maxima_value = sp.sin(maxima)
minima_value = sp.sin(minima)
For part (a), to find the minima and maxima of the function y=sin(x) in the interval [2π, 4π], you can use the SymPy solves
et() function, which takes an equation, a variable and an interval (numn1, num2) as inputs. To do this, you can use the following code:
minima, maxima = sp.solveset(sp.Eq(sp.sin(x), 0), x, (sp.pi*2, sp.pi*4))
For part (b), to determine the x-values at which the maxima and minima occurs, you can use the minima and maxima values from the previous solveset() function and evaluate the sin(x) at those points. For example:
maxima_value = sp.sin(maxima)
minima_value = sp.sin(minima)
Learn more about minima and maxima
brainly.com/question/29562544
#SPJ11
A particles average speed is modeled by the equation
s(t)=T^2-6T+35, determine the average rate of the speeds increase
or decrease from t=2 to t=5
To determine the average rate of the speed's increase or decrease from t=2 to t=5, we need to find the slope of the line connecting the points (2,s(2)) and (5,s(5)) on the graph of the equation s(t)=T^2-6T+35. The slope of a line is given by the formula:
slope = (y2-y1)/(x2-x1)
In this case, x1=2, x2=5, y1=s(2), and y2=s(5).
Plugging in the values of x1 and x2 into the equation s(t)=T^2-6T+35, we get:
y1=s(2)=2^2-6(2)+35=4-12+35=27
y2=s(5)=5^2-6(5)+35=25-30+35=30
Now we can plug in the values of x1, x2, y1, and y2 into the slope formula:
slope = (30-27)/(5-2) = 3/3 = 1
Therefore, the average rate of the speed's increase or decrease from t=2 to t=5 is 1. This means that the speed is increasing at a constant rate of 1 unit per unit of time from t=2 to t=5.
To know more about average rate refer here:
https://brainly.com/question/12395856
#SPJ11
i need helpp pp pp p
Answer:
I CAN NOT SEE THAT OML
Step-by-step explanation:
PLEASE HELP PLSSS
a sequence of transformations that maps DOG to D'O'G' is a (answer choice) followed by a (answer choice)
answer choices:
1. rotation of about 180 degrees of the origin
2.rotation of about 90 degrees of the origin
3. translation 5 units right
4. translation 5 units left
The sequence of transformations that maps DOG to D'O'G' is a rotation of about 90 degrees of the origin, followed by a translation of 5 units right.
What is rotation?Rotation is a physical phenomenon where an object spins around an axis. It is a type of circular motion where an object moves in a circular path around a central point.
To accomplish this transformation, first, the point representing the letter D is rotated 90 degrees clockwise around the origin so that it is now pointing in the same direction as the letter O. After that, the point representing the letter D is translated 5 units to the right, resulting in the final transformation of DOG to D'O'G'.
Thus, the sequence of transformations that maps DOG to D'O'G' is a rotation of about 90 degrees of the origin, followed by a translation of 5 units right.
For more questions related to circular motion,
https://brainly.com/question/2285236
#SPJ1
Help :'( I really need this done 100 points if u do it pls pls help image below pls help :'(
→ the lenght = 13 square units
→ the width = 2 square units
→ the area of the rectangle = 13×2 = 26 square units
→ the area of the triangle = 26 : 2 = 13 square units
Answer:
Step-by-step explanation:
you would copy and paste another triangle on top to form a rectangle. That would make the rectangle's length 13 units and its width 2 units. the area of a rectangle is found by A=length x width which in this case is 26 units^2. A single triangle's area is 1/2 the area of the rectangle making it 26/2 which is 13.
So the area of the triangle is 13 units^2.
