Answer:
12.89
Step-by-step explanation:
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g A pipe of negligible diameter is to be carried horizontally around a corner from a hallway 8 ft wide into a hallway 4 ft wide. What is the longest length that the pipe can be
The length of the longest pipe that can be carried horizontally is given by the minimum value of the function of the length of the pipe.
The longest length that the pipe can be is approximately 16.648 feet.
Reasons:
The length of the pipe, L
Width of the first hallway = 8 ft.
The width of the second hallway = 4 ft.
We have;
(L - a)·sin(θ) = 8
a·cos(θ) = 4
Therefore;
L - a = 8·csc(θ)
a = 4·sec(θ)
L(θ) = 8·csc(θ) + 4·sec(θ)
At the minimum length, we have;
L'(θ) = 4·sec(θ)·tan(θ) - 8·csc(θ)·cot(θ) = 0
4·sec(θ)·tan(θ) = 8·csc(θ)·cot(θ)
Therefore;
[tex]\displaystyle \frac{sec(\theta) \cdot tan(\theta)}{csc(\theta) \cdot cot(\theta)} = \frac{sin(\theta) \cdot tan(\theta) \cdot tan(\theta) }{cos(\theta) } =tan^3(\theta) = \frac{8}{4}[/tex]
[tex]\displaystyle tan(\theta) =\sqrt[3]{\frac{8}{4} } ={\sqrt[3]{2} }[/tex]
θ = arctan([tex]\sqrt[3]{2}[/tex]) ≈ 51.56°
a = 4×sec(arctan([tex]\sqrt[3]{2}[/tex]))
a ≈ 6.434
L = 8·csc(θ) + a = 8 × csc(arctan([tex]\sqrt[3]{2}[/tex])) + 4×sec(arctan([tex]\sqrt[3]{2}[/tex])) ≈ 16.648
The longest length that the pipe can be, L ≈ 16.648 ft.
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The longest length of the pipe is an illustration of trigonometry functions
The longest length of the pipe is 16.64 ft
The widths of the hallways are given as:
[tex]\mathbf{w_1 = 8}[/tex]
[tex]\mathbf{w_2 = 4}[/tex]
See attachment for the diagram that represents the scenario
From the diagram, we have:
[tex]\mathbf{sin(\theta) = \frac 4x}[/tex]
[tex]\mathbf{cos(\theta) = \frac 8y}[/tex]
Make x and y the subject
[tex]\mathbf{x = \frac 4{sin(\theta)}}[/tex]
[tex]\mathbf{y = \frac 8{cos(\theta)}}[/tex]
Where, the total length (L) of the pipe is:
[tex]\mathbf{L = x + y}[/tex]
So, we have:
[tex]\mathbf{L = \frac 4{sin(\theta)} + \frac 8{cos(\theta)}}[/tex]
Differentiate
[tex]\mathbf{L' = -\frac{4cos(\theta)}{sin^2(\theta)} + \frac{8sin(\theta)}{cos^2(\theta)}}[/tex]
Set to 0
[tex]\mathbf{-\frac{4cos(\theta)}{sin^2(\theta)} + \frac{8sin(\theta)}{cos^2(\theta)} = 0}[/tex]
Rewrite as:
[tex]\mathbf{\frac{4cos(\theta)}{sin^2(\theta)} = \frac{8sin(\theta)}{cos^2(\theta)}}[/tex]
Divide through by 4
[tex]\mathbf{\frac{cos(\theta)}{sin^2(\theta)} = \frac{2sin(\theta)}{cos^2(\theta)}}[/tex]
Cross multiply
[tex]\mathbf{2sin^3(\theta) = cos^3(\theta)}[/tex]
Divide both sides by [tex]\mathbf{2cos^3(\theta)}[/tex]
[tex]\mathbf{tan^3(\theta) = \frac 12}[/tex]
Take cube roots of both sides
[tex]\mathbf{tan(\theta) = \sqrt[3]{\frac 12}}[/tex]
[tex]\mathbf{tan(\theta) = 0.7937}[/tex]
Take arc tan of both sides
[tex]\mathbf{\theta = tan^{-1}(0.7937)}[/tex]
[tex]\mathbf{\theta = 38.4}[/tex]
Substitute [tex]\mathbf{\theta = 38.4}[/tex] in [tex]\mathbf{L = \frac 4{sin(\theta)} + \frac 8{cos(\theta)}}[/tex]
[tex]\mathbf{L = \frac 4{sin(38.4)} + \frac 8{cos(38.4)}}[/tex]
Evaluate
[tex]\mathbf{L = 6.43+ 10.21}}[/tex]
[tex]\mathbf{L = 16.64}}[/tex]
Hence, the longest length of the pipe is 16.64 ft
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Change the following numbers to decimals and round to the nearest hundredth
5/9
Answer:
Answer: 5/9 as a decimal is 0.556.
