1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alina [70]
2 years ago
5

Raymond was riding a zip-cable from the top of a viewing post. The cable is 65 yards long. The viewing post is 52 yards high and

forms a right angle with the ground, as shown in the picture below.
Mathematics
2 answers:
grin007 [14]2 years ago
3 0
In order to figure out the horizontal distance Raymond travels using his zip cable, we may simply apply Pythagoras theorem which is, for a right triangle:
hypotenuse² = base² + height²
base = √(hypotenuse² - height²)
base = √(65² - 52²)
base =  39 yards
Raymond will travel a horizontal distance of 39 yards.
rewona [7]2 years ago
3 0

Answer:

B. 33 yards

Step-by-step explanation:

Let x represent the height of the viewing post, y represent the how far the base of the viewing post is from the end of the cable, and z represent the length of the cable. Now, use the Pythagorean theorem.

x2 + y2 = z2

(44 yd)2 + y2 = (55 yd)2

1,936 yd2 + y2 = 3,025 yd2

y2 = 1,089 yd2

y = 33 yd

So, the end of the cable is 33 yards from the base of the viewing post.

You might be interested in
Let f(x)=5x3−60x+5 input the interval(s) on which f is increasing. (-inf,-2)u(2,inf) input the interval(s) on which f is decreas
o-na [289]
Answers:

(a) f is increasing at (-\infty,-2) \cup (2,\infty).

(b) f is decreasing at (-2,2).

(c) f is concave up at (2, \infty)

(d) f is concave down at (-\infty, 2)

Explanations:

(a) f is increasing when the derivative is positive. So, we find values of x such that the derivative is positive. Note that

f'(x) = 15x^2 - 60


So,


f'(x) \ \textgreater \  0
\\
\\ \Leftrightarrow 15x^2 - 60 \ \textgreater \  0
\\
\\ \Leftrightarrow 15(x - 2)(x + 2) \ \textgreater \  0
\\
\\ \Leftrightarrow \boxed{(x - 2)(x + 2) \ \textgreater \  0} \text{   (1)}

The zeroes of (x - 2)(x + 2) are 2 and -2. So we can obtain sign of (x - 2)(x + 2) by considering the following possible values of x:

-->> x < -2
-->> -2 < x < 2
--->> x > 2

If x < -2, then (x - 2) and (x + 2) are both negative. Thus, (x - 2)(x + 2) > 0.

If -2 < x < 2, then x + 2 is positive but x - 2 is negative. So, (x - 2)(x + 2) < 0.
 If x > 2, then (x - 2) and (x + 2) are both positive. Thus, (x - 2)(x + 2) > 0.

So, (x - 2)(x + 2) is positive when x < -2 or x > 2. Since

f'(x) \ \textgreater \  0 \Leftrightarrow (x - 2)(x + 2)  \ \textgreater \  0

Thus, f'(x) > 0 only when x < -2 or x > 2. Hence f is increasing at (-\infty,-2) \cup (2,\infty).

(b) f is decreasing only when the derivative of f is negative. Since

f'(x) = 15x^2 - 60

Using the similar computation in (a), 

f'(x) \ \textless \  \ 0 \\ \\ \Leftrightarrow 15x^2 - 60 \ \textless \  0 \\ \\ \Leftrightarrow 15(x - 2)(x + 2) \ \ \textless \  0 \\ \\ \Leftrightarrow \boxed{(x - 2)(x + 2) \ \textless \  0} \text{ (2)}

Based on the computation in (a), (x - 2)(x + 2) < 0 only when -2 < x < 2.

Thus, f'(x) < 0 if and only if -2 < x < 2. Hence f is decreasing at (-2, 2)

(c) f is concave up if and only if the second derivative of f is positive. Note that

f''(x) = 30x - 60

Since,

f''(x) \ \textgreater \  0&#10;\\&#10;\\ \Leftrightarrow 30x - 60 \ \textgreater \  0&#10;\\&#10;\\ \Leftrightarrow 30(x - 2) \ \textgreater \  0&#10;\\&#10;\\ \Leftrightarrow x - 2 \ \textgreater \  0&#10;\\&#10;\\ \Leftrightarrow \boxed{x \ \textgreater \  2}

Therefore, f is concave up at (2, \infty).

(d) Note that f is concave down if and only if the second derivative of f is negative. Since,

f''(x) = 30x - 60

Using the similar computation in (c), 

f''(x) \ \textless \  0 &#10;\\ \\ \Leftrightarrow 30x - 60 \ \textless \  0 &#10;\\ \\ \Leftrightarrow 30(x - 2) \ \textless \  0 &#10;\\ \\ \Leftrightarrow x - 2 \ \textless \  0 &#10;\\ \\ \Leftrightarrow \boxed{x \ \textless \  2}

Therefore, f is concave down at (-\infty, 2).
3 0
3 years ago
a class has 60 students.Given that 85% passed a science test. Find the number of students who failed and then convert o %
Vanyuwa [196]

Given:

Total students = 60

Student passed = 85%

To find:

The number of students who failed and  then convert it in %.

Solution:

We have,

Number of passed student = 85% of Total students

                                            = \dfrac{85}{100}\times 60

                                            = 51

So, number of passes students is 51.

Number of students who failed = Total students - Passes students

                                                    = 60-51

                                                    = 9

So, number of students who failed is 9.

\text{Fail}\%=\dfrac{\text{Failed students}}{\text{Total students}}\times 100

\text{Fail}\%=\dfrac{9}{60}\times 100

\text{Fail}\%=15

Therefore, 15% students fail in the test.

7 0
2 years ago
Receiving
forsale [732]

Answer: 30.8%

Step-by-step explanation:

Given

Total students receiving financial aid are 6101

Students who are graduate and receiving financial aid are 1879

Probability is the ratio of the favorable and total outcomes

So, the probability is  given by

P=\dfrac{1879}{6101}\\\\P=0.307\ \text{or}\ 30.8\%

8 0
2 years ago
Read 2 more answers
If a coin is flipped three times what is the probability of getting heads at least twice. AND PLS HELP I NEED ANSWERS FOR A 21 P
PSYCHO15rus [73]

Answer:2/3

Step-by-step explanation: the chances are two outa three chances if this dont help at least i tried

5 0
2 years ago
Read 2 more answers
What is the value of a?
ehidna [41]

Answer:

I think it's a= 6.98 I did the solution

4 0
2 years ago
Read 2 more answers
Other questions:
  • What is the simplified form of the following expression?
    8·1 answer
  • Ahhh plz help last question!!! 15 points
    6·2 answers
  • At a New Car Dealership, a particular model comes in 3 different trim levels (CX, DX,
    9·2 answers
  • Carlos says that 17.43 divided by 100 is the same as 174.3 times 0.01<br> Is he correct? Explain
    9·2 answers
  • If a line goes through points (-2,9) and (0,3), what is the slope?
    12·1 answer
  • There are 5 4/5 cups of milk left in a carton . Write 5 4/5 as an improper fraction
    12·2 answers
  • Please help......................
    10·1 answer
  • Look the image below
    5·2 answers
  • 1. At dinner Mr. Murphy’s bill came out to $39.99 before tax and tip sales tax is 6% he wants to also have a 20% tip how much mo
    10·1 answer
  • In how many ways can 13 students be seated in a row of 13 chairs if David, insists on sitting in the first chair?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!