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3 years ago

13

A tree grows vertically on a hillside. The hill is at a 16° angle to the horizontal. The tree casts an 18-meter shadow up the hi

ll when the angle of elevation of the sun measures
68°. How tall is the tree?

1 answer:

elixir [45]3 years ago

8 0

The height of the tree is the sum of the part below the line parallel to the horizontal and the part above the line parallel to the horizontal.

Height of the part below the line parallel to the horizontal = 18 sin16° = 4.96 meters
Horizontal distance of the tip of the of the shadow from the tree = 18 cos16° = 17.30 meters
Height of the part above the line parallel to the horizontal = 17.3 tan68° = 42.83 meters

Height of the tree = 4.96 + 42.83 = 47.79 meters

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as Saturn revolves around the sun, it travels at a speed of approximately 6 miles per second. convert this speed to miles per mi

3241004551 [841]

Given:

Speed = 6 miles per second

If the Saturn revolves 6 miles in 1 second then the speed is:

$\begin{gathered} In\text{ 1 second distance is 6 miles} \\ So\text{ in 60 second distance is =6}\times60\text{ miles} \\ =360 \end{gathered}$

So speed in minutes is 360 miles per min.

In 3 minutes traveling distance is:

$\begin{gathered} =360\times3 \\ =1080 \end{gathered}$

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1 year ago

The sum of the first four terms of an arithmetic sequence is $10$. If the fifth term is $5$, what is the sixth term?

Nookie1986 [14]

The sixth term of an arithmetic sequence is 6

<h3>How to find arithmetic sequence?</h3>

The sum of the first four terms of an arithmetic sequence is 10.

The fifth term is 5.

Therefore,

sum of term = n / 2(2a + (n - 1)d)

where

a = first term
d = common difference
n = number of terms

Therefore,

n = 4

10 = 4 / 2 (2a + 3d)

10 = 2(2a + 3d)

10 = 4a + 6d

4a + 6d = 10

a + 4d = 5

4a + 6d = 10

4a + 16d = 20

10d = 10

d = 1

a + 4(1) = 5

a = 1

Therefore,

6th term = a + 5d

6th term = 1 + 5(1)

6th term = 6

learn more on sequence here: brainly.com/question/24128922

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1 year ago

16x^2+?x+36 perfect square trinomial

Hunter-Best [27]

Answer:

16x² +48x +36

Step-by-step explanation:

A perfect square trinomial is of the form ...

(a +b)² = a² +2ab +b²

We want to match this form.

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<h3>comparing terms</h3>

Comparing the known terms, we see ...

16x² = a² ⇒ a = 4x

36 = b² ⇒ b = 6

<h3>filling in the missing term</h3>

The missing term is the linear term:

2ab = 2(4x)(6) = 48x

? = 48

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2 years ago

What is the prime factorization for 20

NeTakaya

2x2x5 is the prime factorization

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3 years ago

Read 2 more answers

Genetic Defects Data indicate that a particular genetic defect occurs in of every children. The records of a medical clinic show

Dovator [93]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The probability that there exist 60 or more defected children is $P(x \ge 60)=0.0901$

Looking at the value for this probability we see that it is not so small to the point that the observation of this kind would be a rare occurrence

Step-by-step explanation:

From the question we are told that

in every 1000 children a particular genetic defect occurs to 1

The number of sample selected is $n= 50,000$

The probability of observing the defect is mathematically evaluated as

$p = \frac{1}{1000}$

$= 0.001$

The probability of not observing the defect is mathematically evaluated as

$q = 1-p$

$= 1-0.001$

$= 0.999$

The mean of this probability is mathematically represented as

$\mu = np$

Substituting values

$\mu = 50000*0.001$

$= 50$

The standard deviation of this probability is mathematically represented as

$\sigma = \sqrt{npq}$

Substituting values

$= \sqrt{50000 * 0.001 * 0.999}$

$= \sqrt{49.95}$

$= 7.07$

the probability of detecting $x \ge60$ defects can be represented in as normal distribution like

$P(x \ge 60)$

in standardizing the normal distribution the normal area used to approximate $P(x \ge 60)$ is the right of 59.5 instead of 60 because x= 60 is part of the observation

The z -score is obtained mathematically as

$z = \frac{x-\mu }{\sigma }$

$= \frac{59.5 - 50 }{7.07}$

$=1.34$

The area to the left of z = 1.35 on the standardized normal distribution curve is 0.9099 obtained from the z-table shown z value to the left of the standardized normal curve

Note: We are looking for the area to the right i.e 60 or more

The total area under the curve is 1

So

$P(x \ge 60) \approx P(z > 1.34)$

$= 1-P(z \le 1.34)$

$=1-0.9099$

$=0.0901$

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3 years ago