PLEASE HURRY!! WILL GIVE BRAINLIEST
In the space below, use the law of sines or trigonometric ratios to find each length. Round your answer to 1 decimal place. (4 points total: 1 point each)
a. The length of the zip line, z
b. The height of the point on the tree where the top of the ladder rests against it, h
c. The distance between the base of the ladder and the base of the tree, b
d. The distance between the base of the tree and the spot where the zip line is anchored to the ground, B
Answers
Trigonometric ratios are useful in calculating the side lengths of a triangle.
The length of the zip line is 222.5 ftThe height where the ladder rests against the tree is 38.6 ftThe distance between the base of the ladder and that of the tree is 10.4 ftThe distance between the base of the tree and the spot where the zip line is anchored to the ground is 219.1 ft(a) Length, z
First we calculate (h) using the following sine ratio
[tex]\mathbf{sin(75) = \frac{h}{40}}[/tex]
Make h the subject
[tex]\mathbf{h = 40sin(75)}[/tex]
Next, we calculate (z) using the following sine ratio
[tex]\mathbf{sin(10)= \frac{h}{z}}[/tex]
Make z the subject
[tex]\mathbf{z= \frac{h}{sin(10)}}[/tex]
Substitute [tex]\mathbf{h = 40sin(75)}[/tex]
[tex]\mathbf{z= \frac{40sin(75)}{sin(10)}}[/tex]
[tex]\mathbf{z= 222.5 ft}[/tex]
Hence, the length of the zip line is 222.5 ft
(b) The height, h
In (a), we have
[tex]\mathbf{h = 40sin(75)}[/tex]
Evaluate
[tex]\mathbf{h = 38.6}[/tex]
Hence, the height where the ladder rests against the tree is 38.6 ft
(c) The distance, b
To do this, we make use of the following sine ratio
[tex]\mathbf{sin(15) = \frac{b}{40}}[/tex]
Make b the subject
[tex]\mathbf{b = 40sin(15)}[/tex]
[tex]\mathbf{b = 10.4}[/tex]
Hence, the distance between the base of the ladder and that of the tree is 10.4 ft
(d) Distance, B
To do this, we make use of the following sine ratio
[tex]\mathbf{sin(80) = \frac{B}{z}}[/tex]
Make B the subject
[tex]\mathbf{B = z\ sin(80)}[/tex]
Substitute [tex]\mathbf{z= 222.5 ft}[/tex]
[tex]\mathbf{B = 222.5\ sin(80)}[/tex]
[tex]\mathbf{B = 219.1}[/tex]
Hence, the distance between the base of the tree and the spot where the zip line is anchored to the ground is 219.1 ft
Read more about trigonometry ratios at:
https://brainly.com/question/24888715
The length of the zip line is 139.1 ft
The height where the ladder rests against the tree is 24.1 ft
The distance between the base of the ladder and that of the tree is 6.5 ft
The distance between the base of the tree and the spot where the zip line is anchored to the ground is 137.0 ft
(a) Length, z
First we calculate (h) using the following sine ratio
Sin(75)=h/25
Make h the subject
h=25sin(75)
Next, we calculate (z) using the following sine ratio
Sin(10)=h/z
Make z the subject
z=h/sin(10)
Substitute
h=25sin(75)
z= 25sin(75)/sin(10)
z=139.1 ft
Hence, the length of the zip line is 139.1 ft
(b) The height, h
In (a), we have
h=25sin(75)
Evaluate
h=24.1 ft
Hence, the height where the ladder rests against the tree is 24.1 ft
(c) The distance, b
To do this, we make use of the following sine ratio
sin(15)=b/40
Make b the subject
b=25sin(15)
b= 6.5 ft
Hence, the distance between the base of the ladder and that of the tree is 6.5 ft
(d) Distance, B
To do this, we make use of the following sine ratio
sin(80)=B/z
Make B the subject
B=z sin(80)
Substitute
z=139.1 ft
B=139.1 sin(80)
B=137.0 ft
Hence, the distance between the base of the tree and the spot where the zip line is anchored to the ground is 137.0 ft
Credit to the person above me for the format <3
Related Questions
The area of a rectangle is x^2-4/2x in.2, and its length is (x + 2)2/2 in. Find the width.
