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3 years ago

What is the value of a? 9

Mathematics

1 answer:

Vera_Pavlovna [14]3 years ago

6 0

ΔBED and Δ DEC are similar (AAA). Therefore we have the proportion:

$\dfrac{a}{18}=\dfrac{4}{a}$ cross multiply

$a^2=(18)(4)\\\\a^2=72\to a=\sqrt{72}\\\\a=\sqrt{36\cdot2}\\\\a=\sqrt{36}\cdot\sqrt2\\\\\boxed{a=6\sqrt2}$

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You stand a known distance from the base of the tree, measure the angle of elevation the top of the tree to be 15â—¦ , and then

gogolik [260]

Answer:

The maximum possible error of in measurement of the angle is $d\theta_1 =(14.36p)^o$

Step-by-step explanation:

From the question we are told that

The angle of elevation is $\theta_1 = 15 ^o = \frac{\pi}{12}$

The height of the tree is h

The distance from the base is D

h is mathematically represented as

$h = D tan \theta$ Note : this evaluated using SOHCAHTOA i,e

$tan\theta = \frac{h}{D}$

Generally for small angles the series approximation of $tan \theta \ is$

$tan \theta = \theta + \frac{\theta ^3 }{3}$

So given that $\theta = 15 \ which \ is \ small$

$h = D (\theta + \frac{\theta^3}{3} )$

$dh = D (1 + \theta^2) d\theta$

=> $\frac{dh}{h} = \frac{1 + \theta ^2}{\theta + \frac{\theta^3}{3} } d \theta$

Now from the question the relative error of height should be at most

$\pm p$ %

=> $\frac{dh}{h} = \pm p$

=> $\frac{1 + \theta ^2}{\theta + \frac{\theta^3}{3} } d \theta = \pm p$

=> $d\theta = \pm \frac{\theta + \frac{\theta^3}{3} }{1+ \theta ^2} * \ p$

So for $\theta_1$

$d\theta_1 = \pm \frac{\theta_1 + \frac{\theta^3_1 }{3} }{1+ \theta_1 ^2} * \ p$

substituting values

$d [\frac{\pi}{12} ] = \pm \frac{[\frac{\pi}{12} ] + \frac{[\frac{\pi}{12} ]^3 }{3} }{1+ [\frac{\pi}{12} ] ^2} * \ p$

=> $d\theta_1 = 0.25 p$

Converting to degree

$d\theta_1 = (0.25* 57.29) p$

$d\theta_1 =(14.36p)^o$

4 0

3 years ago

Which term below is a "like term" to 2xy2? a, 3xy2 b, -x2y c, -5 d, 4xy

BigorU [14]

Answer:

The answer is

A 3xy^2

Step-by-step explanation:

Im assuming that in the question it is 2xy^2 and that answer choice A is 3xy^2

8 0

3 years ago

Read 2 more answers

A local library claims it has 2.73x103 books. If there are 42 people in the building, how many books per capita are there?

Marizza181 [45]

Answer:

63 books per capita in the library

Step-by-step explanation:

Given

$Books = 2.73 * 10^3$

$People = 43$

Required

Determine the book per capita

To do this, we simply divide the number of books by number of person;

$Average = \frac{Books}{People}$

$Average = \frac{2.73 * 10^3}{43}$

$Average = \frac{2.73 * 1000}{43}$

$Average = \frac{2730}{43}$

$Average = 63.488372093$

$Average = 63$ (Approximated)

Hence;

There are 63 books per capita in the library

7 0

2 years ago

2. If you pay a one-time fee of $30, you can

VikaD [51]

Answer:

Kindly check explanation

Step-by-step explanation:

Given that :

One time fee = $30

Reduced price of ticket after one time fee payment = $17

Regular ticket cost = $25

Write an inequality that can be used to determine the number of reduced price concert tickets you would need to purchase in order for the total cost to be less expensive than the same number of regular tickets

Let the number of tickets needed to purchase = t

Reduced ticket = 30 + 17t

Regular ticket = 25t

30 + 17t < 25t

30 < 25t - 17t

30 < 8t

30/8 < 8t/8

3.75 < t

t > 3.75

Hence number of ticket must be greater than 3.75

t = 4

5 0

3 years ago

Runners in a long distance race start out going 8 kilometers east and then head north for the remainder of the race. The finish

Ilya [14]

B. 6 km

You have to draw it so you can better process it. From there it's just the Pythagorean theorum.
a²+b²=c²
6²+b²=10²
(10 is c because it's the hypotenuse)
64+b²=100
100-64=36
√36 = 6

5 0

3 years ago