A= -1 -1 1 3 -1 -1 1 3 b 5 7 (a) (10 points) Find the QR factorization of A. (b) (5 points) Calculate the orthogonal projection of b onto the range of A. (c) (8 points) Find the solution for least squ
Answers
The least squares problem is [ 192; 192 ].
(a) To find the QR factorization of matrix A, we need to find an orthogonal matrix Q and an upper triangular matrix R such that A = QR.
Let's perform the QR factorization:
Step 1: Find the first column of Q
a1 = A(:,1) = [-1, 3, -1, 1]'
q1 = a1 / ||a1|| = [-1, 3, -1, 1]' / √(6)
Step 2: Find the second column of Q
a2 = A(:,2) = [-1, -1, 1, 3]'
q2 = a2 - (q1' * a2) * q1
= [-1, -1, 1, 3]' - (1/6) * [-1, 3, -1, 1]' * [-1, -1, 1, 3]'
= [-1, -1, 1, 3]' - (1/6) * 18
= [-1, -1, 1, 3]' - [3, 3, -3, -9]'
= [-4, -4, 4, 12]'
q2 = q2 / ||q2|| = [-4, -4, 4, 12]' / √(256) = [-1/4, -1/4, 1/4, 3/4]'
Step 3: Construct Q matrix
Q = [q1, q2] = [ [-1/√6, -1/4], [3/√6, -1/4], [-1/√6, 1/4], [1/√6, 3/4] ]
Step 4: Calculate R matrix
R = Q' * A
R = [ [-1/√6, -1/4], [3/√6, -1/4], [-1/√6, 1/4], [1/√6, 3/4] ]' * [ -1, -1, 1, 3; -1, -1, 1, 3 ]
R = [ [√6, √6, -√6, -√6], [0, -1/2, 1/2, 3/2] ]
Therefore, the QR factorization of matrix A is:
Q = [ [-1/√6, -1/4], [3/√6, -1/4], [-1/√6, 1/4], [1/√6, 3/4] ]
R = [ [√6, √6, -√6, -√6], [0, -1/2, 1/2, 3/2] ]
(b) To calculate the orthogonal projection of b onto the range of A, we can use the formula:
Proj(b) = A * (A' * A)^(-1) * A' * b
Let's calculate it:
b = [5, 7]'
Proj(b) = A * (A' * A)^(-1) * A' * b
= [ -1, -1, 1, 3; -1, -1, 1, 3 ] * ( [ -1, -1, 1, 3; -1, -1, 1, 3 ]' * [ -1, -1, 1, 3;
-1, -1, 1, 3 ] )^(-1) * [ -1, -1, 1, 3; -1, -1, 1, 3 ]' * [5, 7]'
= [ -1, -1, 1, 3; -1, -1, 1, 3 ] * ( [ 10, 10; 10, 10 ] )^(-1) * [ -1, -1, 1, 3; -1, -1, 1, 3 ]' * [5, 7]'
= [ -1, -1, 1, 3; -1, -1, 1, 3 ] * ( [ 1/2, -1/2; -1/2, 1/2 ] ) * [ -1, -1, 1, 3; -1, -1, 1, 3 ]' * [5, 7]'
= [ -1, -1, 1, 3; -1, -1, 1, 3 ] * [ 1, -1; -1, 1 ] * [ -1, -1, 1, 3; -1, -1, 1, 3 ]' * [5, 7]'
= [ -1, -1, 1, 3; -1, -1, 1, 3 ] * [ -2, 0; 0, -2 ] * [ -1, -1, 1, 3; -1, -1, 1, 3 ]' * [5, 7]'
= [ -1, -1, 1, 3; -1, -1, 1, 3 ] * [ -2, 0; 0, -2 ] * [ -1, -1; -1, -1; 1, 1; 3, 3 ] * [5, 7]'
= [ -1, -1, 1, 3; -1, -1, 1, 3 ] * [ -2, 0; 0, -2 ] * [ -12, -12; 12, 12 ] * [5, 7]'
= [ -1, -1, 1, 3; -1, -1, 1, 3 ] * [ -24, -24; 24, 24 ] * [5, 7]'
= [ -1, -1, 1, 3; -1, -1, 1, 3 ] * [ -48, -48; 48, 48]'
= [ -48, -48; -48, -48 ] * [5, 7]'
= [ (-48 * 5) + (-48 * 7); (-48 * 5) + (-48 * 7) ]
= [ -240 - 336; -240 - 336 ]
= [ -576; -576 ].
