A string of a kite is 100 meters long and it makes an angle of 60° with horizontal. Find the height of the kite and then find the ground distance from the kite to the person flying the kite,assuming that there is no slack in the string.
1. Draw a figure for the information given in the problems.
2. Using the correct trig function, write out the mathematical problem.
3. Solve the problem to find the missing sides.
Answers
Answer:
Height of the kite is [tex]=50 \sqrt{3}[/tex] meters.
Ground distance from the kite to the person flying the kite is 50 meters.
Step-by-step explanation:
Given that a string of a kite is 100 meters long and it makes an angle of 60° with horizontal.
Which mans we are getting a shape of right angle triangle as shown in picture. Where "y" is the height of the kite and "x" is the ground distance from the kite to the person flying the kite. Now we can use trigonometric ratios to find the values of x and y.
[tex]\sin\left(60^o\right)=\frac{\left[opposite\right]}{\left[hypotenuse\right]}=\frac{y}{100}[/tex]
[tex]\sin\left(60^o\right)=\frac{y}{100}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{y}{100}[/tex]
[tex]\frac{\sqrt{3}}{2}*100=y[/tex]
[tex]50 \sqrt{3}=y[/tex]
Hence height of the kite is [tex]=50 \sqrt{3}[/tex] meters.
similarly:
[tex]\cos\left(60^o\right)=\frac{\left[adjcent\right]}{\left[hypotenuse\right]}=\frac{x}{100}[/tex]
[tex]\cos\left(60^o\right)=\frac{x}{100}[/tex]
[tex]\frac{1}{2}=\frac{x}{100}[/tex]
[tex]\frac{1}{2}*100=x[/tex]
[tex]50=x[/tex]
Hence ground distance from the kite to the person flying the kite is 50 meters.
The height of the kite and the distance from kite to person are 86.6 meters and 50 meters respectively.
Using Trigonometry concept ;
The height of the kite , y can be obtained thus ;
Sine = opposite / HypotenusSin(60°) = y / 100
y = sin(60°) × 100
y = 86.6 meters
B.)
The distance from the kite to the person would be ;
Tangent = opposite / AdjacentTan(60) = 86.6667 / x
d = 86.6667 / Tan(60)
d = 50 meters
Therefore, the height of the kite and the distance from kite to person are 86.6 meters and 50 meters respectively.
Related Questions
Brian works 40 hours a week. He spends 40% of his time helping customers, 13% doing paperwork, and the remainder performing other store tasks. What percentage of Brian's time is spent on other store tasks?
Answers
40% helping customers + 13% doing paper work = 53% of his time.
This means 100% - 53% = 47% of his time he is doing other tasks.
When solving for x what would (8x-46) + (10x-8)
Answers
Answer:
18x - 54 :) :( :) :)Suppose f(x)=x2 Find the graph of f (x)+1
Answers
You would vertically shift the function up a unit, making it clear that the answer should be graph 3.
Use the image below, red is the original function, and blue is the new function.
What is the remainder when the polynomial f(x)=3x^3-4x^2+2x+8 is divided by (x-5)
Answers
Answer:
remainder = 290
Step-by-step explanation:
[tex]\frac{3x^3-4x^2+2x+8}{x-5}[/tex]
= 3x² + 11x + 57 + [tex]\frac{290}{x-5}[/tex]
quotient = 3x² + 11x + 57 and remainder = 290
I don’t understand all 3 of them
Answers
But maybe someone will know it later
solve and simplify, typing the final answer as a fraction 1/4 ÷ 3/8
Answers
[ Answer ]
2 / 3
[ Explanation ]
1 * 8 / 4 * 3
8 / 12
Simplify:
2 / 3
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What is the sum of 4a^2 − 7a − 5 and −8a^2 − 2a + 7?
Answers
[tex]{ - 4a}^{2} - 5a + 2 [/tex]
steps:
1. gather like terms
all terms with a squared are like, all terms with a are like, all constants are like
2. solve
Solve using substitution
x=2y-6
y= -3x+17
Answers
Answer:
(x, y) = (4, 5)
Step-by-step explanation:
given the 2 equations
x = 2y - 6 → (1)
y = - 3x + 17 → (2)
Either substitute x = 2y - 6 into (2) or y = - 3x + 17 into (1)
substituting y = - 3x + 17 into (1)
x = 2(- 3x + 17) - 6
x = - 6x + 34 - 6
x = - 6x + 28 ( add 6x to both sides )
7x = 28 ( divide both sides by 7 )
x = 4
substitute x = 4 into (2)
y = - 12 + 17 = 5
solution is (4, 5 )
you get to pick 8 of your 12 favorite songs to put on a cd . how many ways 8 songs be arranged from a choice of 12 songs
Answers
D-I are the measurements of the lengths of the sides of triangles. Identify the types of
triangles
d. 45 cm 61 cm 60 cm e. 30 cm, 31cm, 30 cm f. 4 cm, 5ft, 4 cm
g. 89mm, 89mm, 89mm h. 9 in, 5in, 3 in i. 22cm, 22cm, 22in
J-O are the measurements of the angles of triangles. Identify the type of triangle.
