Hi, i need to calculate roots x1 and x2 using the vieta theorem, can anyone help me? I have found the answer for x1 and x2, its 1,5 and 2, all i need is a solution on how to get this answer, the equation is in the picture, will give you brainliest if you type down the correct solution for me, thanks.
I have left a similar equation that i did. The only thing why i cant do the equation, because in front of x2 there’s an number, so i don’t understand.
Answer:
Solution given:
x²-12x+11=0
Comparing above equation with ax²+bx+c
we get
a=1
b=-12
c=11
By using Vieta's theorem
X1+X2=[tex] \frac{-b}{a} [/tex]=[tex] \frac{- -12}{1} [/tex]=12
again
X1X2=[tex] \frac{c}{a} [/tex]=[tex] \frac{11}{1} [/tex]=11
x1.x2=11
x1+x2=12
I need help please.
What is the value of x?
PLEASE HELP FAST WILL MARK BRAINLIEST PLEASEEE
Answer:
[tex]\frac{8x^{18} }{y^{2} }[/tex]
Step-by-step explanation:
Consider the initial value problem my''+cy'+ky=F(t), y(0)=0, y'(0)=0, modeling the motion of a spring mass dashpot system initially at rest and subjected to an applied force F(t), where the unit of force is the Newton (N). Assume that m=2 kilograms, c=8 kilograms per second, k=80 Newtons per meter, and F(t)=20 sin(6t) Newtons.
1. Solve the initial value problem. y(t)=?
2. Determine the long term behavior of the system. Is lim as t goes to infinity of y(t)=0? If it is, enter zero. If not, enter a function that approximates y(t) for very large positive values of t. For very large positive values of t, y(t) is approximately.. ?
Answer:
Hence, the [tex]y(t)=e^{-2 t}\left(\frac{75}{74} \cos 6 t+\frac{75}{148} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t))\end{array}[/tex] and approximately value of [tex]y(t)[/tex] is [tex]-0.844[/tex].
Given :
[tex]my''+cy'+ky=F(t), y(0)=0, y'(0)=0,[/tex]
Where [tex]m=2[/tex] kilograms
[tex]c=8[/tex] kilograms per second
[tex]k=80[/tex] Newtons per meter
[tex]F(t)=20\sin (6t)[/tex] Newtons
Explanation :
(1)
Solve the initial value problem. [tex]y(t)[/tex]
[tex]my''+cy'+ky=F(t), y(0)=0, y'(0)=0,[/tex]
[tex]\Rightarrow 2y''+8y'+80y=20\sin (6t)[/tex]
[tex]\Rightarrow y''+4y'+40y=10\sin (6t)[/tex]
Auxilary equations :[tex]F(t)=0[/tex]
[tex]\Rightarrow r^2+4r+40=0[/tex]
[tex]\Rightarrow r=\frac{-4\pm\sqrt{4^2-4\times 1\times 40}}{2\times 1}[/tex]
[tex]\Rightarrow r=\frac{-4\pm\sqrt{16-160}}{2}[/tex]
[tex]\Rightarrow r=\frac{-4\pm\sqrt{-144}}{2}[/tex]
[tex]\Rightarrow r=\frac{-4\pm12i}{2}[/tex]
[tex]\Rightarrow r=-2\pm6i[/tex]
The complementary solution is [tex]y_c=e^{-2t}\left(c_1\cos 6t+c_2\sin 6t\right)[/tex]
The particular Integral, [tex]y_p=\frac{1}{f(D)}F(t)[/tex]
[tex]y_{y} &=\frac{1}{D^{2}+4 D+40} 25 \sin (6 t) \\\\ y_{y} &=\frac{25}{-6^{2}+4 D+40} \sin (6 t) \quad\left(D^{2} \text { is replaced with }-6^{2}=-36\right) \\\\y_{y} &=\frac{25}{4 D+4} \sin (6 t) \\\\y_{y} &=\frac{25}{4(D+1)} \sin (6 t) \\\\y_{y} &=\frac{25(D-1)}{4(D+1)(D-1)} \sin (6 t) \\\\y_{y} &=\frac{25(D-1)}{4\left(D^{2}-1\right)} \sin (6 t) \\\\y_{y} &=\frac{25(D-1)}{4(-36-1)} \sin (6 t) \\\\y_{y} &=-\frac{25}{148}(D-1) \sin (6 t) \\y_{y} &=-\frac{25}{148}\left(\frac{d}{d t} \sin (6 t)-\sin (6[/tex]
Hence the general solution is :[tex]y=y_c+y_p=e^{-2t}(c_1\cos 6t+c_2\sin 6t)-\frac{25}{148}(6\cos 6t-\sin 6t)[/tex]
Now we use given initial condition.