5/9 ≈ 0.56 rounded to the nearest hundredth, good luck
passes through (2,-3) with a slope of -9/2
Answer:
y = — 9/2x + 6
Step-by-step explanation:
m= —9/2
y — y1 = m (x — x1)
y + 3 = —9/2 (x — 2)
y = — 9/2x + 6
Lauren is at a friend's home that is several miles from her home. She starts walking at a constant rate in a straight line toward her home. The expression −2t + 10 gives the distance, in miles, that Lauren is from her home after t hours. Answer the following questions using the information above.
a. How many miles away from her house did Lauren start?
b. How fast is Lauren moving towards her house?
c. Why is the rate negative?
d. How far away from her house is Lauren after 4 hours?
a.
Lauren was 10 miles away from her house when he started.
Since the expression for Lauren's distance from her house, d = -2t + 10, to determine the number of miles away from his house that Lauren starts, we input t = 0, since this is the time Lauren starts walking.
So, with t = 0, d = -2t + 10
= -2(0) + 10
= 0 + 10
= 10 miles.
So, Lauren was 10 miles away from her house when he started.
b.
Lauren was moving at a rate of -2 mph towards her house.
To find how fast Lauren was moving towards her house, we differentiate d with respect to t.
So, dd/dt = d(-2t + 10)/dt
= d(-2t)/dt + d(10)/dt
= -2 + 0
= -2 mph
So, Lauren was moving at a rate of -2 mph towards her house.
c.
The rate is negative because her distance towards her house is decreasing
The rate is negative because her distance towards her house is decreasing since she is moving towards her house.
d.
Lauren is 2 miles away from her house after 4 hours
To find this, we input t = 4 into the equation for d.
So, d = -2t + 10
= -2(4) + 10
= -8 + 10
= 2 miles.
So, Lauren is 2 miles away from her house after 4 hours
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Solve the equation for B. PLEASE SHOW YOUR WORK.
2(B + 3.5 - B = -3(6 - 2B)
9514 1404 393
Answer:
B = 5
Step-by-step explanation:
The given equation has mismatched parentheses. We assume the intent is ...
2(b +3.5) -b = -3(6 -2b)
Eliminating parentheses, we have ...
2b +7 -b = -18 +6b
25 = 5b . . . . . . . . . . . add 18-b to both sides and collect terms
b = 5 . . . . . . . . . . . . divide both sides by 5
An electrician must use 15 miles of electrical cable between electric poles. How many yards of cable will be used?
13,200
26,400
39,600
79,200
158,400
Answer:
B) 26,400
An electrician must use 15 miles of electrical cable between electric poles. How many yards of cable will be used?
13,200
26,400
39,600
79,200
158,400
26400 yards of cable is used.
the answer is B) 26,400
What is unit conversion?
Unit conversion is the process of changing a physical quantity from one unit of measurement to another. For example, converting kilometers to miles, Celsius to Fahrenheit, or liters to gallons. The process involves multiplying or dividing the original measurement by a conversion factor, which is a ratio of equivalent units
To convert miles to yards, we need to multiply by the conversion factor of 1 mile = 1760 yards.
15 miles * 1760 yards/mile = 26,400 yards
So, the electrician will use 26,400 yards of cable.
Hence, 26400 yards of cable is used.
the answer is B) 26,400
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x^3-3x^2+x-2/10x^4-14x^3-10x^2+6x-10
Answer:
The quotient is 10x+16
The remainder is 28x^2+10x+22
Help!!! Show work!!!!!
Answer:
1. (-2,-5) (-1,-1) (0,3) (1,7) (2,11)
2. (-8,-4) (-4,-3) (0,-2) (4,-1) (8,0)
3. (-4,3) (-2,2) (0,1) (2,0) (4,-1)
4. (-2,-1) (-1,2) (0,5) (1,8) (2,11)
Step-by-step explanation:
1. Slope = (11-7)/(2-1) = 4/1 = 4/1
y-intercept: 7 - (4)(1) = 3
Start in the vertical line (y) on 3, 4 up and 1 to the right (you need to points to trace a line)
2. Slope = (0- - 2)/(8-0) = 1/4
y - intercept = -2-(1/4)(0) = -2
Start on -2 vertical line, 1 up and 4 to the right.
