Consider a window the shape of which is a rectangle of height h surmounted by a triangle having a height t that is 0.9 times the width w of the rectangle. if the cross-sectional area is a, determine the dimensions of the window which minimize the perimeter.
Answers
The cross-sectional area is (h × w ) + ((1 ÷ 2) × 0.9 × w²) and the dimensions of the window which minimize the perimeter is (A - \(c_{0}\)\(w_{0}^{2}\)) ÷ \(w_{0}\) = 2√A\(c_{1}\)(\(c_{2}\) - \(c_{0}c_1\)) = 0.60592√A.
height of rectangle = h
height of the triangle = t
T = 0.9
width of the rectangle = w
The formula of Cross-sectional area is,
A = h × w + (1 ÷ 2)T × w
A = (h × w ) + ((1 ÷ 2) × 0.9 × w²)
Perimeter,
P = w + (2 × h) + 2√(T² + (w ÷ 2)²)
P = w + (2 × h) + 2√((0.9)² + (1 ÷ 2)²)
P = 2h + 2√((0.9)² + (1 ÷ 2)² + 1) × w
Therefore, \(C_{0}\) = 0.9 ÷ 2, \(C_{1}\) = 2, \(C_{2}\) = 2√((0.9)² + (1 ÷ 2)² + 1)
minP=\(c_1\)h+\(c_2\)w
A = (h × w) + \(c_{0}\)w²
substituting h = (A - \(c_{0}\)w²) ÷ hw in P,
P = \(c_1\)w + (\(c_1\)(A - \(c_{0}\)w²) ÷ w)
Differentiating both sides,
(dP ÷ dw) = -2\(c_{0}\)\(c_{1}\) + \(c_{2}\) - (\(c_{2}\)(A - \(c_{0}\)w²) ÷ w²) = 0
\(w_{0}\) = (√\(c_{1}\)A ÷ (√\(c_{2}\) - \(c_{0}c_1\))) = 0.962445√A
and consequently,
\(h_{0}\) = (A - \(c_{0}\)\(w_{0}^{2}\)) ÷ \(w_{0}\) = 2√A\(c_{1}\)(\(c_{2}\) - \(c_{0}c_1\)) = 0.60592√A
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Related Questions
Is A J KL congruent to / MNP? If so, what composition of transformations maps A JKL onto A MNP?
Answers
From this statement, we concluded that ΔJKL is congruent to ΔMNP.
What is a congruent?
When all three corresponding sides and all three corresponding angles are the same sizes, two triangles are said to be congruent.
Here,
ΔJKL go right one, then go to left and then rotate to 180° on JK.
Now rotate 90° counterclockwise with the center of J.
Hence, we concluded that ΔJKL is congruent to ΔMNP because it's all sides are the same.
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Help!! I don’t know the answer
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Linda paid $28 for a sweater that was on sale for 30% off the original price. What was the original price of the sweater? (PLS SHOW WORK BRAINLIEST + 30 PTS TO WHOEVER ANSWERS FIRST)
Answers
Answer:
40 dollars.
Step-by-step explanation:
28=(.7)x
40=x
Thus, the original price was 40 dollars.
Find an equation for a line passing through (10,10) that is perpendicular to the line with equation 5x+8y=-9. Write your equation in
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The equation of a line passing through (10,10) that is perpendicular to the line with equation 5x + 8y = -9 is y - 10 = (8/5)(x - 10) or y = (8/5)x - 6.
Get the slope of the line 5x + 8y = -9 by rewriting it in slope-intercept form. Subtract 5x from both sides and divide by 8.
y = (-5/8)x - (9/8)
The slope of this line is -5/8. The negative reciprocal of -5/8 is 8/5. Therefore, the slope of the line that is perpendicular to 5x + 8y = -9 is 8/5.
Using point-slope form, determine the equation of the line.
y - y₁ = m(x - x₁)
y - 10 = (8/5)(x - 10)
or using the slope-intercept form,
y = mx + b
y = (8/5)x + b
10 = (8/5)10 + b
b = -6
y = (8/5)x - 6
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In this rectangle, the base is 1 cm more than the height. The area of the rectangle is 100 cm². Using a trial and improvement method, find the value of h, correct to 1 decimal place. You must show all of your working
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Let's assume the height of the rectangle is h cm. According to the problem, the base is 1 cm more than the height, so the base would be (h + 1) cm. The formula for the area of a rectangle is given by A = length × width.
