A kite on a 160-foot string is caught on a pole. When the full length of the string is stretched in a straight line to the ground, it touches the ground a distance of 50 feet from the bottom of the pole. The string forms an angle of _______° with the ground when it is stretched like this.
Answers
Answer:
String form an angle of 18.2° with the ground.
Step-by-step explanation:
Given: Length of the string of a kite = 160 ft.
Kite stuck on pole at height of = 50 ft.
We need to find: Measure of angle formed by string of kite with ground.
Attached figure showing the given situation.
let α be the required angle.
In ΔABC,
using trigonometric ratio,
[tex]sin\,\aplha=\frac{AB}{AC}[/tex]
[tex]sin\,\aplha=\frac{50}{160}[/tex]
[tex]sin\,\aplha=\frac{5}{16}[/tex]
[tex]sin\,\aplha=0.3125[/tex]
[tex]\aplha=sin^{-1}(0.3125)[/tex]
[tex]\alpha=18.20995686428301[/tex]
[tex]\alpha=18.21[/tex]
Therefore, String form an angle of 18.2° with the ground.
Related Questions
Marta processed and shipped 424 orders last year. She polled 128 of her customers, 99 of whom replied that they were completely satisfied with their orders.
To the nearest whole percent, the estimated population proportion of the customers who were completely satisfied was ___%
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77% is answer
Answer:
77%
Step-by-step explanation:
in each variety pack of fruit juice, there are 3 voxes of apple juice, 2 boxes of grape juice, and 1 box of orange juice. In a display in the store, there are 16 cases of juice with 8 variety packs in each case. How many boxes of juice are in the display?
Answers
The total number boxes of juice are 768 in the display.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
We have been given that in each variety pack of fruit juice, there are 3 voxes of apple juice, 2 boxes of grape juice, and 1 box of orange juice.
In a display in the store, there are 16 cases of juice with 8 variety packs in each case therefore,
Each variety pack of fruit juice = 3 + 2 + 1 = 6 juice
8 variety packs = 8 x 6 = 48
Now, the total number boxes of juice are in the display
16 x 48
= 768
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Bass - samples: the bass in clear lake have weights that are normally distributed with a mean of 2.1 pounds and a standard deviation of 0.9 pounds. (a) if you catch 3 random bass from clear lake, find the probability that the mean weight is less than 1.0 pound.
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1.825 x 10^-4 write the following number in stand form (decimal).
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Answer: .0001825
what is the inverse of the function below
Answers
Answer:
[tex]f^{-1}=4(x+2)[/tex]
Step-by-step explanation:
[tex]f(x)=\frac{x}{4} -2[/tex]
To find inverse function , replace f(x) with y
[tex]y=\frac{x}{4} -2[/tex]
Swap the variables x and y
[tex]x=\frac{y}{4} -2[/tex], nbw we solve for y
Add 2 on both sides
[tex]x+2=\frac{y}{4}[/tex]
Now to eliminate 4, we multiply 4 on both sides
[tex]y=4(x+2)[/tex]
Replace y with f^-1
[tex]f^{-1}=4(x+2)[/tex]
The sum of three numbers is 142. The first number is 8 less than the second. The third number is 4 times the second. What are the numbers?
Answers
x + y + z = 142
x = y - 8
z = 4y
y - 8 + y + 4y = 142
6y - 8 = 142
6y = 142 + 8
6y = 150
y = 150/6
y = 25 <=== the 2nd number
x = y - 8
x = 25 - 8
x = 17 <== the 1st number
z = 4y
z = 4(25)
z = 100 <=== 3rd number
Help please!! 20 points and brainliest!!
solve the system of linear equations. separate the x- and y- values with a coma. -9x+6y=-30
-12x+9y=-30
Answers
-9x+6y=-30
-12x+9y=-30
Although we might really want to say -9x+6y=-12x+9y, we can't do it that way. We have to get rid of a variable and go from there. Solving for y, we get
-9x+6y=-30
Divide both sides by 3
-3x+2y=-10
Add 3x to both sides
2y=-10+3x
Divide both sides by 2
y=(-10+3x)/2
-12x+9y=-30
Divide both sides by 3
-4x+3y=-10
Add 4x to both sides
-10+4x=3y
Divide both sides by 3
(-10+4x)/3=y
Since we have
(-10+4x)/3=y and y=(-10+3x)/2 , we have
(-10+4x)/3=(-10+3x)/2
Since 3*2=6, we can multiply both sides by 6
-20+8x=-30+9x
Add 30 to both sides
10+8x=9x
Subtract 8x from both sides
x=10
Plug that in to any equation,and you should have your answer! Good luck, and ask if you have any questions!
Makayla's local movie theater has a moviegoer club that charges an annual registration fee of 25 dollars.However, movie tickets are discounted for members at 6 dollars per ticket, instead of 9 dollars per ticket.Let m equal the number of movie tickets Makayla purchases in a year. Write a function to model the amount of money Makayla spent going too the movies during the year she joined the club. C(m)=6x+25 The domain is best represented by: A)integers B)whole numbers C)rational numbers D)real numbers Algebra chestercat
Answers
A large dinosaur was 89 feet long. Convert the length to meters. (Use 1 yd≈0.9144 m.)
