Answer:
Length is 17m and Breadth is also 17mStep-by-step explanation:
The perimeter of a rectangle is expressed as 2(L+B) where;
L is the length and B is the breadth of the triangle.
P = 2(L+B)
68 = 2(L+B)
L+B = 68/2
L+B = 34
L = 34 - B ... 1
Area of the rectangle A = LB... 2
Substituting equation 1 into 2 will give;
A = (34-B)B
A = 34B-B²
To maximize the area of the triangle, dA/dB must be equal to zero i.e
dA/dB = 0
dA/dB = 34 - 2B = 0
34-2B = 0
2B = 34
Dividing both sides of the equation by 2 we will have;
B = 34/2
B = 17
Substituting B = 17 into equation 1 to get the length L
L = 34-17
L = 17m
This shows that the rectangle with maximum area is a square since L = B = 17m
The dimension of the rectangle is Length = 17m and Breadth = 17m
The dimensions are 17m and 17m.
The perimeter of a rectangle is given as:
= 2(length + width)
Since in their case, the lengths have same values, this will be:
Perimeter = 2(l + l)
Perimeter = 4l
4l = 68
L = 68/4
L = 17m
Therefore, the dimensions are 17m and 17m.
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Solve the simultaneous equations 2x-y=7 3x+y=3
Answer:
( 2 , - 3 )Step-by-step explanation:
Using elimination method:
2x - y = 7
3x + y = 3
--------------
5x = 10
Divide both sides of the equation by 5
[tex] \frac{5x}{5} = \frac{10}{5} [/tex]
Calculate
[tex]x = 2[/tex]
Now, substitute the given value of X in the equation
3x + y = 3
[tex]3 \times 2 + y = 3[/tex]
Multiply the numbers
[tex]6 + y = 3[/tex]
Move constant to R.H.S and change it's sign
[tex]y = 3 - 6[/tex]
Calculate
[tex]y = - 3[/tex]
The possible solution of this system is the ordered pair ( x , y )
( x , y ) = ( 2 , -3 )---------------------------------------------------------------------
Check if the given ordered pair is the solution of the system of equation
[tex]2 \times 2 - ( - 3) = 7[/tex]
[tex]3 \times 2 - 3 = 3[/tex]
Simplify the equalities
[tex]7 = 7[/tex]
[tex]3 = 3[/tex]
Since all of the equalities are true, the ordered pair is the solution of the system
( x , y ) = ( 2 , - 3 )Hope this helps..
Best regards!!
Find the 12th term of the following geometric sequence.
10, 30, 90, 270, ...
Answer:
r = 90/30
r = 3
T12 = 10 × 3¹¹
T12 = 1771470
A manager receives 8 applications for a specific position. She wants to narrow it down to 5. In how many ways can she rank 5 applications?
Answer:
56 number of ways
Step-by-step explanation:
This question is a combination question since it involves selection.
Generally, if r objects are to be selected from n pool of objects, this can be done in nCr number of ways.
nCr = n!/(n-r)!r!
If a manager receives 8 applications for a specific position and wants to narrow it down to 5, the number of ways he can do this is 8C5
8C5 = 8!/(8-5)!5!
= 8!/3!5!
= 8*7*6*5!/3*2*5!
= 8*7*6/3*2
= 8*7
= 56 number of ways.
This means that the manager can rank 5 applications in 56 number of ways
The number of ways that can she rank 5 applications should be 6720.
Calculation of the number of ways:Since A manager receives 8 applications for a specific position. She wants to narrow it down to 5.
So here we do apply the permutation here:
[tex]= 8!\div 5!3! \times 5!\div 0!\\\\= 8\times 7\times 6\times 5\times 4[/tex]
= 6720
Hence, The number of ways that can she rank 5 applications should be 6720.
Learn more about ways here: https://brainly.com/question/18988173
A= 63°
C = 7.75 inch
B = 47°
Oblique Triangle
4. Refer to the oblique triangle shown. What's the size of angle C?
O A. 60°
B. 125°
O C. 45°
O D. 70°
Answer:
Option D is correct.
Angle C = 70°
Step-by-step explanation:
The sum of angles in a triangle = 180°
So,
(Angle A) + (Angle B) + (Angle C) = 180°
(Angle A) = 67°
(Angle B) = 43°
(Angle C) = ?
67° + 43° + (Angle C) = 180°
Angle C = 180 - 67 - 43 = 70°
Angle C = 70°
Hope this Helps!!!