Therefore, the orthogonal projection of b onto the range of A is [ -576; -576 ].
(c) To find the solution for the least squares problem, we can use the formula:
x = (A' * A)^(-1) * A' * b
Let's calculate it:
x = (A' * A)^(-1) * A' * b
= ( [ -1, -1, 1, 3; -1, -1
, 1, 3 ]' * [ -1, -1, 1, 3; -1, -1, 1, 3 ] )^(-1) * [ -1, -1, 1, 3; -1, -1, 1, 3 ]' * [5, 7]'
= ( [ 10, 10; 10, 10 ] )^(-1) * [ -1, -1, 1, 3; -1, -1, 1, 3 ]' * [5, 7]'
= ( [ 1/2, -1/2; -1/2, 1/2 ] ) * [ -1, -1, 1, 3; -1, -1, 1, 3 ]' * [5, 7]'
= [ 1, -1; -1, 1 ] * [ -1, -1, 1, 3; -1, -1, 1, 3 ]' * [5, 7]'
= [ -2, 0; 0, -2 ] * [ -1, -1, 1, 3; -1, -1, 1, 3 ]' * [5, 7]'
= [ -2, 0; 0, -2 ] * [ -1, -1; -1, -1; 1, 1; 3, 3 ] * [5, 7]'
= [ -2, 0; 0, -2 ] * [ -12, -12; 12, 12 ] * [5, 7]'
= [ -2, 0; 0, -2 ] * [ -24, -24; 24, 24 ] * [5, 7]'
= [ -2, 0; 0, -2 ] * [ -48, -48; 48, 48]' * [5, 7]'
= [ -96, 96; -96, 96 ] * [5, 7]'
= [ (-96 * 5) + (96 * 7); (-96 * 5) + (96 * 7) ]
= [ -480 + 672; -480 + 672 ]
= [ 192; 192 ].
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Related Questions
A contractor purchases seven dozen pairs of padded work gloves for $101.64 she incorrectly calculated the unit price is $14.52 prepared for the expense report what is the correct unit price what is this error
Answers
Answer:
i got 14.52 as the unit price, Is there some sort of tax or extra expense not included with your question?
Step-by-step explanation:
What is the length of the hypotenuse of the triangle when x=11?
Answers
Answer:
hypotenuse = 93.06
Step-by-step explanation:
\(x = 11\\\\base = 4 \times 11 = 44\\\\height = 7x + 5 = 7 \times 11 + 5 = 77 + 5 = 82\\\\hypotenuse ^2 = base^2 + height^2\\\)
\(=44^2 + 82^2\\\\=8660\)
\(\\\\hypotenuse=93.06\)
What is 25x + 67y if x = 23 and y = 36. Give explanation please!
Answers
Answer:
2987.
Step-by-step explanation:
25(23) + 67(36) = 575 + 2412 = 2987.
Hi there! Hopefully this helps!
------------------------------------------------------------------------------------------------------------
Answer: 2987
First we need to rewrite the equation. Since x = 23 and y = 36 the equation should look like this for easier steps:
25(23) + 67(36) = ?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Now since there numbers by other numbers in parentheses, we need to multiply them.
25 x 23 = 575.
67 x 36 = 2412.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Now that the equation is in its final form, we write it like this for the answer:
575 + 2412 =
2987.Solve thi ytem of linear eqarion. Separate the x-and t-hirt value with a comma
2x=96-14y
9x=40-14y
Answers
The solution which we get for the given question is , x = 5/2 and y = 5/4 answer.