Given that the area is 100 cm², we can write the equation as follows:
100 = h × (h + 1)
To solve this equation using a trial and improvement method, we can start by assuming a value for h and check if it satisfies the equation. Let's try h = 9:
100 = 9 × (9 + 1)
100 = 9 × 10
100 = 90
Since 90 is not equal to 100, we can try a different value. Let's try h = 10:
100 = 10 × (10 + 1)
100 = 10 × 11
100 = 110
Again, 110 is not equal to 100. We can continue this process until we find a value of h that satisfies the equation. Let's try h = 9.5:
100 = 9.5 × (9.5 + 1)
100 = 9.5 × 10.5
100 = 99.75
Now, 99.75 is close to 100 but not exactly. Let's try h = 9.6:
100 = 9.6 × (9.6 + 1)
100 = 9.6 × 10.6
100 = 101.76
101.76 is greater than 100, so we can conclude that the value of h is closer to 9.5 than 9.6. Therefore, the value of h, correct to 1 decimal place, is approximately 9.5 cm.
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solve this please pleaee maths question pleade
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Japanee adult eat about 79 pound of fruit each year. How many year doe it take for a Japanee adult to eat 1100 pound of fruit?
Answers
If it takes 1 year to eat 79lbs and how many years will will take to reach 1100lbs, Divide 1100 by 79. The answer should result around 13.92, rounding up to 14
For an experiment involving 2 Levels of factor A and 3 levels of factor B with a sample of n = 5 in each treatment condition, what is the value for df within treatments?
A 24
B 20
C 29
D 30
Answers
Option A is the correct answer.
For an experiment involving 2 Levels of factor A and 3 levels of factor B with a sample of n = 5 in each treatment condition, we need to calculate the value for df within treatments.
The formula to calculate df within treatments is given by, df within treatments = (A - 1) (B - 1) (n - 1)Where, A = Levels of factor AB = Levels of factor Bn = Sample size= 2 levels of factor A= 3 levels of factor B= 5 in each treatment conditionNow, df within treatments = (A - 1) (B - 1) (n - 1)= (2 - 1) (3 - 1) (5 - 1)= 1 × 2 × 4= 8Hence, the value of df within treatments is 8.
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What's 672 divided by 32
Answers
Answer:
the answer is 21
Step-by-step explanation:
Please Help, this is 20pts worth it.. Please Don’t waste my points.. please help..
Answers
Answer:
1. 7+62+5+4
2. 18+62+5
3.15+4+1
4.5 families
6. three
Step-by-step explanation:
1. Find the equation of a line that passes through the point (4,1) and is perpendicular to the
line that contains the points (3,-7) and (-1,9).
Answers
Answer:
x - 4y = 0 . . . in standard form
y = (1/4)x . . . in slope-intercept form
Step-by-step explanation:
The slope of the given line is ...
m = (y2 -y1)/(x2 -x1) = (9 -(-7))/(-1 -3) = 16/-4 = -4
The slope of the perpendicular line is the negative reciprocal of this:
desired slope = -1/m = -1/-4 = 1/4
This can be used in the point-slope form of the equation of a line:
y -h = m(x -k) . . . . . line with slope m through point (h, k)
Your perpendicular line has a slope of 1/4 and goes through point (4, 1), so its equation can be written as ...
y -1 = (1/4)(x -4)
y = (1/4)x -1 +1
y = (1/4)x
In standard form, this is ...
4y = x
x -4y = 0
jasmine is 5 years younger than twice her sister age of jasmine sister 22 year old then how old is jasmine
Answers
Answer:
100000000000000000000000000
Step-by-step explanation:
Answer:
Step-by-step explanation:
i think the answer is 12
Consider the following undirected, weighted graph (presented in edge list format). Node 1 Node 2 Weight A B 3 A F 5 B C 5 B G 9 CD 2 DE 7 DE 11 E J 8 F G 10 F K 4 G H 4 GL 2 HI 8 IJ 6 IN 3 JO 9 KL 8 K P 7 L M 3 L Q 10 MN 5 MR 5 NO 4 NS 8 OT 4 PQ5 PU 6 QR 4 Q V 8 RS 7 RW 2 SX3 T Y 7 U V 1 V W 7 W X 6 X Y 2 a) Draw the weighted graph. b) Draw the minimal spanning tree on the 5 by 5 square of nodes.
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The given undirected, weighted graph consists of various nodes connected by edges with corresponding weights. To draw the graph, we represent each node as a vertex and connect them with edges labeled with their respective weights.
