Answer:
[tex]1 \rightarrow E, 2\rightarrow B, 3\rightarrow C, 4\rightarrow D, 5\rightarrow A[/tex]
Step-by-step explanation:
1. [tex]\frac{d^2y}{dx^2}+25y=0[/tex]
The characteristic equation for the given differential equation is:
[tex]r^{2} +25=0[/tex]
[tex]\Rightarrow r^2=-25[/tex]
[tex]\Rightarrow r=\pm 5i[/tex]
Since the roots are complex
Now, the general solution is:
[tex]y=A\cos 5x+B\sin 5x[/tex]
2. [tex]\frac{dy}{dx}=\frac {2xy}{x^2}-5y^2[/tex]
[tex]\Rightarrow \frac{dy}{dx}-\frac 2xy=-5y^2[/tex]
Divide both sides by [tex]y^{-1}[/tex]
Let, [tex]v=y^{-1} \Rightarrow \frac{dv}{dx}=-y^{-2}\frac{dy}{dx}[/tex]
[tex]\Rightarrow -\frac{dv}{dx}-\frac 2xv=-5[/tex]
[tex]\Rightarrow \frac{dv}{dx}+\frac 2xv=5[/tex]
Here, [tex]p(x)=\frac 2x\; \text{and}\;\; q(x)=5[/tex]
I.F. [tex]=e^{\int \frac 2xdx}=x^2[/tex]
Now, the general solution is:
[tex]vx^2=\int x^2 5dx=\frac {5x^3}3+c[/tex]
[tex]\Rightarrow \frac {x^2}y-\frac {5x^3}3=c[/tex]
[tex]\Rightarrow 3x^2-5x^3y=Cy[/tex]
3. [tex]\frac{d^2y}{dx^2}+16\frac{dy}{dx}+64y=0[/tex]
The characteristic equation is:
[tex]r^2+16r+64=0[/tex]
[tex]\Rightarrow r^2+8r+8r+64=0[/tex]
[tex]\Rightarrow r(r+8)+8(r+8)=0[/tex]
[tex]\Rightarrow (r+8)(r+8)=0[/tex]
[tex]\Rightarrow r=-8,-8[/tex]
Since the roots are real and repeated.
Now, the general solution is:
[tex]y=Ae^{-8x}+Bxe^{-8x}[/tex]
4. [tex]\frac {dy}{dx}=10xy[/tex]
[tex]\Rightarrow \frac {dy}{y}=10xdx[/tex]
Integrating both sides
[tex]\int\frac {dy}y=\int 10xdx+\log c[/tex]
[tex]\Rightarrow \log y=5x^2+\log c[/tex]
[tex]\Rightarrow y=e^{5x^2}+c[/tex]
5. [tex]\frac {dy}{dx}+24x^2y=24x^2[/tex]
Here, [tex]p(x)=24x^2 \; \text{and}\;\; q(x)=24x^2[/tex]
I.F.[tex]= e^{\int 24x^2dx}=e^{8x^3}[/tex]
Now, the general solution is:
[tex]y.e^{8x^3}=\int 24x^2 e^{8x^3}dx=24\int x^2e^{8x^3}dx[/tex]
Let, [tex]8x^3=t \Rightarrow 24x^2dx=dt\Rightarrow x^2dx=\frac {dt}{24}[/tex]
[tex]\Rightarrow ye^{8x^3}=\int e^tdt[/tex]
[tex]\Rightarrow ye^{8x^3}=e^{8x^3}+c[/tex]
[tex]\Rightarrow y=1+ce^{-8x^3}[/tex]
Given the figure below, find the values of x and z
Answer:
x=14 z=72
Step-by-step explanation:
(8x-40)+(12x-60)=180
20x-100=180
20x=280
x=14
(12x-60)+z=180
(168-60)+z=180
108+z=180
z=72
jess purchased a full tank of gas on thursday.on friday,he took a road trip and used 1/2 of the tank.on saturday,he did some errands and use an 1/3 additional of the tank.how much gas does jess have left?
Answer:
1/3 of the gas.
