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masha68 [24]
2 years ago
5

A tree is growing on a hill. In an attempt to make the tree grow straight up, a 12-foot-long wire is attached to a tree at a poi

nt 6 feet off the ground. The wire is anchored to the ground 10 feet from the base of the tree. At what angle is the tree growing in relation to the hill?

Mathematics
2 answers:
nasty-shy [4]2 years ago
5 0

Answer:

Its 93.8 on ed

melisa1 [442]2 years ago
3 0
For this case what we must do is use the law of cosines.
 We have then:
 12 ^ 2 = 6 ^ 2 + 10 ^ 2 - 2 * (6) * (10) cos (x)
 Clearing we have:
 cos (x) = (12 ^ 2- (6 ^ 2 + 10 ^ 2)) / (- 2 * (6) * (10))
 x = acos ((12 ^ 2- (6 ^ 2 + 10 ^ 2)) / (- 2 * (6) * (10)))
 x = 93.82 degrees
 Answer:
 
The tree is growing in relation to the hill at:
 
x = 93.82 degrees
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Five hundred sixth-grade students
viktelen [127]
<h3>The ratio in three ways are 500 : 125 or 100 : 25 or 4 : 1</h3>

<em><u>Solution:</u></em>

Given that,

Five hundred sixth-grade students  were surveyed

Which means,

sixth-grade students = 500

125 had traveled on an airplane

<em><u>What is the ratio of total sixth-grade students to the number of students who had  traveled on an airplane?</u></em>

Therefore,

total sixth-grade students : students  traveled on airplane = 500 : 125

<h3>Ratio = 500 : 125</h3>

Reduce to lowest terms,

Divide both sides by 5

<h3>Ratio = 100 : 25</h3>

Further reduce to simplest terms,

Divide both sides by 25

<h3>Ratio = 4 : 1</h3>

Thus the ratio in three ways are 500 : 125 or 100 : 25 or 4 : 1

6 0
2 years ago
Choose the function whose graph is given by:
katen-ka-za [31]

Answer:

D. y=\tan (x-\pi)+2

Step-by-step explanation:

We are given the graph of the transformed tangent function.

As, we can see that the graph is shifted 2 units upwards.

That is, the parent function is translated 2 units up.

So, the new function will be of the form, y=\tan (x)+2.

Thus, options A and C are not correct.

Moreover, 'If a function f(x) has period P, then the function cf(bx) will have period \frac{P}{|b|}.

Also, form the figure, we see that the period of the graphed function is \pi.

Since, y=\tan (x) have period \pi.

So, function in option B will have period \frac{\pi}{2}, which is not possible.

<em>Further, function in option D have period \pi.</em>

Thus, the equation of the graphed function is, y=\tan (x-\pi)+2.

7 0
2 years ago
Read 2 more answers
The indicated function y1(x) is a solution of the given differential equation. Use reduction of order or formula (5) in Section
LUCKY_DIMON [66]

Answer:

y2 = C1xe^(4x)

Step-by-step explanation:

Given that y1 = e^(4x) is a solution to the differential equation

y'' - 8y' + 16y = 0

We want to find the second solution y2 of the equation using the method of reduction of order.

Let

y2 = uy1

Because y2 is a solution to the differential equation, it satisfies

y2'' - 8y2' + 16y2 = 0

y2 = ue^(4x)

y2' = u'e^(4x) + 4ue^(4x)

y2'' = u''e^(4x) + 4u'e^(4x) + 4u'e^(4x) + 16ue^(4x)

= u''e^(4x) + 8u'e^(4x) + 16ue^(4x)

Using these,

y2'' - 8y2' + 16y2 =

[u''e^(4x) + 8u'e^(4x) + 16ue^(4x)] - 8[u'e^(4x) + 4ue^(4x)] + 16ue^(4x) = 0

u''e^(4x) = 0

Let w = u', then w' = u''

w'e^(4x) = 0

w' = 0

Integrating this, we have

w = C1

But w = u'

u' = C1

Integrating again, we have

u = C1x

But y2 = ue^(4x)

y2 = C1xe^(4x)

And this is the second solution

5 0
2 years ago
A web page design firm has two designs for an online hardware store. To determine which is the more effective design, the firm u
tatyana61 [14]

Answer:

Explanatory variable : web page design

Response variables : Visitor's rating and amount of time visiting the site.

Kindly check explanation for the rest.

Step-by-step explanation:

The explanatory variable simply means the independent or predictor variable which is used to bring about a change in the dependent or predicted variable. The explanatory variable in the scenario above is the web page design which is used to measure the behavior and changes in the response variable which are the rating given by visitors and the number of visits on each of the two different web page designs available (explanatory variable).

The confounding factor which may affect the study is the different area assigned to test the effectiveness of each page ; designating one page for the Oakland area and the other for Miami. User preferences for each area may itself mask the actual outcome of the experiment.

4 0
2 years ago
Dori and Malory are tracking their steps taken as a health goal. Dori leaves her house at 12:00 p.m. and walks at 50 steps per m
gladu [14]
Let n = minutes since 12:00 pm when Malory catches up to Dori.

Dori travels
(50 steps/min)*(n minutes) = 50n steps

Malory begins walking at 12:20 pm, so she walks for (n - 20) minutes. She travels
(90 steps/min)*(n - 20  min) = 90n - 1800 steps

Equate the steps traveled by Dori and Malory.
90n - 1800 = 50n
40n = 1800
n = 45 min

The time corresponding to n = 45 min is 12:45 pm

Answer: 12:45 pm

7 0
2 years ago
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