Answers
1 foot = 0.305 meter
89 feet = 27.127 meters.
I really hope this helped you! c:
1 yd = 0.9144 m....so 29.67 yds = (29.67 * 0.9144) = 27.13 meters
how many liters of a 20% acid solution must be mixed with a 50% acid solution to obtain 12 liter of a 30% solution?
Answers
Let x = amount of 20% acid solution
Let y = amount of 50% acid solution.
The equation for the solution:
You want a total of 12 liters, so
x + y = 12
The equation for the acid:
The 20% solution has 20% acid, so in x liters of the 20% solution, you have 0.2x liters of acid.
The 50% solution has 50% acid, so in y liters of the 50% solution, you have 0.5y liters of acid.
The combined solution is 12 liters of 30% acid, so it has 30% * 12 liters of acid = 3.6 liters of acid.
0.2x + 0.5y = 3.6
Now you solve the two equations in a system of equations.
x + y = 12
0.2x + 0.5y = 3.6
Multiply the second equation by 10:
2x + 5y = 36
Multiply the first equation by -2:
-2x - 2y = -24
Add the last two equations:
3y = 12
y = 4
Substitute y = 4 in the first original equation:
x + y = 12
x + 4 = 12
x = 8
Answer: 8 liters of 20% solution and 4 liters of 50% solution.
Find all the second partial derivatives. v = e5xey
Answers
Final answer:
The second partial derivatives of v = e⁵x * ey are ∂²v/∂x² = 25e⁵x * ey and ∂²v/∂x² = 5e⁵x * e^y.
Explanation:
To find the second partial derivatives of the function v = e⁵x * ey, we need to differentiate twice with respect to x and y. Let's start with the first partial derivative with respect to x:
∂v/∂x = ∂(e⁵x * ey)/∂x
= 5e⁵x * ey
Next, we differentiate the first partial derivative with respect to x to find the second partial derivative with respect to x:
∂²v/∂x² = ∂(5e⁵x * ey)/∂x
= 25e⁵x * ey
Similarly, the second partial derivative with respect to y is:
∂²v/∂x² = ∂(5e⁵x * ey)/∂y
= 5e⁵x * e^y
David has $425 worth of items in his shopping cart. He receives a discount of 30% for the items at the checkout. If he then has to pay an 8% sales tax, what is the final amount that David paid?
Answers
he paid $321.30
If one million people have equal chances of being called by telephone from a broadcasting show, then the probability of one particular person receiving that call is .
Answers
1/1,000,000 or in decimals 0.000001 is the chance
Need help with this been trying to solve it
x/3ytimes3xy/5dividedby4y^2/5x^2
Fractions,
PLEASE HELP
Answers
[tex]\bf \cfrac{\frac{x}{3y}\cdot \frac{3xy}{5}}{\frac{4y^2}{5x^2}}\implies \cfrac{\quad \frac{3x^2y}{15y}\quad }{\frac{4y^2}{5x^2}}\implies \cfrac{3x^2y}{15y}\cdot \cfrac{5x^2}{4y^2}\implies \cfrac{\underline{15} x^4y}{\underline{15}\cdot 4y^3}\implies \cfrac{x^4y^1}{4y^3} \\\\\\ \cfrac{x^4}{4y^3y^{-1}}\implies \cfrac{x^4}{4y^{3-1}}\implies \cfrac{x^4}{4y^2}[/tex]
3(4x + 3) = 2x - 5(3 - x) + 2
Answers
Here are the steps:
Expand:
12x+9=7x-13
Subtract 9 from both sides:
12x+9-9=7x-13-9
Subtract 7x from both sides:
12x-7x=7x-22-7x
Simplify:
5x=-22
Divide both sides by 5:
5x/5=-22/5
Simplify:
x=-22/5
Thus, x=-22/5.
The solution to the given-equation represented by "3(4x + 6) = 9x + 12" is : (b) x = -2.
To find the solution to the equation 3(4x + 6) = 9x + 12, we simplify and solve for x,
First, we distribute the 3 to both terms,
12x + 18 = 9x + 12
Next, we separate variable-term by subtracting 9x from both sides:
12x - 9x + 18 = 9x - 9x + 12,
Simplifying further:
We get,
3x + 18 = 12,
Next, we separate "x" by subtracting 18 from both sides,
3x + 18 - 18 = 12 - 18,
3x = -6,
(3x) / 3 = (-6) / 3,
x = -2
Therefore, the correct answer is (b) x = -2.
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The given question is incomplete, the complete question is
What is the solution to the equation 3(4x + 6) = 9x + 12?
(a) x = 2,
(b) x = -2,
(c) x = 10,
(d) x = -10.
Jacob, Kylie, and Manuel each bought a sandwich and drink. The total bill to $21, and each drink cost $2. Of each sandwich cost the same amount, what is the cost of one sandwich?
Answers
Subtract 6 from both sides
15 = 3x
Divide 3 from both sides
x = 5
The price of each sandwich was $dollars.
