Two towers A and B are 45m and 30m high. Tower A lies to the west and B to the east of a man 1.5m tall. From the mans eye level, the angle of elevation of the top of A and B are 66° and 28° respectively. Calculate correct to three signigicant fugures the distance between A and B.
Answers
Answer:
73.0m
Step-by-step explanation:
see the attachment. Hope it helps.
Related Questions
The Molokai Nut Company (MNC) makes four different products from macadamia nuts grown in the Hawaiian Islands: chocolate-coated whole nuts (Whole), chocolate-coated nut clusters (Cluster), chocolate-coated nut crunch bars (Crunch), and plain roasted nuts (Roasted). The company is barely able to keep up with the increasing demand for these products. However, increasing raw material prices and foreign competition are forcing MNC to watch its margins to ensure it is operating in the most efficient manner possible. To meet marketing demands for the coming week, MNC needs to produce at least 1,000 pounds of the Whole product, between 400 and 500 pounds of the Cluster product, no more than 150 pounds of the Crunch product, and no more than 200 pounds of the Roasted product. Each pound of the Whole, Cluster, Crunch, and Roasted product contains, respectively, 60%, 40%, 20%, and 100% macadamia nuts with the remaining weight made up of chocolate coating. The company has 1,100 pounds of nuts and 800 pounds of chocolate available for use in the next week. The various products are made using four different machines that hull the nuts, roast the nuts, coat the nuts in chocolate (if needed), and package the products. The following table summarizes the time required by each product on each machine. Each machine has 60 hours of time available in the coming week.
Machine Minutes Required per Pound
Whole Cluster Crunch Roasted
Hulling 1 1 1 1
Roasting 2 1.5 1 1.75
Coating 1 0.7 0.2 0
Packaging 2.5 1.6 1.25 1
The selling price and variable cost associated with each pound of product is summarized in the following table:
Per Pound Revenue and Costs
Whole Cluster Crunch Roasted
Selling Price $5.00 $4.00 $3.20 $4.50
Variable Cost $3.15 $2.60 $2.16 $3.10
Required:
a. Formulate an LP model for this problem.
b. Create a spreadsheet model for this problem, and solve it using Solver.
c. What is the optimal solution?
Answers
Answer:
Profit = Selling price - Variable cost
Formulas:
F2 =SUMPRODUCT(B2:E2,$B$16:$E$16) copy to F2:F12, F14
Optimal solution: The company should produce the following quantities (in pounds) of the four varieties of nuts.
Whole = 1000
Cluster = 500
Crunch = 80
Roasted = 200
Total profit = $ 2913.20
Step-by-step explanation:
Find the simple interest on a loan of $34,500 at 6.9% interest for 11 months
Give your answer to the nearest cent
Answers
Answer:
$2182.13
Step-by-step explanation:
Simple interest (I) is calculated as
I = [tex]\frac{PRT}{100}[/tex] ( P is principal, R is rate of interest, T is time in years )
Here P = $34,500 , R = 6.9 and T = [tex]\frac{11}{12}[/tex] , then
I = [tex]\frac{34500(6.9)(\frac{11}{12}) }{100}[/tex]
= 345 × 6.9 × [tex]\frac{11}{12}[/tex]
= $2182.13
please helpppppppppppp
Answers
Answer:
3
Step-by-step explanation:
4.5x 2 = 9
[tex]\sqrt{9}[/tex]= 3
(x-2)(-5x^2+x)=(x)(-5x^2)+(x)(x)+(-2)(-5x^2)+(-2)(x) is an exsample of
Answers
this is an example of linear equations is one variable
In a class of 40 students, 2/5
of the total number of students like to study English and 3/5
of the
total students like to study Mathematics.
a) How many students like to study English?
b)How many students like to study Mathematics?