3. Slope = (1-0)/(0-2 = -1/2
y-Intercept: 0 - (-1/2)(2)=1
Start on 1 vertical line then 1 down and two to the right (the slope is negative, the line goes downhill)
4. Slope: (8-1)/(1-0) = 7/1
y-intercept = 1 - (7)(0) = 1
Start on 1 vertical line (y) , seven up and 1 to the right.
if 1 dollar equals 0.72p what is the exchange rate from pounds to dollars
Answer:
1 pound = 1.389 dollars ( to nearest thousandth)
Step-by-step explanation:
1 pound = 1/0.72 = 1.388888...
a car travels at 56 km per hour find the time it takes to travel 300 metres give your answer in seconds correct to the nearest second
1km = 1000 m , thus 56km = 56000 m
1hr = 60 mins
1min = 60 secs, therefore 60 mins = 60*60 seconds = 3600 seconds = 1hr
so then, we know the car travels 56000 meters in 3600 secs, how many seconds will that be for 300 meters?
[tex]\begin{array}{ccll} meters&seconds\\ \cline{1-2} 56000&3600\\ 300&x \end{array}\implies \cfrac{56000}{300}=\cfrac{3600}{x}\implies \cfrac{560}{3}=\cfrac{3600}{x} \implies 560x=10800 \\\\\\ x = \cfrac{10800}{560}\implies x = \cfrac{135}{7}\implies x \approx 19.286\implies \stackrel{\textit{rounded up}}{x = 19}[/tex]
Let be an angle in quadrant I such that sin +10 Find the exact values of sec 0 and tan 0.
Answer:
just look at picture's That's the answer
Nine more than the product of a number and 3 is equal to 6
Answer:
x = - 3
Step-by-step explanation:
9 more than the product of a number and three is equal 6.
9 + (x · 3) = 6
9 + 3x = 6
3x = -9 + 6
3x = - 3
x = - 3
Answer:
3x + 9 =6
Step-by-step explanation:
Simply the expression
-2.4f + 0.4f -15-3
Answer:-2.4f + 0.4f -15-3Step-by-step explanation:
Answer:
-1.8f - 19
Step-by-step explanation:
Sara has only nickels in her hand, and David has exactly the same
number of dimes and no other coins. Together, they have a total of $1.05. How many nickels does Sara have? How many dimes does David have? Show your work
using numbers, labeled sketches, or words.
Peter has 18 oranges, 27 pears and 12 bananas. He wants to make fruit baskets with
the same number of each fruit in each basket. What is the greatest number of fruit
baskets he can make? How many of each type of fruit will be in the baskets?
Answer:
3 baskets and 6 oranges, 9 pears, 4 bananas
Step-by-step explanation:
the common denominator is 3
write the fraction as a decimal use bar notatin if necessary
-2 5/22
Answer:
1.13
Step-by-step explanation:
to turn a fraction to a decimal divide the denomitator by the numerator [tex]\frac{-25}{22}[/tex] can also be written as -25÷22 which equals 1.13 or 1.136 with a line over it
Hope this helps!
Plz help!! Given: DE is a midsegment of ABC. Show all work.
Find the value of x and y.
And What is the length of AC? !Please show all work!
Incase photo is blurry
AE-y+6
EC-x-3
DE-x+2
BC-24
Answer:
AC=14
X=10
Y=1
Hoped this helped!
Step-by-step explanation:
DE is half of BC, therefore x=10. AE and EC have to be the same length, which is 7. SO, y=1 and x is 10.
Below is an excerpt from the home loan contract Kyle signed with his bank.
“The sum of the principal of the loan and all applicable interest will be divided into 360 monthly payments according to the amortization schedule.
The Buyer shall make each monthly payment by the first day of the month it is due. A payment not received by the first day of the month it is due will be considered delinquent. A payment not received by the fifteenth day of the month it is due will be subject to a late charge of $75.00. If a payment is not received by the last day of the month it is due, the Buyer and transaction shall be reported to the appropriate credit agencies.
In the event of delinquency, the Buyer may divide any payment not received into not more than three equal installments to be included on the next consecutive monthly payments. Notification of the Buyer’s intent to do so must be made by written letter or phone call to the phone number and address listed below within one business week of delinquency.”
