A point H is 20m away from the foot of a tower on the same horizontal ground. From the point H, the angle of elevation of the point (P) on the tower and the top(T) of the tower are 30° and 50° respectively.
( a) draw a diagram to illustrate the information above.
(b) calculate correct to 3 s.f,
( I) /PT/
(ii) the distance between H and the too of the tower.
(III) the position of H if the angle of depression of H from the too of the tower is to be 40°
Answers
Answer:
a. See Attachment 1
b. [tex]PT = 12.3\ m[/tex]
c. [tex]HT = 31.1\ m[/tex]
d. [tex]OH = 28.4\ m[/tex]
Step-by-step explanation:
Calculating PT
To calculate PT, we need to get distance OT and OP
Calculating OT;
We have to consider angle 50, distance OH and distance OT
The relationship between these parameters is;
[tex]tan50 = \frac{OT}{20}[/tex]
Multiply both sides by 20
[tex]20 * tan50 = \frac{OT}{20} * 20[/tex]
[tex]20 * tan50 = OT[/tex]
[tex]20 * 1.1918 = OT[/tex]
[tex]23.836 = OT[/tex]
[tex]OT = 23.836[/tex]
Calculating OP;
We have to consider angle 30, distance OH and distance OP
The relationship between these parameters is;
[tex]tan30 = \frac{OP}{20}[/tex]
Multiply both sides by 20
[tex]20 * tan30 = \frac{OP}{20} * 20[/tex]
[tex]20 * tan30 = OP[/tex]
[tex]20 * 0.5774= OP[/tex]
[tex]11.548 = OP[/tex]
[tex]OP = 11.548[/tex]
[tex]PT = OT - OP[/tex]
[tex]PT = 23.836 - 11.548[/tex]
[tex]PT = 12.288[/tex]
[tex]PT = 12.3\ m[/tex] (Approximated)
--------------------------------------------------------
Calculating the distance between H and the top of the tower
This is represented by HT
HT can be calculated using Pythagoras theorem
[tex]HT^2 = OT^2 + OH^2[/tex]
Substitute 20 for OH and [tex]OT = 23.836[/tex]
[tex]HT^2 = 20^2 + 23.836^2[/tex]
[tex]HT^2 = 400 + 568.154896[/tex]
[tex]HT^2 = 968.154896[/tex]
Take Square Root of both sides
[tex]HT = \sqrt{968.154896}[/tex]
[tex]HT = 31.1\ m[/tex] (Approximated)
--------------------------------------------------------
Calculating the position of H
This is represented by OH
See Attachment 2
We have to consider angle 50, distance OH and distance OT
The relationship between these parameters is;
[tex]tan50 = \frac{OH}{OT}[/tex]
Multiply both sides by OT
[tex]OT * tan50 = \frac{OH}{OT} * OT[/tex]
[tex]OT * tan50 = {OH[/tex]
[tex]OT * 1.1918 = OH[/tex]
Substitute [tex]OT = 23.836[/tex]
[tex]23.836 * 1.1918 = OH[/tex]
[tex]28.4= OH[/tex]
[tex]OH = 28.4\ m[/tex] (Approximated)
Related Questions
Find the output, y, when the input, x, is 666.
Answers
Answer:
y = 8
Step-by-step explanation:
The question is simply asking for the y-value when x = 6. We look at the graph when x = 6 and see what y-value it gives us. We find that when x = 6, we have y = 8.
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Answers
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30 POINTS!! Given triangle ABC shown below, which graph shows the transformation (x-2, y+4)?
Answers
Answer:
Its C
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Take point A at ( 4,-1)
We are shifting down 2 and to the right 4
(4-2, -1+4) becomes ( 2,3)
Choice C has A' at ( 2,3)
Please can someone help me asap
Answers
Answer:
48
Step-by-step explanation:
Because you add 20 cm, 15 cm, and lastly 13 cm. Then you add it all together and get the answer.