Answers
A tank contains 1000L of pure water. Brine that contains 0.04kg of salt per liter enters the tank at a rate of 5L/min. Also, brine that contains 0.06kg of salt per liter enters the tank at a rate of 10L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15L/min. Answer the following questions. 1. How much salt is in the tank after t minutes
Answers
Answer:
s(t) = 160/3 ( 1 - e^(-3t / 200) )
Step-by-step explanation:
volume of pure water in tank = 1000 L
Brine contains 0.04kg of salt/L
Inflow rate of Brine containing 0.04kg of salt/L = 5L/min
Brine containing 0.06 kg of salt/L
Inflow rate of Brine containing 0.06 kg of salt/L = 10L/min
Solution is thoroughly mixed and drains from tank at 15L/min
a) Determine the amount of salt is in the tank after t minutes
rate of salt entering = 0.2 + 0.6 = 0.8 kg/min
rate of salt leaving = s/1000 * 15
amount of salt at time (t) = s(t)
initial condition s( 0 ) = 0
ds/dt = 0.8 - 15s/1000 = 0.8 - 3s/200
200 ds/dt = ( 160 - 3s )
-200/3 In ( 160 - 3s ) = t + c
Given that ; t = 0 , s = 0
c = - 200/3 In ( 160 )
∴ -200/3 In ( 160 - 3s ) = t - 200/3 In ( 160 )
- 200/3 [ In ( 60 - 3s ) - In ( 160 ) ] = t
therefore:
In ( 160 - 3s / 160 ) = -3t/200
= ( 160 - 3s / 160 ) = e ^ (-3t/200 )
Hence amount of salt in tank after t minutes
s(t) = 160/3 ( 1 - e^(-3t / 200) )
Show that the set of nonsingluar 2 by 2 matrices is not a vector space. Show also that the set of singular 2 by 2 matrices is not a vector space.
Answers
Answer:
a) 2 nonsingular 2 by 2 matrices are not closed when added together hence it is not a vector space( i.e. their sum = singular and not nonsingular )
b) 2 singular 2 by 2 matrices is not closed under addition, hence they are not a vector space. ( i.e. their sum = nonsingular )
Step-by-step explanation:
a) Prove that nonsingular 2 by 2 matrices is not a vector space
2 nonsingular matrices are not closed when added together hence it is not a vector space ( i.e. their sum = singular and not nonsingular )
vector A = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex] + vector B = [tex]\left[\begin{array}{ccc}0&1\\1&0\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&1\\1&1\\\end{array}\right][/tex] ( singular vector )
b) Prove that singular 2 by 2 matrices is not a vector space
2 singular 2 by 2 matrices is not closed under addition, hence they are not a vector space. ( i.e. their sum = nonsingular )
Vector C = [tex]\left[\begin{array}{ccc}1&0\\0&0\\\end{array}\right][/tex] + vector D = [tex]\left[\begin{array}{ccc}0&0\\0&1\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex] ( nonsingular vector )
Find the area for me pls
Answers
this figure can be divided into three parts one is rectangle other one is semicircle and the third one is one fourth of the circle .so let's find the area of each figure one by one. For the rectangle 12×8 =96
for semicircle that is on the top it has the radius 6 which is a half of 12
so area of the semicircle is
[tex] \frac{1}{2} \pi \: r {}^{2} \\ \frac{1}{2} \times 3.14 \times 6 {}^{2} \\ 3.14 \times 18 \\ 56.52[/tex]
no that's fine. 80 of the 1/4 of the other Circle
[tex] \frac{1}{4} \pi {}^{2} \\ \frac{1}{4} 3.14 \times 8 {}^{2} \\ 3.14 \times 16 \\ 50.24[/tex]
add all these areas
96+56.52+50.24 =202.76
An expression is shown below:
3(m + 5 + 9m)
Part A: Write two expressions that are equivalent to the given expression. (3 points)
Part B: Show that one of your expressions in Part A is equivalent to the given expression using algebraic properties. Explain which properties you used. (4 points)
Part C: Show that your other expression from Part A is equivalent to the given expression by substituting a number for m. (3 points)
Answers
The answers are as follows part A = 30m+15 part B =3m+15+27m
and partC = 30m+15
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition,substraction, multiplication and division.