In an episode of the old school version of the game show Family Feud, 43 out of a random sample of 100 people said they pick their noses at red lights. Find a 95% confidence interval of the proportion of all people who pick their noses at red lights.
Answer:
95% of confidence interval of the proportion of all people who pick their noses at red lights
(0.3342 , 0.5258)
Step-by-step explanation:
Step(i):-
Given sample size 'n' = 100
Given data 43 out of a random sample of 100 people said they pick their noses at red lights.
sample proportion
[tex]p^{-} = \frac{x}{n} = \frac{43}{100} = 0.43[/tex]
Level of significance = 0.05
Z₀.₀₅ = 1.96
Step(ii):-
95% of confidence interval of the proportion of all people who pick their noses at red lights
[tex](p^{-} -Z_{\alpha } \sqrt{\frac{p(1-p)}{n} } ,p^{-} +Z_{\alpha } \sqrt{\frac{p(1-p)}{n} })[/tex]
[tex](0.43 -1.96 \sqrt{\frac{0.43(1-0.43)}{100} } ,0.43 +1.96 \sqrt{\frac{0.43(1-0.43)}{100} })[/tex]
( 0.43 - 0.0958 , 0.43 + 0.0958)
(0.3342 , 0.5258)
Conclusion:-
95% of confidence interval of the proportion of all people who pick their noses at red lights
(0.3342 , 0.5258)
Help !!! Need answer fast. Find the value of x.
Answer:
x=60
Step-by-step explanation:
We know that when two secant lines, or a secant line and a tangent line, intersect at a point outside the circle, the measure of the angle formed at the point of intersection is half the difference between measures of the intercepted arcs.
So, we can set up the equation [tex]55=\frac{1}{2} (170-x)[/tex], which will come out to [tex]x=60[/tex].
hope this helps!
The drama club is selling T-shirts and caps to raise money for a spring trip. The caps sell for $5.00 each, and the T-shirts sell for $10.00 each. The drama club needs to raise at least $500.00 for the trip. The inequality that represents this situation is graphed, with x representing the number of caps sold and y representing the number of T-shirts sold. Which solution is valid within the context of the situation?
Answer:
The correct answer to this question is C: (72,24).
Step-by-step explanation:
We are given that:
The cost of 1 cap is $5 each
The cost of 1 t-shirt is $10 each
Let x be the number of caps sold
Let y be the number of t-shirt sold
In the context we are given that the drama club needs to raise at least $500 to go on the trip.
So based on this information we can create a inequality as:
the number of caps sold x (times) the cost of a single cap + the number of shirts x (times) the cost of a single t-shirt ≥ (greater than or equal to) 500
Inequality: 5x+10y ≥ 500 ( We used a greater than or equal to symbol because it said that the drama club need at least $500 for the trip.
Next we need to figure out how many caps and t-shirt were sold.
- We can already take out two of the options which are the two answer with negatives in them because we know that when you multiply a positive number with a negative number we get a negative number and we don't want that. (So Option A and Option D are out.)
Now all we do is plug x and y into our inequality equation ( 5x+10y ≥ 500 )
B) x=65 caps, y= 17.5 t-shirts ----> 5(65)+10(17.5) =500 which you get $500
YOU MAY THINK THIS IS THE ANSWER BUT! if you look closely at variable y it said they sold 17.5 t-shirt, but here there thing how do you sell 17 shirts and a half of shirt? Which means this option is also wrong!
C) x =72 caps, y =24 t-shirts ------> 5(72)+ 10(24)= $600 which is more than the original amount they were going for because it said at least $500.
So the correct option to this question is C, they sold 72 caps and 24 t-shirts and earned $600 dollars.
Answer: C
Step-by-step explanation: Each coordinate point is located within the solution set, as shown on the graph.
First, take out any solution that includes a negative number, since there cannot be a negative number of bags. So, (-2,10) and (9,-3) are not solutions.
Next, take out any solution that does not have all whole numbers because the bags are whole objects. So, (4.5,9) is not a solution.
So, (8,5) is a valid solution in the context of the situation.
Samuel needs to replace a portion of his rain gutter. The height of the roof is 25 feet and the
length of his ladder is 30 feet. What is the maximum distance away from house that he can place
the ladder? Round your answer to the nearest foot.
Answer:
16.6 ftStep-by-step explanation:
The height of the house, the ground and the ladder forms a right angle triangle, with the following parameters stated below.