To find the minimal spanning tree (MST) on the 5 by 5 square of nodes, we need to select the subset of edges that connect all the nodes with the minimum total weight.
a) Drawing the weighted graph: Based on the given edge list, we draw the graph by representing each node as a vertex and connecting them with edges labeled with their corresponding weights. We consider the nodes A, B, C, D, ..., and draw the edges with the respective weights between the corresponding vertices.
b) Drawing the minimal spanning tree (MST): To find the MST on the 5 by 5 square of nodes, we need to select the subset of edges that connect all the nodes with the minimum total weight. Starting from any node, we choose the edge with the minimum weight to connect it to another node. We continue this process, ensuring that we do not form cycles and include all the nodes until we have connected all the nodes with the minimum total weight.
By considering the weights and following the process described above, we draw the minimal spanning tree on the 5 by 5 square of nodes, connecting them with the minimum weight edges.
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PLS WHAT IS THE REAL ANSWWR ASAP
Answers
the answer is t<-48
i hope this helped you if you need the explanation lmk
A radio is #5400 when a discount of 14%is given for each.What is the cash price?
Answers
The cash price of one radio after a 14% discount is $4644.
The price of a radio is $5400. After giving a 14% discount for each radio, what will be the cash price?
Solution: The given price of the radio is $5400. The discount given on each radio is 14%.
Let's calculate the discount: Discount% = 14% Discount = (Discount%/100%) × Selling Price Discount = (14/100) × $5400 Discount = $756 Therefore, the discount on one radio is $756.
The cash price of one radio after a 14% discount is: Cash Price = Selling Price - Discount Cash Price = $5400 - $756Cash Price = $4644 Therefore, the cash price of one radio after a 14% discount is $4644.
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f (x) = x2 + 4
What is the value of x when f (x) = 42
A. -2
В. 0
C 12
D. 20
Answers
Answer:
f(x)=X^2+4
f(x)=42
42=X^2+4
X^2+4=42
X^2=42-4
X^2=38
X=sqrt(38)=6.16
\( \sqrt{?} \)
Jabal and Michael are walking to school and agree to leave their homes at the same time.
Jabal leaves his house walking 2.5 meters per second. Michael leaves his house walking 5 meters per second.
Jabal's house is 15 meters closer to school than Michael's house, therefore he is starting 15 meters closer than Michael.
After how long are the boys walking together? Use any strategy you'd like to solve.
Answers
Answer: 6 seconds
Step-by-step explanation:
Time Jabal (2.5mps) Michael (5mps)
Start 15 0
1 sec 17.50 5
2 20 10
3 22.5 15
4 25 20
5 27.5 25
6 30 30
7
8
9
10
Answer:
6 sec
Step-by-step explanation:
Let d = distance for Jabal
d + 15 = distance for Michael
t = d/r
d/2.5 = time for Jabal
(d + 15)/5 = time for Michael
The times are equal since they both started walking at the same time.
(d + 15/5 = d/2.5
2.5(d + 15) = 5d
2.5d + 37.5 = 5d
37.5 = 2.5d
d = 15 m. = Jabal's distance
15/2.5 = 6 sec.
Complete the square to rewrite x^2+y^2+2x+6y-6=0 in graphing form
Answers
Answer:
(x + 1)² + (y + 3)² = 16
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
x² + y² + 2x + 6y - 6 = 0
Collect the x and y terms together and add 6 to both sides
x² + 2x + y² + 6y = 6
To complete the square
add ( half the coefficient of the x/ y terms )² to both sides
x² + 2(1)x + 1 + y² + 2(3)y + 9 = 6 + 1 + 9
(x + 1)² + (y + 3)² = 16
with centre = (- 1, - 3) and r = \(\sqrt{16}\) = 4
What is 1/20 as a percentage
Answers
Answer:
1/20 = 5%
Hope this helps with your question :)
Step-by-step explanation:
1. Multiply numerator and denominator by 5 to get 100 in the denominator.
1/20 = 5/100
2. A number over 100 means it is that number on top of 100.
5/100 = 5% out of 100%
3. So final answer is 5%
Classifiy the triangle by using its side lengths
Answers
Answer: Where is the triangle?
Step-by-step explanation: Brainliest pls:)
5×62+6×33-68 (help pls I need it
Answers
Answer:
440
Step-by-step explanation:
To do this problem, you have to follow the PEMDAS order.
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
We have to do 5x62 first, which is 310. Next, we multiply 6 and 33, which gets us 198. Then, we add 310 to 198, which is 508. Finally, we subtract 68 from 508 to get 440.
Hope this helps!
