The fundamental matrix Φ(t) satisfying Φ(0) = I for the given first-order system x' = [[-1, 1], [-4, -1]]x is Φ(t) = [[e^(-t), te^(-t)], [-4te^(-t), e^(-t)]].
The fundamental matrix is a matrix whose columns are the linearly independent solutions of the given system of differential equations. In this case, we are given the matrix representation of the system and we need to find the fundamental matrix Φ(t).
To find Φ(t), we first need to find the eigenvalues and eigenvectors of the coefficient matrix A = [[-1, 1], [-4, -1]]. The eigenvalues can be found by solving the characteristic equation det(A - λI) = 0, where λ is the eigenvalue and I is the identity matrix.
Solving det(A - λI) = 0, we find that the eigenvalues are λ₁ = -2 and λ₂ = -3.
Next, we find the corresponding eigenvectors. For λ₁ = -2, we solve the equation (A - λ₁I)v₁ = 0, where v₁ is the eigenvector. Similarly, for λ₂ = -3, we solve (A - λ₂I)v₂ = 0, where v₂ is the eigenvector.
After finding the eigenvectors, we construct the fundamental matrix Φ(t) using the formula Φ(t) = [v₁ e^(λ₁t), v₂ e^(λ₂t)], where e^(λ₁t) and e^(λ₂t) are the exponential terms corresponding to the eigenvalues.
Finally, we substitute the eigenvalues and eigenvectors into the formula and simplify to obtain the fundamental matrix Φ(t) = [[e^(-t), te^(-t)], [-4te^(-t), e^(-t)]], which satisfies Φ(0) = I.
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Zane buys a rope that is 50 feet long. The cost of the rope is $0.35 per foot, including tax. What is the total cost, in dollars, of Zane’s rope?
Answer:
50x.35=17.50
Step-by-step explanation:
multiply length times amount per foot equals total cost
Simplify the following expression. (52x + 61y) + (-6x + 47y)
Answer:
46x + 108y
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
(52x + 61y) + (-6x + 47y)
Step 2: Simplify
Combine like terms (x): 46x + 61y + 47yCombine like terms (y): 46x + 108yWhen the angle of elevation of the sun is 78 degrees, a tree casts a 13 foot shadow. How tall is the tree?
Answer: 61.16 ft
Step-by-step explanation:
We can think in this situation as a triangle rectangle.
where:
The height of the tree is one cathetus
The shadow of the tree is the other cathetus.
We know that the angle of elevation of the sun is 78°, an angle of elevation is measured from the ground, then the adjacent cathetus to this angle is the shadow of the tree. And the opposite cathetus will be the height of the tree.
Now we can remember the relationship:
Tg(A) = (opposite cathetus)/(adjacent cathetus)
Where:
A = 78°
Adjacent cathetus = 13ft
opposite cathetus = height of the tree = H
Then we have the equation:
Tg(78°) = H/13ft
Tg(78°)*13ft = H = 61.16 ft
4^x. 2^y =128,find x and y .please needed urgently
Mitchell went to the grocery store and bought 30 bagels. If there are 3 bagels in each pack, how many packs of bagels did Mitchell buy?
Answer: 10
Step-by-step explanation: 30/3=10
Answer:
10
Step-by-step explanation:
Take the total number of bagels and divide by the number of bagels per package to determine the number of packs
30/3 = 10
He will buy 10 packs
mid-segment definition
Answer:
A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle.
Step-by-step explanation:
hope this helps :)
Which of the following formulas is NOT used for finding the volume of sphere, cylinder, or cone?
Answer:
i think C
Step-by-step explanation:
Mutiply to get the answer
Altogether, 360 schoolchildren sit down for their exams.
Five percent of them have one pen. Of the remaining 95
percent, half of them have two pens and the other half
have none. How many pens do the children have between
all of them?
HEL MEEEE
Answer:
A esta así no puedo xd ._.
Total Pens, owned by all students between all of them = 360
Percentage wise calculation of Pens
Total children = 360
Students having one pen = 95% of 360 = 18
Remaining 95% = 360 - 18 = 342
Half of remaining ie 342 = 171, have two pens
Other half of remaining ie 171 have no pens
Total pens, all children have between all of them = Summation (number of students x number of pens)
= (18 x 1) + (171 x 2) + (171 x 0)
= 18 + 342
= 360
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A right triangle has side lengths,8,15,17 and as shown below.
Use these lengths to find, tan b, cos b, sin b
Remember the chant "soh cah toa"
sine = opposite ÷ hypotheneus
cosine = adjacent ÷ hypotheneus
tangent = opposite ÷ adjacent
remember that hypotheneus is the slanty side, opposite and adjacent side is in COMPARISON with the angle you want to find.
