The equation of the polynomial P3 is p3(t) = 5/6t³− 17/6t
Equation:
In algebra, an equation consists of variable, number and constants.
Given,
Here we need to find the polynomial P3 such that {P0, P1, P2, P3} is an orthogonal basis for the subspace P3 of P4.
And the scale the polynomial p3 so that its vector of values is (-1,2,0, -2,1).
Here we know that the polynomial (before the scaling) p3 is just the difference between t³ and its orthogonal projection on the span of 1,t,t²−2.
Then we showed that the projection is , hence
p3(t) = t³− 17/5t
When here we have the scale this polynomial such that the vector of values at t=−2,−1,0,1,2 is (−1,2,0,−2,1).
Now, we need to find the scalar α, it can be written as,
=> α⋅p3(−2)=−1
=> α⋅p3(−1)=2
=> α⋅p3(0)=0
=> α⋅p3(1)=−2
=> α⋅p3(2)=1
Here from the 4-th equation we have the value of
=> α⋅(1- 17/5) = -2
=> α = 5/6
And it is easy to check that all the equations are satisfied with this α.
Therefore, the required polynomial p3 is
=> p3(t) = 5/6(t³− 17/5t)
=> p3(t) = 5/6t³− 17/6t
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8x³ +16x² + 12x+13)÷(2x+2)
Find quotient and remainder
The degree of the remainder is less than the degree of the divisor, we have found the complete remainder. Therefore, the quotient is 4x² + 8x + 6, and the remainder is -16x² -16x.
What is the quotient?
The number we obtain when we divide one number by another is the quotient. For example, in 8 ÷ 4 = 2; here, the result of the division is 2, so it is the quotient. 8 is the dividend and 4 is the divisor.
To find the quotient and remainder when dividing 8x³ +16x² + 12x+13 by 2x+2, we can use polynomial long division.
First, we divide the leading coefficient of the dividend (8x³) by the leading coefficient of the divisor (2x). This gives us a quotient of 4x². We then multiply the divisor (2x+2) by this quotient and subtract it from the dividend to get the first term of the remainder:
8x³ +16x² + 12x + 13
(2x+2)(4x²)
8x³ - 8x³ -8x² -8x² +12x+13
This leaves us with 12x+13 as the first term of the remainder.
Next, we bring down the next term of the dividend (16x²) and divide it by the leading coefficient of the divisor (2x). This gives us a quotient of 8x. We then multiply the divisor (2x+2) by this quotient and subtract it from the dividend to get the next term of the remainder:
12x+13
(2x+2)(8x)
12x+13 - 16x² - 16x
-4x² -4x
This leaves us with -4x² -4x as the next term of the remainder.
Finally, we bring down the last term of the dividend (12x) and divide it by the leading coefficient of the divisor (2x). This gives us a quotient of 6. We then multiply the divisor (2x+2) by this quotient and subtract it from the dividend to get the final term of the remainder:
-4x² -4x
(2x+2)(6)
-4x² -4x -12x -12
-16x² -16x
This leaves us with -16x² -16x as the final term of the remainder.
Hence, the degree of the remainder is less than the degree of the divisor, we have found the complete remainder. Therefore, the quotient is 4x² + 8x + 6, and the remainder is -16x² -16x.
We can write the result of the division as:
(8x³ + 16x² + 12x + 13) ÷ (2x+2) = (4x² + 8x + 6) + (-16x² -16x)/(2x+2)
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Find the measure of angle b.
59°
A) 69°
C) 21°
B) 121°
D) 159
Answer:
he answer is B
Step-by-step explanation:
Total angle is 180°
angle a=59°angle b=180°-59°=121°
Q1 - Similar shapes and area
Work out the missing area in each pair of similar shapes.
The answer for the first shape would be 24cm^2.
The answer for the second shape would be 20cm^2.
The answer for the third shape would be 30cm^2. "30".
What are Shapes?
A shape in geometry can be characterized as an object's form, outline, outer border, or outer surface.