j. 900, 350, 550 k. 600, 600, 600 l. 700, 550, 550
m. 350, 400, 1000 n. 460, 460, 440 o. 1200, 300, 300,
Answers
Answer:
The sum of the interior angles of a triangle is 180 degrees.
d. Scalene
e. Isosceles
f. Isosceles
g. Equilateral
h. Scalene
i. Equilateral
j. Right
l. Acute
m. Obtuse - doesn't add to 180 not a triangle
n. Acute - doesn't add to 180 not a triangle
o. Obtuse
Step-by-step explanation:
The interior angles of a triangle add to 180 degrees. There are two ways we classify triangle by side lengths and angle measures.
Side lengths: Compare the side lengths and see if any are equal to determine the type.
Scalene: 3 different lengthsIsosceles: 2 equal lengths and 1 differentEquilateral : 3 equal sidesAngle Measures: Compare the angles measures to 90 degrees.
Right: If one angle is equal to 90Acute: All angles are less than 90 degreesObtuse: One angle is greater than 90 degreesa fruit stand has to decide what to charge for their produce. They need $10 for 4 apples and 4 oranges. They also need $12 for 6 apples and 6 oranges. We put information into a system of linear equations.
Answers
Answer:
X = apple
y = orange
4x + 4y = 10
6x + 6y = 12
Step-by-step explanation:
Answer:
4a+4r = 10
6a + 6r = 12
No solutions
Step-by-step explanation:
a = cost of the apple
r = cost of the orange
4a+4r = 10
6a + 6r = 12
Divide the first equation by 2 and the second equation by 6
2a+2r = 5
a +r = 2
Multiply the second equation by -2 so we can eliminate a
-2a -2r = -4
Add the first equation
2a+2r = 5
-2a -2r = -4
---------------------
0 = 1
This system is inconsistent and has no solutions
Linda received a $ 90 gift card for a coffee store. She used it in buying some coffee that cost $ 7.63 per pound. After buying the coffee, she had $ 51.85 left on her card. How many pounds of coffee did she buy?
Answers
Answer:
5 pounds
Step-by-step explanation:
:'>
Answer:
She bought 5 pounds of coffee.
Step-by-step explanation:
At the art fair, 95 artists exhibited their work. Of those 95 artists, 25 showed sculptures and 48 showed paintings. If 12 showed both sculptures and paintings, how many artists showed only sculptures or paintings?
Answers
To determine the number of artists who showed only sculptures or paintings at the art fair, we use the formula for the principle of inclusion-exclusion, resulting in 61 artists.
Explanation:To find out how many artists showed only sculptures or paintings at the art fair, we apply the principle of inclusion-exclusion. First, we add the number of artists who showed sculptures (25) to those who showed paintings (48), which gives us a total of 73 artists. However, this counts the 12 artists who showed both sculptures and paintings twice, so we subtract 12 from this total to correct for the double counting. Therefore, the number of artists who showed only sculptures or paintings is 73 - 12, which equals 61 artists.
Three snacks bars contain 1/5,0.22, and 19 percent of their Calories from fat. Which snack bar contains the least amount of calories from fat?
Answers
Answer:
19 percent
Step-by-step explanation: First we need to convert them all the a similar format. Fractions would be easiest.
.22 = 22/100
1/5 = 20/100
19% = 19/ 100
The one that contains the least is 19/100 or 19%.
At the beginning of the week Fayez writes down the mileage of his limo at 2529 at the end of the week the mileage is 2834, Fayez knows he used 75.2 litres of petrol during this week. The handbook states the limo uses 1 gallon of petrol for every 20 miles. Fayez wants to know if his limo uses 1 gallon of petrol for every 20 miles that week. 1 gallon = 4.54 litres . Did his limo use 1 gallon of petrol every 20miles that week. Show your answer clearly
Answers
Answer:
No. It used 1 gallon in 18.41 miles.
Step-by-step explanation:
He travelled 2834 - 2529 = 305 miles.