List three additional combos of length width and height that have a volume of 24 and please include the surface area too
The solution is then:
l = 6cm
w = 2cm
h = 2cm
What is the total surface area of cuboid?The surface area of a cuboid is the total area of all of the faces of a cuboid. If, the length (l), width (w), and height (h) of the cuboid
then, use the formula: surface area (SA)=2lw+2lh+2hw.
here, we have,
We know that the formula for the volume of a box is:
V = l*w*h
Where:
l = length
w = width
h = height
The formula of the surface area of a box is:
SA = 2(lw+lh+wh)
Based on the given we know the following:
24 = l*w*h
and
56 = 2(lw+lh+wh)
If we factor out the given volume, you can come up with 3 numbers that will satisfy the surface area formula:
24 = 6*2*2
Let:
l = 6cm
w =2cm
h =2cm
Now let's try this on the surface area formula:
56 = 2(6*2+6*2+2*2)
so, 56 = 56
The answer is then:
l = 6cm
w = 2cm
h = 2cm
To learn more on total surface area of cuboid click:
brainly.com/question/27226519
#SPJ1
Exercise 2.4.28 LetAbe ann×nmatrix and letIbe then×nidentity matrix. a. IfA2=0, verify that(I−A)−1=I+A. b. IfA3=0, verify that(I−A)−1=I+A+A2.
a. For A2 = 0, it is proved that (I - A)-1 = I + A.
b. For A3 = 0, (I - A)-1 = I + A + A2.
a. If A2 = 0, then (I - A)-1 = I + A
Proof:
(I - A)-1 = (I + A)-1
(I + A)-1 = (I + A)(I - A)-1
(I + A)(I - A)-1 = I + A
Therefore, (I - A)-1 = I + A
b. If A3 = 0 then (I - A)-1 = I + A + A2
Proof:
(I - A)-1 = (I + A + A2)-1
(I + A + A2)-1 = (I + A + A2)(I - A)-1
(I + A + A2)(I - A)-1 = I + A + A2
Therefore, (I - A)-1 = I + A + A2
You can learn more about matrix at
https://brainly.com/question/28777961
#SPJ11
Please help I’ll give brainliest!!
Answer:
[tex]\large\boxed{\tt (3x+4)(x+7)=3x^{2}+25x+28}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to factor the given trinomial.}[/tex]
[tex]\large\underline{\textsf{What is a Trinomial?}}[/tex]
[tex]\textsf{A Trinomial is an expression that has 3 terms. No more, and no less.}[/tex]
[tex]\large\underline{\textsf{What is Factoring?}}[/tex]
[tex]\textsf{Factoring is a way to split a trinomial into 2 binomials. Binomials have 2 terms.}[/tex]
[tex]\textsf{Factoring helps us to find the possible values of x, setting the binomials equal to 0.}[/tex]
[tex]\textsf{We don't have to do this for our problem though.}[/tex]
[tex]\large\underline{\textsf{Factoring Looks Like;}}[/tex]
[tex]\tt x^{2} + x + 1 = (x+?)(x+?)[/tex]
[tex]\tt The \ 2 x's \ multiply \ to \ equal \ x^{2}.[/tex]
[tex]\textsf{The x's multiply with the whole numbers inside the opposite binomial.}[/tex]
[tex]\large\underline{\textsf{To Factor;}}[/tex]
[tex]\textsf{Factoring is a little tedious, we must be careful and make sure we are finding}[/tex]
[tex]\textsf{the correct factors for factoring to work out. Remember that the trinomial has to}[/tex]
[tex]\textsf{equal the 2 binomials being multiplied.}[/tex]
[tex]\large\underline{\textsf{Solving;}}[/tex]
[tex]\tt 3x^{2} + 25x + 28[/tex]
[tex]\textsf{3x can't be split apart in 2 whole numbers, so it remains 3 in one of the binomials.}[/tex]
[tex]\underline{\textsf{We should have;}}[/tex]
[tex]\tt (3x+?)(x+?)[/tex]
[tex]\textsf{We don't have to worry about} \ \tt 3x^{2} \ \textsf{anymore.}[/tex]
[tex]\textsf{Our goal is to find factors of 28 that multiply to get to 25x and 28.}[/tex]
[tex]\textsf{We might need to try many factor pairs before we have our factored expression.}[/tex]
[tex]\underline{\textsf{Factors of 28;}}[/tex]
[tex]\tt 28: 1, 2, 4, 7, 14, 28.[/tex]
[tex]\textsf{We should substitute the factor pairs in, then FOIL.}[/tex]
[tex]\textsf{Foiling is multiplying 2 binomials together.}[/tex]
[tex]\underline{\textsf{Substitute;}}[/tex]
[tex]\tt (3x+1)(x+28) = 3x^{2}+85x+28[/tex]
[tex]\textsf{Incorrect Factor Pair Whether Flipped or Not.}[/tex]
[tex]\tt (3x+2)(x+14)=3x^{2}+44x+28[/tex]
[tex]\textsf{Incorrect Factor Pair Whether Flipped or Not.}[/tex]
[tex]\large\boxed{\tt (3x+4)(x+7)=3x^{2}+25x+28}[/tex]
[tex]\textsf{Correct Factor Pair. If these factors were flipped it would be incorrect.}[/tex]
Why might a person open a savings account?