To find the number of units that gives break-even for the product, solve the equation R C. Round your answer to the nearest whole unit A manufacturer has total revenue given by the function R = 90x and has total cost given by C 35x + 17,000, where x is the number of units produced and sold. A, 55 units
B. 125 units
C. 136 units
D. 309 units
Answers
Answer:
The correct answer is D.
Step-by-step explanation:
Giving the following information:
R = 90x
Total cost= 35x + 17,000
x= is the number of units produced and sold
Now, we know that:
Unitary variable cost= 35
Fixed costs= 17,000
Selling price per unit= 90
To calculate the break-even point in units, we need to use the following formula:
Break-even point in units= fixed costs/ contribution margin per unit
Break-even point in units= 17,000 / (90 - 35)
Break-even point in units= 309 units
At the toy store, you could get 4 board games for $25.84. Online, the price for 5 board games is $32.15. Which place has the highest price for a board game?
Answers
Answer:
The board game store
Step-by-step explanation:
Just divide the store price by 4 and online by 5
Answer:
Toy store
Step-by-step explanation:
Let's find the unit rates for the toy store and the online store. To find the unit rate, divide the price by the number of board games.
price/board games
Toy Store
price/board games
The toy store sells 4 board games for $25.84
$25.84 / 4 board games
25.84/5
6.46
Online Store
price/ board games
The online store sells 5 board games for $32.15
$32.15 / 5 board games
32.15/5
6.43
At the toy store, a board game costs $6.46. Online, it costs $6.43.
6.46 is greater than 5.43, therefore, the toy store has the higher price for a board game.
I need you to answer ASAP
Line R: 2x + 2y = 18
Line M: x + y = 9
Which statement is true about the solution to the set of equatic
It is (189)
It is (9, 18)
There are infinitely many solutions
There is no solution
Answers
Answer:
infinitely many solutions
Step-by-step explanation:
2x + 2y = 18
x + y = 9
multiply Line M equation by -2 to eliminate at least one variable:
2x + 2y = 18
-2x - 2y = -18
use elimination:
2x + 2y = 18
-2x - 2y = -18
__________
0 + 0 = 0
since this statement is true, there are infinitely many solutions.
Please answer this question now
Answers
Answer:
[tex]\boxed{u = 6.0}[/tex]
Step-by-step explanation:
Using the cosine rule
[tex]c^2= a^2+b^2-2abCosC[/tex]
Here c = u , a = 11 , b = 12 and C = 30
[tex]u^2 = 11^2+12^2-2(11)(12)\ Cos 30\\u^2 = 121+144-2(132)(0.866)\\u^2 = 265-228.6\\u^2 = 36.37[/tex]
Taking sqrt on both sides
u = 6.0 (To nearest tenth)
Plzzzz help me
Consider the function below.
Х
-1
0
1
2
(x)
3
oo
13
N
Which of the following functions could be the inverse of function ?
Answers
Answer:
i think its option b but im not sure
Type the correct answer in each box. If necessary, use / for the fraction bar. Complete the statements about series A and B. Series A: 10+4+8/5+16/25+32/125+⋯ Series B: 15+3/5+9/5+27/5+81/5+⋯ Series__ has an r value of___where 0<|r|<1. So, we can find the sum of the series. The sum of the series is___ need help guys please :/
Answers
Answer:
Series A has an r value of 2/5 and series A has an r value of 3. The sum of the series A is 50/3
Step-by-step explanation:
A geometric sequence is in the form a, ar, ar², ar³, . . .