[tex]y(t) &=e^{-2 t}\left(c_{1} \cos 6 t+c_{2} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\\y(0) &=e^{-\alpha 0)}\left(c_{1} \cos (0)+c_{2} \sin (0)\right)-\frac{25}{148}(6 \cos (0)-\sin (0)) \\\\0 &=\left(c_{1}\right)-\frac{25}{148}(6) \\\\c_{1} &=\frac{75}{74} \\\\y(t) &=e^{-2 t}\left(c_{1} \cos 6 t+c_{2} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\[/tex]
[tex]y^{\prime}(t)=-2 e^{-2 t}\left(c_{1} \cos 6 t+c_{2} \sin 6 t\right)+e^{-2 t}\left(-6 c_{1} \sin 6 t+6 c_{2} \cos 6 t\right)-\frac{25}{148}(-36 \sin (6 t)-6 \cos (6 t)) \\\\y^{\prime}(0)=-2 e^{0}\left(c_{1} \cos 0+c_{2} \sin 0\right)+e^{0}\left(-6 c_{1} \sin 0+6 c_{2} \cos 0\right)-\frac{25}{148}(-36 \sin 0-6 \cos 0) \\\\0=-2\left(c_{1}\right)+\left(6 c_{2}\right)-\frac{25}{148}(-6) \\\\0=-2 c_{1}+6 c_{2}+\frac{75}{74} \\\\0=-2\left(\frac{75}{74}\right)+6 c_{2}+\frac{75}{74} \\\\[/tex][tex]\begin{array}{l}0=-\frac{150}{74}+6 c_{2}+\frac{75}{74} \\\\\frac{150}{74}-\frac{75}{74}=6 c_{2}\end{array}[/tex]
[tex]\begin{array}{l}c_{2}=\frac{25}{148}\\\\\text { Substitute } c_{1} \text { and } c_{2} \text { in } y(t) \text { . Then }\\\\y(t)=e^{-2 t}\left(\frac{75}{74} \cos 6 t+\frac{75}{148} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t))\end{array}[/tex]
(2)
[tex]y(t)=e^{-2 t}\left(\frac{75}{74} \cos 6 t+\frac{75}{148} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\y(t)=\left(\frac{75}{74} e^{-2 t} \cos 6 t+\frac{75}{148} e^{-2 t} \sin 6 t\right)-\frac{25}{148}(6 \cos (6 t)-\sin (6 t)) \\\\y(t)=\frac{75}{74}\left(e^{-2 t}-1\right) \cos 6 t+\frac{25}{148}\left(3 e^{-2 t}+1\right) \sin 6 t \\\\|y(t)| \leq \frac{75}{74} e^{-2 t}-1|\cos 6 t|+\frac{25}{148}\left|3 e^{-2 t}+1\right||\sin 6 t| \\\\[/tex]
[tex]|y(t)| \leq \frac{75}{74}\left|e^{-2 t}-1\right|+\frac{25}{148}\left|3 e^{-2 t}+1\right| \\\\\lim _{t \rightarrow \infty} y(t) \leq \lim _{t \rightarrow \infty}\left\{\frac{75}{74}\left|e^{-2 t}-1\right|+\frac{25}{148}\left|3 e^{-2 t}+1\right|\right\} \\\\\lim _{t \rightarrow \infty} y(t)=\left\{\frac{75}{74}\left|\lim _{t \rightarrow \infty}\left(e^{-2 t}-1\right)\right|+\frac{25}{148}\left|\lim _{t \rightarrow \infty}\left(3 e^{-2 t}+1\right)\right|\right\} \\[/tex]
[tex]\lim _{t \rightarrow \infty} y(t)=\left\{\frac{75}{74}(-1)+\frac{25}{148}(1)\right\}=-\frac{75}{74}+\frac{25}{148}=-\frac{-150+25}{148}=-\frac{125}{148} \approx-0.844[/tex]
SOLVE THR SIMULTANEOUS EQUATIONS
3X+Y=8
X-3Y=11
ANSWER PLEASE
Answer:
if you just wanted the equations fixed: y= -3x + 8 & y= 1/3x - 11/3
but if you wanted x then x = 7/2
Step-by-step explanation:
3x + y = 8 *subtract 3x from both sides*
y = -3x + 8
x - 3y = 11 *add 3y to both sides*
x = 3y + 11 subtract 11 from both sides*
x - 11 = 3y * divide both sides by 3*
1/3x - 11/3 = y --> y = 1/3x - 11/3
and to solve for x i just used ma thway but if you did want to solve it you'd need to put the equations equal to each other --> -3x + 8 = 1/3x - 11/3