Step-by-step explanation:
1 - 1/2 = 1/2
1/3 - 3/3 = 2/3
2/3 ( 1/2 ) = 1/3
The amount of gas left with Jess is given by the equation A = 1/6 of the total gas
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total amount of the gas be represented as A
Now , the equation will be
The amount of gas utilized by Jess on Friday = 1/2 of the initial gas
So , The amount of gas left on Friday = A - ( 1/2 ) A
On simplifying the equation , we get
The amount of gas left on Friday = ( 1/2 )A
Now ,
Amount of gas utilized by Jess on Saturday = ( 1/3 ) of the remaining gas
On simplifying the equation , we get
The remaining gas = ( 1/2 ) A - ( 1/3 ) A
So , the remaining amount of gas with Jess = ( 1/6 ) of the total gas
Hence , the equation is ( 1/6 ) of the total gas is remaining
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the height of the house is 26 feet what is the height x of each story?
Answer:
1 story=26, 2 stories=13 3 stories= 8.666666 4 stories= 6.5 5 stories=5.2
Step-by-step explanation:
(b) Heera sold a pen at the loss of 15%. Had she sold it in Rs. 3 more, she should have 5%
profit. What would be the cost price of the pen? Find it.
Answer:
Cost price= Rs. 15
Step-by-step explanation:
Please see attached picture for full solution.
A market research company wishes to know how many energy drinks adults drink each week. They want to construct a 80% confidence interval for the mean and are assuming that the population standard deviation for the number of energy drinks consumed each week is 0.9. The study found that for a sample of 164 adults the mean number of energy drinks consumed per week is 7.9. Construct the desired confidence interval. Round your answers to one decimal place.
Answer:
The confidence interval = (7.8 , 8.0)
Step-by-step explanation:
Confidence Interval formula =
Mean ± z × Standard deviation/√n
Mean = 7.9
Standard deviation = 0.9
n = number of samples = 164
z = z score of an 80% confidence interval = 1.282
Confidence Interval = 7.9 ± 1.282 × 0.9/√164
= 7.9 ± 0.0900966432
Confidence Interval
= 7.9 - 0.0900966432
= 7.8099033568
Approximately to 1 decimal place = 7.8
7.9 + 0.0900966432
= 7.9900966432
Approximately to 1 decimal place = 8.0
Therefore, the confidence interval = (7.8 , 8.0)
You have five pieces of wood. The lengths of these are shown below.
325 cm
4.04 m
73 cm
1.6 m
2.87 m
What is the total length of the wood?
Answer:
1,249 cm or 12.49
Whichever one it asks for
Step-by-step explanation:
First, we need to convert all of the m to cm.
4.04 m = 404 cm
1.6 m = 160 cm
2.87 m = 287 cm
Next, add them all up.
325 + 404 + 73 + 160 + 287 =
1,249 cm
If it asks to convert to m again, then the answer would be 12.49 m
Hope this helps!!!
Answer:
1,249 cm (or) 12.49 m
Step-by-step explanation:
1m = 100cm
4.04m = 404cm
1.6m = 160 cm
2.87m = 287 cm
So, 325 + 404 + 73 + 160 + 287 = 1,249 cm
If u want the answer in meters, [tex]\frac{1249}{100}[/tex]
So, it will be 12.49 m
1. Graph the line y=2x+5 on the graph.
Answer:
See below
Step-by-step explanation:
We can simply use a graphing calculator to carry it out.
See the attached file for more explanation!
Another way is that we can take the values of x as 1,2 and 3 and so on and put it in the equation to get the value of y. We have some coordinates now so we'll plot them in the graph to get the line of y = 2x+5.
Step-by-step explanation:
Hope this helps........
Find the pattern and use inductive reasoning to predict the next number in the sequence 5,5,10,30,120,…
Answer:
afdgdfdf
Step-by-step explanation:
Answer:
its going up by 1 each time theres a new number so next youll multiply 4 by 120 which is 480
Step-by-step explanation:
Use any of the methods to determine whether the series converges or diverges. Give reasons for your answer.
∑[infinity]n=17n2−4n+3
12+2n6
Answer:
It means [tex]\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}[/tex] also converges.
Step-by-step explanation:
The actual Series is::
[tex]\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}[/tex]
The method we are going to use is comparison method:
According to comparison method, we have:
[tex]\sum_{n=1}^{inf}a_n\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n[/tex]
If series one converges, the second converges and if second diverges series, one diverges
Now Simplify the given series:
Taking"n^2"common from numerator and "n^6"from denominator.
