Any vector of the form v = [6z, 2z, z] is orthogonal to each of u1, u2, and u3, and hence belongs to the orthogonal complement of W. A basis for this subspace can be obtained
(a) Let W = Span{u1, ..., up} be a subspace of a vector space V. Suppose v is a vector in W, then by definition, there exist scalars c1, c2, ..., cp such that v = c1u1 + c2u2 + ... + cpup. To show that v is orthogonal to each of u1, ..., up, we need to show that their inner products are all zero, i.e., v · u1 = 0, v · u2 = 0, ..., v · up = 0. We have:
v · u1 = (c1u1 + c2u2 + ... + cpup) · u1 = c1(u1 · u1) + c2(u2 · u1) + ... + cp(up · u1) = c1||u1||^2 + c2(u2 · u1) + ... + cp(up · u1)
Since v is in W, we have v = c1u1 + c2u2 + ... + cpup, so we can substitute this into the above equation and get:
v · u1 = c1||u1||^2 + c2(u2 · u1) + ... + cp(up · u1) = 0
Similarly, we can show that v · u2 = 0, ..., v · up = 0. Therefore, v is orthogonal to each of u1, ..., up.
Conversely, suppose v is a vector in V that is orthogonal to each of u1, ..., up. We need to show that v lies in W = Span{u1, ..., up}. Since v is orthogonal to u1, we have v · u1 = 0, which implies that v can be written as:
v = c2u2 + ... + cpup
where c2, ..., cp are scalars. Similarly, since v is orthogonal to u2, we have v · u2 = 0, which implies that v can also be written as:
v = c1u1 + c3u3 + ... + cpup
where c1, c3, ..., cp are scalars. Combining these two expressions for v, we get:
v = c1u1 + c2u2 + c3u3 + ... + cpup
which shows that v lies in W = Span{u1, ..., up}. Therefore, we have shown that v lies in W if and only if v is orthogonal to each of u1, ..., up.
(b) We are given that W = Span{u1, u2, u3}, where u1 = [-1, 0, 2], u2 = [0, 1, -3], and u3 = [-4, 3, 1]. To find a basis for the orthogonal complement of W, we need to find all vectors that are orthogonal to each of u1, u2, and u3. Let v = [x, y, z] be such a vector. Then we have:
v · u1 = -x + 2z = 0
v · u2 = y - 3z = 0
v · u3 = -4x + 3y + z = 0
Solving these equations, we get:
x = 6z
y = 2z
z = z
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Help ASAP!!!!! ILL GIVE BRANILYLEST!
Answer: Area: (100+75π/2)cm^2 Perimeter: (10+75π/2)cm
Step-by-step explanation:
Area of total shape
= square+3 semi-circles
=100cm^2 + 5*5πcm^2*3/2 = 100cm^2+75/2*πcm^2
= (100+75π/2)cm^2
Perimeter of shape
= 10cm + 25/2π*3cm
= (10+75π/2)cm
Step-by-step explanation:
in this figure you can observe 1 cube and 3 half cirles
the flield of the square would by using a formula a(lenght) * b(height)
in this case it would be 10m * 10m = 100m
and the formula for a cirle would be
A = pir^2
knowing that we can connect two of the halfs and make a cirle with a radius of 5
A= pi 5^2
A= pi 25
25pi approximatly equals to 78.53982m
knowing that information we can devide that value by 2 and get the value of the 3rd half cirlce
which is 39.26991m
than we add all the values we collected
39.26991m + 78.53982m + 100m = 217.80973 m
At a Cambridge College, 65% of the math tudent are from England. If there are 240 math tudent, how many are not from England?
84 math students are not from England
Given that
In mathematics, a percentage (from Latin: per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%",although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number (pure number); it has no unit of measurement.
The term "percent" is derived from the Latin per centum, meaning "hundred" or "by the hundred". The sign for "percent" evolved by gradual contraction of the Italian term per cento, meaning "for a hundred". The "per" was often abbreviated as "p."—eventually disappeared entirely. The "cento" was contracted to two circles separated by a horizontal line, from which the modern "%" symbol is derived.