So his consumption is 305 / 75.2 = 4.056 miles/litre.
This equals 4.056*4.54 = 18.41 miles / gallon.
So this is less than the 1 gallon every 20 miles stated by the handbook.
Answer: His limo used 1 gallon fuel for 18.4136 miles.
Step-by-step explanation:
Fayez covered distance:
2834 - 2529 = 305 miles.
He used fuel = 75.2 litres
75.2/4.54 = 16.5638 gallons petrol used.
His limo covered distance / total petrol used = 305 miles / 16.5638 gallons petrol = 18.4136 miles per gallon.
That is less than 20 miles per gallon
Please answer with calculations
Answers
Answer:
Step-by-step explanation:
Given that a storage rack has dimensions as 25x12x5 ft.
Box has dimensions as 15x8x10 inches
Volume of each box = 15(8)(10) = 1200 inches = 1200x12^(-3) feet^3
Volume of 5000 boxes = 5000 (1200x12^(-3) ) = 3472.22 cubic feet
Volume of storage rack = 25(12)(5) = 1500 cubic feet
Volume of 25 storage racks 1500(25) = 37500 cubic feet.
SInce storage racks have sufficient volume it is concluded that enough storage is there.
Answer:
Yes, we have enough storage space.
Step-by-step explanation:
25 storage racks that are:
Length: Lsr = 25 ft = 25 ft (12 in / 1 ft) → Lsr = 300 in
Width: Wsr = 3 ft = 3 ft (12 in / 1 ft) → Wsr = 36 in
Height: Hsr = 12 ft = 12 ft (12 in / 1 ft) → Hsr = 144 in
5000 boxes 15x8x10 in
Length: Lb = 15 in
Width: Wb = 8 in
Height: Hb = 10 in
In the length of each storage rack we can put:
Nl=Lsr/Lb=300 in / 15 in → Nl = 20
In the width of each storage rack we can put:
Nw=Wsr/Wb=36 in / 8 in = 4.5 → Nw = 4
In the height of each storage rack we can put:
Nh=Hsr/Hb=144 in / 10 in = 14.4 → Nh = 14
Then we can put in each storage rack:
N = Nl Nw Nh = (20)(4)(14) → N=1,120 boxes
And we have 25 storage racks, then we can storage in total:
Nt=25N=25(1,120)→Nt=28,000 boxes
And we have 5,000 boxes, then we have enough storage space
There are 90 fith-grade students going on a feild trip. Each student gives the teacher $9.25 to cover admission to the theater and for lunch. Admission for all the students will cost $315, and each student will get an equal amount to spend on lunch. How much will each fifth grader get to spend on lunch?
Answers
Answer:
they each get $5.75 for lunch
Step-by-step explanation:
9.25 x 90 students = 832.50
832.50 -315 = 517.50
517.50 / 90 = 5.75
Divide (x^3-8x^2+17x-10)/(x-5)
Answers
Answer:
(x - 2)*(x - 1) is the answer
Step-by-step explanation:
We have to divide the polynomial f(x) = x^{3}-8x^{2}+17x-10 by (x-5).
Now, after dividing f(x) gets simplified into (x-5)*(x^{2}-3x+2).
So, we need to factorize the quadratic equation x^{2}-3x+2.
i.e. x^{2} - 3x + 2 = x^{2} - x - 2x + 2 = x(x-1) - 2(x-1) = (x - 2)*(x - 1)
Therefore, f(x) again gets simplified into (x-5)*(x - 2)*(x - 1)
Now eliminating the common factor (x-5).
We get, [tex]\frac{x^{3}-8x^{2}+17x-10}{x-5}[/tex] = (x - 2)*(x - 1)
Answer:
[tex]x^{2}-3x+2[/tex]
Step-by-step explanation:
Use synthetic division.
Reverse the sign of -5 and write the coefficients of the polynomial.Multiply the coefficient by the divisor, then add to the next coefficient.Continue through the last coefficient.5 | 1 -8 17 -10
+ 5 -15 10
1 -3 2 0
The quotient is [tex]x^{2} -3x+2[/tex].
How many batches of soup can Marcia make
Answers
Answer:
400 divided by 5 is how you get the answer.
