Savannah is flying a kite, holding her hands a distance of 2.5 feet above the ground
and letting all the kite's string play out. She measures the angle of elevation from her
hand to the kite to be 32. If the string from the kite to her hand is 75 feet long, how
many feet is the kite above the ground? Round your answer to the nearest tenth of a
foot if necessary.
Answer:
feet Submit Prowes
Z
Answers
Answer:
42.2 ft
Step-by-step explanation:
The given scenario can be modelled as a right triangle (see attached diagram), where the angle of elevation is 32°, and the length of the kite string (75 ft) is the hypotenuse.
We want to find the distance the kite is above the ground, so we want to find the side of the right triangle that is opposite the given angle. To do this, we can use the sine trigonometric ratio.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
Substituting θ = 32° and H = 75 into the ratio, we get:
[tex]\sin 32^{\circ}=\dfrac{\sf O}{75}[/tex]
[tex]\textsf{O}=75\sin 32^{\circ}[/tex]
[tex]\textsf{O}=39.7439448...\; \sf ft[/tex]
The angle of elevation is the angle between the horizontal plane and the line of sight from an observer to an object located at a higher position.
In this scenario, the angle of elevation is measured from Savannah's hand, which is a distance of 2.5 ft above the ground. Therefore, we need to add 2.5 ft to the value of O found using the sine ratio.
[tex]\implies 39.7439448...+2.5=42.2\; \sf ft\;(nearest\;tenth)[/tex]
Therefore, the kite is 42.2 ft above the ground (rounded to the nearest tenth).
Related Questions
Select the correct answer. The equations y = 1 2 x + 1 and y = 2 x + 4 are graphed on the coordinate grid. A nonlinear function starting from the line (minus 2, 0), and (0, 2) another line intercepts the x and y-axis (minus 2, 0), and (0, 1) How many real solutions does the equation 2 x + 4 = 1 2 x + 1 have? A. 0 B. 1 C. 2 D. cannot be determined from the graph
Answers
These lines y = 12x + 1 and y = 2x + 4 intersect at only one point, therefore, this system of equations has a unique solution and also one real solution.
What are the types of solutions in a system of equations?If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.
There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.
Given are two equations y = 12x + 1 and y = 2x + 4.
Now by graphing we conclude that these lines intersect at only one point, therefore, this system of equations has a unique solution and also one real solution.
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Eve is going to buy 30 pens from either shop A or shop B.
Shop A: pack of 10 pens for £2
Shop B: pack of 5 for £1.10 buy 1 pack and get 1 half price.
What is the difference in cost for all 30 pens between the two shops?
PLSS HELPPPP
Answers
The difference in the cost of all 30 pens between two shops is,
£1.05
Given, Eve is going to buy 30 pens from either shop A or shop B.
Shop A: pack of 10 pens for £2
Shop B: pack of 5 for £1.10 buy 1 pack and get 1 half price.
So, the cost of 30 pens from the shop A is,
as, a pack of 10 pens is of £2
1 pen = 2/10
30 pens = £6
Now, the cost of 30 pens from the shop B is,
as, a pack of 5 for £1.10
1 pen = 1.10/5 = £0.22
also buy 1 and get 1 at half price.
So, 2 pens = 0.22 + 0.11 = £0.33
Therefore, 30 pens = £4.95
So, the cost of 30 pens from shop A is £6 and from shop B is £4.95.
Hence, the difference in the cost of all 30 pens between two shops is,
£1.05
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Write an equation for a parabola with x-intercepts (-4,0) and (3,0) which passes through the point (2, -12).
Answers
Answer:
y = 2(x + 4)(x - 3)
Step-by-step explanation:
Knowing the x-intercepts, we can set up the equation:
y = (x + 4)(x - 3)
However, we are unaware of whether there is a dilation applied to it, so we input a point on the parabola. "a = dilation"
-12 = a(2 + 4)(2 - 3)
-12 = a(6)(-1)
-12 = -6a
2 = a
Now, we can write the equation for the parabola:
y = 2(x + 4)(x - 3)
Select the true statement about the following linear equation.
y= -2x + 4
The graph is a curve
The y-intercept is -2
The slope is -2
The slope is 2
Answers
The general form of a linear equation is slope m and y-intercept c is given as y = mx + c thus the slope of the line y = -2x + 4 is -2 so option (C) is correct.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given line,
y = -2x + 4
The general form of a linear equation is the slope(m) and y-intercept (c) is given as
y = mx + c
Compare,
m = -2 and c = 4
Slope = -2 and y-intercept = 4
Hence "The slope of the line y = -2x + 4 is -2 and y-intercept is 4".