At a Cambridge College,65% of the math student are from England
If there are 240 math student
now we need to find how many are not from England
= (100 - 65)% = 35% percentage
= [tex]\frac{35}{100}[/tex] * 240
= 84
84 math students are not from England
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What is the formula to find position of image?
The formula to find the position of an image is x = (width of the canvas - width of the image)/2 and y = (height of the canvas - height of the image)/2.
1. First, calculate the width of the canvas by subtracting the x-coordinate of the right side of the canvas from the x-coordinate of the left side.
2. Then, calculate the height of the canvas by subtracting the y-coordinate of the top side of the canvas from the y-coordinate of the bottom side.
3. Next, calculate the width of the image by subtracting the x-coordinate of the right side of the image from the x-coordinate of the left side.
4. Then, calculate the height of the image by subtracting the y-coordinate of the top side of the image from the y-coordinate of the bottom side.
5. Finally, calculate the x-coordinate of the position of the image by dividing the width of the canvas by two and subtracting the width of the image from that result.
6. Calculate the y-coordinate of the position of the image by dividing the height of the canvas by two and subtracting the height of the image from that result.
Therefore, the formula for finding the position of an image is x = (width of the canvas - width of the image)/2 and y = (height of the canvas - height of the image)/2.
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How to solve factor by grouping. Step by step.
solving factor by grouping, The final factored form of the expression is n(n + 3) - 10.
What is factor?A factor is a number that divides into another number exactly with no remainder. For example, the factors of 8 are 1, 2, 4, and 8.
What is factor by grouping?Factor by grouping is a method of factoring polynomials, which is used to find the common factors in an expression. The idea is to group the terms of the polynomial in such a way that the common factors can be factored out of them. In other words, it is a way to simplify an algebraic expression by finding common factors among the terms and then grouping them together. For example, the polynomial 2x^2 + 6x can be factored by grouping as (2x^2 + 6x) = 2x(x + 3). This is the most common way to factor a polynomial with four terms.
To solve the problem "factor by grouping" for the expression "n^2+3n-10", you can follow these steps:
Write the expression in the form of (n^2 + An + B) + (Cn + D)
(n^2 + 3n - 10) = (n^2 + 3n) + (-10)
Factor out the greatest common factor (GCF) of the terms in the first set of parentheses.
(n^2 + 3n) = n(n + 3)
Factor out the GCF of the terms in the second set of parentheses, if possible. In this case, there is no GCF.
Combine the factored expressions from step 2 and step 3 to get the final factored form.
n(n + 3) + (-10)
The final factored form of the expression is n(n + 3) - 10.
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How do you find the terms and factors of an algebraic expression?
A term can be a number, a variable, a product of two or more variables, or a number and a variable product. A factor is anything that is multiplied by another item. A factor might be a number, a variable, a word, or a more complicated statement. The numbers or variables that are multiplied together to generate a word are referred to as its factors.
What is algebraic expression?An expression, also known as an algebraic expression, is a mathematical statement made up of numbers, variables, and an arithmetic operation between them. For example, 4m + 5 is an expression in which the words 4m and 5 are separated by the arithmetic sign + and m is the variable of the provided expression.
Here,
A term can be a number, a variable, the product of two or more variables, or the product of a number and a variable. Anything that is multiplied by another object is referred to as a factor. A factor might be a number, a variable, a word, or a longer statement. The factors are the numbers or variables that are multiplied together to form a word.
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The area of the base of a cylinder is found by dividing the volume of the cylinder by its height. if the volume of the cylinder is represented by 5x2 15x 2 and the height is 5x, which expression represents the area of the base? x2 3x 5x (5x2 15x 2) x 3 x (x2 3x 2)
Answer:4x5
Step-by-step explanation:
Answer:
The area of the base of a cylinder is found by dividing the volume of the cylinder by its height.If the volume of the cylinder is represented by 5x2 +15x + 2 and the height is 5x, which expression represents the area of the base?x2 + 3x + 5x (5x2 + 15x + 2)x + 3 + x (x2 + 3x +2)
Step-by-step explanation:
x+3+x+2
Consider the equation `q=4+0.8p`.