Isolating x,
2x = 9x - 14y
2x-9x = 9x-9x -14y
-7x = -14y
-7x/-7 = -14y/-7
x = 2y
Therefore substituting value of x on equation 2,
9(2y) = 40 - 14y
18y = 40 - 14y
18y+14y = 40 -14y+14y
32y = 40
32y/32 = 40/32
y = 5/4
Therefore , x = 10/4 = 5/2
as because x =2y.
An equation is a mathematical statement which equated two value using the equal sign. Eg.) 2x = y
These expressions on either side of the equals sign are referred to as the equation's "left" and "right" sides. The right-hand side of an equation is usually assumed to be zero. The generality will still be there as because we can balance it by subtracting the right-hand side expression from the expressions on both sides.
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Help me asaaaaappppppppppp please
Answers
Answer:
-29
Step-by-step explanation:
2(b-4)=3(b+7)
2b-8=3b+21
2b-3b=21+8
-b=29
b=-29
C
f
33 mi
44 mi
What is the length of the hypotenuse?
C =
miles
Answers
Answer:
The hypotenuse is 55 miles
Step-by-step explanation:
Given the sides of a right angle triangle as 33 and 44 miles, we want to get the hypotenuse
Mathematically, by Pythagoras’ theorem, the hypotenuse square is the sum of the squares of the other two sides
So we have;
h^2 = 33^2 + 44^2
h^2 = 3025
h = √3025
h =55 miles
9 - 6(x+1) = 2(x-4) + 27
Answers
1) Use the distributive property to multiply −6 by x + 1
9−6x −6 = 2(x−4) +27
2) Subtract 6 from 9 to get 3
3−6x =2(x−4) +27
3) Use the distributive property to multiply 2 by x−4
3−6x =2x−8 +27
4) Add −8 and 27 to get 19
3−6x = 2x +19
5) Subtract 2x from both sides
3−6x −2x = 19
6) Combine −6x and −2x to get −8x
3−8x = 19
7) Subtract 3 from both sides
−8x= 19−3
8) Subtract 3 from 19 to get 16
−8x = 16
9) Divide both sides by −8
x= 16/-8
10) Divide 16 by −8 to get −2
x=−2
Hope this helps :D
List the two outliers in this graph.
Answers
Answer:
(10.5,14) and (15,3.5)
Step-by-step explanation:
solve (8.5) . (-3) =a
Answers
Answer:
The answer is a = -25.5
Step-by-step explanation:
(8.5) . (-3) =a
-25.5 = a
a = -25.5 is your answer
Answer:
a = -25.5
Step-by-step explanation:
7. The quality control division of Rothschild's Blueberry Farm randomly inspects 100 of the containers in the truck being
sent to Stop and Shop. Identify the population and sample given in this scenario.
Answers
The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.
Population: The containers of blueberries that are being sent to Stop and Shop.
Sample: The 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.
Therefore, the 100 containers that the quality control division of Rothschild's Blueberry Farm randomly inspects.
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Which ordered pair is included in the solution set to the following system?y < x^2 + 3y > x^2 – 2x + 8(–4, 2)(0, 6)(1, 12)(4, 18)
Answers
To determine which of the 4 pairs is part of the solution set, let's simply replace the value of "x" in the inequalities above and see if it makes the expression true or not.
Let's start with (-4, 2). Replace "x" with -4 and "y" with 2. Let's use the first inequality.
\(\begin{gathered} yLet's check the second inequality. Replace "x" with -4 and "y" with 2.\(\begin{gathered} y>x^2-2x+8 \\ 2>(-4)^2-2(-4)+8 \\ 2>16+8+8 \\ 2>32-FALSE \end{gathered}\)Since it is false for the second inequality, (-4, 2) is not part of the solution set.
Let's move on to (0, 6). Replace "x" with 0 and "y" with 6.
\(\begin{gathered} ySince it is false in the first inequality, (0, 6) is also not part of the solution set. No need to check for the second inequality.Let's move on to (1, 12). Replace "x" with 1 and "y" with 12.