Will mark brainliest
A) Savings accounts are designed for a short term such as paying monthly bills.
B)Savings accounts provide high interest rates in exchange for taking on a great deal of risk.
C)Savings accounts are designed to earn interest to encourage depositors to keep their money in the bank.
D)Savings accounts provide a quick way to pay monthly bills.
Answer:
C) Savings accounts are designed to earn interest to encourage depositors to keep their money in the bank. Savings accounts provide a safe and secure way to store money for use in the future. They also offer the opportunity to earn interest over time, which can be used to grow your savings. As a result, savings accounts are a great way to save for long-term goals such as retirement, a child's education, or a down payment on a home.
Answer:
C)Savings accounts are designed to earn interest to encourage depositors to keep their money in the bank.
Step-by-step explanation:
Savings accounts are designed to keep your money safe and to hold it for as long as you want. Ex for the future, such as collage or something you really want like a car. A saving account will will hold your money until you want to deposit it out of your account.
Write equivalent fractions for 5/12,1/2 and 5/6 using the least common denominator.
We have the following response after answering the given question: Hence, the comparable fractions with 12 as the denominator are: 5/12= 60/144 and 1/2 and 5/6 = 10/12
What is the equation?
In a mathematical equation, the equals sign (=), which connects two claims and denotes equality, is utilized. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For instance, in equation 3x + 5 = 14, the equal sign separates the numbers by a space. Mathematical expressions can be used to describe the relationship between the two sentences on either side of a letter. The logo and the particular piece of software frequently correspond. like, for instance, 2x - 4 = 2.
2 x 2 x 3 is the prime factorization of 12.
2 x 1 is the prime factorization of the number 2.
Two by three is the prime factorization of six.
The LCD is the sum of all the prime factors with the largest powers, giving us 2 × 2 × 3
5/12 = 5/(12 * 1) = 5/12 * 12/12 = 60/144
1/2 = 1/2 * 6/6 = 6/12
5/6 = 5/6 * 2/2 = 10/12
Hence, the comparable fractions with 12 as the denominator are:
5/12 = 60/144
1/2 = 6/12
5/6 = 10/12
To know more about equation visit:
brainly.com/question/649785
#SPJ1
need to find the volume in both terms of π and the nearest tenth
Answer: why do u need help again? this is easy boy
Step-by-step explanation:
if 37 out of 66 students were boys l, what percent of the group was boys?
I think it would be 56%
Answer:56.06%
Step-by-step explanation:
Divide 37 by 66 to get it in decimal form
37 ÷ 66 ≈0.5606
Then multiply the answer from the previous step by 100 to get an answer as %
0.5606 x 100 = 56.06%
The proof answer is correct by taking 56.06 % of 66 to get 37
(66 x 56.06) ÷ 100 ≈ 37
If there is a rectanglure pyramid that is 8 units tall, 12 units long, and 10 units wide, how big is it
The size or volume of the rectangular pyramid hat is 8 units tall, 12 units long, and 10 units wide is 320 cubic units.