Part A:- Two expressions that are equivalent to the given expressions are:-
3m + 15 + 27m
30m + 15
Part B: Show that one of your expressions in Part A is equivalent to the given expression using algebraic properties.
3 ( m + 5 + 9m )
Open the bracket by multiplying 3 by what is in the bracket
3m + 15 + 27m
Part C: Show that your other expression from Part A is equivalent to the given expression by substituting a number for m.
3 ( m + 5 + 9m )
Open the bracket by multiplying 3 by what is in the bracket
3m + 15 + 27m
Collect like terms together
3m + 27m + 15
= 30m + 15
To know more about Expression follow
https://brainly.com/question/723406
#SPJ2
Share 30 000 bags of 20kg rice in the ratio 2:3:4:6 among Villages A, B, C and D in that order. (2 marks) How many bags of 20 kg rice will Villages B and C get?
Answers
Answer:
2+3+4+6 = 15 parts
Village B gets 3 of 15 parts
3/15 * 30000 = 6000 bags
Village C gets 4 of 15 parts
4/15 * 6000 = 8000 bags
Answer:
each "share" needs "15" (2+3+4+6) "portions/bags"
2000 distributions
A-4000 bags/80000 kg
B-6000 bags/120000 kg
C-8000 bags/1680000 kg
D-12000 bags/240000 kg
Step-by-step explanation:
(a+b)²=hihihihihihihihiihihihi
Answers
Answer:
(a+b)²=a²+b²+2ab
Step-by-step explanation:
The square of sum of two terms is equal to the squared plus squared plus times product of and . In mathematics, the plus whole squared algebraic identity is called in three ways. The square of sum of two terms identity.
A certain medicine is given in an amount proportional to a patient's body weight. Suppose a patient weighing 150 pound requires 144 milligrams of medicine. what is the weight of a patient who requires 174.72 milligrams of medicine
Answers
9514 1404 393
Answer:
182 lbs
Step-by-step explanation:
You can write the proportion for the required patient weight (w) as ...
weight/medicine = w/(174.72 mg) = (150 lb)/(144 mg)
w = (150 lb)(174.72/144) . . . . . multiply by 174.72 mg
w ≈ 182 lb
The patient's weight is 182 pounds.
A cyclist travels at a rate of 12 kilometers per hour. What is the rate in kilometers per minute? How many kilometers will the cyclist travel in 20 minutes? Do not round your answer.
Answers
Answer:
0.2&4
Step-by-step explanation:
There are 60 minutes in one hour, so 12 divided by 60 is the answer.
0.2 kilometers * 20 = 4
A college admissions officer takes a simple random sample of 90 entering freshman and computes their mean mathematics sat score to be 436. assume the population standard deviation is σ = 101. Based on a 99% confidence interval for the mean mathematics SAT score, is it likely that the mean mathematics SAT score for entering freshmen class is greater than 460?
Answers
Answer:
460 is part of the confidence interval, which means that we cannot say that there is significant evidence that the mean mathematics SAT score for entering freshmen class is greater than 460
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.575\frac{101}{\sqrt{90}} = 27.4[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 436 - 27.4 = 408.6.
The upper end of the interval is the sample mean added to M. So it is 436 + 27.4 = 463.4.
460 is part of the confidence interval, which means that we cannot say that there is significant evidence that the mean mathematics SAT score for entering freshmen class is greater than 460
How would I solve this?
Answers
Answer:
20°
Step-by-step explanation:
perpendicular from the center on a chord of a circle always bisects the chord.
AR=BR
∴m arcAC=m arc BC=20°
I need help on this too please it’s hard
Answers
Answer:
Y=x
Step-by-step explanation:
The y and x values are the same
Answer:
y = x
Step-by-step explanation:
a 45° line with the origin passing through the origin has the equation y=x.
Have a nice day.
How tall is the table?