\(\begin{gathered} yOnce again, (1, 12) is false for the first inequality. Hence, (1,12) is not part of the solution set.Lastly, let's check the 4th pair (4, 18). Replace "x" with 4 and "y" with 18.
\(\begin{gathered} yLet's also check if it is true for the second inequality,\(\begin{gathered} y>x^2-2x+8 \\ 18>4^2-2(4)+8 \\ 18>16-8+8 \\ 18>16-TRUE \end{gathered}\)As we can see above, the ordered pair (4, 18) makes both inequalities true hence, (4, 18) is included in the solution set of the given system of inequalities. (Option 4)
Shayla decides to have a bbq for her birthday and purchased sodas and juice pouches. She paid $6 for each soda and the price of each juice pouch was 50% of each soda. She paid no more than $70.
Write an inequality that represents all possible combinations of x, the number of sodas, and y, the number of juice pouches purchased.
Answers
Answer:
Juice is 3 dollars
Step-by-step explanation:
If soda is 6 dollars then juice is 3 dollars. So dividing 70 we get 35$, she could get around 6 sodas and 12 jucies
Please help me....Could you answer these 2 questions correctly?
Answers
Answer:
A
Step-by-step explanation:
for the two of them, the first answer is the answer
Answer:
#1 - First option: y + 7 = \(\frac{-1}{4}\)(x -4)
#2 - First option: y = 2x - 5
Step-by-step explanation:
#1
Given: (x1,y1) = (4,-7) and m = \(\frac{-1}{4}\);
To find the point slope form which is
y - y1 = m(x - x1); substitute (x1,y1) and m
y - (-7) = \(\frac{-1}{4}\)(x -4)
y + 7 = \(\frac{-1}{4}\)(x -4)
#2
Given: points (x1,y1) = (0, -5) and (x2,y2)=(4,3)
To find the slope we use
m = \(\frac{(y2-y1)}{(x2-x1)}\) = \(\frac{(3-(-5))}{(4-0)}\) = \(\frac{8}{4}\) = 2
Now pick a number to find b
y = mx + b
y1 = mx1 + b
-5 = 2(0) + b
b = -5
now plug into y = mx + b; which is
y = 2x - 5
solve for x
x/4 - 3 = 0
Answers
Answer:
Step-by-step explanation:
x/4 - 3 = 0
x/4 = 3
x = 12
Answer:
12
Step-by-step explanation:
x/4-3 =0 /×4
x - 12 =0
x=12
1. A traveling wave A snapshot (frozen in time) of a water wave is described by the function z=1+sin(x - y) where z gives the height of the wave and (x, y) are coordinates in the horizontal plane z=0. a) Use Mathematica to graph z =1+sin(x - y). b) The crests and the troughs of the waves are aligned in the direction in which the height function has zero change. Find the direction in which the crests and troughs are aligned. c) If you were surfing on this wave and wanted the steepest descent from a crest to a trough, in which direction would you point your surfboard (given in terms of a unit vector in the xy-plane)? d) Check that your answers to parts (b) and (c) are consistent with the graph of part (a).
Answers
The partial derivatives with respect to x and y, we obtain dz/dx = cos(x - y) and dz/dy = -cos(x - y), respectively. When dz/dx and dz/dy are both zero, the crests and troughs are aligned.
The given water wave function is graphed as z = 1 + sin(x - y) using Mathematica. The crests and troughs of the wave are aligned in the direction of zero change in the height function, which can be determined by analyzing the partial derivatives. The steepest descent from a crest to a trough corresponds to the direction perpendicular to the alignment of crests and troughs. These conclusions are consistent with the graph of the wave.
The water wave function z = 1 + sin(x - y) represents a snapshot of a frozen water wave. To graph this function using Mathematica, the x and y coordinates are assigned appropriate ranges, and the resulting z-values are plotted.