Where a is the first term and r is the common ratio = [tex]\frac{a_{n+1}}{a_n}[/tex]
For series A: 10+4+8/5+16/25+32/125+⋯ The common ratio r is given as:
[tex]r=\frac{a_{n+1}}{a_n}=\frac{4}{10} =\frac{2}{5}[/tex]
For series B: 1/5+3/5+9/5+27/5+81/5+⋯ The common ratio r is given as:
[tex]r=\frac{a_{n+1}}{a_n}=\frac{3/5}{1/5} =3[/tex]
For series A a = 10, r = 2/5, which mean 0 < r < 1, the sum of the series is given as:
[tex]S_{\infty}=\frac{a}{1-r}=\frac{10}{1-\frac{2}{5} } =\frac{50}{3}[/tex]
help me please, explanation not necessary but would be appreciated
Answers
Answer:
55°
Step-by-step explanation:
The following data were obtained from the diagram given above:
Adjacent = 4
Hypothenus = 7
Angle A =?
The value of angle A can be obtained as follow:
Cos A = Adjacent / Hypothenus
Cos A = 4/7
Take the inverse of Cos.
A = Cos¯¹(4/7)
A = 55.1° ≈ 55°
Therefore, the value of angle A is approximately 55°.
Someone pls help if you want more points just go to my other questions and answer them pls
Answers
Answer:
I would say the answer is C.
2. Hessa was playing a computer game. She scored 43 points in Round 1 and 26 points in Round 2. Which sum could she use to add the points together? a. 40 + 20 + 3 + 6 b. 4 + 3 + 2 + 6 c. 40 + 30 + 20 + 60 d. 30 + 4 + 60 + 2
Answers
Answer:
a. 40 + 20 + 3 + 6Step-by-step explanation:
Points scored by Hessa is as shown below;
Round 1 = 43 points
Round 2 = 26 points
Total points for both rounds = 43 + 26 = 69 points
To determine the sum she could use to add the points together, we must select the sum that will give us the same total of points for both rounds i.e 69 points.
The Round 1 score (43 pt)can also be expressed as (40+3) points
The Round 2 score (26 pt)can also be expressed as (20+6) points
The sum she could use to add the points together will be (40+3)+(20+6)
which is also equal to 40 + 20 + 3 + 6 = 69points
Hence, option a is correct
The Big Telescope Company sells circular mirrors. Their largest mirrors have radii of 5 meters and their smallest mirrors have radii of 1 meter. The cost of every mirror is proportional to the cube of the mirror's radius. What is the ratio of the total cost of 25 of the company's smallest mirrors to the cost of one of the company's largest mirrors? Express your answer as a common fraction.
Answers
Answer:
The answer is 1/5
Step-by-step explanation:
What is the y-intercept of the function, represented by the table of values
below?
x
у
-2
16
1
4.
2
0
4
-8
7
-20
Answers
Answer:
8
Step-by-step explanation:
The y-intercept (b) of the function is the point at which the line of the graph of the given values of the table above crosses the y-axis, for which x = 0.
To find the y-intercept of the function represented by the tables, recall the equation of a straight line which is given as:
y = mx + b
Where, m is the slope = (y2 - y1)/(x2 - x1)
b = the y-intercept we are to find
y and x could be any values of a point on the graph which is represented in the table of values.
First, let's find the slope (m):
Let's use any 2 given pairs of the values in the table above.
Using,
(1, 4), (2, 0),
y1 = 4,
y2 = 0
x1 = 1
x2 = 2
m = (0 - 4)/(2 - 1)
m = -4/1 = -4
=>Using, y = mx + b, let's find the y-intercept (b), taking any of the coordinate pairs from the table of values given.
Let's use, (1, 4) as our x and y values.
Thus,
4 = -4(1) + b
4 = -4 + b
Add 4 to both sides to solve for b
4 + 4 = -4 + b + 4
8 = b
y-intercept of the function represented by the table of values = 8
Simplify the expression.
–6.5(–4.9)
Answers
Answer:
31.85
Step-by-step explanation:
Hey there!
Well to simplify the given expression we do,
-6.5 * -4.9
= 31.85
Hope this helps :)
ASAP!!! PLEASE help me with this question! It is really urgent...
Answers
Answer:
0.987
Step-by-step explanation:
use stat on calculator
Clark collected 200 fruits from his orchard. 56 of the fruits were durians and the rest were mangoes. What percentage of the fruits were mangoes?