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Calculate the standard score (z-score) of the given sample mean. Round your answer to two decimal places.
μ = 35 and o = 9; n = 60; x = 32
Answers
The standard score (z-score) of the given sample is -20.
Given,
[tex]u[/tex] = 35
[tex]o[/tex] = 9
n = 60
x = 32
To calculate standard score (z-score) use formula,
[tex]z=\frac{x-u}{\frac{o}{n} }\\\\z=\frac{32-35}{\frac{9}{60} }\\\\z=\frac{-3}{0.15}\\ \\z=-20[/tex]
Thus, the standard score(z-score) of given sample mean is -20.
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explain how the value of a digit changes if the digit moves one place to the right or left.
Answers
When talking about a number line, the farther right the digit moves, the large the number. The farther left it goes, the smaller the number.
For example, 81 would be to the right of 80. And 79 would be on the left. The larger the negative number, the smaller it is. So -70 is smaller than -20.
I hope this helps!
Two students share 8 markers equally enter the numerical expressions in he box that models the situation
Answers
Answer: 8÷2 or 8/2 and also just in case, the answer is 4
Step-by-step explanation: Ok, 8 markers split equally between 2 students, this means that for each marker that student one takes, student two also takes one. they repeat this until there are no more markers left. This ends up with the two students each having four markers. Now, what is 8 divided by 2? Why yes, the answer is 4, just like the word problems answer. So the word problem "Two students share 8 markers equally" translates to 8÷2.
Hope this helps!
12²+6² ÷2 =
please help me
Answers
Answer:
162
Step-by-step explanation:
12²+6² ÷ 2
= 144 + 36 ÷ 2
= 144 + 18
= 162
Work out M and C for the line:
Y=2x+5
M= C=
Answers
In the given equation we get the following values:
M = 2
C = 5
Given, we have the equation:
Y = 2x + 5
we are asked to determine the following values of m and c.
The given equation is in the form of slope intercept form.
slope intercept form is given as:
y = mx+c
hence :
M = 2 and
C = 5
One of the most popular ways to represent a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis).
The slope intercept form is a technique for figuring out a straight line's equation in the coordinate plane. This relationship will be the equation of a straight line:
the line must satisfy the coordinates of every point along it.Any location that is not on the line will not satisfyhence we get the required values.
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Ed and Flo share money in
the ratio 3:5. Flo gets £40
more than Ed. How much
money was shared in total?
Answers
5x - 3x = 2x
2x = 40
x = 20
x * 8 = 160
Which of the following expressions contains only 1 constant? Select TWO that apply.
A 18+5r³
B
C.
90(h - 4)
766
D. 41y-8y + 7y
Answers
The expressions which have only one constant are:
A. 18+5r³
B. 90(h-4)
Given: we have a set of equations.
an equation is a combination of variables and constants.
In the given set of equations we have a single variable with a single constant.
those are:
→ 18+5r³
→ 90(h-4)
In the other equations we don't have constants.
A constant is defined as an object whose value is fixed regardless of changes in its usage.
Even after the expression is changed, these values stay the same.
Natural numbers, whole numbers, real numbers, integers, and decimal numbers are examples of constants in mathematics.
A variable is a thing whose value changes depending on how it's used and isn't fixed.
Hence we get the required answer.
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In 1965, the population of a certain town was 2010. In 1995, the population was 3620. If the population during this time period grew according to an exponential model, what will the population be in 2050?
Answers
According to the growth function, the population be in 2050 will be 10,635
Growth function:
The growth function refers the pattern of data that shows greater increases with passing time, creating the curve of an exponential function.
Given,
In 1965, the population of a certain town was 2010. In 1995, the population was 3620.
Here we need to find the population in 2050.
While we looking into the given problem, let us consider,
P refers the final population
A refers the the starting population, and
x refers the time passed
Now, we need to determine the value of the growth factor n and it can be calculated using the information for the years 1965 and 2010.
Here we know that, in 1965, the population of a certain town was 2010. In 1995, the population was 3620.