Have a wonderful day! :D
First multiple 62x5 by using calculator then add that total with 6 then multiple with the result u got by 33 then subtract-that total with 68. And u will get answer 440
find the hcf of 91 , 112 , 49
Answers
Answer: The highest common factor of 91, 112 and 49 is 7
hope this helps :)
Help please
Brainiest answer to whoever is first
Answers
Answer:
84 inches squared
Step-by-step explanation:
perimeter = 6+7+5+10+15
= 43
HW 3: Problem 9 Previous Problem List Next (1 point) Suppose that X is normally distributed with mean 110 and standard deviation 21. A. What is the probability that X is greater than 145.28? Probabili
Answers
The probability that X is greater than 145.28 is approximately 0.0465.
Given that X is normally distributed with mean (μ) of 110 and standard deviation (σ) of 21. We are to find the probability that X is greater than 145.28. It can be calculated as follows: We can calculate the Z-score value with the help of the following formula, Z = (X - μ) / σWhere X is the random variable value, μ is the mean, and σ is the standard deviation. Substituting the values in the formula, we get: Z = (145.28 - 110) / 21Z = 1.68476 Using the Z-table, we can find the probability that X is greater than 145.28 as follows: From the Z-table, we get: P(Z > 1.68) = 0.0465
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
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Given the following linear function sketch the graph of the function and find the domain and range.
\(f\left(x\right)\ =\ \frac{2}{7}x\-21)
Answers
A graph of the given linear function (y = 2x/7 - 2)is shown in the image attached below.
The domain of the given linear function is (-∞, ∞).
The range of the given linear function is (-∞, ∞).
How to determine the domain and range?In Mathematics, the horizontal extent of a graph represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.
Furthermore, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph of this function shown in the image attached below, we can reasonably and logically deduce the following domain and range:
Domain = -∞ < x < ∞ or (-∞, ∞).
Range = -∞ < y < -∞ or (-∞, ∞).
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Complete Question:
Given the following linear function sketch the graph of the function and find the domain and range. y = 2x/7 - 2
Does anybody know this?Put the following numbers in order from least to greatest.
Answers
Answer:
\(-\sqrt{12}; -\frac{12}{5}; -1.5; 0; 0.3\)
P.S. Hope it helps. If you have any questions, feel free to ask them in the comment section below. I'll be happy to help with whatever I can. Have a wonderful day!
Find the interquartile range of these data.
5, 12, 9, 8, 6, 2, 6
Answers
Answer: 7
Step-by-step explanation:
HELLP I need this question
Answers
Answer:5^15
Step-by-step explanation: I am Smart :>
Answer:
\(5^{15}\)
Step-by-step explanation:
\(\frac{(5^3)^9}{5^{12}} \\\\\frac{5^{27}}{5^{12}} \\\\5^{15}\)
3 x 9 = 27
27 - 12 = 15
NEED HELP ASAP Let the function f(x) have the form f(x) = Acos(x+C). To produce a graph that matches the one shown below, what must the value of C be?
Answers
Answer:
\(C = 2\) (A)
Step-by-step explanation:
We assume the constant A is different than 0
We notice that the graph of the function intercepts the x-axis when x = -0.5
we know that cos(x) = 0 when x = π/2 or x = -π/2
thus, \(-0.5 + C = \pi /2\) or \(-0.5 + C = -\pi /2\)
then \(C = \pi /2 + 0.5 = 2\) or \(C = -\pi /2 = 0.5 = -1\)
so \(C = 2\)
There are five vowels (a,e,i,o,u) along with 21 consonants. Suppose that you decide to make up a password where the first seven characters alternate - consonant, vowel, consonant, vowel, consonant, vowel - with repetitions allowed, and a digit as the eighth character. How many different passwords can be make up
Answers
There are 1,602,562,500 different passwords that can be made up using the given pattern and character choices.
We need to make a password with eight characters, where the first seven characters follow the pattern CVCVCVC, and the eighth character is a digit. There are 21 consonants and 5 vowels available, and there are 10 digits (0-9) available for the eighth character.
To find the number of possible passwords, we can count the number of choices for each character in the password, and then multiply the choices together.
For the first character, we can choose from 21 consonants. For the second character, we can choose from 5 vowels. For the third character, we can choose from 21 consonants again, and so on, alternating between consonants and vowels. For the eighth character, we can choose from 10 digits.
Therefore, the total number of possible passwords is:
21 x 5 x 21 x 5 x 21 x 5 x 21 x 10 = 1,602,562,500
So there are 1,602,562,500 different passwords that can be made up using the given pattern and character choices.
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