Answers
Step-by-step explanation:
the area (length × width) is
A = (x² - 4)/2x in² = (x + 2)(x - 2)/2x
length = (x + 2)²/2 = (x + 2)(x + 2)/2
width = A/length = 2(x+2)(x-2) / 2x(x+2)(x+2) =
= (x-2)/x(x+2) = (x-2)/(x²+2x)
One student solved the inequality -4 > x/-7 and got 28 < x. Another student solved the inequality and got x > 28. Are they both correct? Explain.
Answers
Answer: solutions are the same, just written differently, inequality sign is reversed when multiplying. Yes, both students are correct. When multiplying by –7, the inequality symbol+ is reversed. The answers are the same, just written differently.
Step-by-step explanation: Happy to Help. Brainliest Please
A boat sails directly toward a 250-m skyscraper that stands on the
edge of a harbor. The angular size of the building is the angle
formed by lines from the top and bottom of the building to the
observer (see figure). Complete parts (a) and (b) below.
Answers
a) The value of [tex]\theta[/tex] as a function of "x" is [tex]\theta = tan^{-1}\frac{250}{x}[/tex]
b) The rate of change of the angle with respect to x is -0.000308rad/m
Find the complete question and diagram attached
Form the right-angled triangle shown:
Adjacent side = x
Opposite side = 250m
angle of elevation = [tex]\theta[/tex]
Using the SOH CAH TOA identity
[tex]tan\theta = \frac{opposite}{hypotenuse} \\tan \theta = \frac{250}{x} \\\theta = tan^{-1}\frac{250}{x}[/tex]
Hence the value of [tex]\theta[/tex] as a function of "x" is [tex]\theta = tan^{-1}\frac{250}{x}[/tex]
b) If x = 450m
[tex]\theta = tan^{-1}\frac{250}{x}\\tan \theta = \frac{250}{x}\\[/tex]
Differentiate both sides with respect to "x"
[tex]sec^2 \theta \frac{d\theta}{dx} = \frac{-250}{x^2} \\ \frac{d\theta}{dx} = \frac{1}{sec^2\theta} \times \frac{-250}{x^2}[/tex]
Substitute x = 450m and [tex]\theta = 60^0[/tex] into the resulting expression to have:
[tex]\frac{d\theta}{dx} = \frac{1}{sec^260^0} \times \frac{-250}{450^2}\\\frac{d\theta}{dx} = (cos60)^2\times \frac{-250}{202,500}\\\frac{d\theta}{dx} = 0.5^2\times \frac{-250}{202,500}\\\frac{d\theta}{dx} =-0.000308[/tex]
Hence the rate of change of the angle with respect to x is -0.000308rad/m
Learn more here: https://brainly.com/question/15580615
What is the distance between the points (7, 8) and (-8, 0) on a coordinate grid?
Answers
Answer:
17 units
Step-by-step explanation:
Answer:
17
Step-by-step explanation:
The function g(x) = 8|x – 15| - 30 is a transformation of the parent function p(x) = x. Which of the following correctly describes the transformation of function p that generates function g?
A p is translated 30 units down, then has a vertical shrink by a factor of 8, and then is translated 15 units right.
B. p has a vertical shrink by a factor of 8, then is translated 15 units down, and then is translated 30 units left
c. p is translated 15 units left, then has a vertical stretch by a factor of 8, and then is translated 30 units up.
D. p is translated 15 units right, then has a vertical stretch by a factor of 8, and then is translated 30 units down.
Answers
Using translation concepts, it is found that the correct option, which represents the transformation made to function [tex]g(x) = 8|x - 15| - 30[/tex], is given by:
D. p is translated 15 units right, then has a vertical stretch by a factor of 8, and then is translated 30 units down.
The parent function is:
[tex]p(x) = |x|[/tex]
The first transformation was [tex]x \rightarrow x - 15[/tex], which means that it was shifted 15 units to the right.