plzzzzzzzz help for a brainly
Answer:
The first one is supplementary
The second one is complementary
The third one is vertical
Step-by-step explanation:
Answer:
First answer is supplementary.
second answer is complementary.
Third answer is Vertical.
help how to do this due in a few hours
Answer:
x=52 y=116
Step-by-step explanation:
because they give you the angle 116.
those two are actually equal.
y=116
since that is true, you can do 180-116=64.
now, you subtract 64-12
which is 52.
Joelle bought some fruit at the store. They bought 5 apples and a bunch of bananas. The bananas cost $1.50, and the total cost was $5.24. How much did each apple cost?
Define your variable: a represents…
Write an equation using your variable that matches the situation.
Solve your equation. Show all your steps.
Write your answer in a complete sentence.
Answer:
$3.74
Step-by-step explanation:
we already know the cost of the banana's and it gives us the total price including apples. So $5.24 - $1.50 = $3.74, and the 3.74 is the cost of apples
In a regression analysis, the actual values of Y may be found above or below the regression line. These deviations are called the _____. slope error term variance standard error of the mean standard deviation
Answer:
Error term
Step-by-step explanation:
Given :
In a regression analysis, the actual values of Y may be found above or below the regression line. These deviations are called the _____. slope error term variance standard error of the mean standard deviation
To find :
Fill in the blanks.
Now, In a regression analysis, the actual values of Y may be found above or below the regression line. These deviations are called the Error term.
Because we use the error term in the regression analysis difference between the actual value of [tex]Y[/tex] and the approximate value of [tex]Y[/tex] which is above of actual value or below of actual value.
As [tex]Y[/tex]is an actual value and [tex]Y_0[/tex] is an approximate value then,
[tex]|Y-Y_0|[/tex] is an error.
It is a vertical distance between the actual value and the approximate value of [tex]Y[/tex].
So, the error term is always positive.
The scale on a map is 55 cm : 88 km.
If the distance between two cities is 5656 km, how far apart in cm are the two cities on the map?
Answer:
look at the picture i have sent
Answer:
The cities are 35 cm apart in map.
The scale on a map is 5 cm : 8 km.
Step-by-step explanation:
mrk me brainliest please
Which phrase describes the expression 505n ?
Answer:
I believe it would be "505 times n"
Step-by-step explanation:
If tis is not what you are looking for I am sorry, but the question was vague.
Can someone help me really please
Answer:
b
Step-by-step explanation:
3/3 = 1
Answer:
C
Step-by-step explanation:
The diagram shows two right angled triangles, joined together along a common side.
Calculate the area of the triangle ACD.
you must show all your working.
(Pleaseee it’s really urgent!)