In this case, tan B would be 15/8
sinB = 15/17
cosB = 8/17
Calculate the simple interest on $ 6400 at 10% p.a. for 9 months.
Step-by-step explanation:
SI=P×T×R÷100
SI= 6400×9×10÷100
SI=576000÷100
SI=5760
The height of a doorway is 7 yards. What is the height of the doorway in inches?
The height of the doorway is ____ inches.
(100 POINTS!!) Help me on this please! (I will mark you brainliest!)
Answer:
its the 3rd and 5th check mark
Step-by-step explanation:
It is the 3rd and 5th answer check mark thingy!
Hope this helped, thanks so much for the points :)
find compound interest on12600rupees for 2years at10% per annum compounded anually
Answer:
₹2520
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 10%/100 = 0.1 per year,
then, solving our equation
I = 12600 × 0.1 × 2 = 2520
I = ₹ 2,520.00
The simple interest accumulated
on a principal of ₹ 12,600.00
at a rate of 10% per year
for 2 years is ₹ 2,520.00.
What is the equation of this line?
Answer:
y = -x +2
Hope that helps
A toy store sells accessories to go with the latest action figure. The store projects that it will sell a certain number of accessories for every box of a dozen action figures it orders. Let d represent one box of a dozen action figures. Use the table to write an expression to represent the actual number of each accessory sold per box of action figures.
The equation that can be used to represent the turbo jet pack will be 6b + 7.
How to calculate the equationFrom the information given, the turbo jet pack is given as six times the number of boxes plus seven. This will be:
= (6 × b) + 7
= 6b + 7
The x-ray vision glass is given as five fewer than two times the number of boxes. This will be:
= (2 × b) - 5
= 2b - 5
The invisible shield is given as one more than ten times the number of boxes. This will be:
= (10 × b) + 1
= 10b + 1
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Find the zeros 7x(x-11)-2(x-11)=0
(x-11)(7x-2)=0
x=11 or x=2/7
Answer:
x = [tex]\frac{2}{7}[/tex], x = 11
Step-by-step explanation:
Given
7x(x - 11) - 2(x - 11) = 0 ← factor out (x - 11) from each term
(x - 11)(7x - 2) = 0
Equate each factor to zero and solve for x
x - 11 = 0 ⇒ x = 11
7x - 2 = 0 ⇒ 7x = 2 ⇒ x = [tex]\frac{2}{7}[/tex]
The mall is having a sale on all shoes. Each pair is $3.50 off the original price. Which expression shows the final price of a pair of shoes?
3.5+x
x- 3.5
3.5x
which is the answer???
and could anybody help me with a few more questions?
Answer:
x-3.5
Step-by-step explanation:
I suppose that x= the orginal cost of the pairs of shoes.
The expression that shows the final price of a pair of shoes is given by f(x) = (x - 3.5).
What is a mathematical function, equation and expression? function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that the mall is having a sale on all shoes. Each pair is $3.50 off the original price.
Assume the original price of the shoes is $x. So, the expression that shows the final price of a pair of shoes is given by -
f(x) = (x - 3.5)
Therefore, the expression that shows the final price of a pair of shoes is given by f(x) = (x - 3.5).
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A sno-cone machine priced at $139 is on sale for 20% off. The sales tax rate is 6.75%. What is the price of the sno-cone machine after the discount and sales tax?
Answer:
$127.03
Step-by-step explanation:
A snow cone machine price at $139 is on after for 20 off.
The price after discount=139-20=$199
The sale tax rate 6.75%
Price with sales tax=199+(6.75%×199)
=199+(0.0675×199)
= 199+8.03
=$127.03
Yep here we go again:
The x-axis represents the number of hours before or afternoon, and the y-axis represents the temperature in degrees Celsius.
At 9 a.m., it was below freezing. In what quadrant would this point be plotted? Use Roman Numerals in your answer: Either I, II, III, or IV
At 11 a.m., it was 10 degrees Celsius. In what quadrant would this point be plotted?
Here is the image T ^ T ( I will also give brainliest!)
Answer:
9 am it will be IV quadrant
11 it will be I quadrant
hope it helps u
If at 9 a.m. the temperature was below freezing, which means below 0 degrees Celsius, then the point would be plotted in the third quadrant (III).
What is coordinate plane?The coordinate plane has four quadrants, which are numbered using Roman numerals I, II, III, and IV, and they are separated by the x-axis and y-axis.
In this case, the temperature was below freezing at 9 a.m., which means it was less than 0 degrees Celsius.
The point would be plotted in the third quadrant (III), where the x-value is negative and the y-value is negative, because the x-axis represents the time in hours before noon and the temperature is negative.