Think of it, 5 + 5 + 5 = 15 (sandwiches)
15 + 2 + 2 + 2 = 21 (Drinks and the total sandwich amount)
Hope this makes sense, ask if you need more help! :)
The radius of a circle is increasing at a rate of 3 cm per minute. find the rate of change of the area when
Answers
A dress is sold for $980 plus 15% GCT. what is the total cost of the dress
Answers
Your friend has $100 when he goes to the fair. He spends $10 to enter the fair and $20 on food. Rides at the fair cost $2.00 per ride. Which function can be used to determine how much money he has left over after x rides?
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i hope that correct
A coral reef grows 0.13m every week. How much does it grow in 9 weeks?
Answers
An electrician has 4.1 meters of wire. How many strips 7/10 meters long can he cut?
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Every 23 hour, Harris can sew 16 pair of jeans. What is Harris's rate in pairs of jeans per hour?
Answers
rate = 2/3 pairs of jeans per hour
Solve -2 (x+5)=1/4(x-10)
Answers
-8(x+5)=x-10
-8x-40=x-10
-9x=30
x=-10/3
-10
x= ------
3
In a biology lab, a student has measured the lengths of 30 palmetto bugs in inches. he computes the mean and standard deviation as 4.1 inches and 1.2 inches, respectively. he later finds out that he was supposed to calculate the mean and standard deviation in centimeters instead of in inches. what is the new standard deviation of his sample, in centimeters? (note: 1 in = 2.54 cm)
Answers
Solution:
Mean = 4.1 inches x (2.54 cm/1 inch) = 10.41 cm
Standard deviation = 1.2 inches x (2.54 cm/1 inch) = 3.05 cm
ANSWERS: Mean = 10.41 cm; Standard Deviation = 3.05 cm
Consider the solid shaped like an ice cream cone that is bounded by the functions z=x2+y2‾‾‾‾‾‾‾√ and z=50−x2−y2‾‾‾‾‾‾‾‾‾‾‾‾√. set up an integral in polar coordinates to find the volume of this ice cream cone.
Answers
To calculate the volume of a solid bounded by two functions, set up an integral in polar coordinates. The volume is found by integrating the difference of the two volumes described by the functions (50 - sqrt(x²+y²) - sqrt(x²+y²)) over r, θ, and z within their appropriate limits.
Explanation:The subject of the question is mathematics, more specifically, integral calculus in spherical or polar coordinates. Calculating the volume of a solid bounded by two functions can be done by taking the difference of the two function volumes.
The integrals, using polar coordinates (r and θ), are set up as follows:
Volume = ∫∫∫(50 - sqrt(x²+y²) - sqrt(x²+y²)) r dr dθ dz,
where the limits for r are [0, sqrt(50)], for θ are [0, 2π], and for z are [0, 50]. Also, note that 'x²+y²' is replaced with 'r²' because in polar coordinates, 'r' represents the square root of x^2 plus y^2.
This integral, when solved, gives the volume of the ice cream cone-shaped solid.
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The volume of the ice cream shaped solid can be found by converting the limits of the cone to polar coordinates and performing a double integral. The limits of the cone are represented by the expressions z = r and z = sqrt(50 - r^2). The volume integral will be ∫ _(theta=0 to 2*pi) ∫ _(r=0 to sqrt(50)) [(sqrt(50 - r^2)) - r] r dr dθ.
Explanation:To evaluate the volume of the solid resembling an ice cream cone, we can use the method of double integration in polar coordinates. Because we're dealing with a cone, polar coordinates are suitable as they're related to circular symmetry.
The limits of the cone are given by the functions z = sqrt(x^2 + y^2) and z = sqrt(50 - x^2 - y^2). In polar coordinates these become z = r and z = sqrt(50 - r^2).
To evaluate the volume of the cone, we need to subtract the volume of the lower cone (given by z = r) from the volume of the upper cone (given by z = sqrt(50 - r^2)). We convert the values to polar coordinates and use double integration as follows:
V = ∫ _(theta=0 to 2*pi) ∫ _(r=0 to sqrt(50)) [(sqrt(50 - r^2)) - r] r dr dθ
This integral, once solved, will give the volume of the ice cream shaped solid.
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Approximate to pi 13.0909091
Answers
3.14159265359 x 4 = 12.5663706144
so 13.0909091 is not approximate to pi
Spence Ferris, a sales representative, drove 4 1/2 hours on the first day of his business trip, 8 3/4 hours on the second day, 6 2/3 hours on the third day, and 5 1/6 hours on the fourth day. If he must drive a total of 30 hours in five days, how much hours must Spence drive on the fifth day.
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360 miles driven on 12 gallons of fuel; 270 miles driven on 9 gallons of fuel. Use ratios or rates are equivalent. Explain your reasoning. Show all your work.
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Is (-2,5) a solution to the inequality y<-3x+4 show steps
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Estimate 615-342 please help me
Answers
615 rounds to 600
342 rounds to 300
Answer 900
620 - 340 = 280 (if you're rounding to the nearest tenth)