What value of `q` would make the equation true when `p` is 100?
q = 84
q = 4 + 0.8p (where "p" = 100)
q = 4 + 0.8 × 100
q = 4 + 80
q = 84
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q = 84 for the equation q = 4 + 0.8p to be true, when `p` is 100.
q=4+0.8p (given)
If 'p' is equal to 100
Putting p = 100 into the above equation,
q = 4 + 0.8p
q = 4 + 0.8 × 100
q = 4 + 80
q = 84
Hence, when 'p' is 100, q would be 84 to make the equation true.
What triangle is formed when the sides are 5/12 13?
The triangle formed when the sides are 5, 12, 13 is a right-angled triangle. The Pythagorean theorem can be used to verify this.
From Pythagorean theorem, it can be said that, the square of hypotenuse side is equal to the sum of other two sides of a right angled triangle.
Let AB, CA and BC be the sides of a right triangle. CA is the hypotenuse side, AB and BC are the base and height sides of the right triangle. The equation can then be expressed as,
CA² = AB² + BC²
Now, let us check this rule for the above given sides of the triangle.
Longest side² = Sum of squares of other two sides
13² = 12² + 5²
169 = 144 + 25
169 = 169
Thus, the sides 5 cm, 12 cm and 13 cm can form a right-angled triangle.
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Help please im not sure which one to choose from
Answer:
85
Step-by-step explanation:
First, take your 400 and minus the 60 on the floor.
Then take your 340 and divide it by 4.
Which then leads to your final answer of 85 per box.
A baker sells bread for $6 a loaf and rolls for $2 each. The baker needs to sell $60 worth of baked goods by
the end of the day.
Use the graph to approximate how many loaves of bread the baker must sell if 24 rolls are sold, where b
is the number of loaves of bread and r is the number of rolls.
Number of
rolls sold
6b+2r=60
Answer: We can start solving this problem by using the information given in the equation 6b + 2r = 60. This equation represents the total cost of the bread and rolls sold, with 6b representing the cost of the bread (6 dollars per loaf) and 2r representing the cost of the rolls (2 dollars each). The goal is to find the value of b, the number of loaves of bread sold.
We can use the information that the baker sold 24 rolls. If we substitute this value into the equation, we get:
6b + 2(24) = 60
Next, we can simplify the equation by substituting in the value of 24 for r:
6b + 48 = 60
Now we can subtract 48 from both sides of the equation to find the value of b:
6b = 12
Finally, we can divide both sides of the equation by 6 to find the value of b:
b = 12/6 = 2
So the graph suggests that the baker must sell approximately 2 loaves of bread if 24 rolls are sold.
We can check this by substituting this value in the equation to make sure that it works and total cost of the bread and rolls sold is $60
6(2) + 2(24) = 60, which is true
It is important to note that this is an approximation based on the information given, and it is possible that the baker may have sold a different number of loaves of bread while selling 24 rolls.
Step-by-step explanation:
3.045 simplify is equal to 3 ? am i correct if not what it's the correct answer
Answer:
Yes, you are correct!
Step-by-step explanation:
When you see a number after the decimal is larger than 5 you will round up; when you see a number after the decimal is smaller than 5, you will round down.
In this case
3.045
The number after the decimal is 0, which is smaller than 5, so we round down and get the answer 3.
What is an equation of the line that passes through the point (-4,5) and is perpendicular to the line 4X + Y = seven
The equation of the line is y = x + 6.
What is slope?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.
here, we have,
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
4x + y = 7 ( subtract 4x from both sides )
y = - 4x + 7 ← in slope- intercept form
with slope m = - 4
given a line with slope m then the slope of a line perpendicular to it is
= 1/-m =1/ 4
then,
y = x/4 + c ← is the partial equation of the perpendicular line
to find c substitute )- 4, 5 ) into the partial equation
5 = - 1 + c ⇒ c = 5 + 1 = 6
hence, y = x/4 + 6 ← equation of perpendicular line.
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You have 20 quarters. You find 40% more quarters in your room. Then you go shopping and spend 50% of the total number of quarters. Write an expression to represent the total number of quarters you take with you shopping. Calculate, in dollars, the amount of money you have left
The expression for the quarters you take is (1 - 0.50) x 28
The money you have left is $3.50.