1. the hypotenuse is the length of the ladder which is 30 feet
2.the opposite is the height of the house, which is 25 feet
3. the adjacent is the distance of the ladder away from the building, this is the parameter we are solving for.
Since we have two sides of the triangle given, we can employ Pythagoras theorem to solve for the third side of the triangle
let the the opposite be x
we know that
[tex]hyp^2= opp^2+adj^2\\\\ 30^2= x^2+25^2\\\\ 900= 625+x^2\\[/tex]
Solving for x we have
[tex]x^2= 900-625\\\\X^2= 275\\\\x=\sqrt{275} \\\\x= 16.58[/tex]
Hence the maximum distance away from house that he can place
the ladder is 16.6 ft to the nearest foot
Solve for x: ( 1/2 )^(x−1)=2^(3x−4)
Answer:
[tex]\huge\boxed{x=\dfrac{5}{4}}[/tex]
Step-by-step explanation:
[tex]\left(\dfrac{1}{2}\right)^{x-1}=2^{3x-4}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\\left(2^{-1}\right)^{x-1}=2^{3x-4}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{(-1)(x-1)}=2^{3x-4}\qquad\text{use the distributive property}:\ a(b+c)=ab+ac\\\\2^{(-1)(x)+(-1)(-1)}=2^{3x-4}\\\\2^{-x+1}=2^{3x-4}\iff-x+1=3x-4\qquad\text{subtract 1 from both sides}\\\\-x+1-1=3x-4-1\\\\-x=3x-5\qquad\text{subtract}\ 3x\ \text{from both sides}\\\\-x-3x=3x-3x-5\\\\-4x=-5\qquad\text{divide both sides by (-4)}[/tex]
[tex]\dfrac{-4x}{-4}=\dfrac{-5}{-4}\\\\x=\dfrac{5}{4}[/tex]
Solve the system by the substitution method.
X-2y=6
Y=2x-21
Answer:
Hey there!
We have two equations, x-2y=6, and y=2x-21.
Thus, we can substitute all y's in the first equation for 2x-21.
x-2(2x-21)=6
x-4x+42=6
-3x+42=6
-3x=-36
3x=36
x=12
y=2(12)-21
y=24-21
y=3
x=12, and y=3.
Hope this helps :)
Answer:
[tex]\boxed{x=12, y=3}[/tex]
Step-by-step explanation:
[tex]x-2y=6\\y=2x-21[/tex]
Plug y as 2x-21 in the first equation.
[tex]x-2(2x-21)=6\\x-4x+42=6\\-3x+42=6\\-3x=-36\\x=12[/tex]
Plug x as 12 in the second equation.
[tex]y=2(12)-21\\y=24-21\\y=3[/tex]
Suppose a car depreciates linearly the second you drive it off the lot. If you purchased the car for $31,500 and after 5 years the car is worth $20,500, find the slope of the depreciation line.
Answer: m = - 2200
Step-by-step explanation: Slope of a line is a number which describes the steepness and direction of a linear graph. It is represented by the letter m.
The year a car is bought and its price means:
f(0) = 31,500
Five years later, the price is $20,500, i.e.:
f(5) = 20,500
With these two pairs of value, slope is calculated as:
[tex]m = \frac{y-y_{0}}{x-x_{0}}[/tex]
[tex]m = \frac{20500-31500}{5-0}[/tex]
[tex]m = \frac{- 1100}{5}[/tex]
m = - 2200
The slope of the depreciation line is m = -2200 and it is negative because the line decreases along time.
A cubical container measures 9 ft on each edge. What does it cost to fill the container at $2.58 per cubic ft?
Answer:
1,880.82
Step-by-step explanation:
If the secant value is 37^ * , the cosine value to the hundredths degree is: A 0.80 B1.25 C0.60
Answer:
The value of the cosine function at 37º is 0.80. A. 0.80
Step-by-step explanation:
The correct statement is: "If the secant of 37º is 1.25, the cosine value to the hundredths degree is:"
Secant and cosine functions are related by the following trigonometric identity:
[tex]\sec 37^{\circ} = \frac{1}{\cos 37^{\circ}}[/tex]
[tex]\cos 37^{\circ} = \frac{1}{\sec 37^{\circ}}[/tex]
[tex]\cos 37^{\circ} =\frac{1}{1.25}[/tex]
[tex]\cos 37^{\circ} = 0.80[/tex]
The value of the cosine function at 37º is 0.80. The right answer is A.