120cm
90cm
I
Answers
The values of variables, such as the height of the table can be found by writing equations of their relationships
The height of the table is 105 cm
The reason the above height value is correct is as follows;
Known parameters:
The diagram shows a table, a cat and a mice
Let x, represent the height of the table, let y represent the height of the cat, and let z represent the height of the mice
From the given diagram, we have;
Height of the table + Height of the cat - Height of the mice = 120 cm
∴ x + y - z = 120...(1)
Height of the table + Height of the mice - Height of the cat = 90 cm
∴ x + z - y = 90...(2)
Adding equation (1) to equation (2) gives;
x + y - z + (x + z - y) = 120 + 90 = 210
x + y - z + (x + z - y) = 210
However;
x + y - z + (x + z - y) = x + x + y - y - z + z = 2·x
∴ x + y - z + (x + z - y) = 2·x = 210
x = 210/2 = 105
Therefore;
The height of the table, x = 105 cm
Learn more about word problems leading on simultaneous equations here:
https://brainly.com/question/16513646
The half life of Co-60 is 5.20 years. How many milligrams of a 1.00mg sample remains after 6.55 years
Answers
Answer:
For cobalt-60, which has a half-life of 5.27 years, 50% remains after 5.27 years (one half-life), 25% remains after 10.54 years (two half-lives), 12.5% remains after 15.81 years (three half-lives), and so on.
Step-by-step explanation:
You can figue out the rest.
Last question! Please show work. Really need to get this done in 1 hour
Answers
Answer:
x = 1, y = 2 , z = 3
Step-by-step explanation:
[tex]6x\:+\:2y\:-4z\:=\:-2 \ \ \ \ \ \ \ \ \ -----( 1 ) \:\\\\-3x-4y\:+2z\:=\:-5 \ \ \ \ \ \ ------( 2 ) \:\\\\4x-\:6y\:+3z\:=\:1 \ \ \ \ \ \ \ \ \ \ \ \ ------- ( 3 ) \\\\( 2 ) \times 2=> -6x -8y + 4z = -10 \ \ \ \ \ \ \ -----( 4)[/tex]
Now add ( 1 ) and (4)
[tex]6x +2y -4z = - 2\\\\-6x-8y - 4z = -10\\\\=>0x -6y + 0 = - 12\\\\-6y = -12[/tex]
y = 2
Now multiply ( 1 ) by 2 and (3) by 3
[tex](1) \times 2 => 12x + 4y -8z = -4\\\\(3) \times 3 => 12x -18y +9z = 3\\\\Subtract \ the \ equation : ( 1) - ( 3) => 0x +22y -17z = -7[/tex] ------ ( 5 )
Substitute y = 2 in ( 5 ) :
[tex]22(2) - 17z = - 7\\\\ 44 - 17z = - 7\\\\ -17z = - 7 - 44\\\\ -17z = -51\\\\[/tex]
z = 3
Substitute z = 3 and y = 2 in ( 1 ) :
[tex]6x + 2y - 4z = - 2\\\\6x + 2( 2) -4( 3) = -2\\\\6x + 4 - 12 = -2\\\\6x - 8 = - 2\\\\6x = - 2 + 8 \\\\6x = 6\\[/tex]
x = 1
What’s an example for y=1/2x-6 real world problems
Answers
Max is participating at a school bake sale. Each cookie he sells costs 50 cents. Unfortunately, it took 6 dollars to buy the materials for the cookies. Find how much money would it take for Max to break even.
Answer:
Step-by-step explanation:
4 years ago when Mary was 6, she was one half the age of her brother.
How old is her brother now?
Solution :
Let brother's age be = x
Four years ago, brothers age was = (x - 4)
Four years ago Mary was = 6
She was half the age of her brother
[tex]6 = \frac{1}{2} (x - 4)[/tex]
The senior classes at High School A and High School B planned separate trips to Yellowstone National Park. The senior class at High School A rented and filled 9 vans and 14 buses with 710 students. High School B rented and filled 13 vans and 5 buses with 371 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus.
Answers
Answer:
Buses - 43 people
Vans - 12 people
For this question I am sure the answer is 81% as you divide 45 and 55. However, it is stating my answer is incorrect even though I put 0.81% as well. Did I round wrong or is the answer wrong completely?
