Answer:
316 ls the next term greater than 312. in the sequence you are adding 4 to the preceding term
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.
Learn more here:
https://brainly.com/question/13602432
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
Read more about lengths at:
https://brainly.com/question/13147699
PLEASEEEE HELP! MY MOM IS GONNA KILL ME
Answer:
16
Step-by-step explanation:
Since the perimeter of the rectangle is 80, we can set up the perimeter formula:
80=2L+2W=2(3x+3)+2(2x+2)=6x+6+4x+4=10x+10
10x=70
x=7
AB=2x+2=2(7)+2=14+2=16
Answer:
AB= 16
Step-by-step explanation:
2x+2+3x+3=40
Add like terms: 2x+3x= 5x and 2+3=5
New equation: 5x+5=40
Solve: 40-5= 35
35 divided by 5= 7Now we know that x is equal to 7.
2(7)+2= 16
Side DC equals 16.
Side AB has the same length as side DC since it's a rectangle.
Side AB equals 16.
Let's check: 16+16=32 (side DC and side AB)
80-32=483(7)+3= 2424 must be the length of the other sides.
24+24= 48So, when you add all the sides together...
16+16+24+24= 80
You get 80, the perimeter!
I hope this helped!
For a weekly car rental, a car rental company charges customers a flat fee of $100 plus
10 cents for every mile traveled.
15 Write an equation for the amount, A dollars, of a weekly rental for a car that travels
m miles
The way you typed out this sentence was a bit confusing but I think you were saying...
For a weekly car rental, a car rental company charges customers a flat fee of $100 + and charges 10 cents for every mile traveled. write an equation for the amount of a weekly rental car that travels 15 miles (Please let me know if I am wrong)
The equation would be
10+10 +10+ 10+ 10+ 10+ 10+ 10+ 10+ 10+ 10+ 10+ 10+ 10+ 10 = 150 cents
so they would be charging $1.50
Hoped this helped!
Have a great day/night! :)
I really need help this is due in a little bit and I need to finish
Answer:
The correct form is [tex]y = -2x + 24[/tex]
Step-by-step explanation:
First we need to interpret the equation of Nolan.
The [tex]y[/tex] means the current value in the bank accountThe [tex]x[/tex] means the past days-2 means that spend each dayand 12 the initial amount in the bankHow you can see the initial amount in the bank is incorrect because Nolan started with 24 instead of 12.
So the correct form of the equation is:
[tex]y = -2x + 24[/tex]
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]
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:
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
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
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.
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:
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
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
Read and analyze the following. Write the correct answer.
1. What is a way of comparing two or more quantities?
2. What is the statement of equality between two ratio? Write a ratio of the following:
3. ?
4. ?
5. Compare the number of balloons to party hats. 三
6. Express the ratio in its simplest form the given figure in number 4. 7. Express the given ratio of four one-peso coins to Php80.00 coins in its simplest form using colon form. answer it with solution pls
Ratios are simply used to compare two or more related quantities
(a) Comparing quantities
To compare quantities, we make use of ratios.
Hence, a way to compare two or more quantities is by using ratio
(b) Statement of equality between ratios
When two or more ratios are equal, the ratios are said to be equivalent ratios
Hence, the statement of equality between ratios is equivalent ratios
(c) Express (3) and (4) as ratios
There are 10 stars and 8 crosses.
So, the ratio is 10 : 8
There are 3 toys and 9 books.
So, the ratio is 3 : 9
(d) Compare balloons and party hats
There are 12 balloons and 18 party hats.
So, the ratio is 12 : 18
Reduce the ratio as follows:
12 : 18 = 2 : 3 ---- this is done by dividing 12 and 18 by 6
So, the comparison is:
There are 2 balloons for every 3 party hats
(e) Simplify (4)
In (4), we have:
Ratio = 3 : 9
Divide by 3
Ratio = 1 : 3
Hence, the simplified ratio is 1 3
(f) Express the currency ratio in its simplest form
The ratio is given as:
Ratio = 4 * 1 peso coin : Php80.00 coin
Evaluate the product
Ratio = 4 peso coin : Php80.00 coin
Divide both sides by 4
Ratio = 1 peso coin : Php20.00 coin
Hence, the simplest form of the ratio is 1 : 20
Read more about ratios at:
https://brainly.com/question/25326254
workout the size of angle x
Answer:
Where is it?
Step-by-step explanation:
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
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...
Line /1 and line /2 are parallel lines. Determine the measures of <1 though <12
Answer:
1=56⁰
2=56⁰
3=68⁰
4=68⁰
5=56⁰
6=112⁰
7=180-124 Ans=56⁰
8=68+56 Ans=124⁰
9=68⁰
10=112⁰
11=124⁰
12=56⁰
MARK ME BRAINLIEST PLSSS ITS FREE
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!
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
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:
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
Learn more about distance travelled here:
https://brainly.com/question/17997145
Find m∠BXY.
HELPPPPP PLS
Answer:
60°
Step-by-step explanation:
Connecting the mid points of the three sides of the triangle makes four more triangles all similar and half the size of the original. Corresponding angles of similar triangles have the same measure.
What is the simplified form of the expression? 7r - 8r + 13 -2r + 5? Please help me
Answer:
- 3r + 18
Step-by-step explanation:
7r - 8r - 2r + 13 + 5 = 7r - 10r + 18
Determine the length of the model.
-60 ft-
1 in. = 8 ft
=
Does this graph represent a function? Why or why not?
Ay
10
8
8+
2+
1
-10-8-64
2
+ c
240
-
ON
10
4
-8-
-8-
-10
O A. No, because it fails the vertical line test.
O B. Yes, because it passes the vertical line test.
O C. No, because it is not a straight line.
O D. Yes, because it passes the horizontal line test.
The answer would e number B.
Please help and explain if you can the answer because I don’t know what I’m doing
Answer:
Step-by-step explanation:
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
solve for a?
a
+
-
If a
a
= 2
6 3
=
4
Step-by-step explanation:
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
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.