Answer:
AC² = 10.8²+14.4² = 324
AC = √324= 18
area = AC.DC÷2
area=18×24÷2
area=216
Answer:
216 centimeters squared
Step-by-step explanation:
working is above
I NEEED SOMEBODY TO HELP ME OUT WITH THIS QUESTION THXS
Answer:
The answer is less than that is the answer
There are 50 pennies in a roll. If you have 150 rolls of pennies, how many pennies do you have?
Answer: 7500
Step-by-step explanation:
multiply 150 by 50
HELP NEEDED ASAP!! Please CAN SOMEONE HELP
Answer:
Part 1:
y= 23
Part 2:
x=20
Step-by-step explanation:
Part 1:
cos(y) = 48/52
y=cos^-1(48/52)
y=22.619864948~23
Part 2:
48^2+x^2=52^2
x^2=2704-2304
x=sqrt(400)
x=20 or -20.
A negative length makes no sense, so x=20
Answer:
y = 23º
x = 20 cm
Step-by-step explanation:
Cos∅ = adj/hyp
cosy = 48/52
∅ = arccos48/52
use calculator
∅ = 22.619864948040426
Rounded
∅ = 23º
----------------------------------
a² + b² = c²
x² + 48² = 52²
x² = 52² - 48²
x² = 400
x = 20 cm
Find the measure of the missing angles. Help please
Answer:
< 1 = 92º
< 2 = 24º
< 3 = 35º
< 4 = 35º
< 5 = 81º
Step-by-step explanation:
< 1 = 180 - 88 = 92
< 3 = 64 corresponding angle due to parallel lines
< 2 = 180 - (92 + 64) = 24
< 4 = 180 - (64 - 81) = 35
< 5 = 180 - (64 + 35) = 81
Convert the rectangular coordinates (-9, 3V3) into polar form. Express the angle
using radians in terms of te over the interval 0
Answer:
[tex](6\sqrt{3},\,\frac{5\pi}{6})[/tex]
Step-by-step explanation:
The radius r can be found from the relationship
[tex]r^2=x^2+y^2\\r^2=(-9)^2+(3\sqrt{3})^2\\r^2=81+27=108\\r=\sqrt{108}\\r=6\sqrt{3}[/tex]
The point is in Quadrant II (-, +), so use the inverse cosine function to find the angle.
[tex]\cos{\theta}=\frac{x}{r}=\frac{-9}{6\sqrt{3}}\\\cos{\theta}=-\frac{9}{6\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}\\\cos{\theta}=-\frac{9\sqrt{3}}{6\cdot3}\\\cos{\theta}=-\frac{\sqrt{3}}{2}\\\\\cos^{-1}\frac{-\sqrt{3}}{2}}=\frac{5\pi}{6}[/tex]
See the attached image.
e If M P = Rs 420,SP. 405 then
find discount
Answer:
discount=MP-SP
=Rs420-Rs405
=Rs15
Step-by-step explanation:
Find the component form of the resultant vector.
u=-12i + 35j
Find: -8u
A) 10V 47 - 1 + 10j
B) -40i + 35j
C) 961 – 280j
D) 151 – 5V3.j
Answer:
C) 96i – 280j
Step-by-step explanation:
Multiplying vector by constant:
When a vector is multiplied by a constant, each component of the vector is multiplied by this constant.
In this question:
u = -12i + 35j
-8u = -8(-12i + 35j) = (8*12i - 8*35j) = 96i - 280j.
The answer is C) 96i – 280j
An isosceles right triangle has legs of equal length. If the
hypotenuse is 10 centimeters long, find the length of each leg.
Answer:
[tex] \displaystyle 5\sqrt{2}[/tex]
Step-by-step explanation:
we have a right angle isosceles triangle
in order to figure out the length of each leg we can consider Pythagoras theorem given by
[tex] \displaystyle {a}^{2} + {b}^{2} = {c}^{2} [/tex]
remember that,
isosceles triangle has two equal legs so a=b and given that the the hypotenuse is 10
substitute:
[tex] \displaystyle {a}^{2} + {a}^{2} = {10}^{2} [/tex]
simplify addition:
[tex] \displaystyle {2a}^{2}= 100[/tex]
simplify square:
divide both sides by 2:
[tex] \displaystyle {a}^{2}= 50[/tex]
square root both sides:
[tex] \displaystyle {a}^{}= \sqrt{50}[/tex]
[tex] \displaystyle {a}^{}= 5\sqrt{2}[/tex]
hence,
the length of each leg is 5√2
5% equals what fraction, in lowest terms?