Every object we notice in the world has a form. The objects we see around us may be broken down into several fundamental forms, such as the two-dimensional square, rectangle, and oval, or the three-dimensional rectangular prism, cylinder, and sphere few types of Shape.Shapes establish an object's perimeter and may be distinguished in a variety of ways depending on their characteristics. In a Shape a border that is created by merging the curves, points, and line segments surrounds these forms. The name of each form depends on the structure. Circle, square, rectangle, triangle, and other simple forms are few types of Shape.The first shape seems to be scaling up. From 3cm to 12cm. So for this you need to multiply. Using the formula that I gave you last time.
3cm times ___ = 12cm. 4 fits in there,
therefore 6cm^2 times 4 = 24cm^2.
The answer for the first one would be 24cm^2. "24" in the blank.
The second shape seems to be scaling down. From 16cm to 8cm. So for this you need to divide.
16cm divided by ___ = 8cm. 2 fits in there,
therefore 40cm^2 divided 2 = 20cm^2.
The answer for the second one would be 20cm^2. "20" in the blank.
The third shape seems to be scaling up.
From 3cm to 4.5cm.
So for this you need to multiply. 3cm times ___ = 4.5cm.
Now since we're dealing with decimals, not whole numbers this time you can't really use guess and check as efficiently. So you do the opposite operation, which in this case the opposite of multiplication is division.
You take 3cm (the original shape's number) and divide it into 4.5cm. So 4.5cm divided by 3cm = 1.5. 1.5 fits in there,
therefore 20cm^2 times 1.5 = 30cm^2.
The answer for the third one would be 30cm^2. "30" in the blank.
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Legs have length of 4 find the length of the hypotenuse
Answer:
4√2
Step-by-step explanation:
hypotenuse = [tex]\sqrt{4^2 + 4^2} = \sqrt{16 + 16} =\sqrt{2*16} = 4\sqrt{2}[/tex]
The packages a and b together weigh 6kg
Package a is twice as heavy as package b
Find the weight of package a and find the weight of package b
The Bateria in a culture increases according to the law [tex]\frac{ds}{dt} = \frac{N}{4}[/tex]
if intially N = 200, then what is thevalue of N when t = 200
The required value of N when t = 200 is given as 10,000.
Given that,
The Bateria in culture increases according to the law ds/dt = N/4
if intially N = 200, then what is the value of N when t = 200 is to be determined.
Rate of change is defined as the change in value with rest to the time is called rate of change.
Here,
ds/dt = N/4 = 200/4 = 50
Now,
N = 50t
N = 50[200]
N = 10,000
Thus, the required value of N when t = 200 is given as 10,000.
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A boat is heading towards a lighthouse, where Jeremiah is watching from a a vertical distance of 126 feet above the water. Jeremiah measures an angle of depression to the boat at point A to be 11. The other measurement at point B is 78. Find the distance from point A to point B.
Using the given information, the distance from point A to point B is 568ft
How to find distance between two points?You should know that Distance is defined as the numerical or occasionally qualitative measurement of how far apart points are from each other.
The distance between A and B can be measured using the Trigonometric ratio of angles.
The drawing formed a right angled triangle.
Using the tangent function
Tan∅=[tex]\frac{opposite}{adjacent}[/tex]
Tan11⁰=x/126
x=126tan11⁰
Also, in the second angle of depression,
Using the tangent ratio as stated above,
y=126tan78⁰
The distance between A and B is given thus:
AB =126tan78⁰-126tan11⁰
AB =126*4.7046-126*0.1944
AB =592.78-24.4944
AB =568.28553
AB =568ft
In conclusion, the distance from point A to point B is 568ft
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La suma del triple de un número más el doble de otro número distinto al cuadrado
Procedimiento:
Empezamos separando el problema por partes. En este caso, a "un número" le daremos el nombre "x", y al "otro número distinto" le daremos el nombre "y".