How much do you have left?The expression that is used to represent the total number of quarters is:
Total number of quarters = number of quarters you have x ( 1 + percent you find/100)
Total number of quarters = 20 x (1 + 40/100)
Total number of quarters = 20 x 1.40 = 28 quarters
Number of quarters you have left = (1 - percentage spent/100) x number of quarters
= (1 - 50%/100) x 28
(1 - 0.50) x 28
0.50 x 28 = 14 quarters
Value of 14 quarters in dollars = 14 x 0.25 = $3.50
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Please help me out with this one !!! Evaluate the integral.
1
∫
0
r3
over
⩗ 16 + r2
dr
The definite integral is [tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r$[/tex][tex]=[/tex][tex]\frac{128}{3}-\frac{31 \sqrt{17}}{3}$[/tex]
Definite Integral helps to find the area of a curve in a graph. It has limits, which are the start and the endpoints, within which the area under a curve is calculated. The limit points can be taken as [a, b], to find the area of the curve f(x), with respect to the x-axis.
Here,
∫ = Integration symbol
a = Lower limit
b = Upper limit
f(x) = Integrand
dx = Integrating agent
Thus, ∫ab f(x) dx is read as the definite integral of f(x) with respect to dx from a to b.
Indefinite integrals are implemented when the boundaries of the integrand are not specified.
To find [tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r$[/tex]
Put [tex]$16+r^2=t^2$[/tex]
[tex]$2 r d r=2 t d t$\\[/tex]
[tex]$r d r=d t$[/tex][tex]$r=0 \Rightarrow t=4$[/tex]
[tex]$r=1 \Rightarrow t=\sqrt{17}$[/tex]
[tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r=\int_4^{\sqrt{17}} \frac{t^2-16}{t} d t$[/tex]
[tex]$=\left[\frac{t^3}{3}-16 t\right]_t^{\sqrt{17}}$[/tex]
[tex]$=\frac{(\sqrt{17})^3}{3}-16(\sqrt{17})-\frac{(4)^3}{3}+64$[/tex]
[tex]$=\frac{128}{3}-\frac{31 \sqrt{17}}{3}$[/tex]
[tex]$\int_0^1 \frac{r^3}{\sqrt{16+r^2}} d r=\frac{128}{3}-\frac{31 \sqrt{17}}{3}$[/tex]
Therefore, the evaluated integral is [tex]\frac{31 \sqrt{17}}{3}$[/tex].
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A school choir needs to make T-shirts for its 75 members and has set aside some money in their budget to pay for them. The members of the choir decided to order from a printing company that charges $3 per shirt, plus a $50 fee for each color to be printed on the shirts.
1. Write an equation that represents the relationship between the number of T-shirts ordered, the number of colors on the shirts, and the total cost of the order. If you use a variable, specify what it represents.
variable X represent the number of colors in T-shirt. The equation of the
Total cost = 75 ( $3+$50 X)
what is equation?It is a mathematical statement that shows the equality between two or more expressions. There are various types of equation such as linear, polynomial, quadratic, exponential and so on. By using equation, the value of unknown variable is determined.
Here,
What will be the equation that representing the given relationship?
given, number of T-shirt = number of members = 75
charges of each T-shirt = $ 3
$50 fee for each color printed in the shirt.
let, X be the number of colors on the T-shirt.
The equation that represents the total cost of the order.
75($3 + $50 X) = total cost
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Given the points P(2, -3) & Q(-5, -3), what are the coordinates of the point on the directed line segment
Given the points P(2, -3) & Q(-5, -3), what are the coordinates of the point on the directed line segment
The equation of the line passing through the points P(2, -3) & Q(-5, -3) is y = -3
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
The standard form of a linear equation is:
y = mx + b
Where m is the rate of change and b is the y intercept
The equation of the line passing through P(2, -3) & Q(-5, -3) is:
y - (-3) = [(-3-(-3))/(-5-2)](x-2)
y + 3 = 0(x - 2)
y = -3
The equation of the line is y = -3
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Solve for y
2x-3y=-15
identify
the slope
and y-intercept
Answer:
The slope is -2/3 and the y-intercept is 5
Is it possible to have a triangle with the side lengths 4cm 7cm 8cm?
It is possible to construct a triangle whose sides are 4 cm, 7 cm and 8 cm because the sum of two sides are greater than third sides.