Please answer this correctly without making mistakes
Simplify the correct answer
Answer:
[tex]\frac{109}{122}[/tex]
Step-by-step explanation:
Well first we need to find the total amount of Winter Olympic medals won.
550 + 540 + 130
= 1220
Now we need to find the amount won from the Western and Northern Europe.
550 + 540
= 1090
Now we can make the following fraction,
1090/1220
Simplify
= 109/122
Thus,
the answer is [tex]\frac{109}{122}[/tex].
Hope this helps :)
Hi there!! (✿◕‿◕)
⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐
Northern Europe: 550 medals
Western Europe: 540 medals
550 + 540 = 1,090
Northern Europe and Western Europe: 1,090
Other: 130
1,090 + 130 = 1,220
European Regions: 1,220 medals
1,090/1,220 = 109/122
Hope this helped!! ٩(◕‿◕｡)۶
please need help with this math question
Answer:
third option
Step-by-step explanation:
We just have to calculate 2x² - 4x - (x² + 6x). 2x² - x² = x² and -4x - 6x = -10x so the answer is x² - 10x.
Answer:
x^2-10x
Step-by-step explanation:
f(x)-g(x)
(2x^2-4x)-(x^2+6x)
carry through the negative
2x^2-4x-x^2-6x
x^2-10x
72 students choose to attend one of three after school activities: football, tennis or running.
There are 25 boys.
27 students choose football, of which 17 are girls.
18 students choose tennis.
24 girls choose running.
A student is selected at random.
What is the probability this student chose running?
Give your answer in its simplest form.
Answer:
P = 0,3749 or P = 37,49 %
Step-by-step explanation:
17 girls play football 10 boys do ⇒ 27 students
24 girls running 3 boys do ⇒ 27 students
then 6 girls play tennis and 12 boys do ⇒ 18 students
Probability of student running P is equal to P1 (probability of student (boy) running ) plus P2 (probability of student (girl) running )
P = P1 + P2
P1 (probability of girl running ) is equal to choose a girl out of 72 students, times the probability of the girl running
Probability of girl 47/72 = 0,6528
Probability of running is equal to 24/47 = 0,5106
Then the probability of girl running is equal to
P2 = 0,6528*0,5106 = 0,3333 or 33,33 %
P2 = 0,3333 or P2 = 33,33 %
Now we have 72 students 25 boys, then the probability of choosing a boy is = 25/72 = 0,3472
And the probability of running is 3/25 = 0,12
Then
P1 = 0,3472*0,12
P1 = 0,04166 and
P = P1 + P2
P = 0,04166 + 0,3333
P = 0,3749 or P = 37,49 %
How many times would a coin have to show heads in 50 tosses to have an experimental probability of 20% more than the theoretical probability of getting heads? Which of the following represents a function
Answer: The required number of heads = 30
Step-by-step explanation:
Given, Total tosses = 50
The theoretical probability of getting head = [tex]\dfrac{1}{2}[/tex]
As per given,
Experimental probability = Theoretical probability + 20% of Theoretical probability
= [tex]\dfrac{1}{2}+\dfrac{20}{100}\times\dfrac{1}{2}[/tex]
= [tex]\dfrac{1}{2}+\dfrac{1}{10}=0.5+0.1=0.6[/tex]
Required number of heads = (Experimental probability) x (Total tosses )
= 0.6 x 50
= 30
Hence, the required number of heads = 30
A relation is said to be a function if each input value corresponds to a unique output value.For example: {(1,2), (3,4), (2,3), (4,1))}
Answer:
35 is the Answer
A random sample of 61 Foreign Language movies made in the last 10 years has a mean length of 135.7 minutes with a standard deviation of 13.7 minutes. Construct a 95% confidence interval.
Answer:
95% confidensce interval of the mean (two-tail) = [132.2, 139.2]
Step-by-step explanation:
Given:
N = size of sample = 61
m = sample mean = 135.7
s = sample standard deviation 13.7
Need 95% confidence interval
Solution.
alpha (95% confidence interval) = 0.05
(1-alpha/2) = 0.975 [two sided]
Equation for confidence interval of the mean
= m +/- t(1-alpha/2,N-1) * s / sqrt(N)
= 135.7 +/- 2.0003 * 13.7 / sqrt(60)
= [132.16, 139.24]
What is the equation of the parabola with focus (1, -3) and directrix y = 2?