1. Entonces, "el triple de un número" significa que es el triple de "x". En otras palabras, es 3 veces "x", osea:
3x
2.Como dice "la suma", entonces sabemos que nuestro 3x se va a sumar con otro término, entonces nuestro enunciado está quedando así:
3x+
3.El segundo término de la suma es "el doble de otro número distinto al cuadrado". Si el "otro número distinto" es "y", tenemos que "el doble" de "y" es 2 veces "y", osea, "2y".
Finalmente, se explica que este término está al cuadrado, lo cual daría que nuestro segundo término sea (2y)^2.
4.Entonces, la expresión completa es:
3x+(2y)^2
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
please help ASP ....
Answer:
B. Reflexive Property
Step-by-step explanation:
The statement is that BC ~= BC. That is, that BC is congruent to itself. The reason is that all numbers are equal to themself. Angle measures are equal to themself. Segments are equal to themself.
Like looking at a reflection in a mirror. The word "reflection" can help you memorize the reason why something is equal to itself:
Reflexive Property
If 3000 dollars is invested in a bank account at an interest rate of 10 per cent per year, Find the amount in the bank after 10 years if interest is compounded annually:
Find the amount in the bank after 10 years if interest is compounded quaterly:
Find the amount in the bank after 10 years if interest is compounded monthly:
Answer:
Step-by-step explanation:
100%-10%=90%
90/100=0.9%
3000*0.9^10 years= 1046.04
Step-by-step explanation:
For annually,
3000×(1.10)^10= 7781.23
For quarterly,
3000×(1.10)^40= 135777.77
For montly,
3000×(1.10)^120=278127206.5
Find the slope of the line that passes through all of the points on the table.
Help Please!!!!!!!!!!!!
(a) Complete this synthetic division table.
-2√-1 2 12 0 -16
(b) Write your answer in the following form: Quotient + Remainder / x+2
-x⁴+2 x³+12 x²-16 / x+2= ____+ _____ / x+2
a) The synthetic division table is given by the image shown at the end of the answer.
b) The result of the division is given as follows:
-x³ + 4x² + 4x - 8 + 0/x + 2.
How to apply the synthetic division algorithm?In the synthetic division algorithm, the coefficients of a polynomial, which is the dividend, are each divided by a value.This divisor is the goes into the far left box.In this problem, the dividend is given as follows:
-x^4 + 2x³ + 12x² - 16.
Hence the coefficients are given, respectively, by:
-1, 2, 12, 0 and -16.
The divisor is of:
x + 2.
Hence the term on the left box is of:
x + 2 = 0 -> x = -2.
Then the procedure goes as follows:
-1 is multiplied by -2 and added to 2, result of 4.4 is multiplied by -2 and added to 12, result of 4.And the same logic follows until the last term.From the coefficients of the bottom box, we have that:
The quotient is of -x³ + 4x² + 4x - 8.The remainder is of zero.Learn more about synthetic division at brainly.com/question/24662212
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Consider the conversion facts 1 inch = 2.54 centimeters and 1 centimeter = 0.39 inch.
a. Write an expression for the exact number of inches in 1 centimeter.
1 cm = -in.
b. Use a calculator to evaluate your expression in part (a). Round to the nearest ten thousandths if necessary.
1 cm =
in.
he clightly different when converting botung
The expression for the exact number of inches in 1 centimeter is 2.54/2.54 cm = 1/2.54 in and the number of inches is 0.39
How to determine the expression?From the question, we have the following parameters that can be used in our computation:
1 inch = 2.54 centimeters and 1 centimeter = 0.39 inch.
To calculate the number of inches expression, we make use of the following equation
1 inch = 2.54 centimeters
Divide both sides of the equation by 2.54
So, we have the following representation
1/2.54 inch = 2.54/2.54 centimeters
Rewrite the expression as
2.54/2.54 centimeters = 1/2.54 inch
So, we have
2.54/2.54 cm = 1/2.54 in
So, the expression is 2.54/2.54 cm = 1/2.54 in
The value of the expressionIn (a), we have'
Expression: 2.54/2.54 cm = 1/2.54 in
This implies that
2.54/2.54 cm = 1/2.54 in
Evaluate the quotients
1 cm = 0.39 in
Hence, the value is 0.39 inches
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I need help badly.
