=π(6)^2(17)

V=1922.65

Rounding to the nearest tenth:

V=1922.7 cubic inches

3 0
2 years ago
Whats the answers to these tables
AVprozaik [17]

Answer:

You would just plug in the x’s for the equations above and that will equal your x

Step-by-step explanation:

for example x=1

the equation is x+5

so y equals 1+5=6

y=6

8 0
2 years ago
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