Step-by-step explanation:
400 / 5 = 80
80 batches of soup.
jordan is chopping wood for the winter. for 10 days on a row he follows the same process: in the morning he chops 20 pieces of wood and in the evening he chops an additional 30 pieces of wood on the 11th day jordan chops only 5 pices of wood write a numerical expression with parentheses for the total number of pieces of wood jordan chopped. (do not simplify your expression)
Answers
[tex](20 + 30) \times 10 + 5[/tex]
I'm 90% sure that's right, sorry if I'm wrong :/
Will give brainliest please help ASAP
Answers
Answer:
D
Step-by-step explanation:
y>-3x+1 Negative slope
y<x+2 Positive slope
< or > have dotted line
< or > have a solid line
> or > means solutions are above the line
< or < means solutions are below the line
The one with negative slope has a dotted line and solutions above it.
The one with positive slope has a solid line and solutions below it.
Natasha is observing the growth of a population of bacteria. She started out with 250 bacteria cells. The population of bacteria quadruples every hour. Use x to represent the number of hours and y to represent the population of the bacteria. Enter an equation that represents this scenario in the box.
Answers
Answer:
[tex]y=250(5)^x[/tex]
Step-by-step explanation:
The growth of a population of bacteria can be represented by exponential growth function,
[tex]y=a(1+r)^x[/tex]
where,
y = the population of the bacteria after x hours,
x = the number of hours,
a = initial population of bacteria,
r = rate of growth,
At the beginning the number bacteria was 250 and the population of bacteria quadruples every hour i.e rate of growth is 400% or 4 per hour.
Putting all the values,
[tex]y=250(1+4)^x[/tex]
[tex]\Rightarrow y=250(5)^x[/tex]
Answer please ?!?!?!
Answers
Answer: -9
Step-by-step explanation: -91/6 ≈ -9.167
21/3 ≈ 2.33333
-17/8 ≈ -1.875
-9.167 + 2.3333 + -1.875 = -8.71
Rounded, the answer is -9.
You are making sets of pens and pencils to sell. You want each set to contain the same combination of pens and pencils. You have 28 pens and 80 pencils, and you want to use them all. What is the greatest number of these sets you can make?
Answers
The greatest number of sets of pens and pencils that can be made, using all of the given 28 pens and 80 pencils in each set, is 4. Each set would contain 7 pens and 20 pencils.
Explanation:In the problem, we are looking to find the Greatest Common Divisor (GCD), which is the greatest number that can evenly divide both the number of pens (28) and the number of pencils (80). The GCD between 28 and 80 is 4.
Thus, the most sets of pens and pencils you can make would be equal to the GCD, which in this case is 4.
This means you can put together 4 sets with an equal number of pens and pencils in each set. In each of these sets, there would be 7 pens (28 pens ÷ 4 sets) and 20 pencils (80 pencils ÷ 4 sets).
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Final answer:
To maximize the number of sets with 28 pens and 80 pencils, find the greatest common divisor and divide the total by it. You can create 27 sets of 4 pens and 10 pencils each.
Explanation:
To find the greatest number of sets you can make with 28 pens and 80 pencils, you need to determine the highest common factor of the two quantities.
Calculate the greatest common divisor (GCD) of 28 and 80, which is 4.
Divide the total number of pens and pencils by the GCD: (28 + 80) ÷ 4 = 27.
You can make 27 sets, each consisting of 4 pens and 10 pencils.
How do you solve for a²+b²=289 when b+a=23
Answers
Answer:
1 Use Product Rule: {x}^{a}{x}^{b}={x}^{a+b}x
a
x
b
=x
a+b
{a}^{2}+bb=289a
2
+bb=289
2 Use Product Rule: {x}^{a}{x}^{b}={x}^{a+b}x
a
x
b
=x
a+b
{a}^{2}+{b}^{2}=289a
2
+b
2
=289
3 Subtract {b}^{2}b
2
from both sides
{a}^{2}=289-{b}^{2}a
2
=289−b
2
4 Take the square root of both sides
a=\pm \sqrt{289-{b}^{2}}a=±√
289−b
2
5 Rewrite 289-{b}^{2}289−b
2
in the form {a}^{2}-{b}^{2}a
2
−b
2
, where a=17a=17 and b=bb=b
a=\pm \sqrt{{17}^{2}-{b}^{2}}a=±√
17
2
−b
2
6 Use Difference of Squares: {a}^{2}-{b}^{2}=(a+b)(a-b)a
2
−b
2
=(a+b)(a−b)
a=\pm \sqrt{(17+b)(17-b)}a=±√
(17+b)(17−b)
crate a list of steps, in order, that will solve the following equation. 2(x+3/4)^2 -5 =123
Answers
Answer:
x = -8.75; x = 7.25
Step-by-step explanation:
2(x + ¾)² - 5 = 123
Add 5 to each side: 2(x+ ¾)² = 128 Divide each side by 2: (x+ ¾)² = 64 Take the square root of each side: x + ¾ = 8 x + ¾ = -8 Subtract ¾ from each side: x = 8 - ¾ x = -8 - ¾ Convert to decimal fraction: x = 8 - 0.75 x = -8 – 0.75 Subtract: x = 7.25 x = -8.75The graph of your equation is a parabola with x-intercepts at x = -8.75
and x = 7.25.