At 11 a.m., however, the temperature was 10 degrees Celsius, which is a positive value.
Thus, the point would be plotted in the first quadrant (I), where both the x-value and the y-value are positive, because the x-axis represents the time in hours before noon and the temperature is positive.
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Exercice 1:
Voici un programme de calcul :
Choisir un nombre
Multiplier ce nombre par 4
Ajouter 8
Multiplier le résultat par 2
1. Vérifier que si on choisit le nombre -0,5, ce programme donne 12 comme résultat final.
2. Le programme donne 34 comme résultat final, quel est le nombre choisi au départ ?
Dans la suite de l'exercice, on nomme x le nombre choisi au départ.
3. L'expression A = 2(4x + 8) donne le résultat du programme de calcul précédent pour un nombre x
donné.
On pose B = (4 + x)2 – x2
Prouver que les expressions A et B sont égales pour toutes les valeurs de x.
4. Pour chacune des affirmations suivantes, indiquer si elle est vraie ou fausse.
On rappelle que les réponses doivent être justifiées.
Affirmation 1: Ce programme donne un résultat positif pour toutes les valeurs de x.
Affirmation 2 : Si le nombre x choisi est un nombre entier, le résultat obtenu est un multiple de 8.
If anyone could answer any of these that would be awesome
Answer:
10
Step-by-step explanation:
12.)
m = -2 n = -3
Evaluate: m(m + n)
Substitute!
-2(-2 + -3)
Do the parenthesis
-2(-2 -3)
(-2)(-5)
= 10
I hoped this helped
can someone please help me with thiss!?
I would first find the volume of the hole and multiply that by 2 because there's 2 holes.
[tex]v = lwh[/tex]
[tex]v = (5)(8)(5)[/tex]
[tex]v = 200[/tex]
[tex]200 \times 2 = 400[/tex]
//
I would then find the volume of the entire cinder block.
[tex]v = lwh[/tex]
[tex]v = (16)(8)(8)[/tex]
[tex]v = 1024[/tex]
//
I would then substract.
[tex]1024 - 400 = 624[/tex]
The volume of the cinder blocks is 624 inches³
SOMEBODY PLEASE HELP ASAP PLEASE PLEASE PLEASE WILL GIVE YOU A GIFTCARD OF YOUR CHOICE
Answer:
what grade are u in
Step-by-step explanation:
Answer: I hope this helps!! It would mean the world to me if i got an Amazon or Xbox giftcard thanks!! :D
Step-by-step explanation:
Translate the following verbal expression into an algebraic expression.
“Three times the sum of a number and seven”
Answer:
3 * (x + 7)
Step-by-step explanation:
Mark number as x
Then the sum of a number and seven is x + 7
Three times x + 7 can be written as
3 * (x + 7)
Parentheses mean that we first add x and 7 and then multiply their sum by 3
Alternatively you can write it as 3x + 21, since
3 * (x + 7) = 3 * x + 3 * 7 = 3x + 21
The spinner below is spun. Find the probability,
P(D greater than 1)
What is the numerator for the probability?
What is the denominator for the probability?
Answer:
5 - numerator
6 - denominator
Find the area of this rectangle.
6 m
9 m
A = [?] m2
Answer:
The area would be 54 m^2.
HELP I NEED HELP ASAP
Answer:
constant... I think... sorry if it's wrong... just trying to help ;-;
Step-by-step explanation:
Hope this helped! Good luck! :)
Answer:
linear
Step-by-step explanation:
if you put it into an equation, it would be y = 5 + 2x, which is a linear (straight line) equation
Can you find the midpoint of the segment with the following endpoints.
(-7,-5) and (-4,2)
9514 1404 393
Answer:
(-5.5, -1.5)
Step-by-step explanation:
The midpoint is the average of the end points:
((-7, -5) +(-4, 2))/2 = (-7-4, -5+2)/2 = (-11, -3)/2 = (-5.5, -1.5)
The midpoint of the segment is (-5.5, -1.5).
John makes 2 cookies a day. Write an equation that shows the relationship between the days and number of cookes John
makes. Write an equation
Answer:
2x
x = each day
Step-by-step explanation:
Answer:
y= 2(x)
Step-by-step explanation:
The Y is the cookies. X is the days. Every day that John bakes, he makes 2 cookies. So you multiply the days by 2 to find the number of cookies he bakes.
Marie is saving $75 each week so she can buy a new laptop which costs $1200. She has already saved $125. Find the minimum number of weeks she will have to save in order to be able to make this purchase.
Answer:
Step-by-step explanation:
[tex]125+75w\ge 1200\\ \\ 75w\ge 1075\\ \\ w\ge 14.33\\ \\ \text{So she must save for at least 15 weeks.}[/tex]