Answers
Answer:
72%
Step-by-step explanation:
First find the number of mangoes
200 -56 = 144
Take the number of mangoes over the total
144/200
.72
Change to percent by multiplying by 100
72%
Answer:
72%
Step-by-step explanation:
If 56 of the 200 fruits were durians, then [tex]200-56[/tex] of the fruits were mangoes. Therefore, 144 of the fruits were mangoes.
Now we can set up a percentage proportion to find what percent of 200 144 is.
[tex]\frac{144}{200} = \frac{x}{100}[/tex]
Multiply the cross values and divide by the value thats diagonal to the variable.
[tex]144\cdot100=14400\\14400\div200=72[/tex]
So, the answer is 72%
Hope this helped!
If you have the answer pls screenshot and put each pare in one color pls
Answers
Step-by-step explanation:
(2 / 3)(-4)(9) = (2 / 3) * 9 * (-4) = 6 * (-4) = -24.
(-3 / 4)(7 / 8) = (-3 * 7) / (4 * 8) = -21 / 32.
(2 and 3/5)(7 / 9) = (10/5 + 3/5)(7/9) = (13/5)(7/9) = 91 / 45.
(5 / 16)(-2)(-4)(-4/5) = (5 / 16)(4 / 5)(2)(-4) = (1 / 4)(2)(-4) = (-1)(2) = -2.
Hope this helps!
can someone help me fill out this chart
Answers
Answer:
is there a y part of this equation?
Step-by-step explanation:
T models the temperature (in degrees Celsius) in New York City when it's t hours after midnight on a given day. Match each statement with the feature of the graph that most closely corresponds to it.
Answers
Answer:
Y Intercept: It was 3C at the beginning of the day.
Positive or negative interval: The temperature was above zero between 8 am and 8 pm.
Increasing or decreasing interval: It was getting warmer between 2 am and 2 pm
Step-by-step explanation:
Features matching the correct statements are:
y intercept: It was ₋3°C at the beginning of the day.
Positive or negative interval: The temperature was above zero between 8 am and 8 pm.
Increasing or decreasing interval: It was getting warmer between 2am and 2 pm.
What is the temperature graph over time?
The x-axis in a time-temperature graph, sometimes known as a "x-y graph," depicts time, and the y-axis the temperature. The temperature's relationship to time is depicted on the graph.
we can notice in the given graph that T(t) represents the time and t represents the temperature of the city.
So we see when lowercase t when time is zero(0), zero hours after midnight the temperature in the New York city is negative 3°C(₋3°C) so it was ₋3°C at the beginning of the day since the true beginning of the day is right at midnight. Hence y intercept tells us that it was ₋3°C at the beginning of the day. Then about the positive or negative interval we can notice from the graph that we have a negative interval from time equals zero to time equals eight which means the temperature is negative as it goes below zero and from 8 am to 8 pm we can see that the temperature goes positive and then it dips down to negative again. So a positive or negative interval tells us about when the temperature was above xero between 8 am and 8 pm.The increasing and decreasing interval, here we see that the function is increasing as t increases so does the temperature, all the way to 2 pm. Hence, we are just using the increasing interval to match the statement that it was getting warmer between 2 am and 2 pm.Hence we get the statements match to their features.
Learn more about"temperature problems" here-
https://brainly.com/question/24746268
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Please help. I will give out brainliest
Answers
Answer:
the table is correct
the graph will look like:
I NEED SOMEONES HELP HELP ME PLEACE
Answers
Answer:
He needs to paint 12 inches in height
and 42 inches in width
This is really confusing I need help with this.
Answers
Answer:
Step-by-step explanation:
can you at least telllus what is in the drop box
The y-axis is horizontal line , the slope of the line is zero
The x-axis is x=0 , the slope of the line is undefined
answer : horizontal line , zero
Answer: x=0 , undefined
The second step by step is below
Hopefully this help you
If you have any other questions let me know
Have a great day :)
If two digit number, the digit at unit place is
2 more the digit at tens place. If three times
the sum of digits is added to the number, the
number will be reversed. Find the number.