In the given question, we have to check that it is possible to construct a triangle whose sides are 4 cm, 7 cm and 8 cm.
To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always grater than the third side.
To check this we firstly add the 4 and 7
4 + 7 > 8
11 > 8
Now we add 7 and 8
7 + 8 > 4
15 > 4
Now we add 4 and 8
4 + 8 > 7
12 > 7
It is possible to construct a triangle whose sides are 4 cm, 7 cm and 8 cm because the sum of two sides are greater than third sides.
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Which line segment is congruent to HF?
Answer:
C) DF
Step-by-step explanation:
since the HF is the diameter of the top circle because the line is formed from the centre of the circle (c)
therefore,
the line made from the centre of (b), DF is the diameter
both DF and HF are congruent aswell as HD but thats not the option available in this question.
HELPPPPPP
Hailey walked 2.32 miles in the morning and 1.5 miles in the afternoon. She walked miles in all.
Hailey walked a total of 3.82 miles.
What is Addition?Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.
The process of doing addition is also called as finding the sum.
Given that,
Distance Hailey walked in the morning = 2.32 miles
Distance Hailey walked in the evening = 1.5 miles
Total distance she walked = 2.32 miles + 1.5 miles
= 3.82 miles
Hence the distance Hailey walked in total is equal to 3.82 miles.
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Which is a true statement about the given ratios? PLEASE IS TIMED
StartFraction 9 Over 14 EndFraction, StartFraction 22 Over 28 EndFraction, StartFraction 5 Over 7 EndFraction, StartFraction 12 Over 14 EndFraction
StartFraction 9 Over 14 EndFraction greater-than StartFraction 5 Over 7 EndFraction
StartFraction 5 Over 7 EndFraction greater-than StartFraction 22 Over 28 EndFraction
StartFraction 12 Over 14 EndFraction greater-than StartFraction 22 Over 28 EndFraction
StartFraction 9 Over 14 EndFraction greater-than StartFraction 12 Over 14 EndFraction
A statement which is true about the given ratios include the following: C. 12/14 > 22/28.
What is a ratio?In order to determine the statement that is true, we would evaluate each of the given ratios as follows by converting the fractions into a decimal number as follows;
9/14 is greater than 5/7 i.e 9/14 > 5/7;
Dividing both denominators by 7, we have the following:
9/2 > 5/1 = 4.5 > 5 (False).
9/14 > 5/7 = 0.64 > 0.71 (False).
5/7 is greater than 22/28 i.e 5/7 > 22/28;
Dividing both denominators by 7, we have the following:
5/1 > 22/4 = 5 > 5.5 (False).
5/7 > 22/28 = 0.71 > 0.79 (False).
12/14 is greater than 22/28 i.e 12/14 > 22/28;
Dividing both denominators by 14, we have the following:
12/14 > 22/28 = 12 > 22/2
12 > 22/2 = 12 > 11 (True).
9/14 is greater than 12/14 i.e 9/14 > 12/14;
Dividing both denominators by 14, we have the following:
9/14 > 12/14 = 9 > 12
9 > 12 (False).
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Complete Question:
Which is a true statement about the given ratios?
9/14, 22/28, 5/7, 12,14
A. 9/14>5/7
B. 5/7>22/28
C. 12/14 > 22/28
D. 9/14>12/14
Which graph represents the linear equation y equals one fourth times x plus 1 on the coordinate plane? graph of a line passing through the points 0 comma negative 2 and 2 comma negative 1 graph of a line passing through the points negative 4 comma 0 and 0 comma 2 graph of a line passing through the points negative 5 comma 0 and 0 comma 1 graph of a line passing through the points 0 comma 1 and negative 4 comma 0
The graph which represents the linear equation; y = (1/4)x + 1 as required in the task content is; the graph of a line passing through the points 0 comma 1 and negative 4 comma 0.
Which graph best represents the given linear equation?It follows from the task content that the graph which represents the given linear equation be determined.
Since the given linear equation is; y = (1/4)x + 1.
By comparison of the given equation to the slope-intercept form equation of a straight line, the y-intercept is; ( 0, 1).
Additionally, by checking (-4, 0); we have that;
0 = { (1/4) × -4 } + 1
0 = -1 + 1
0 = 0.