And the value of x is 30
So, it can be written as,
=> 3620 = 2010eⁿˣ³⁰
=> 3620/2010 = e³⁰ⁿ
=> 362/201 = e³⁰ⁿ
Here by applying ln to both sides of the equation:
⇒ln(362/201) = ln(e³⁰ⁿ)
By, using the laws of logarithms:
=> 30n = ln(362) - ln(201)
=> n = [ln(362) - ln(201)] / 30
=> n = 0.0196
Here we have to use this information to determine P in 2050.
Here the value of A will still be 2010, but x will be 85 years.
Here we have to apply these values then we get,
=> P = 2010e⁰°⁰¹⁹⁶ˣ⁸⁵
=> P = 2010e¹°⁶⁶⁶
=> P = 2010 x 5.2909
=> P = 10635
Therefore, there are 10635 in 2050.
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Solve the equation by using the square root property. Express all radicals in simplest form.
k²=17
Answers
The simplest form of radicals is [tex]k \ \epsilon \ \{17^{\frac{1}{2}} ,-17^{\frac{1}{2} } \}[/tex]
What is a radical expression?
An nth root of a number x is a number r that, when multiplied by n, equals x, where n is a positive integer, also known as the degree of the root. Degree 3 roots are referred to as cube roots, while degree 2 roots are known as square roots.
We have,
k² = 17
The variable in this non-linear equation needs to be separated. This is achieved by exponentiating both sides by the reciprocal of the exponent of the variable, which in our example is equal to 1/2.
[tex](k^{2} )^{\frac{1}{2} } = 17^{\frac{1}{2} }[/tex]
[tex](k^{2} )^{\frac{1}{2} } = -17^{\frac{1}{2} }[/tex]
[tex]k= 17^{\frac{1}{2} }[/tex]
[tex]k = -17^{\frac{1}{2} }[/tex]
Hence, the simplest form of radicals is [tex]k \ \epsilon \ \{17^{\frac{1}{2}} ,-17^{\frac{1}{2} } \}[/tex]
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Write an slope equation form of the equation of the line through the given points
through: (0, -3) and (-5, 4)
Answers
The slope equation form is :
m = - 7/5
Slope Solution
To calculate the slope use the slope formula.
m = (y2- y1)/(x2- x1)
Where (x1,y1) and (x2,y2) are 2 coordinate points.
Here the 2 points are (0,-3) and (-5,4)
let (x1,y1) = (0,-3) and (x2,y2) = (-5,4)
m = (4 - (-3))/((-5) - 0)
m = 7/((-5) )
m = - 7/5
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. You lean a 16 foot ladder against the wall. If the base is 4 feet from the wall, what angle does
the ladder make with the ground? Round your answer to the nearest tenth.
Answers
Check the picture below.
[tex]cos(\theta )=\cfrac{\stackrel{adjacent}{4}}{\underset{hypotenuse}{16}}\implies cos(\theta )=\cfrac{1}{4}\implies \theta =cos^{-1}\left( \cfrac{1}{4} \right)\implies \theta \approx 75.5^o[/tex]
Make sure your calculator is in Degree mode.
A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days: f(d) = 11(1.01)°
Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm.
What is a reasonable domain tc plot the growth function?
(4 points)
Part B: What does the y-intercept of the graph of the function f(c) represent? (2 points)
Part C: What is the average rate of change of the function f(d) from d = 2 to d = 7, and what does it represent? (4 points)
Answers
Answer:
Step-by-step explanation:
a.
f(d)=11(1.01^d
d=6.97 days
b.
t
f(c) represents the size of algae after c days
c.
f(2)=11(1.01)^2
f(7)=11(1.01)^7
[tex]rate=\frac{f(7)-f(2)}{7-2} \\=\frac{11(1.01)^7-11(1.01)^2}{5} \\=\frac{11[(1.01)^7-(1.01)^2]}{5} \\\approx 0.0104 ~mm[/tex]
An applicant receives a job offer from two different companies. Offer A is a starting salary of $55,000 and 5% increase for 5 years. Offer B is a starting salary of
$56,000 and an increase of $2,000 per year.