Answers
Answer:
24
Step-by-step explanation:
let the 2 digit number be ab then digit in unit place is 2 more than ten place
2 digit number is a a + 2 where b = a + 2.
Thus sum of digits = a + a + 2 = 2a + 2, then
ab + 3(2a + 2) = ba ← using place value of digits
10a + b + 6a + 6 = 10b + a, that is
16a + 6 + b = 10b + a ( subtract 10b + a from both sides
15a - 9b + 6 = 0 ← substitute b = a + 2
15a - 9(a + 2) + 6 = 0
15a - 9a - 18 + 6 = 0
6a - 12 = 0 ( add 12 to both sides )
6a = 12 ( divide both sides by 6 )
a = 2
Thus the number is 24
I need the answers to B and C please and thank you! :)
Answers
Answer:
2/9 and 4/9
Step-by-step explanation:
There are 3 * 3 = 9 possible outcomes of spinning the spinners. Out of those, there are only 2 ways to achieve a product of 6 (2 and 3 or 6 and 1) so the answer to B is 2/9. For C, there are 4 ways for the total to be greater than 10 (12, 18, 20, 30) so the answer is 4/9.
Answer:
b=2/9
c=4/9
Step-by-step explanation:
b: 2/3(there are two options you can land on that have a pair that multiplies to six)*1/3(each only has one pair)= 2/9
c: 2/3(6 or 4)*2/3(3 or 5) =4/9
Find the width of a rectangle if the diagonal is 19 and the length is 16
Answers
Answer:
≈10.25
Step-by-step explanation:
use the Pythagorean Theorem: a² + b² = c²
c is the hypotenuse, the diagonal, or the longest side of the triangle
a = 16
b = ?
c = 19
(16)² + b² = (19)²
256 + b² = 361
b² = 105
b = √105 ≈ 10.25
Any fake answers will get reported but if u do good u get brainliest:) ----------------------------------- Fred's coffee shop sells two blends of beans at the following prices. a) House Blend ($3.50/lb) b) Exotic Blend ($4.00/lb). House blend is 1/2 Costa Rican beans and 1/2 Ethiopian beans. Exotic blend is 1/4 Costa Rican beans and 3/4 Ethiopian beans. Every day Fred receives 200 lbs of Costa Rican Beans and 330 lbs of Ethiopian beans. What are the common sense constraints? ------ ---------------------------------- x or = 530 ---- x > or = 0, and y > or = 0
Answers
Since he needs beans to sell. The common sense constraints would be that both x and y need to be equal to or greater than 0, otherwise he wouldn’t have anything to sell.
The answer is the last choice
Answer:
x>=0, and
y>=0
Step-by-step explanation:
Let
x = pounds of house blend he sells/makes every day
y = pounds of exoted blend he makes/sells every day
constraint for costa rican beans
x/2 + y/4 <= 200 ...............(1)
constraint for Ethiopian beans
x/2 + 3y/4 <=330..................(2)
Total weight per day
x+y <= 200+330 = 530............(3)
common sense constraints, cannot have negative weight for coffee
x>=0, and
y>=0
which geometric solid is formed by rotating the rectangle about line m?
Answers
Answer:
rectangular prism
Step-by-step explanation:
check by rotating the shape in images
3 8 3 ÷9=3, start fraction, 3, divided by, 8, end fraction, divided by, 9, equals
Answers
Answer:
1/24
Step-by-step explanation:
In the above question, we are asked to solve for:
start fraction, 3, divided by, 8, end fraction, divided by, 9, equals
Mathematically, this is represented as:
(3/8) ÷ 9
= (3/8) × 1/9
= 3/72
= 1/24
Therefore, start fraction, 3, divided by, 8, end fraction, divided by, 9, equals 1/24