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iren2701 [21]
3 years ago
13

Giulia unreels her kite string until the kite is flying on a string of length 50 m. A light breeze holds the kite such that the

string makes an angle of 60° with the ground. After a few minutes, the wind picks up speed. The wind now pushes the kite until the string makes an angle of 45° with the ground. What distance has the kite changed position horizontally over the ground. Determine an exact expression.

Mathematics
1 answer:
ehidna [41]3 years ago
4 0
25(1-2^1/2) it is right ?XD

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Need help with radical expression!!! It’s asking for a set of all x where the expression is defined in interval form!
gayaneshka [121]

Answer:  (0, 25) ∪ (25, ∞)

<u>Step-by-step explanation:</u>

The expression is undefined when the denominator is equal to zero and when the radicand (expression inside the radical) is less than zero.

Let's deal with the denominator first by finding the x-values that would make the denominator equal to zero (these are the values that will NOT be included in the interval notation)

x - 5√x = 0

x = 5√x          <em>added 5√x to both sides</em>

x² = 25x              <em>squared both sides</em>

x² - 25x = 0             <em>subtracted 25x from both sides</em>

x(x - 25) = 0                 <em>factored the quadratic equation</em>

x = 0   and   x - 25 = 0     <em>applied the Zero Product Property</em>

x = 0   and    x = 25              <em>solved for x</em>

<em />

So, x ≠ 0 and x ≠ 25

Next, let's deal with the radicand by setting the expressions inside the radicals to "greater than or equal to zero".

2√x   and   5√x     both have a radicand of x

x ≥ 0

Now, let's put it all together

x ≥ 0  and    x ≠ 0    and    x ≠ 25    

so, x is between 0 and ∞  but not including 0 or 25.

Interval Notation: (0, 25) ∪ (25, ∞)

Reminder that interval notation uses a bracket [ ] when the value is included and a parenthesis ( ) when the value is not included.  Infinity always uses a parenthesis since it is not an actual number.

6 0
3 years ago
Alfonso runs 10 km at an average speed of x km/h.
puteri [66]

Step-by-step explanation:

Note that t = d/r where t is time, d is distance, and r is rate/speed.

We can come up with two equations with the information given and the equation:

t_1 hr = (10 km)/(x km/hr)

t_2 hr = (12 km)/(x - 1 km/hr)

<em>where t_1 is the time taken to run the 10km the first day and t_2 is the time taken to run the 12km the second day.</em>

We know that 30 minutes is 1/2 of an hour and that t_1 is 30 minutes less than t_2 (as stated in the question). Therefore, we can write:

t_1 = t_2 - 1/2

Substituting the values we derived:

(10 km)/(x km/hr) = (12 km)/(x - 1 km/hr) -1/2

Then we can evaluate by multiplying by 2x(x-1) on both sides:

20(x-1) = 24x - (x)(x-1)

20x - 20 = 24x - x^2 + x

x^2 -5x -20 = 0

And we are done.

I hope this helps! :)

6 0
2 years ago
A grocery store advertises that 15 cups of granola cost $6.75. Which are equivalent prices
fgiga [73]

which of what are equivilent prices?

6 0
3 years ago
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Can some help me with this question
Luden [163]

To find the equation of this line in slope-intercept form (y = mx + b, where m is its slope and b is its y-intercept), we naturally need the slope and the y-intercept. We can see that the line intersects the y-axis at the point (0, 4) so our y-intercept is 4, and the line rises 4 along the y-axis for every 2 it runs along the x-axis, so its slope is 4/2 = 2. With this in mind, we can write the line's equation as

y = 2x + 4

7 0
3 years ago
How many ounces are in a pound?
Naddika [18.5K]
16 ounces is the correct [email protected]
4 0
3 years ago
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