Answers
Answer:
it says round to the nearest 10th so it wouldn't be 81, it would be 81.8%
Find the greatest common factor of 8a and 6a?
Answers
Answer:
2a.
Step-by-step explanation:
6 = 2 * 3
8 = 2 * 2 * 2 - 2 is common to both sets of factors.
So the GCF of 6 and 8 is 2.
For the 2 a's it is a.
There are 38 Legs in a group of goat and hens. How many goats and hens are there?
1) 13 Goats , 3 hens
2) 11 goats ,3hens
3) 7 goats,3 hens
4) 8 goats,3 hens
Answers
Answer:
4)8 goats, 3 hens.
Step-by-step explanation:
8*4=32
3*2=6
32+6=38
A set of numbers is shown below:
{0, 0.6, 2, 4, 6}
Which of the following shows all the numbers from the set that make the inequality 2x + 3 ≥ 7 true?
{4, 6}
{0, 0.6, 2}
{0, 0.6}
{2, 4, 6}
Answers
Answer:
{2,4,6}
Step-by-step explanation:
Hope it helps you
if a labour earns Rs 6360 in a year find his earning in one month
Answers
There are 12 month in a year :
6360 ÷ 12 = 530
Thus the labour earns Rs 530 in a month .
To find this out we will divide 6360 by 12 (as there are 12 months in an year) 6360/12 = 530 . Therefore answer = rs 530
Pls follow and mark brainliest.
(Right angle) Trigonometry
please help!
Answers
Answer:
A = 41.4°
Step-by-step explanation:
Reference angle = A
Length of Adjacent side = 6
Length of Hypotenuse = 8
Apply the trigonometric function, CAH.
Cos A = Adj/Hyp
Substitute
[tex] Cos(A) = \frac{6}{8} [/tex]
[tex] A = Cos^{-1}(\frac{6}{8}) [/tex]
A = 41.4° (approximated to the nearest tenth)
help me find the perimeter of this square. if you can do it step by step please!
Answers
Answer:
396
Step-by-step explanation:
It's a square.
That means that all four sides are equal.
So the two expressions you have been given are equal.
2.5x + 76.5 = 12x - 9 Subtract 2.5x from both sides.
-2.5x -2.5x
76.5 = 9.5x - 9 Add 9 to both sides
9 9
85.5 = 9.5x Divide by 9.5
85.5/9.5 = x
x = 9
That is just the value for x. It is not the answer
Side = 12x - 9
Side = 12*9 - 9
Side = 108 - 9
Side = 99
The perimeter = 4 * Side
The perimeter = 4 * 99
Perimeter = 396
Hellllllllllp! Someone help
Answers
Answer:
4. (2, 3)
5. (0, 1)
7. (-1, 2)
Step-by-step explanation:
I hope this helps! Have a nice dayy! :)
You're very close. Choices D and E are two of the three answers. The third answer is choice G (-1,2)
In short, the 3 answers are Choices D, E and GIf you plug the coordinates of the points into the inequality, you should get a true statement.
For instance, let's try the coordinates of choice G
[tex]-2x + 3y\ge 3\\\\-2(-1) + 3(2)\ge 3\\\\2 + 6\ge 3\\\\8\ge 3\\\\[/tex]
Which is true since 8 is indeed greater than 3. That verifies point G is a solution point. A similar story happens with points D and E as well.
----------
If you tried something like choice A, then,
[tex]-2x + 3y\ge 3\\\\-2*(2) + 3(-3)\ge 3\\\\-4 - 9\ge 3\\\\-13\ge 3\\\\[/tex]
Which is false because -13 is not greater than 3, and -13 is not equal to 3 either. So choice A is a non-answer. You should find that choices B, C, and F are also non-answers.
----------
The graph is below. Notice how points D, E and G are either in the blue shaded region or on the boundary. The boundary line is solid (due to the "or equal to" as part of the inequality sign), so points on the solid boundary line are part of the solution set. The graph is a quick way to visually confirm the answers. I used GeoGebra to make the graph.
So that's why the 3 answers are D, E and G.
PLZ I NEED HELPPPPPPPP