To determine the alignment of the crests and troughs, we examine the rate of change of the height function. Taking the partial derivatives with respect to x and y, we obtain dz/dx = cos(x - y) and dz/dy = -cos(x - y), respectively. When dz/dx and dz/dy are both zero, the crests and troughs are aligned. Setting dz/dx = 0 gives cos(x - y) = 0, which implies x - y = (2n + 1)π/2, where n is an integer. This equation represents lines in the xy-plane along which the crests and troughs are aligned.
For the steepest descent from a crest to a trough, we need to find the direction of maximum decrease in the height function. This direction corresponds to the negative gradient of the height function, which can be obtained by taking the partial derivatives dz/dx and dz/dy and forming the vector (-dz/dx, -dz/dy). Simplifying this vector, we get (-cos(x - y), cos(x - y)), which represents the direction perpendicular to the alignment of crests and troughs.
Upon examining the graph of the wave, we can observe that the lines of alignment for the crests and troughs match the lines where the height function has zero change, confirming our conclusion from part (b). Similarly, the direction of steepest descent from a crest to a trough, indicated by the negative gradient, aligns with the steepest downward slopes on the graph.
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a rectangular box with square base and top is to be constructed using sturdy metal. the volume is to be 16 m3 3 . the material used for the sides costs $4 per square meter, and the material used for the top and bottom costs $1 per square meter. what is the least amount of money that can be spent to construct the box?
Answers
The least amount of money used to construct the rectangular box with volume of 16 m³ is equal to $61.4 ( approximately ).
Let x be the length of one side of the square base, and let y be the height of the box.
Since the volume of the box is given as 16 m³, we have,
Volume = (Area of base) × Height
⇒16 = x²y
We want to minimize the cost of constructing the box, which is a function of the surface area of the box.
The surface area consists of the area of the top and bottom which are squares with side length x.
Area of the four sides which are rectangles with width y and height x
Surface area = 2(x²) + 4(xy)
Express the cost of constructing the box in terms of x and y, using the given costs of the materials,
Cost = 4(2xy) + 1(2x²)
= 8xy + 2x²
Minimize this cost subject to the constraint on the volume,
16 = x²y
Use the constraint to eliminate y from the cost function,
y = 16/x²
Substituting this into the cost function, we get,
Cost = 8x(16/x²) + 2x²
= 128/x + 2x²
To minimize this function,
Take the derivative with respect to x, set it equal to zero, and solve for x,
d(Cost)/dx = -128/x² + 4x
⇒= -128/x² + 4x = 0
⇒ 4x³ = 128
⇒ x = 2∛4
⇒x = 3.174
⇒ x ≈ 3.2
Use the constraint to find y,
16 = x²y
⇒ 16 = (2∛4)²y
⇒ y = 16/(2∛4)²
⇒ y = 1.5874
⇒ y ≈ 1.6
The dimensions of the box that minimize the cost are x = 3.2 meters, y = 1.6 meter.
The minimum cost is equal to,
Cost = 8xy + 2x²
= 8(3.2)(1.6) + 2(3.2)²
= 61.44
≈ $61.4
Therefore, the least amount of money that can be spent to construct the box with given volume is $61.4.
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What is the yield to maturity of a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons if this bond is currently trading for a price of $884?
5.02%
6.23%
6.82%
12.46%
G
5.20%
Answers
The yield to maturity of a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons, if the =bond is currently trading for a price of $884, is 6.23%. Thus, option a and option b is correct
Yield to maturity (YTM) is the anticipated overall return on a bond if it is held until maturity, considering all interest payments. To calculate YTM, you need to know the bond's price, coupon rate, face value, and the number of years until maturity.
The formula for calculating YTM is as follows:
YTM = (C + (F-P)/n) / ((F+P)/2) x 100
Where:
C = Interest payment
F = Face value
P = Market price
n = Number of coupon payments
Given that the bond has a coupon rate of 5.2%, a face value of $1000, a maturity of ten years, semi-annual coupon payments, and is currently trading at a price of $884, we can calculate the yield to maturity.