Then, the function was multiplied by 8, which means that it was stretched vertically by a factor of 8.
Finally, 30 was subtracted from the function, which means that it was shifted down 30 units.
Hence, the correct option is given by:
D. p is translated 15 units right, then has a vertical stretch by a factor of 8, and then is translated 30 units down.
A similar problem is given at https://brainly.com/question/18405655
(0,3) and (2,4) are on the line
Answers
The slope can be found by dividing y(2) - y(1) by x(2) - x(1).
4 - 3 = 1
2 - 0 = 2
m = 1/2
Since the first point has an x-coordinate of 0, the y-coordinate is the y-intercept of the line.
b = 3
Equation: y = 1/2x + 3
Two particles are projected simultaneously towards each other from opposite ends of a straight horizontal tube. One particle travels 97 cm in the 1st 2 seconds, 93 cm in next 2 seconds , 89 cm in another next 2 seconds, etc. The other particle travels 49 cm in the 1st 2 seconds, 47 cm in the next 2 seconds , 45 cm in another next 2 seconds, etc. Find how long it takes for the particles to meet and hence, determine the distances travelled by each particle.
Answers
This shows that it will take the particle 23 secs to meet.
The distance travelled by each particle is 50cm
If two particles are projected simultaneously towards each other from opposite ends of a straight horizontal tube,
The first particle distances are 97cm, 93cm, 89cm... every 2secs
This form an arithmetic sequence and the nth term is expressed as:
Tn = a + (n - 1)d
a is the first term = 97
d is the common difference = 4
Substitute
Tn = 97+(n - 1)(4)
Tn = 97 + 4n -4
Tn = 4n + 93
Similarly for the distances 49 cm, 47 cm, 45cm .....
This also forms an arithmetic sequence and the nth term is expressed as:
Tn = a + (n - 1)d
a is the first term = 49
d is the common difference = 2
Substitute
Tn = 49+(n - 1)(2)
Tn = 49 + 2n -2
Tn = 2n + 47
For the particles to meet, this means that 4n + 93 = 2n + 47
4n - 2n = 47 - 93
2n = -46
n = -23
This shows that it will take the particle 23 secs to meet.
To get the distance travelled by each particle
Tn = 4n + 93
T2 = 4(2) + 93
T2 = 101
For the other sequence;
Tn = 2n + 47
T2 = 2(2) + 47
T2 = 51
Taking the difference;
D = 101 - 51 = 50cm
Hence the distance travelled by each particle is 50cm
Learn more here: https://brainly.com/question/13989292
.Factor 20x2 + 68x - 160
Answers
Answer:
4(5x-8) (x+5)
Step-by-step explanation:
4(5x^2+17x-40)
4(5x-8) (x+5)
20000 divided by 2 x 56 x 7898 - 100
First to Answer gets brainliest!!!
NO LINKS PLEASE!!!!
Answers
Answer:
0.0226122585576093
Jimin wants to know whether if there is a difference in proportion of people who like mint chocolate chip-flavored ice cream between Americans and Koreans. She takes a random sample of 46 Americans and find that 30 of them like the flavor, and then she takes a random sample of 53 Koreans and find that 24 of them like the flavor. For a 95% confidence interval of the true difference in proportion of people who like this ice cream flavor, what is the margin of error (MOE)
Answers
Answer:
5hj
m5Step-by-step explanation:
How to solve x/m = n/p. Solve for x. Please include steps for solving. Thank you
Answers
Answer:
[tex]x=\frac{n}{p}m[/tex]
Step-by-step explanation:
Since we have two variables on the left side (x and p), and they are being divided, we need to do the opposite in order to get it to the other side. Therefore, we multiply both sides of the equation by m.
