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
Juliette [100K]
3 years ago
8

The angle of elevation from the top of a house to a jet flying 2 miles above the house is x radians. If d represents the horizon

tal distance, in miles, of the jet from the house, express d in terms of a trigonometric function of x.
Mathematics
1 answer:
alisha [4.7K]3 years ago
6 0

Answer:

d = 2cot(x) or d = 2/tan(x)

Step-by-step explanation:

The vertical distance from the jet to the top of the house represents the opposite side to the 'x' angle, while the horizontal distance, d, represents the adjacent side. Since we do not know the hypotenuse, the tangent and cotangent functions are the preferable choices:

tan (x) = \frac{2}{d}\\d = \frac{2}{tan (x) }\\cot (x) = \frac{d}{2} \\d= 2cot(x)

Therefore, the distance 'd' can be expressed as d = 2cot(x) or d = 2/tan(x).

You might be interested in
A merchant buys a television for $125 and sells it for $75 more. what is the percent of markup?
guajiro [1.7K]
Since he sold it for $75 more,

% Mark Up = Mark Up/ Cost Price   * 100%

% Mark Up =   75 / 125 * 100%
            
                   =   0.6  * 100% = 60%

Percent Mark Up = 60%.

Hope this explains it.

4 0
3 years ago
Find negative square root of 16. (4 points) a −4 b 4 c ±4 d −8
Tom [10]

Step-by-step explanation:

Find negative square root of 16. (4 points) a −4 b 4 c ±4 d −8

3 0
2 years ago
the derivative of the function f is given by f'(x)=x^2cos(x^2). How many points of inflection does the graph of f have on the op
Vsevolod [243]
The point of inflection is calculated by equating the second derivative to zero and determining x from there.

f"(x) = -x²2xsinx² + cosx²(2x) = 0

2xcosx² - 2x³sinx² = 0
2x (cosx² - xsinx²) = 0

2x = 0   ⇒  x = 0
cosx² - xsinx² = 0   ⇒ x = 3.82 (if you use shift+solve in your scientific calculator)

Thus, the function only has 1 point of inflection and it is at x = 0.
5 0
3 years ago
How you find the answer
lozanna [386]

Answer:

cut up the shape

Step-by-step explanation:

if you are looking for area make the 18 yard a triangle so then you have a rectangle and add them together. try this for practice so you can do it on your own next time:)

6 0
3 years ago
Read 2 more answers
What is a quick and easy way to remember explicit and recursive formulas?
Oliga [24]
I always found derivation to be helpful in remembering. Since this question is tagged as at the middle school level, I assume you've only learned about arithmetic and geometric sequences.

First, remember what these names mean. An arithmetic sequence is a sequence in which consecutive terms are increased by a fixed amount; in other words, it is an additive sequence. If a_n is the nth term in the sequence, then the next term a_{n+1} is a fixed constant (the common difference d) added to the previous term. As a recursive formula, that's

a_{n+1}=a_n+d

This is the part that's probably easier for you to remember. The explicit formula is easily derived from this definition. Since a_{n+1}=a_n+d, this means that a_n=a_{n-1}+d, so you plug this into the recursive formula and end up with 

a_{n+1}=(a_{n-1}+d)+d=a_{n-1}+2d

You can continue in this pattern, since every term in the sequence follows this rule:

a_{n+1}=a_{n-1}+2d
a_{n+1}=(a_{n-2}+d)+2d
a_{n+1}=a_{n-2}+3d
a_{n+1}=(a_{n-3}+d)+3d
a_{n+1}=a_{n-3}+4d

and so on. You start to notice a pattern: the subscript of the earlier term in the sequence (on the right side) and the coefficient of the common difference always add up to n+1. You have, for example, (n-2)+3=n+1 in the third equation above.

Continuing this pattern, you can write the formula in terms of a known number in the sequence, typically the first one a_1. In order for the pattern mentioned above to hold, you would end up with

a_{n+1}=a_1+nd

or, shifting the index by one so that the formula gives the nth term explicitly,

a_n=a_1+(n-1)d

Now, geometric sequences behave similarly, but instead of changing additively, the terms of the sequence are scaled or changed multiplicatively. In other words, there is some fixed common ratio r between terms that scales the next term in the sequence relative to the previous one. As a recursive formula,

a_{n+1}=ra_n

Well, since a_n is just the term after a_{n-1} scaled by r, you can write

a_{n+1}=r(ra_{n-1})=r^2a_{n-1}

Doing this again and again, you'll see a similar pattern emerge:

a_{n+1}=r^2a_{n-1}
a_{n+1}=r^2(ra_{n-2})
a_{n+1}=r^3a_{n-2}
a_{n+1}=r^3(ra_{n-3})
a_{n+1}=r^4a_{n-3}

and so on. Notice that the subscript and the exponent of the common ratio both add up to n+1. For instance, in the third equation, 3+(n-2)=n+1. Extrapolating from this, you can write the explicit rule in terms of the first number in the sequence:

a_{n+1}=r^na_1

or, to give the formula for a_n explicitly,

a_n=r^{n-1}a_1
6 0
3 years ago
Other questions:
  • An investment is currently worth 2.125×104 dollars . Ten years ago, the investment was worth ​ 1.25×103 ​ dollars. How many time
    12·2 answers
  • What is a mathematic expresion for 43 more than d
    6·1 answer
  • Ethan burns 659 calories when he runs for 1 hour. Suppose he runs for 5 houtse in one week. How many calories does Ethan burn in
    9·2 answers
  • Henry's wage is £450 per week.
    13·1 answer
  • A store uses a selling price of 125% of the cost of an item. If a pair of jeans has a sale price of $52.50, what does the store
    10·1 answer
  • Solve for k.
    5·2 answers
  • Can i please get help on 46,66,66, and 74
    5·1 answer
  • The speed s (in miles per hour) of a car driving on dry asphalt can be given by s=4.74d√, where d is the stopping distance (in f
    7·1 answer
  • Point 7,2 is translated vertically 2 units and horizontally -5 units. Where is the new point located?
    15·1 answer
  • In which number is the value of the 5 ten times the value of the 5 in 10.059?
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!