Part A: Determine whether offer A can be represented by an arithmetic or geometric series and write the equation lor A, that represents the total salary received after
n years. Justity your reasoning mathematically. (3 points)
Part B: Determine whether offer B can be represented by an arithmetic or geometric series and write the equation for B, that represents the total: salary received
after n years. Justity your reasoning mathematically. (3 points)
Part C: Which offer will provide a greater total income after years? Show all necessary math work. (4 points)
Answers
After 5 years, Offer A will offer a higher total salary.
What is arithmetic mean?The result of adding together and dividing by the total number of numbers or variables is the arithmetic mean, which is also known as the average or average value.
What is geometric mean?The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers. In essence, we multiply the numbers together and calculate their nth root, where n is the total number of data values.
Given
a) that a candidate receives job offers from two different companies, with Offer A offering a starting salary of $ 55,000 and a 5% increase for 5 years and Offer B offering a starting salary of $ 56,000 and an increase of $ 2,000 per year, it is necessary to perform the following calculation to determine which offer will result in a higher total income after 5 years:
b) Offer A -> Arithmetic
=>55000 x 1.05 ^ 5 = X
=>55000 x 1.2762 = X
70,195.48 = X
Offer B -> Geometric
=>56000 + (5 x 2000) = X
=>56000 + 10000 = X
66,000 = X
c) Hence comparing the above 2, Offer A will provide a greater total income after 5 years.
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A package contains 12 electrical locks, each with a unique key. A package is delivered to 16 job site superintendents. How many unique keys will result from the distribution
Answers
Using the multiplication, 192 unique keys will result from the distribution.
In the given question we have to find the number of unique keys will result from the distribution.
As given that a package contains 12 electrical locks, each with a unique key. A package is delivered to 16 job site superintendents.
So 1 package have 12 electrical locks with a unique key.
Package delivered to 16 job site.
We can find the total number of unique keys y multiplying the total number of electrical locks with a unique key in a pckage to the total number of site of package delivery.
So total keys=12×16
Total keys=192
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Which statement about the ordered pairs (-9, 3) and (2, 4) is true for the equation 6x = 14?
(-9, 3) is a solution to the equation. O Both ordered pairs are solutions.
O Neither ordered pair is a solution.
(2, 4) is a solution to the equation.
Answers
The correct statement will be "Neither ordered pair is a solution".
What are ordered pairs?
An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.In order to understand a point visually, it can be helpful to position it on the Cartesian plane.An ordered pair's numerical values may be fractions or integers.Ordered Pair is equal to (x,y), where x is the distance between a point and the principal axis (x).Additionally, y = ordinate measures how far a point is from the secondary axis "y."Given equation is: 6x = 14
For ordered pair (-9, 3) , the values of x=-9 and y=3
Plugging these values into the given equation
6(-9) = 14
-54 = 14 (False)
Now for ordered pair (2, -4) , the values of x=2 and y=-4
Plugging these values into the given equation
6(2) = 14
12 = 14 (False)
The correct statement will be "Neither ordered pair is a solution".
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The graph below represents the paths of a squirrel traveling up and down a tree over time. The position of the squirrel can be calculated using the function p(t)=at^2+bt+c. What is the value of a? What is the value of b? What is the value of c?
Answers
The values of the variables a, b and c are; a = 5/19, b = -160/19, c = 960/19
How to interpret Quadratic graphs?
We are given the quadratic function formula as;
p(t) = at² + bt + c
Thus, the equation is now;
p(t) = at² + bt + 0
p(t) = at² + bt
From the graph, we see that when x = 8, y = 0. Thus;
p(8) = a(8²) + 8b + c = 0
64a + 8b + c = 0 ------(1)
From the graph, we know that the axis of symmetry is;
x = -b/2a
Thus;
16 = -b/2a
b = -32a -----(2)
From the graph, we see that when x = 5, y = 15. Thus;
p(8) = a(5²) + 5b + c = 0
25a + 5b + c = 15 ------(3)
Put -32a for b in eq 1 and 3 to get;
64a + 8(-32a) + c = 0
-192a + c = 0 ------(4)
25a + 5(-32a) + c = 15
-135a + c = 15 ------(5)
Subtract eq 4 from eq 5 to get;
192a - 135a = 15
57a = 15
a = 15/57
a = 5/19
Thus;
b = -32(5/19) = -160/19
-135(5/19) + c = 15
15 + (675/19) = c
c = 960/19
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Simplify: (A + C)(AD + AD) + AC + C
Answers
Answer:
It looks just fine! Well done!