First, let's calculate the semi-annual coupon payment:
Semi-annual coupon rate = 5.2% / 2 = 2.6%
Face value = $1000
Market price = $884
Number of years remaining until maturity = 10 years
Number of semi-annual coupon payments = 2 x 10 = 20
Semi-annual coupon payment = Semi-annual coupon rate x Face value
Semi-annual coupon payment = 2.6% x $1000 = $26
Now, we can calculate the yield to maturity using the formula:
YTM = (C + (F-P)/n) / ((F+P)/2) x 100
YTM = (2 x $26 + ($1000-$884)/20) / (($1000+$884)/2) x 100
YTM = 6.23%
Therefore, If a ten-year, $1000 bond with a 5.2% coupon rate and semi-annual coupons is now selling at $884, the yield to maturity is 6.23%.
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Lisa represented the phrase '9 less than a number' with the expression 9-n.
Is her expression correct? Explain why or why not.
Answers
Each triangle in the STL file is defined by the vertices and inward pointing surface normal vector True O False Since the STL file is created from the Solid Model, it can be reconverted into the original CAD model O True False Which one of the following is NOT an advantage of using lattice structure? Reducing the weight Saving the material cost Simplifying the design and manufacturing process Increasing the heat exchange area for a heat exchanger
Answers
False. Each triangle in the STL file is defined by the vertices, but not necessarily by the inward pointing surface normal vector. The surface normal vector is often calculated based on the vertex positions.
False. The STL file is a mesh representation of the CAD model, and it does not contain all the information needed to fully reconstruct the original CAD model. It lacks information such as parametric features, assembly relationships, and design intent, making it difficult to recreate the exact original model.
The option "Increasing the heat exchange area for a heat exchanger" is NOT an advantage of using a lattice structure. Lattice structures are known for their lightweight properties, material-saving benefits, and simplified design and manufacturing processes.
However, increasing the heat exchange area for a heat exchanger is not typically associated with lattice structures. Heat exchangers usually rely on other design considerations, such as fin arrays or extended surfaces, to enhance heat transfer efficiency, rather than lattice structures.
Therefore, increasing heat exchange area is not a direct advantage of lattice structures.
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If a truss has 12 joints, what is the maximum number of members the truss can have and still be statically determinate? a. 24 b.18 c. 21 d. 12
Answers
The maximum number of members the truss can have and still be statically determinate if a truss has 12 joints is 21.
How to determine the maximum number of members of a truss?The maximum number of members that a truss can have and still be statically determinate can be found using the following formula:
Maximum number of members = 2j - 3
Where j represents the number of joints in the truss. If a truss has 12 joints, the maximum number of members it can have can be calculated as;
Maximum number of members = 2j - 3
Maximum number of members = 2(12) - 3
Maximum number of members = 21
Hence, maximum number of members the truss can have and still be statically determinate is 21.
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I need the answer for both questions btw its 1 problem I'll give you brainlist if you get it correct i need it asap
Answers
Answer:
1.) B (Real Numbers)
2.) A
Step-by-step explanation:
Describe what the graph would look like for the inequality.
x < -6 or x >= 4
Answers
Answer:
Step-by-step explanation:
on a number line
open circle on the -6 and draw a line to the left to ten with the arrow on the end
make a closed circle on positive 4 and draw a line to the right to 10 with arrow at the end
pls help me i’ll give brainliest
Answers
Answer:
25/0 aka infinity
Step-by-step explanation:
Equation used:
(y2-y1)/(x2-x1)
1. Plug in the values to get (27-2)/(9-9)
2. Simplify to get 25/0
3. This results in an infinity
Hi can someone please tell me what the answer is thanks!
Answers
Answer:
B. 6
Step-by-step explanation:
50 times 3/5 = 150/5 = 30
30 times 4/5 = 120/5 = 24
24 times 1/4 = 24/4 = 6
Lanthanum -144 becomes cerium- 144 when it undergoes a beta decay (write an equation)
Answers
Beta decay is a type of radioactive decay that occurs in certain atomic nuclei. It involves the transformation of a neutron or proton within the nucleus into the other.