Doing that, we get
[tex]\frac{x}{m} m=\frac{n}{p}m\\\\\\So,x= \frac{n}{p}m\\[/tex]
Can someone please help me with this problem
Answers
Answer:
A is the right one
Step-by-step explanation:
if not I'm sorry I'm here to help
Which of the following are perfect squares? 2, 4, 6, 16, 20,25, x², x³, x¹⁵, x²⁰, x²⁵
Answers
Answer:
4, 16, 25, [tex]x^{2}[/tex], [tex]x^{20}\\[/tex].
Step-by-step explanation:
Answer:
16, 4, 25, x², x ²⁰
. . . . . . . .
Carson has a smart phone data plan that costs $35 per month that includes 10 GB of data, but will charge an extra $15 per GB over the included amount. How much would Carson have to pay in a month where he used 3 GB over the limit? How much would Carson have to pay in a month where he used went over by x GB?
Answers
Answer:
3 GB over: $80 x GB over: $35+$15x
Step-by-step explanation:
3 GB over is 3 times 15 plus 35, which equals 80, x GB over is x times 15 plus 35. Boom, answer.
Your welcome!
Answer:
$80
Step-by-step explanation:
please help me with this sum
Answers
Answer:
391 × 5 = 1955
621 × 3 = 1863
481 × 7 = 3367
531 × 6 = 3186
981 × 2 = 1962
761 × 9 = 6849
581 × 8 = 4648
431 × 3 = 1293
271 × 4 = 1084
821 × 4 = 3284
what should she do next?
Answers
Answer:
(-2) *6 = -12
Step-by-step explanation:
4 + (2-4) *6 , solve the subtraction in parenthesis
4 + (-2)*6, solve the multiplication of (-2) *6
4 - 12, solve the subtraction
-8
Please answer this question
Answers
Answer:
See explanation below:
see attached file below
TIME REMAININO
58:40
Which graph could represent a constant balance in a bank account over time?
Daily Balance
Daily Balance
Daily Balance
de
10
$
1378
Time (day)
1 2 3 4 5
Time day)
O
Daily Balance
35
Save and Exit
NE
Suband
Mark this and return
Answers
Thanks hope you have a good day
What is the distance from (-4, 0) to (2, 5)? Round your answer to the nearest hundredth.
Answers
Answer:
7.81
Step-by-step explanation:
Step-by-step explanation:
[tex]distance = \sqrt{(x2 - x1) ^{2} + (y2 - y1) ^{2} } [/tex]
Now, substitute the numbers into the equation,
[tex] \sqrt{(2 + 4) ^{2} +( 5 - 0)^{2} } [/tex]
distance = 7.81
brianlist me??
Erin ran 5 km in 25 minutes. What is her speed in km per minute? (Answer as a decimal)
Answers
Answer:
what what what what what what what what
(I NEED THE ANSWER FAST PLS) Explain how to use place value and the distributive property to find the product of 828 and 9. (also, please do not give the edge sample answer)
Answers
Answer:
7452
Step-by-step explanation:
Answer:
Sample Response: First, write 828 as a sum of 800 + 20 + 8. Next, multiply each number by 9. Add the products to get 7,452.
Step-by-step explanation: edge 2021
Which word is a synonym of verify?
consent or confirm
Answers
Answer:
confirm is the correct answer
Plz mark as Brainliest
_+_+_+_+_+_=300,684 how could I do this with 6 digits to equal 300,684 .?
Answers
Answer:
Number 300,684 spell , write in words: three hundred thousand, six hundred and eighty-four . Ordinal number 300684th is said and write: three hundred thousand, six hundred and eighty-fourth. Color #300684. The meaning of number 300684 in Maths: Is Prime? Factorization and dividers. The square root and cube root of 300684. The meaning in computer science, numerology, codes and images, writing and naming in other languages, other interesting facts.
hop it helps:) :(Two particles are projected simultaneously towards each other from opposite ends of a straight horizontal tube. One particle travels 97 cm in the 1st 2 seconds, 93 cm in next 2 seconds , 89 cm in another next 2 seconds, etc. The other particle travels 49 cm in the 1st 2 seconds, 47 cm in the next 2 seconds , 45 cm in another next 2 seconds, etc. Find how long it takes for the particles to meet and hence, determine the distances travelled by each particle.