To find the size of a rectangular pyramid, we need to find its volume. The formula for the volume of a rectangular pyramid is given:
Volume = (1/3) x base area x height
Here, the height of the pyramid is 8 units. The base is a rectangle with a length of 12 units and a width of 10 units. Therefore, the area of the base is:
Base area = length x width = 12 x 10 = 120 square units
Now we can substitute the values in the formula for volume:
Volume = (1/3) x base area x height
= (1/3) x 120 x 8
= 320 cubic units.
Learn more about rectangular pyramids at
https://brainly.com/question/21416050
#SPJ4
A pendulums horizontal distance from rest is given by the function det d(t)= 7 sin (πt/3 - 2) inches, where t is the time in seconds. a. Find the velocity of the pendulum in 6 seconds. b. Find the acceleration of the pendulum in 6 seconds.
The velocity of the pendulum is approximately -2.45 inches/second.
The acceleration of the pendulum is approximately 5.13 inches/second².
To find the velocity and acceleration of the pendulum, we need to find the first and second derivatives of the function d(t).
a. The velocity of the pendulum is given by the first derivative of the function d(t):
v(t) = d'(t) = 7 * (π/3) * cos(πt/3 - 2)
To find the velocity at t = 6 seconds, we simply plug in 6 for t:
v(6) = 7 * (π/3) * cos(π(6)/3 - 2) = 7 * (π/3) * cos(4) ≈ -2.45 inches/second
So the velocity of the pendulum at 6 seconds is approximately -2.45 inches/second.
b. The acceleration of the pendulum is given by the second derivative of the function d(t):
a(t) = d''(t) = -7 * (π/3)² * sin(πt/3 - 2)
To find the acceleration at t = 6 seconds, we simply plug in 6 for t:
a(6) = -7 * (π/3)² * sin(π(6)/3 - 2) = -7 * (π/3)² * sin(4) ≈ 5.13 inches/second²
So the acceleration of the pendulum at 6 seconds is approximately 5.13 inches/second².
Learn more about pendulum: https://brainly.com/question/30899808
#SPJ11
Factorising a quastatic Perfect iectargler fiea of rectangle Area of iedangle 11= Aica of rectangle 111= Area of 1V= Area of 1+11+1v
If you have a rectangle with a length of 5 and a width of 3, the area would be 5 * 3 = 15.
To factorise a quadratic equation, you need to find two numbers that multiply to give the constant term and add to give the coefficient of the x term.
For example, if you have the equation x^2 + 5x + 6 = 0, the two numbers you need to find are 2 and 3, because 2 * 3 = 6 and 2 + 3 = 5. So the equation can be factorised as (x + 2)(x + 3) = 0.
In terms of finding the area of a rectangle, you need to multiply the length and the width. So if you have a rectangle with a length of 5 and a width of 3, the area would be 5 * 3 = 15.
For more such questions on Quadratic equation.
https://brainly.com/question/1863222#
#SPJ11
There are 88 seats in the theater. The seating in the theater is split in to 4 identical section has 14 red seats and some blue seats.
The theater has a tοtal οf 56 red seats and 32 blue seats, making a tοtal οf 88 seats.
Hοw tο find the number οf red seats?If each sectiοn has 14 red seats, then there are a tοtal οf 4 x 14 = <<4 × 14=56>>56 red seats in the theater.
Tο find οut hοw many blue seats are in each sectiοn, we need tο subtract the number οf red seats frοm the tοtal number οf seats in each sectiοn:
88 tοtal seats / 4 sectiοns = 22 seats per sectiοn
22 seats per sectiοn - 14 red seats per sectiοn = 8 blue seats per sectiοn
Therefοre, each sectiοn has 8 blue seats, and the theater has a tοtal οf 4 x 8 = <<4 × 8=32>>32 blue seats.