0.000236 to 3 significant figures.
Answer:
It is rounded to 3 sig figs already
Step-by-step explanation:
What is 136 simplified. Use the fx button above to access the button.
Rewatch
Next question
The simplified expression of √136 is 2√34
How to determine the simplified expression?From the question, we have the following parameters that can be used in our computation:
√136
Expand the expression
So, we have the following representation
√136 = √68 * 2
Further, expand the expression
So, we have the following representation
√136 = √34 * 2 * 2
So, we have
√136 = √34 * 4
Take the square root
√136 = 2√34
The expression cannot be further simplified
Hence, the solution is 2√34
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Station 2: Unit 3 and Unit Linear Functions given the table x 9,3,-3,-9 y 2,-2,-6,-10 ,
Find equation slope form answer the following questions.
Answer:
y = (2/3)x - 4
Step-by-step explanation:
To find the equation of the line in slope-intercept form given a table of values, you will need to calculate the slope of the line and the y-intercept. The slope of a line is a measure of its steepness, and it is calculated as the rise (change in y-values) divided by the run (change in x-values) between two points on the line. The y-intercept is the point at which the line crosses the y-axis.
Given the table x: 9, 3, -3, -9 and y: 2, -2, -6, -10, you can use any two points to calculate the slope. For example, you could use the points (9, 2) and (3, -2) to calculate the slope:
slope = (y2 - y1) / (x2 - x1) = (-2 - 2) / (3 - 9) = -4 / -6 = 2/3
To find the y-intercept, you can use the slope and one of the points from the table to substitute into the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
Using the slope and the point (9, 2), you can solve for b:
y = mx + b
2 = (2/3) * 9 + b
2 = 6 + b
b = -4
Therefore, the equation of the line in slope-intercept form is y = (2/3)x - 4.
To answer the other questions, you can use this equation to determine the y-value for a given x-value or the x-value for a given y-value. You can also use the equation to graph the line on the coordinate plane.
The length of rectangle is twice its width.How many times long as the width of the rectangle is the perimeter of the rectangle.
Step-by-step explanation:
w=x
l=2x
p=2(l+w)
p=2(2x+x)
p=6x
Xavier is riding on his bike at a constant speed of 15
miles per hour. What is the closest approximation of
how long it will take Xavier to ride 5 miles?
A. 0.15 hour
B. 0.2 hour
C. 0.33 hour
D. 0.5 hour
Answer:
C. 0.33 hour
Step-by-step explanation:
15 miles = 1 hr
5 miles = x hr
cross multiply
5 = 15x
x = 5/15
x = 0.333 hr
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4. Which statement best describes the relationship in the table?
Months 12 24 36 48
Years 1 2 3 4
a. The constant of proportionality is 0.
b.The constant of proportionality is 4.
c. The number of months is proportional to the number of years?
d. The number of months is not proportional to the number of years?
On solving the provided question, we got that the number of months is proportional to the number of years
What is proportionality>When two quantities or variables are linearly related in mathematics, the term "proportional" is used. Both quantities increase by two times when one increases by two. Each variable decreases in proportion to the other when it falls to 1/100th of its previous value.
What do you think about proportionality?We must determine the ratio of the two quantities for each value supplied in order to determine if two quantities are proportionate. The proportionate link between them is evident if their proportions are equal. Their connection is not proportionate if all the ratios are out of balance.
Here,
12/1 = 12
24/2 = 12
36/3 = 12
48/4 = 12
So, They are proportional to each other.
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A garden table and a bench cost $821 combined. The garden table costs $71 more than the bench. What is the cost of the bench?