The list of steps, in order, that will solve the equation is:
Addition of 5 to both sides to eliminate the value of -5Division of both sides of the equation by 2 to eliminate the coefficient of 2 from the left-hand sideTaking the square root of both sidessubtract 3/4 from each sideConvert the answer to decimalThe given expression is raised to a power of 2, so we can say that the given expression is a quadratic equation.
What is a quadratic equation?A quadratic equation is a form of an algebraic expression in which the variable is usually raised to the power of its second degree.
From the parameters given:
[tex]\mathbf{2(x + \dfrac{3}{4})^2 -5 = 123 }[/tex]
Addition of +5 to both sides[tex]\mathbf{2(x + \dfrac{3}{4})^2 -5 +5 = 123+5 }[/tex]
[tex]\mathbf{2(x + \dfrac{3}{4})^2 = 128}[/tex]
Division of both sides by 2[tex]\mathbf{\dfrac{2(x + \dfrac{3}{4})^2 }{2} =\dfrac{ 128}{2}}[/tex]
[tex]\mathbf{(x + \dfrac{3}{4})^2 = 64}[/tex]
Taking the square root of both sides[tex]\mathbf{\sqrt{(x + \dfrac{3}{4})^2} =\sqrt{ 64}}[/tex]
[tex]\mathbf{(x + \dfrac{3}{4})} =\pm8}[/tex]
Subtract 3/4 from both sides[tex]\mathbf{(x + \dfrac{3}{4} - \dfrac{3}{4}) }\mathbf{= \pm 8-\dfrac{3}{4}}[/tex]
[tex]\mathbf{x= \pm 8-\dfrac{3}{4}}[/tex]
[tex]\mathbf{x= +8-\dfrac{3}{4} \ \ OR \ \ x= -8-\dfrac{3}{4}} [/tex]
[tex]\mathbf{x=7.25 \ \ OR \ \ -8.75} [/tex]
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If quadrilateral ABCD is congruent to quadrilateral EFGH, then what corresponding side is congruent to side EF? (5 points)
Answers
Answer:
Side AB
Step-by-step explanation:
Draw two congruent quadrilaterals.
Label the sides of one A,B,C,and D.
Label the sides of the other E,F,G,and H
Because the sides match up with the order in which they appear in if they are congruent, The first two letters(E and F) should be equivalent to the first two letters of the other shape(A and B).
explain whether a quadratic function can have both a maximum value and a minimum value
Answers
A quadratic function can not have a maximum and minimum value. It can only take on one of those. The quadratic only makes one turn, so if the quadratic opens upwards, there is a minimum. If the quadratic opens downwards, there is a maximum.
A quadratic function can have either a maximum value or a minimum value, but not both.
Explanation:A quadratic function can have either a maximum value or a minimum value, but not both. Whether it has a maximum or minimum value depends on the coefficient of the quadratic term (a) in the function. If a is positive, the graph of the quadratic function opens upwards and has a minimum value. If a is negative, the graph opens downwards and has a maximum value.
For example, the function y = x² has a minimum value of 0 at the vertex of the parabola, while the function y = -x^2 has a maximum value of 0 at the vertex.
Therefore, a quadratic function cannot have both a maximum value and a minimum value.
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Two runners start 30 kilometers apart and run toward each other. They meet after 3 hours. One runner runs 2 kilometers per hour faster than the other runner. What rate do they run?
2 km/hr and 4 km/hr
3 km/hr and 5 km/hr
5 km/hr and 7 km/hr
4 km/hr and 6 km/hr
Answers
Answer: 4 km/hr and 6 km/hr
Step-by-step explanation:
A runner = 4km/hr
A runner covered distance after 3 hours = 12 km
B runner = 6km/hr
B runnet covered distance after 3 hours = 18 km
Total distance = 12 + 18 = 30km
i dont understand this help me :( What is the equation of a line with a slope of 3 and a point (3, 1) on the line?
Express the equation in the form of y=mx+b where m is the slope and b is the y-intercept.
Answers
[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{1})~\hspace{10em} slope = m\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-1=3(x-3) \\\\\\ y-1=3x-9\implies y=3x-8[/tex]