On this note, the graph which represents the linear equation is the; graph of a line passing through the ( 0, 1 ) and (-4, 0).
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The graph which represents the linear equation; y = (1/4)x + 1 as required in the task content is; the graph of a line passing through the points 0 comma 1 and negative 4 comma 0.
Which graph best represents the given linear equation?
It follows from the task content that the graph which represents the given linear equation be determined.
Since the given linear equation is; y = (1/4)x + 1.
By comparison of the given equation to the slope-intercept form equation of a straight line, the y-intercept is; ( 0, 1).
Additionally, by checking (-4, 0); we have that;
0 = { (1/4) × -4 } + 1
0 = -1 + 1
0 = 0.
On this note, the graph which represents the linear equation is the; graph of a line passing through the ( 0, 1 ) and (-4, 0).
Two rental car companies are running specials this month. At Eliana's Rentals, customers will pay $60 to rent a mid-sized car for the first day, plus $6 for each additional day. At Arcadia Rent-a-Car, the price for a mid-sized car is $30 for the first day and $12 for every additional day beyond that. At some point, renting from either one of the companies would cost a customer the same amount. How much would the customer pay?
On the 5th day, renting a mid-sized car from either Eliana's Rentals or Arcadia Rent-a-Car would cost the customer $90.
What is the linear equation in one variable?
A linear equation in one variable is an equation in which the highest power of the variable is 1. A linear equation in one variable can be written in the form of y = mx + b, where m is the slope and b is the y-intercept. The graph of a linear equation in one variable is a straight line.
In the given problem, the rental cost of a mid-sized car from Eliana's Rentals can be represented by the equation:
y = 60 + 6x (where y is the total cost and x is the number of days)
The rental cost of a mid-sized car from Arcadia Rent-a-Car can be represented by the equation:
y = 30 + 12x (where y is the total cost and x is the number of days)
At some point, renting from either one of the companies would cost the customer the same amount, so we can set both equations equal to each other and solve for x:
60 + 6x = 30 + 12x
Solving for x:
30 = 6x
x = 5
Hence, on the 5th day, renting a mid-sized car from either Eliana's Rentals or Arcadia Rent-a-Car would cost the customer $90.
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How do you find the length of the third side of a triangle for Class 7?
Answer:
To find the length of the third side of a triangle for class 7, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
The theorem can be written as: c^2 = a^2 + b^2, where c is the hypotenuse and a,b are the other two sides.
So, if you know the lengths of the other two sides, you can use this theorem to find the length of the third side. For example, if you know the lengths of sides a and b, you can use the following formula to find the length of side c: c = √(a^2 + b^2)
You can also use the converse of the Pythagorean theorem, which states that if the square of the length of one side is equal to the sum of the squares of the other two sides, the triangle is a right triangle.
It is always a good idea to draw a diagram to help you understand the problem and to double check the answer.
Step-by-step explanation:
O if you had to explain why finding the leat common denominator i important in working with factor what would it be
The term least common denominator (LCD) is used when referring to the denominators in fractions.
The smallest common denominator shared by two or more fractions is referred to as the least common denominator (LCD).
They are the same when the common denominator also happens to be the smallest common denominator. The least common denominator will always be smaller than the common denominator if this is not the case.
There are numerators and denominators in fractions. The fraction's top and bottom halves are called the numerator and denominator, respectively.
A common denominator is a denominator that is shared by two or more fractions. They all require common denominators before two or more fractions may be added together or subtracted.
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A.Direct
B.Inverse
C.Neither
Answer:
Inverse most likely
Step-by-step explanation:
What is the table method in math?
The numbers in a function table follow a pattern and have inputs and outputs. By constructing an equation using variables .
what is sequence ?A collection of numbers, or "terms," is referred to as a sequence. Examples of terms include 2, 5, and 8. Some sequences can be made endlessly long by taking advantage of a particular pattern they follow. Use the example of 2,5,8 and add 3 to continue the series. There are formulas that demonstrate where to look for words within a sequence. A collection of objects that are in some order is known as a sequence in mathematics (or events). It resembles a set in that it has pieces (also called elements or terms). the act of placing two or more items in a logical order. Chronological.
given
The numbers in a function table follow a pattern and have inputs and outputs.