Answer:
(x-1)²=-10(y-0.5)
Step-by-step explanation:
Investment: Suppose you receive a gift of $1,000 and decide to open a CD (certificate of
deposit) as a low risk investment. The best CD rate you could find is 2.25%, which means that
your original investment will grow at a rate of 2.25% each year.
Assuming the rate of increase does not change, which of the following statements is TRUE
about your CD account balance?
It will no longer grow after several years.
It will triple in approximately 3 years.
O 4 years after the original investment, it is approximately $1,093.
O It will double in approximately 10 years.
Answer: 4 years after the original investment, it is approximately $1,093.
Step-by-step explanation:
Hi, to answer this question we have to apply the simple interest formula:
I = p x r x t
Where:
I = interest
P = Principal Amount
r = Interest Rate (decimal form)
t= years
Replacing with the values given
I = 1000x (2.25/100) x t
It will triple in approximately 3 years. FALSEI = 1000x (2.25/100) x 3 =67.5
1000+67.5 = 1067.5
It will no longer grow after several years: False, it will grow because it has a growth rate.4 years after the original investment, it is approximately $1,093. TRUEI = 1000x (2.25/100) x 4 =90
1000+90 = $1090
It will double in approximately 10 years.I = 1000x (2.25/100) x 10 =225
1000+90 = $1225
Feel free to ask for more if needed or if you did not understand something.
Which phrase best describes the graph of a proportional relationship?
A) a straight line passing
B) a straight line
C) a curve
D) not a straight line
Answer:
A. a straight line passing
Step-by-step explanation:
Answer:
a straight line passing
Step-by-step explanation:
xdy+ydx= ? (a) d(x+y) (b) d(x/y) (c) d(x-y) (d) d(xy)
Answer:
d) d(x)
Step-by-step explanation:
Derivative Rules
Product Rule xy -> d(xy) = xdy + ydxAn epidemiologist wishes to know what proportion of adults living in a large metropolitan area have subtype ayr hepatitis B virus. Determine the sample size that would be required to estimate the true proportion to within 3% margin of error with 95 percent confidence.
Answer:
Sample size 'n' = 1067
Step-by-step explanation:
Explanation:-
Given margin of error of the true proportion
M.E = 0.03
The margin of error is determined by
[tex]M.E =Z_{\alpha } \frac{\sqrt{p(1-p)} }{\sqrt{n} }[/tex]
Level of significance = 0.95
The critical value Z₀.₀₅ = 1.96
The margin of error is
[tex]0.03 =1.96 \frac{\sqrt{p(1-p)} }{\sqrt{n} }[/tex]
we know that
[tex]\sqrt{p(1-p} \leq \frac{1}{2}[/tex]
[tex]0.03 =\frac{1.96 X\frac{1}{2} }{\sqrt{n} }[/tex]
on cross multiplication , we get
√n = 32.66
Squaring on both sides, we get
n = 1066.6≅1067
Determine a differential equation that models the growth of a population of fish as a function of time in days under each of the following hypotheses:
a) The rate of population increase is proportional to the size of the population. The population increases by 2 percent per day. (Treat time in days as a continuous variable, i.e. the rate at which the population increases is .02 times the population size.) dP/dt =
b) The rate of population increase is again proportional to the size of the population with the same constant of proportionality but 4 percent of the population is harvested each day. dP/dt =
c) The rate of population increase is again proportional to the size of the population with the same constant of proportionality but 1000 fish are harvested each day. dP/dt =
d) The equation in part c) has a threshhold. What is it?
Step-by-step explanation:
a).
It is given that rate at which the population increases is directly proportional to size of the population. Thus we have,
[tex]\frac{dP}{dt}\propto P[/tex]
It is given in the question that the population increases by 2% in one day. Now we know that the time in days is a continuous variable, so we have
2% of P = [tex]$\frac{2}{100}\times P$[/tex]
[tex]$\therefore \frac{dP}{dt}=0.02 P $[/tex]
b).
It is given that the population is harvested by 4 % in one day
[tex]$\therefore \frac{dP}{dt} =0.02P-0.04P$[/tex]
(Since 4% of the P is harvested.)
[tex]$\therefore \frac{dP}{dt}=-0.02P$[/tex]
c).
It is given that 1000 fish are being harvested or removed in one day.
[tex]$\therefore \frac{dP}{dt}= 0.02 P-1000$[/tex]
d).