It looks just fine! Well done!A bit more simply,
It looks just fine! Well done!A bit more simply,(A+C)(AD+AD)+AC+C=(A+C)AD+AC+C=AAD+CAD+AC+C=AD+(AD+A+1)C=AD+C
Step-by-step explanation:
Hope this helped
Out of 5,000 students 1,000 preferred diet drinks over sugared sodas. What percent preferred non diet drinks?
Answers
what expression is equivalent to 3x+3(x+y)
Answers
Answer:
6x + 3y
Step-by-step explanation:
Distribute:
=3x + (3)(x) + (3)(y)
=3x + 3x + 3y
Combine Like Terms:=3x + 3x +3y
=(3x + 3x) + (3y)
=6x + 3y
Answer:
I do not see the choices. There could be more than one right answer
6x + 3y
Step-by-step explanation:
3x + 3(x+y)
3x + 3x + 3y
6x + 3y
Simplify x^2-4/x^2+2
Answers
Answer:x^4+6
Step-by-step explanation:
you must combined both x squared to get x^4 and then add the opposite of -4 Which is +4 and what you do to one side you must do to the other therefore you add the 2 to it as well. in conclusion you get x^4+6. hope this helps:)
A toaster oven usually sells for $60. If the toaster oven is 20% off, and sales tax is 7%, what is the total price of the toaster oven, including tax?
Answers
Work:
About 65% of American teenagers wear orthodontal corrective devices..
In Heritage High School, there are about 1,800 teenagers. How many of them would you expect to have corrective devices?
Answers
Answer:
1170 teenagers would have corrective devices
Step-by-step explanation:
hope this helps :)
A 40-foot rope is cut into 2 pieces. Seven less than four times the length of the longer rope piece x is five times the length of the shorter piece, which is (40 − x) ft. Find the length of the longer rope piece x (in ft). (Enter an exact number.)
Answers
If a 40-foot rope is cut into 2 pieces. the length of the longer rope piece x is 23ft.
How to find the length?Seven less than 4 times = 4x-7
4x-7=5(40-x)
4x-7=200-5x
Collect like terms
9x=207
Divide both side by 9x
x = 207 /9
x=23 ft (longer part of the rope)
Shorter part of the rope
40-x where x is 23
40 -23
= 17ft
Therefore the longer part is 23ft.
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Determine whether (-9,-5) is a solution of 9x + 4y = 10.
...
Answers
Answer:
It is not a solution
Step-by-step explanation:
put in (-9,-5) in for x and y
9(-9)+4(-5)=10
-81-20=10
-101=10
This is false so (-9,-5) is not a solution to the equation 9x+4y=10
I need help fast please!
The time it takes to cover the distance between two cities by car varies inversely with the speed of the car.
The trip takes 7 hours for a car moving at 36 mph.
What is the speed of a car that makes the trip in 9 hours?
Answers
Answer:
28 mph
Step-by-step explanation:
Given that a car moving 36 mph takes 7 hours for a trip, you want to know the speed if the trip takes 9 hours.
Time and SpeedThe speed and time vary inversely for the same distance. If the time goes up by a factor of 9/7, the speed will go down by the inverse factor: 7/9.
7/9 × 36 mph = 28 mph
The speed of the car is 28 mph for the 9-hour trip.
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Logic
Consider the following statements:
Alex's bag is heavier than Hisham's bag
Hisham's bag is lighter than both Aya's bag
and Irene's bag
Aya's bag is heavier than Alex's bag and
Irene's bag
Whose bag is the heaviest?
Aya
Answers
In given order puzzle Aya's bag is the heaviest bag .
What is order puzzle?
A puzzle is a thing that is difficult to understand or explain. The term also refers to a game, toy, or problem designed to test ingenuity or knowledge. Math puzzles are problems that require mathematical logic and calculation. These types of puzzles carry recreational as well as educational value for the pupils.
Here the given statements ,
=> Alex bag > Hisham bag
And Hisham bag < Aya bag and Irene bag
Now ,
=> Aya bag > Alex bag and Irene bag
Then combine the given ,
=> Aya bag> Alex bag>Irene bag>Hisham bag.
Therefore Aya's bag is the heaviest bag.
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