By constructing an equation using variables, you may determine the rule. Make sure your rule is applicable to all possible combinations of inputs and outputs .
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A sequence starts with: 312500, 62500, 12500, 2500
Calculate the next four terms!
My brain isnt working, please help
The next four terms in the geometric sequence are 500, 100, 20 and 4
What is SequenceSequence is a set or series of related items or events in a particular order. It can refer to a number of different things, such as a set of numbers, a set of events, or a set of objects. In mathematics, a sequence is a series of numbers or other mathematical objects that follow a particular pattern.
In the given problem, the sequence is;
312,500, 62,500, 12,500, 2,500
This is most likely a geometric sequence and we have to find the common ratio.
r = 62500 / 312500 = 0.2 or 2500 / 12500 = 0.2
The common ratio is 0.2
The next term will be the 5th term
Tₙ = arⁿ⁻¹
T₅ = ar⁴
a = first term = 312500
T₅ = 312500(0.2)⁴
T₅ = 500
The next term is 6th term
T₆ = ar⁵
T₆ = 312500(0.2)⁵
T₆ = 100
T₇ = ar⁶
T₇ = 312500(0.2)⁶
T₇ = 20
T₈ = 312500(0.2)⁷
T₈ = 4
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You are standing next to a table and looking down on a record player sitting on the table. Take the spindle (axis of rotation) to be the center of your coordinate system and the y axis to be perpendicular to the side of the player you are standing next to. Long-playing records revolve 3313 times per minute. You put a small blob of clay at the edge of a record that has a radius of 0. 15 m, positioning the clay such that it is at its greatest value of y at t = 0.
Answer:
a) The rotational speed of the clay: 3.45 rad/s.
b) The value of A in the equation of motion: 0.15 m.
c) The value of ϕi: 90° or π/2 rad.
Given that;
Revolution per minute( rpm) is = 33( 1/3) = 100/3
The frequency ( f) is= 100 / 3(60) = 0.55 Hz
a) Rotational speed W = 2πf
we substitute
W = 2π × 0.55
W = 3.45 rad/s
So, the rotational speed of the clay is 3.45 rad/s.
b) given equation; y(t)=Asin(ωt+ϕi)
given that radius = 0.15 m
y(t)=(0.2)sin(ωt+ϕi)
So, the value of A in the equation of motion is 0.15 m.
c) since y(t) has the maximum value at t =0
so at t=0
y(0) = (0.15)sin(ω(0)+ϕi)
= 0.15sin(ϕi)
this gives maximum value when ϕi = 90°
so,
y(0) = (0.15)sin(ω(0)+ϕi)
= 0.15sin(90°)
= 0.15
So, the value of ϕi is 90° or π/2 rad.
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The complete question is:
You are standing next to a table and looking down at a record player sitting on the table. Take the spindle (axis of rotation) to be the center of your coordinate system and the y-axis to be perpendicular to the side of the player you are standing next to. Long-playing records revolve 33(1/3) times per minute. You put a small blob of clay at the edge of a record that has a radius of 0.15 m, positioning the clay such that it is at its greatest value of y at t = 0.
Equation of motion for the y component of the clay's position: y(t)=Asin(ωt+ϕi)
Required:
a. What is the rotational speed of the clay?
b. Determine the value of A in the equation of motion.
c. Determine the value of ϕi in the equation of motion. Suppose that −π<ϕi≤π
____relate the side lengths of a right triangle to an acute angle
Sine function relates side lengths of a right triangle to an acute angle.
In a right triangle, the side lengths are related to the acute angles through the trigonometric functions. The side opposite the acute angle is related to the angle through the sine function, the side adjacent to the acute angle is related to the angle through the cosine function, and the hypotenuse is related to the angle through the tangent function.
More specifically, if θ is an acute angle in a right triangle and a and b are the lengths of the side opposite and adjacent to the angle respectively, and c is the length of the hypotenuse, we have:
sin(θ) = a/c
cos(θ) = b/c
tan(θ) = a/b
Thus, we can use these functions to find the length of any side of the right triangle if we know the measure of one of the acute angles and the length of one of the other sides.
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