Answer:
1/20
Step-by-step explanation:
According to G0ogle 5 percent equals 1/20 in lowest terms.
Answer:
5% equals 5/100 which is 1/20 in lowest terms.
Step-by-step explanation:
5% is basically equivalent to 5/100. 5/100 in lowest terms is 1/20 since you divide the numerator and denominator by 5.
I hope this helps, have a nice day.
Voce 2x-u - 1x2-3x+3 = 2
Answer:
u=−x2−x+1
Step-by-step explanation:
Let's solve for u.
2x−u−1x^2−3x+3=2
Step 1: Add x^2 to both sides.
−x2−u−x+3+x2=2+x2
−u−x+3=x2+2
Step 2: Add x to both sides.
−u−x+3+x=x2+2+x
−u+3=x2+x+2
Step 3: Add -3 to both sides.
−u+3+−3=x2+x+2+−3
−u=x2+x−1
Step 4: Divide both sides by -1.
−u/−1=x2+x−1
−1/u=−x2−x+1
Answer:
u=−x2−x+1
Find the volume of the prism. round to the nearest tenth
Answer:
V = 310.5 cm³
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Volume of a Prism Formula: V = lwh
l is lengthw is widthh is heightStep-by-step explanation:
Step 1: Define
Identify variables
l = 13.8 cm
w = 4.5 cm
h = 5 cm
Step 2: Solve for V
Substitute in variables [Volume of a Prism Formula]: V = (13.8 cm)(4.5 cm)(5 cm)Multiply: V = (62.1 cm²)(5 cm)Multiply: V = 310.5 cm³HELP HELP HELP PLS ✨
Answer:
C. 18
Step-by-step explanation:
4-6 paris = about 23
10-12 pairs = about 5
28 - 5 = 18
How much is three times two
Answer:
the answer is 6.
Step-by-step explanation:
Answer:
6.
Step-by-step explanation:
3+3=6 = 2×3=6
you can do draw 3 circles 2 times and add it all together.
please help I'll give brilliantist:)
Answer:
-7
Step-by-step explanation:
The full coordinate is (-7,3) the dot is on the line between -6 and -8
Answer:
-7
Step-by-step explanation:
x = 3
y = -7
the answer is just -7
Simran has a bag containing white and yellow marbles. Simran randomly selects one marble from the bag,
records the result, and returns the marble to the bag. The results of the first 65 selections are shown below.
A white marble was selected 41 times.
A yellow marble was selected 24 times.
Based on these results, what is the probability that the next marble Simran selects, rounded to the nearest
Answer:
d. 63%
Step-by-step explanation:
percent, will be white?
A41% b50% c59% d63%
The probability of white = P (w) = 41/65= 0.63
The probability of yellow = P (y)= 24/65= 0.369=0.37
The probability of choosing white is 0.63 . When rounded to nearest percent gives
0.63*100/100
=0.63*100 percent
= 63 percent
= 63%
the probability of getting the next marble white is the same as the probability of getting a white.
Find the exact value of sin A in simplest radical form.
Using the sine rule,
[tex] \frac{a}{sin(a)} = \frac{b}{sin(b)} = \frac{c}{sin(c)} [/tex]
Here we are going to use the values of A and C,
[tex] \frac{12}{sin(a)} = \frac{14}{sin(90)} \\ \frac{12}{sin(a)} = \frac{14}{1} \\ sin(a) = 12 \div 14 \\ sin(a) = 0.8571[/tex]
So sin(A) = 12/14 = 6/7 = 0.8571, but since the question says in its simplest radical form, I think the closest answer to it should be
[tex] \frac{ \sqrt{3} }{2} [/tex]