The threshold is given by
[tex]$0.02 P_{eq}-1000=0$[/tex]
[tex]$\therefore P_{eq}=\frac{1000}{0.02}$[/tex]
or [tex]$P_{eq}=5\times 10^4$[/tex]
Which equation shows a=bc^2+d solved for c
Answer:
[tex]\large \boxed{c=\pm \sqrt{\dfrac{a-d}{b}}}[/tex]
Step-by-step explanation:
Hello,
[tex]a=bc^2+d \\ \\ <=> a-d=bc^2+d-d=bc^2 \ \text{ subtract d }\\ \\ <=> c^2=\dfrac{a-d}{b} \ \text{ divide by b, assuming b is different from 0}\\ \\<=>\large \boxed{c=\pm \sqrt{\dfrac{a-d}{b}}} \ \ \text{ take the root of both parts}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Examine today’s stock listing for SFT Legal, shown below. 52 wk High 52 wk Low Symbol Div. Close Net Change 74.80 44.61 SFT 8.94 56.11 5.74 What was the price of SFT Legal yesterday? a. $47.17 b. $56.11 c. $50.37 d. $61.85
Answer:
c. $50.37
Step-by-step explanation:
Close price was $56.11 and net change was $5.74. so subtract the net change from the close to get yesterday's price.
Answer:
c.50.37
Step-by-step explanation:
The original price of a 2018 Honda Shadow to the dealer is $17,715, but the dealer will pay only $16,985 after rebate. If the dealer pays Honda within 15 days, there is a 2% cash discount.
Answer:
The final price to be paid after the 2% discount has been made will be $ 16,645.30.
Step-by-step explanation:
Since there is a 2% discount on the price of the Honda Shadow in the event that the dealer pays Honda within 15 days, and that after a rebate the price of the vehicle is $ 16,985, to obtain the value of the discount and the final amount to be paid must be calculated as follows:
16,985 x 2/100 = X
33,970 / 100 = X
339.70 = X
Thus, the discount to be made will be $ 339.70, with which the final price to be paid after the 2% discount has been made will be $ 16,645.30.
7. A large population of ALOHA users manages to generate 60 requests/s, including originals and retransmissions. Time is slotted in units of 50 ms. (Page 265 in the book may provide some help with this question.) (12 pts) a) What is the chance of success on the first attempt
Answer:
P(success at first attempt) = 0.1353
Step-by-step explanation:
This question follows poisson distribution. Thus, the formula is;
P(k) = (e^(-G) × (G)k)/k!
where;
G is number of frames generated in one frame transmission time(or frame slot time)
Let's find G.
To do this, we need to find number of frames generated in 1 slot time which is given as 50 ms.
Now, in 1000 ms, the number of frames generated = 50
Thus; number of frames generated in 50 ms is;
G = (50/1000) × 50
G = 2.5
To find the chance of success on the first attempt will be given by;
P(success at first attempt) = P(0) = e^(-G) = e^(-2) = 0.1353
What the answer now fast
sine(X) = opposite side / hypotenuse
sine(X) = (2√11) / (4√11)
sine(X) = (2/4)
sine(X) = 0.5
X = arcsine(0.5)
X = 30°
Answer: m∠x = 30°
Step-by-step explanation:
In a right triangle, if the short side of the right angle is Half the length of the hypotenuse, the triangle has angles of 30°, 60° and 90°
∠x is the smallest one, so m∠x = 30°
It is possible to figure the sine and get the angle from that, but in this case it might not be necessary. ;-)
Solve application problems using radical equations. A hang glider dropped his cell phone from a height of 450 feet. How many seconds did it take for the cell phone to reach the ground?
Answer:
[tex]\large \boxed{\text{5.29 s}}[/tex]
Step-by-step explanation:
The appropriate free fall equation is
y = v₀t + ½gt²
Data:
v₀ = 0
g = 32.17 ft·s⁻²
Calculation:
[tex]\begin{array}{rcl}450 &=& v_{0}t + \dfrac{1}{2}gt^{2}\\\\& = & 0 \times t + \dfrac{1}{2}\times 32.17t^{2}\\\\& = & 16.08t^2\\t^{2}& = & \dfrac{450}{16.08}\\\\& = & 27.97\\t & = & \textbf{5.29 s}\\\end{array}\\\text{It took $\large \boxed{\textbf{5.29 s}}$ for the phone to reach the ground.}[/tex]