In the case of Lanthanum-144 (La-144), a neutron undergoes beta decay to convert into a proton, resulting in the formation of Cerium-144 (Ce-144).
The equation for the beta decay of La-144 into Ce-144 is as follows:
La-144 → Ce-144 + β¯
In this equation, the La-144 nucleus decays into the Ce-144 nucleus. To conserve charge, a beta particle (β¯) is emitted. The beta particle can be either an electron (β-) or a positron (β+), depending on the specific type of beta decay occurring in the nuclide.
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A gardener wants to divide a square piece of lawn in half diagonally. What is the length of the diagonal if the side of the square is ? Leave your answer in simplest radical form.Viruses
a. 16√8
b. 2√8
c. 8√8
d. 4
Answers
The correct response is c. 8√2 . The length of the diagonal if the side of the square is 8√2.
A polygon's opposed vertices (or corners) are connected by a line segment known as a diagonal. Or to put it another way, a diagonal is a line segment joining two polygonal vertices that are not neighbouring. With the exception of the figure's edges, it connects a polygon's vertices. For instance, a diagonal line or movement runs slopingly from one corner of a square to the other corner. a type of straight line called a diagonal. Straight up, down, or across are not possible on a diagonal line. It is a line that joins the corners of a form at two points. Instead of running straight up or across, a diagonal is formed by a straight line that is positioned at an angle.
Right isosceles triangles with both legs 8 feet long would make up each half.
The hypotenuse that both of those triangles would share is the diagonal.
We must determine the hypotenuse's length, d, in feet.
According to the Pythagorean theorem, the lengths of the legs' squares sum up to the length of the hypotenuse's square, so
\(8^{2} +8^{2} =8\sqrt{2}\)
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A gardener wants to divide a square piece of lawn in half diagonally. What is the length of the diagonal if the side of the square is 8ft? Leave your answer in simplest radical form.
a. 16√8
b. 2√8
c. 8√2
d. 4
The width of this rectangle is measured as 19.4mm correct to 1 decimal place.
b) What is the
lower bound for the area of the rectangle?
Answers
Answer:
reducing 9.35 to 19.44 is rounded to 19.4
Step-by-step explanation:
9.35 to 19.44 is rounded to 19.4
19.35 = 19.4
19.36 = 19.4
19.37 = 19.4
19.38 = 19.4
19.39 = 19.4
19.40 = 19.4
19.41 = 19.4
19.42 = 19.4
19.43 = 19.4
19.44 = 19.4
Hence Lower bound of of the rectangle = 19.35 mm
In AMNO, m = 41 cm, o = 98 cm and Angle O=22º. Find all possible values of Angle M, to the nearest degree.
Answers
Answer:
Answer:
85t
Step-by-step explanation:
1. Volume of a cone: 1. V = (1/3)πr2h 2. Slant height of a cone: 1. s = √(r2 + h2) 3. Lateral surface area of a cone: 1. L = πrs = πr√(r2 + h2) 4. Base surface area of a cone (a circle): 1. B = πr2 5. Total surface area of a cone: 1. A = L + B = πrs + πr2 = πr(s + r) = πr(r + √(r2 + h2))
hope this helps
Answer:
9
Step-by-step explanation:
sin(M)/41 = sin(22)/98
sin(M)=41sin(22)/98 = 0.1567232
sin^-1(0.1567232) = 9.02 = 9
5th grade math. Correct answer will be marked brainliest. Yes or no questions (decimals)
Answers
Answer:
Yes
Step-by-step explanation:
Answer:
NO! (first two are yes)
Step-by-step explanation:
He did not buy 2.4 pounds of potato salad, 2.32 rounds down to 2.3.
what is 1/4+3/8+1/2+5/8+3/4+7/8+1+1 1/4
Answers
Answer:
5.625 which is 5 5/8.
Step-by-step explanation: