Answer:
18
Step-by-step explanation:
3:2 means 3/2 or 3÷2
but its better to leave it as
3/2
Find a homogeneous second-order Cauchy-Euler equation with real coefficients if the given number is a root of its auxiliary equation.
mi= i
C1cos(ln(x)) + C2sin(ln(x))
I'm going to assume that you mean to say that i = √(-1) is a root of the auxiliary equation. That is, if the Cauchy-Euler DE is
x ²y'' + axy' + by = 0
then the auxiliary equation obtained by substituting y = xᵐ is
x ² (m (m - 1) xᵐ ⁻ ²) + ax (m xᵐ ⁻ ¹) + bxᵐ = 0
which reduces to
m (m - 1) + am + b = 0
or
m ² + (a - 1) m + b = 0
By the fundamental theorem of algebra, we can write the quadratic in terms of its roots r₁ and r₂,
(m - r₁) (m - r₂) = 0
Given that one root is the imaginary unit i, and the coefficients of the aux. equation are real, it follows that the other root is -i, because complex roots must occur with their conjugates. So we have as our aux. equation,
(m - i ) (m + i ) = 0
or
m ² + 1 = 0
Then a - 1 = 0 and b = 1, so that the given root and general solution correspond to the DE,
x ²y'' + xy' + y = 0
What is the total cost of a $28 pair of jeans if the sales tax is 7.5%?
Answer:
30.10
Step-by-step explanation:
First find the amount of tax
28 * 7.5%
28 * .075
2.10
Add this to the price of the pants
28+2.10 =30.10
Which of the following is equivalent to 0 equals 3 x squared minus 12 x minus 15 when completing the square?
After completing the square the quadratic equation [tex]3x^{2} -12x-15=0[/tex] is equivalent to [tex](x-2)^2=3^2[/tex].
What is a quadratic equation?"It is a polynomial equation with degree two."
What is completing the square method?"It is a method that is used for converting a quadratic expression of the form [tex]ax^2 + bx + c[/tex] to [tex]a(x - h)^2 + k[/tex] "
For given example,
We have been given a quadratic equation.
[tex]3x^{2} -12x-15=0[/tex]
First we divide above quadratic equation by 3,
[tex]x^{2} -4x-5=0\\\\x^2-4x=5[/tex] ................(i)
Now for completing the square first find [tex](\frac{-b}{2a} )[/tex]
[tex]\frac{-b}{2a}\\=\frac{-(-4)}{(2)(1)}\\\\ =\frac{4}{2}\\\\ =2[/tex]
Add [tex](\frac{-b}{2a} )^2[/tex] on both the sides of equation (i),
[tex]x^{2} -4x+4=5+4\\\\(x-2)^2=9\\\\(x-2)^2=3^2[/tex]
Therefore, after completing the square the quadratic equation [tex]3x^{2} -12x-15=0[/tex] is equivalent to [tex](x-2)^2=3^2[/tex].
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Fewer and fewer customers have been coming into the restaurant, so Bill, the manager, decides to change the entire menu. After he does this, he finds out that people loved the food, but the service has been driving people away. This represents what kind of problem in the decision-making process? O a) Failure to develop enough options O b) Failure to correctly define the problem c) Failure to act on a decision O d) Failure to evaluate the decision
Answer:
failure to correctly define the problem
Step-by-step explanation:
He changes the menu without identify that the real problem was the service.
6. How many rational number are there Between ⅕and⁹/⁵
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Answer:
an infinite number
Step-by-step explanation:
Between any pair of numbers, there are ...
an infinite number of rational numbers, and
an infinite number of irrational numbers
Expand (2+x)^-3
....
Answer:
1/(x^3 + 6x^2 + 12x + 8)
Step-by-step explanation:
The first thing we do is rationalize this expression. (2+x)^-3 is written as
1/(2+x)^3
Then from there we can foil out the denominator. It is easiest to foil (2+x)(2+x) first and then multiply that product by (2+x).
(2+x)(2+x) = 4 + 4x + x^2
(4+4x+x^2)(2+x) = 8+8x+2x^2+4x+4x^2+x^3.
Then we combine like terms and put them in order to get:
x^3 + 6x^2 + 12x + 8
And of course we can't forget that this was raised to the negative third power, so our answer is 1/(x^3 + 6x^2 + 12x + 8)
Answer:
Hello,
Step-by-step explanation:
[tex](a+x)^n=a^n+\left(\begin{array}{c}n\\ 1\end{array}\right)*a^{n-1}*x+\left(\begin{array}{c}n\\ 2\end{array}\right)*a^{n-2}*x^2+\left(\begin{array}{c}n\\ 3\end{array}\right)*a^{n-3}*x^3+\left(\begin{array}{c}n\\ 4\end{array}\right)*a^{n-4}*x^4+...+\left(\begin{array}{c}n\\ n\end{array}\right)*a^{n-n}*x^n[/tex]
[tex]with \\\\\left(\begin{array}{c}n\\ 1\end{array}\right)=n\\\\\left(\begin{array}{c}n\\ 2\end{array}\right)=\dfrac{n(n-1)}{2!} \\\\\left(\begin{array}{c}n\\3 \end{array}\right)=\dfrac{n(n-1)(n-2)}{3!} \\\\...\\[/tex]
[tex]\dfrac{1}{(2+x)^3} =\dfrac{1}{8} +3*\dfrac{x}{4}+3\dfrac{x^2}{2}+x^3\\\\[/tex]
Correct the formula
Please
Answer:
The addition should be divided by 4 and not 3 since there are 4 meals.
Step-by-step explanation:
A rectangle auditorium seats 1260 people. The number of seats in each row exceeds the number of rows by 12. Find the number of seats in each row
Answer:
Easy, all you ha
Step-by-step explanation:
Find the L.C.M. of: a2 + 2a +1, a? + 3a + 2
Step-by-step explanation:
sorrry .......................
help pls!!! Classify the following question: “President, vice president, and secretary are being chosen for the Environmental Club. In how many different ways can these three offices be filled from a list of ten members?”
the answer is: combation
Write the phrase as an algebraic expression: 3 less than 4 times a number
Answer:
4x-3 is the expression to your question
Answer:
3[tex]\leq[/tex]4x
Step-by-step explanation:
What is the value of the expression, written in standard form?
Answer:
200
Step-by-step explanation:
6.6/3.3 = 2
10^-2 - (-4) = 10^2
The answer is 2 * 10^2 or 200.
At what points do these graphs intersect
y=x²-x-6
y=x+2
Answer:
Solve algebraicallyEliminate y:
x² - x - 6 = x + 2x² - 2x = 8x² - 2x + 1 = 9(x - 1)² = 3²1) x - 1 = 3 ⇒ x = 4 ⇒ y = 62) x - 1 = -3 ⇒ x = -2 ⇒ y = 0The solution is:
(-2, 0), (4, 6)Solve graphicallySee the attached
Answer:
[tex]thank \: you[/tex]
[tex] \frac{2}{4} + 5 \times 36 + 2 \frac{6}{3 } = [/tex]
what is answer
Step-by-step explanation:
[tex] \frac{2}{4} + 5 \times 36 + 2 \frac{6}{3} [/tex]
[tex] = \frac{1}{2} + 180 + 2 \times \frac{2}{1} [/tex]
[tex] = \frac{1}{2} + 180 + 4[/tex]
[tex] = \frac{1 + 360 + 8}{2} [/tex]
[tex] = \frac{369}{2} [/tex]
[tex] = 184 \frac{1}{2} \: or \: 184.5(ans)[/tex]
Sandy used these rules to write a 6-digit number.
• 3 in the tens place
• 6 in the hundreds place
1 in the thousands place
• 8 in the ten thousands place
4 in the ones place
• 2 in the hundred thousands place
.
What number did she write?
A. 281,634
B. 361.842
C. 681,234
D. 864,321
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Answer:
A. 281,634
Step-by-step explanation:
You can identify the number after the first two "rules".
Choices A and C have 3 in the tens place.
Choice A has 6 in the hundreds place.
Find the lengths of the other two sides of the isosceles right triangle
Answer:
h²=p²+b²
(7√2)²=x²+x²
(49×2)=2x²
2x²=49ײ
x²=49×2/2
x²=49
x=√49=7
x=7
OAmalOHopeO
Which of the following are exterior angles? Check all that apply.
Answer:
<5
Step-by-step explanation:
exterior angles + the corresponding interior angle of the triangle = 180º or a straight angle
the only exterior angle shown in the diagram is <5, which corresponds to the interior <2
hope this helps!
Answer:
<5
Step-by-step explanation:
everything else is matched up perfectly so it has to be <5
14. The area of 10 square plots is 160 ares. Find the length in metres of the side of each plot (3mks)
Answer:
Step-by-step explanation:
1 are = 100 m²
Assuming the ten squares are congruent, the area of each square is 160/10 = 16 are
16 are × 100 m²/are = 1600 m²
each side is √1600 = 40 m
The length of side of plot is 40 meters.
What is area?The total space occupied by a flat (2-D) surface or shape of an object is known as area.
Draw a square on a piece of paper with a pencil. It has two dimensions. The term "area" refers to the area that the shape occupies on the paper.