Sο, the theater has a tοtal οf 56 red seats and 32 blue seats, making a tοtal οf 88 seats.
Learn more about theater
https://brainly.com/question/27779790
#SPJ1
What are the following Sets, Factors, Real numbers for these two
rational expressions: 22x + 11 x2 – 3x – 10
1 – 2c 20c2 + 10c
Its set of factors would include all real numbers and the complex roots of the polynomial.
The first rational expression, 22x + 11 x2 – 3x – 10, is a polynomial of degree 2. Its set of factors would include all real numbers, since it has no real-number roots. The second rational expression, 1 – 2c 20c2 + 10c, is a polynomial of degree 3. Its set of factors would include all real numbers and the complex roots of the polynomial.
Learn more about polynomial
brainly.com/question/11536910
#SPJ11
Mark invested $3,200 at 7% simple interest. How much interest did his account earn at the end of the four years
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$3200\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\dotfill &4 \end{cases} \\\\\\ I = (3200)(0.07)(4) \implies I = 896[/tex]
At a county fair, 60% of the entries are livestock. Of those entries, 70% are sold at the auction. If
130 entries of livestock are sold at the auction, how many total entries were there at the fair?
Answer:
Let's start by using algebra to solve the problem.
Let x be the total number of entries at the fair.
Given that 60% of the entries are livestock, we can write:
0.6x = number of livestock entries
Of those livestock entries, 70% are sold at the auction, which means:
0.7(0.6x) = 130
Simplifying the second equation, we get:
0.42x = 130
Solving for x, we can divide both sides by 0.42:
x = 309.52
Since we can't have a fractional number of entries, we can round up to the nearest whole number, giving us:
x = 310
Therefore, there were a total of 310 entries at the fair.
Step-by-step explanation:
Set up (do not solve ) the partial fraction decomposition for (4x-3)/(x^(2)(x+3)(x^(2)+2x+9)(x^(2)+1)^(3)).
To find the values of these constants, we need to multiply both sides of the equation by the denominator of the original fraction and then equate the numerators. This will give us a system of equations that we can solve for the constants.
The partial fraction decomposition for the given fraction is:
(4x-3)/(x^(2)(x+3)(x^(2)+2x+9)(x^(2)+1)^(3)) = A/x + B/x^(2) + C/(x+3) + D/(x^(2)+2x+9) + E/(x^(2)+1) + F/(x^(2)+1)^(2) + G/(x^(2)+1)^(3)
Where A, B, C, D, E, F, and G are constants that need to be determined.
To find the values of these constants, we need to multiply both sides of the equation by the denominator of the original fraction and then equate the numerators. This will give us a system of equations that we can solve for the constants.
However, since the question only asks to set up the partial fraction decomposition, we do not need to solve for the constants at this time.
Learn more about Partial fraction
brainly.com/question/30763571
#SPJ11
Homework:6.3 Applications of Systems of Linear Equations Question 4, 6.3.13-BE
Part 1 Jim took clothes to the cleaners three times last month. First, he brought 3 shirts and 2 pairs of slacks and paid $18.45. Then, he brought 7 shirts, 2 pairs of slacks, and 1 sports coat and paid $35.40. Finally, he brought 4 shirts and 2 sports coats and paid $23.94. How much was he charged for each shirt, each pair of slacks, and each sports coat?
Jim was charged$____ for each shirt, $____for each pair of slacks, and $____for each sports coat.
Therefore, it is not possible to determine how much Jim was charged for each shirt, each pair of slacks, and each sports coat with the given information.