Answers
This shows that it will take the particle 23 secs to meet.
The distance travelled by each particle is 50cm
If two particles are projected simultaneously towards each other from opposite ends of a straight horizontal tube,
The first particle distances are 97cm, 93cm, 89cm... every 2secs
This form an arithmetic sequence and the nth term is expressed as:
Tn = a + (n - 1)d
a is the first term = 97
d is the common difference = 4
Substitute
Tn = 97+(n - 1)(4)
Tn = 97 + 4n -4
Tn = 4n + 93
Similarly for the distances 49 cm, 47 cm, 45cm .....
This also forms an arithmetic sequence and the nth term is expressed as:
Tn = a + (n - 1)d
a is the first term = 49
d is the common difference = 2
Substitute
Tn = 49+(n - 1)(2)
Tn = 49 + 2n -2
Tn = 2n + 47
For the particles to meet, this means that 4n + 93 = 2n + 47
4n - 2n = 47 - 93
2n = -46
n = -23
This shows that it will take the particle 23 secs to meet.
To get the distance travelled by each particle
Tn = 4n + 93
T2 = 4(2) + 93
T2 = 101
For the other sequence;
Tn = 2n + 47
T2 = 2(2) + 47
T2 = 51
Taking the difference;
D = 101 - 51 = 50cm
Hence the distance travelled by each particle is 50cm
Learn more here: https://brainly.com/question/13989292
-14 + 6x = 1 - 3x what is x
Answers
Answer:
X = 5/3
Step-by-step explanation:
-14 + 6x = 1 - 3x
-14 + 9x = 1
9x = 15
x = 5/3
Hope this helps! Pls give brainliest!
Answer:
[tex]x = 1\frac{2}{3} [/tex]Step-by-step explanation:
To find:Value of x
Equation:-14 + 6x = 1 - 3x
=> 6x + 3x = 1 + 14
=> 9x = 15
[tex] = > x = \frac{15}{9} [/tex]
[tex] = > x = \frac{5}{3} [/tex]
[tex] = > x = 1 \frac{2}{3} (ans)[/tex]
12. Determine the slope of the line having the equation 2x + y = 12
a. 2
b. -2
c. ½
d. -½
Answers
Answer:
b. -2
Step-by-step explanation:
Note the slope-intercept form: y = mx + b
Note that:
y = (x , y)
m = slope
x = (x , y)
b = y-intercept
First, isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Subtract 2x from both sides of the equation:
2x (-2x) + y = (-2x) + 12
y = -2x + 12
Remember, m is the variable for the term that stands for the slope (directly next to the x variable). In this case, your answer will be -2
b. -2 is your answer.
~
Answer:
b. -2
Step-by-step explanation:
2x+y=12
add -2x to both sides
y = -2x + 12
this is in slope intercept form y = mx + b
m meaning the slope
in this case the slope is -2
the answer will be b. -2
"The quotient of five less than a number and 6, is -4."
Answers
Answer:
The number is 20
Step-by-step explanation:
x represents the missing number
The equation would be:
[tex]\frac{x-5}{6} =-4[/tex]
Then isolate the variable and solve,
First multiply both sides by 6...
[tex]x-5=-25[/tex]
Add 5 to both sides.
x=20
Pls help and answer the question in the photo
Answers
Answer:
Cam
Step-by-step explanation:
Cam first multiplied both sides by 3 which removed the fraction on the left. They then correctly added 5 to both sides to get x on its own.
Hope this helps!
Helppp I’m in class and need answers
Answers
Answer:
Need answers for what? I would LOVE to help you hun but I cant help because there is nothing to answer.
Step-by-step explanation:
Helppppppppppppppppppppppppppppppppppp
Answers
Answer:
The answer would be 7 I hope this helps! : )
Answer:
it's 2
Step-by-step explanation:
if we solve 3×2×1/3
then we will get 2 .