Due to some changes at his job and the resulting loss of income, Kyle will not be able to make his monthly payment by the first of the month. He does expect to be able to make it by the 9th of the month. According to the contract, what does Kyle need to do?
a.
Other than pay the monthly payment, Kyle does not need to do anything.
b.
Notify the bank to let them know that his payment is going to be eight days late
c.
Divide this payment into three payments to be included in future monthly payments.
d.
Include an extra $75.00 with his payment to cover the late fee that will be assessed.
9514 1404 393
Answer:
a. Other than pay the monthly payment, Kyle does not need to do anything.
Step-by-step explanation:
If Kyle plans to make a payment by the 15th of the month, he need do nothing, except make the payment.
If he plans to divide the payment into 3 parts, he needs to contact the bank within a week of the first of the month. If he plans to make a payment after the 15th, he needs to add $75 to it for the late charge.
Answer:
i would think it would be [A Other than pay the monthly payment, Kyle does not need to do anything.]
Step-by-step explanation:
Determine the length of the model.
-60 ft-
1 in. = 8 ft
=
What is the property of this math problem please help
Answer:
distributive property
Step-by-step explanation:
Because distributive property formula is a(b+c) = ab + ac
meaning that w(6+5) = 6w + 5w
Please help and explain if you can the answer because I don’t know what I’m doing
Answer:
Step-by-step explanation:
Jamal had $25.00. He spent $9.00. Which decimal represents the fraction of the $25.00 that
Jamal spent?
A. 0.64
B. 0.36
C. 04
D. 06
Answer:
B. 0.36
Step-by-step explanation:
9/25 = x/100
9x100= 900
900 divided by 25 will be 36/100, so 0.36
A food store is making 60 jars of vegetables. Each jar will get 7.83 ounces of peas and carrots
combined. The food store has 384 ounces of peas for all the jars, and the carrots will be divided
equally among the jars. How many ounces of carrots will go into each jar?
Answer:
1.43 ounces
Step-by-step explanation:
384 / 60 = 6.4
7.83 - 6.4 = 1.43
Complete the table for an object that goes 3/4 mile in 6 minutes .
solve for a?
a
+
-
If a
a
= 2
6 3
=
4
Step-by-step explanation:
X+y=6 x-y=-2 solve by elimination
Step-by-step explanation:
x + y = 6
+ x - y = -2
------------------
2x + 0 = 4
x = 2
2 + y = 6
y = 4
How many solutions does this equation have
-4(5-3x)=12x+20
A) no solution
B) one solution
C) two solutions
D) infinitely many solutions
Answer:
A) no solution
Step-by-step explanation:
It’s A Contradiction
Answer:
its one solution
Step-by-step explanation:
-20+12
Celia's scores in the 5 quizzes Math are 18,12,15,19. What is her average score in Math?
d. 18
a. 15
c. 17
b. 16
Step-by-step explanation:
(18+12+15+19)÷5
64÷5
15
The population in millions of a city t years after 1990 is given by the equation p(t) = 2.9+0.08t in this function
Answer:
The answer would be 2.9 million is the population of the city in 1990 and 0.08 million is the increase per year in the population.
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1 3/10 x 18 please show work and answer
Answer:
Step-by-step explanation:
1 3/10 x 18
(1 x 10 +3)/10 = 13/10
13/10 x 18 = (13 x 18) / 10 = 234/10 = (234/2) / (10/2) = 117/5 = 23 2/5 (a fraction is a division)
The answer to the expression showing the product of 1 3/10 x 18 is 23 2/5.
Given is an expression showing the product of 1 3/10 x 18, we need to solve it,
To multiply a mixed number by a whole number, you can convert the mixed number to an improper fraction and then multiply the fractions.
Here's how you can solve the problem:
Step 1: Convert the mixed number to an improper fraction:
1 3/10 = (1 × 10 + 3) / 10 = 13/10
Step 2: Multiply the fractions:
13/10 x 18/1 = (13 x 18) / (10 x 1) = 234 / 10
Step 3: Simplify the fraction, if possible:
234/10 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2:
234/10 = (234 ÷ 2) / (10 ÷ 2) = 117/5
Therefore, 1 3/10 x 18 = 117/5.
Alternatively, you can express the answer as a mixed number by dividing the numerator by the denominator:
117 ÷ 5 = 23 with a remainder of 2
So, the final answer is 23 2/5.
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