To solve this problem, we can use a system of linear equations. Let x be the cost of each shirt, y be the cost of each pair of slacks, and z be the cost of each sports coat. Then we can write the following equations based on the information given in the problem:
3x + 2y = 18.45 (equation 1)
7x + 2y + z = 35.40 (equation 2)
4x + 2z = 23.94 (equation 3)
Now we can use the elimination method to solve for the variables. First, we can subtract equation 1 from equation 2 to eliminate the y variable:
4x + z = 16.95 (equation 4)
Next, we can multiply equation 1 by -2 and add it to equation 3 to eliminate the y variable:
-6x - 4y + 4x + 2z = -36.9 + 23.94
-2x + 2z = -12.96 (equation 5)
Now we can subtract equation 4 from equation 5 to eliminate the x variable:
2z - z = -12.96 - 16.95
z = -29.91
This value for z does not make sense, so there must be a mistake in the calculations or the original problem. Therefore, it is not possible to determine how much Jim was charged for each shirt, each pair of slacks, and each sports coat with the given information.
Learn more about problem
https://brainly.com/question/30137696
#SPJ11
Andy has $1,000 in an account. The interest rate is 15% compounded annually.
To the nearest cent, how much will he have in 2 years?
He will have $1322.5 in 2 years.
What is Compound Interest?Compound Interest is the interest calculated on the principal and the interest accumulated over the previous period. It is also the interest-based on the initial principal amount and the interest collected over the period of time.
The formula is A = P(1 + r/n)^nt
Where A = Amount compounded annually
P = Principal = $1000
r = Rate of interest = 15%
n = Number of times interest is compounded per year
t = Time in years
So, A = 1000(1 + 15%/1)^1*2
A = 1000(1 + 0.15)^2
A = 1000(1.15)^2
A = 1000(1.3225)
A = $1322.5
Therefore, the amount he will have in 2 years is $1322.5
Read more about Compound Interest
https://brainly.com/question/30852400
#SPJ1
What is 5x + 4y = -16 in slope-intercept form?
If I know that 40% of a number is 100 and I multiply that number by 2, what's 40% of that new number?
Answer: 200
Step-by-step explanation:
40% of y = 100
40/100 of y = 100
40y/100 = 100
40y = 100 multiplied by 100
40y/40 = 10000
y = 250.
40% of 2 multiplied by 250
40/100 of 500
40 multiplied by 5
answer = 200.
what is the rule multiplying with same sign
Answer:
When you multiply two numbers with the same sign (either both positive or both negative), the rule is that the result is always positive.
For example, if you multiply +2 and +3, the result is +6 because both numbers have the same positive sign. Likewise, if you multiply -4 and -5, the result is +20 because both numbers have the same negative sign.
This rule applies to any two numbers with the same sign, regardless of their values or whether they are whole numbers, fractions, or decimals.
The quotient is positive if the divisor and dividend have the same signs and negative if they have opposite signs. The quotient of any integers (with a nonzero divisor) will be a rational number
It is true that the quotient of two integers will always result in a rational numbers, as the quotient of two integers is in fact a fraction.
What are rational and irrational numbers?Rational numbers are numbers that can be represented by a ratio of two integers, which is in fact a fraction, such as numbers that have no decimal parts, or numbers in which the decimal parts are terminating or repeating. Examples are integers, fractions and mixed numbers.Irrational numbers are numbers that cannot be represented by a ratio of two integers, that is, they cannot be represented by fractions. They are non-terminating and non-repeating decimals, such as non-exact square roots.More can be learned about rational and irrational numbers at brainly.com/question/5186493
#SPJ1
The average salary of 36 employee was 4650. Using historical data, we will assume that the population standard deviation is 165. Find the 98% confidence interval for the population mean salary.
Select one:
a. 4650±63.97
b. 4650±67.05
c. 4650±70.84
d. 4650±45.24
e. 4650±74.91
f. 4650±53.90
g. 4650±46.48
h. 4650±55.83
The average salary of 36 employee was 4650. Using historical data, we will assume that the population standard deviation is 165. The 98% confidence interval for the population mean salary is 4650±70.84. The correct answer is option c. 4650±70.84.