X
The cost of the bench is $ 375 and the Cost of the garden table is $ 446.
Calculating Unknown Quantity:We can Calculate unknown quantities mathematically using Algebra Expressions. Unknown values in an equation are represented by variables, which are often represented by a letter of the alphabet like x, y, and z or a, b, and c, etc.
Here we have
A garden table and a bench cost $ 821 combined
Let x, and y be the cost of the garden table and bench
Given that
The garden table costs $71 more than the bench.
=> x = y + $ 71 ---- (1)
It is also given that
The total cost of the garden table and a bench = $ 821
=> x + y = 821
=> y + 71 + y = 821
=> 2y = 821 - 71
=> 2y = 750
=> y = 375
=> Cost of bench, y = $ 375
=> The cost of the garden table, x = $ 375 + $ 71 = $ 446
Therefore,
The cost of the bench is $ 375 and the Cost of the garden table is $ 446.
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fhyyyyyyyyyyyyyyyyyyyyytttttttttttttttttttttttttttttttttttttttttgsdddddddddddddtttttttt
Answer:
Step-by-step explanation:
there is no answer it just a bunch of f,h,y and t this is not math this is something
1 - O produto das raízes reais da equação é igual a :
A) - 1,5
B) -0,5
C) 0,5
D) 1,5
for any relation r, if, for every valid instance of a, that value of a uniquely determines the value of b:
"In a relation r, for every instance of a, that value of a uniquely determines the value of b then a primary dependency exists in the relation.
Relation:
In math relation means the relationship between sets of values of ordered pairs.
Given,
Here we need to find if for every valid instance of a, that value of a uniquely determines the value of b in the relation.
As per the definition of relation, for every relation has two set of data ad each of the element in one set is uniquely refers the other one's element.
Here we have to identify the type of relation between a an b.
Here we have given that the relation a uniquely determines the value in b.
So, this type primarily refers the dependency of the relation.
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El primer término en una serie geométrica es 64 y la razón común es 0.75
Answer:
Si...
En una progresión geométrica se conocen a1 = 64 y r = 0,75
6x^3+2x^2+3x -(3x^3-2x^2-3x)
The simplest form of the given expression is 3x³+4x²+6x
What is arithmetic?
Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, mathematical operation, and extraction of roots.
Main body:
according to question ,
6x³+2x²+3x -(3x³-2x²-3x)
we need to simplify the given equation.
firstly opening the bracket and taking care of sign,
⇒6x³+2x²+3x -3x³ +2x² +3x
taking like terms seperately,
⇒6x³ -3x³ +2x²+2x²+3x+3x
⇒3x³+4x²+6x
Hence the simplest form of the given expression is 3x³+4x²+6x
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Consider the equation 5y + 9 =
Which value or expression can you write in the blank so the equation
has no solution?
0
9
5y
+2.
7y
The equation has no solution if the blank is filled with 5y, so option c is correct.
What is equation?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign. It shows that the expressions printed on the left and right sides have an equal relationship.
Given equation:
5y + 9 = _
Use the hit and trial method and put the value zero,
5y + 9 = 0
y = -9 / 5
So the equation has a solution,
Again put
5y + 9 = 5y
9 = 0, which is not possible
Therefore, the equation has no solution if we fill the blank with 5y.
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changing tne value of m in f(x)=mx+b resulst in a (translation or rotation) of the graph
?????
Answer:
Rotation
Step-by-step explanation:
The function [tex]f(x)=mx+b[/tex] , is the equation of a line given in slope-intercept form. Where m is the slope of the line and b is the y-intercept of the line. If you were to change the value of m, while keeping the value of b the same, that would result in a rotation. If you were to change the value of b, while keeping the value of m the same, that would result in a translation (specifically a vertical translation).
Help help help help help help
Answer:
Andre walks more steps
Step-by-step explanation:
Step-by-step explanation:
dawn step rate=8400/60=140step/he
dawn step=140×240=33600 steps
teddl step=142 ×240 =34080