Now picture your square as being comprised of smaller unit squares. The number of unit squares required to cover a 2-D shape's total surface area is used to calculate its area.
Given the area of 10 square plot is 160 are,
here 1 are = 100 m²
area of 10 square plot = 160 x 100 = 16,000 m²
area of 1 square plot = 16000/10 = 1600 m²
area of square is "a²"
where a is side of square
area = a² = 1600 m²
a = √1600
a = 40 m
Hence the length of side of each plot is 40 meters.
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|x|+|x+1|+|x+2|+|x+3|+...+|x+2021=2021x
Answer:
jo pahle wale X hai na na X + x plus 1 unhen Yad Karke answer 1 aaega FIR X + 2 =_= + 3 X + 3 yah answer Aaya 1 or 2 X + ka ok
Step-by-step explanation:
FIR hai x+ x and ++ 2021 x
2021x
FIR + Kannan donon ko x
ans
x - 3 X
x - 4042
yah answer aayega ine donon ka the solve this question ok friend
a. 8
b. 9
c. 7
d. 6
Answer:
a. 8
Step-by-step explanation:
1+1 = 2
1+2 = 3
2+3 = 5
3+5 = 8
Find the probability. A calculator requires a keystroke assembly and a logic circuit. Assume that 75% of the keystroke assemblies and 94% of the logic circuits are satisfactory. Find the probability that a finished calculator will be satisfactory.
Answer:
0.705 = 70.5% probability that a finished calculator will be satisfactory.
Step-by-step explanation:
Probability of independent events:
If two events, A and B, are independent, the probability of both happening is the multiplication of the probabilities of each happening, that is:
[tex]P(A \cap B) = P(A)P(B)[/tex]
In this question:
Event A: Keystroke assembly are satisfactory.
Event B: Logic circuits are satisfactory.
75% of the keystroke assemblies and 94% of the logic circuits are satisfactory.
This means that [tex]P(A) = 0.75, P(B) = 0.94[/tex]
Find the probability that a finished calculator will be satisfactory.
Both satisfactory, and since they are independent:
[tex]P(A \cap B) = P(A)P(B) = 0.75*0.94 = 0.705[/tex]
0.705 = 70.5% probability that a finished calculator will be satisfactory.
In 20P4 how many choices are
there for vice-president from a
state of four officers?
Note: The vice president is the second officer
to be elected.
Acellus
Explanation:
There are 20 choices for president, and 20-1 = 19 choices for vice president. You count down by 1 each time you fill a seat. So that means you'll have 19-1 = 18 choices for the third seat, and 18-1 = 17 choices for the fourth seat.
if x = -5
x2 + 3
x - 2
Answer:
Step-by-step explanation:
f(x) = x - 1. Find the inverse of f(x).
Answer:
f^-1 (x) = x+1
Step-by-step explanation:
f(x) = x-1
y = x-1
Exchange x and y
x = y-1
Solve for y
Add 1 to each side
x+1 = y-1+1
x+1 = y
The inverse is x+1
f^-1 (x) = x+1
which function is positive for the entire interval (-3,-2)
Answer:
There can be several such functions; however, the basic condition that needs to be met for a function to be positive for the interval [–3, –2] is that it should be multiplied by (-1) Hence, one such function that is positive for the entire interval is f(x) = -x
Step-by-step explanation:
Help only #31,33, please thank you
Answer:
31) 4d + 28 33) 10 + 5
Step-by-step explanation:
31) 4 ( d + 7) = 4 x 7 = 28 = 4d + 28
33) 5 ( 2m + 1 ) = 5. 2m + 5 . 1: 10m + 5
round 12.5478 to the nearest hundredths
Answer:
12.04
Step-by-step explanation:
Find the number in the hundredth place 4 and look one place to the right for the rounding digit 1 . Round up if this number is greater than or equal to 5 and round down if it is less than 5 .
Copy center charges $0.08 a page for machine fed copies and $0.20 for hand fed copies.If Logan's bill for 80 copies of his movie script is $13, how many copies of each type were made?
Answer:
machine fed copies = 25, hand fed copies = 55
Step-by-step explanation:
let machine fed = x, hand fed = y
0.08x+0.2y = 13 (1)
x+y = 80
x= 80-y (2)
sub (2) into (1)
0.08(80-y)+0.2y=13
6.4-0.08y+0.2y=13
0.12y=6.6
y = 55
sub y=55 into eqn 2
x = 80-55 = 25
Jackson gets $3,600 worth of new toy cars each toy car is worth $18 how many toy cars did Jackson get
Answer:
200 I think
Step-by-step explanation:
i need help on this PLS
Answer:
25 miles (The pattern is m = 25g where m is miles and g is gallons.)