To find the 98% confidence interval for the population mean salary, we will use the formula:
CI = X ± Z* (σ/√n)
Where:
CI = Confidence Interval
X = Sample mean
Z = Z-score for the given confidence level
σ = Population standard deviation
n = Sample size
Plugging in the given values, we get:
CI = 4650 ± 2.33* (165/√36)
CI = 4650 ± 70.84
Therefore, the 98% confidence interval for the population mean salary is 4650±70.84. The correct answer is C.
Learn me about confidence interval here: brainly.com/question/17097944.
#SPJ11
PLSSSS HELP IF YOU TURLY KNOW THISSS
Answer:
x = -6
Step-by-step explanation:
-4 + 2x = 4x+8
-4-8 = 4x - 2x
-12 = 2x
x = -6
Answer:
x = - 6
Step-by-step explanation:
Hope this helps! <33
select the number line that shows that two oppsite numbers have the sum of 0
Answer: I'd say A
Step-by-step explanation:
-1+1=0
Calculus Problem…
Suppose a and b span R². Determine the values of x and y, given that (2-x)a + b is
equal to ya + (x-3)b.
The values of x and y that satisfy the given equation are x = 2 and y = 1.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.
Since a and b span R², any vector in R² can be expressed as a linear combination of a and b.
Let's call the coefficients of this linear combination c₁ and c₂ so that any vector v in R² can be expressed as:
v = c₁a + c₂b
Now let's use this fact to solve the given equation:
(2-x)a + b = ya + (x-3)b
We can rearrange this equation to get all the terms with an on one side and all the terms with b on the other side:
(2-x)a - ya = (3-x)b
Now we can write both sides of the equation as linear combinations of a and b:
(2-x)a - ya = 2a - xa - ya = (2-x)a - (x-2)a - ya = (2-x - x + 2)a - ya = (4 - 2x)a - ya
(3-x)b = 3b - xb = 3b - xb + 3b - 3b = (6 - x)b - 3b = (6 - x - 3)b = (3 - x)b
So now we have:
(4 - 2x)a - ya = (3 - x)b
Since a and b span R², we know that any vector in R² can be expressed as a linear combination of a and b. Therefore, we can write:
(4 - 2x)a - ya = c₁a + c₂b
(3 - x)b = c₁a + c₂b
Now we can set the coefficients of a and b equal to each other and solve for x and y:
4 - 2x = c₁
-y = c₂
3 - x = c₂
Substituting the third equation into the second equation, we get:
-y = 3 - x
Solving for x and y, we get
x = 2
y = 1
Therefore, the values are x = 2 and y = 1.
To learn more about the system of equations;
brainly.com/question/13729904
#SPJ1
How do I solve these two ?
Geometry
The length of the sides x and y of the right-angled triangles using the trigonometric ratio of sine and cosine are:
11). x = 11√3 and y = 33
12). x = 4√7 and y = 8√7
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
recall that sin60° = √3/2 and cos60° = 1/2
For question 11:
sin 60° = y/22√3 {opposite/hypotenuse}
y = 22√3 × sin 60° {cross multiplication}
y = 22√3 × √3/2
y = 11 × 3
y = 33
cos 60° = x/22√3 {adjacent/hypotenuse}
x = 22√3 × cos 60° {cross multiplication}
x = 22√3 × 1/2
x = 11√3.
For question 12:
sin 60° = 4√21/y {opposite/hypotenuse}
y = 4√21/sin 60° {cross multiplication}
y = 4√21 ÷ √3/2
y = 4√21 × 2/√3
y = 4√7 × 2
y = 8√7
cos 60° = x/8√7 {adjacent/hypotenuse}
x = 8√7 × cos 60° {cross multiplication}
x = 8√7 × 1/2
x = 4√7
Therefore, the length of the sides x and y of the right-angled triangles using the trigonometric ratio of sine and cosine are:
11). x = 11√3 and y = 33
12). x = 4√7 and y = 8√7
Know more about trigonometric ratios here: https://brainly.com/question/11967894
#SPJ1