[tex]=\frac{n^2[7-\frac{4}{n}+\frac{3}{n^2}]}{n^6[\frac{12}{n^6}+2]} \\\\=\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{n^4[\frac{12}{n^6}+2]}[/tex]
[tex]\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n=\sum_{n=1}^{inf} \frac{1}{n^4}[/tex]
Now:
[tex]\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\ \\\lim_{n \to \infty} a_n = \lim_{n \to \infty} \frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\=\frac{7-\frac{4}{inf}+\frac{3}{inf}}{\frac{12}{inf}+2}\\\\=\frac{7}{2}[/tex]
So a_n is finite, so it converges.
Similarly b_n converges according to p-test.
P-test:
General form:
[tex]\sum_{n=1}^{inf}\frac{1}{n^p}[/tex]
if p>1 then series converges. In oue case we have:
[tex]\sum_{n=1}^{inf}b_n=\frac{1}{n^4}[/tex]
p=4 >1, so b_n also converges.
According to comparison test if both series converges, the final series also converges.
It means [tex]\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}[/tex] also converges.
what is 4+2+-8+-6?
Answer:
-8
Step-by-step explanation:
+-8 = -8
+-6 = -6
then:
4 + 2 + -8 + -6 = 4 + 2 - 8 - 6 = 6 - 14
= -8
Answer:
-8
Step-by-step explanation:
Simplify: 4 + 2 - 8 - 64 + 2 = 6Plug 6 in: 6 - 8 - 66 - 8 = -2Plug -2 in: -2 - 6-2 - 6 = -8Therefore, the answer is -8.
Question in the picture please help me.
Answer:
1) [tex]50=2(x+5)+2(x)[/tex]
2) [tex]x=10[/tex]
3) [tex]15\text{ units}[/tex]
Step-by-step explanation:
So we know that the perimeter of the rectangle is 50.
The formula for the perimeter of a rectangle is given by:
[tex]P=2l+2w[/tex]
Where l is the length and w is the width.
The length is (x+5) and the width is (x).
Thus, substitute (x+5) for l and (x) for w. Also substitute 50 for P. Therefore:
[tex]50=2(x+5)+2(x)[/tex]
And that's our equation.
To solve, first distribute:
[tex]50=2x+10+2x[/tex]
Combine like terms:
[tex]50=4x+10[/tex]
Subtract 10 from both sides:
[tex]40=4x[/tex]
Divide everything by 4:
[tex]x=10[/tex]
So, the value of x is 10.
The length is the longer side. Thus, it is (x+5).
We now know that x is 10, substitute:
[tex]x+5\\=(10)+5\\=15[/tex]
So, the length is 15 units.
Answer:
Below
Step-by-step explanation:
The perimeter of a rectangle is the sum of its 4 sides.
Let P be the perimeter
● P = x + (x+5) + x + (x+5)
● P = x+x+x+x+5+5
The perimeter is 50 units
● 50 = 4x +10
So this the equation that would model how to find x.
Let's solve it
● 4x + 10 = 50
Substract 10 from both sides
● 4x + 10 - 10 = 50-10
● 4x = 40
Divide both sides by 4
● 4x/4 = 40/4
● x = 10
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's find the length.
The length is x+5
Replace x by 10 to find the value of the length.
● 10 + 5 = 15
So the length is 15 units
what is the probability that a randomly selected driver fatality who was female was 55 to 69 years old
Answer:
0.1354
Step-by-step explanation:
Relevant data provided as per the requirement is shown below:-
Female probability of age between 55 to 69 = 2058
Male probability of age between 55 to 69 = 4571
According to the given situation, the calculation of probability is shown below:-
[tex]= \frac{Female\ from\ 55\ to\ 69 }{Total\ female}[/tex]
where,
Total female is
= 143 + 2333 + 4027 + 5178 + 2058 + 1459
= 15,198
And, the female is 2058
So, the probability is
[tex]= \frac{2058}{15,198}[/tex]
= 0.1354
Therefore for computing the probability of female that lies between 55 to 69 we simply applied the above formula.
five thousand two hundred sixty-seven. standard form
Answer:
5,267
Step-by-step explanation:
Five thousand: 5,000
Two hundred: 200
Sixty: 60
Seven: 7
Put them together: 5,267
Five thousand two hundred sixty-seven in standard form is 5,267.
Standard form is the way of written down number in simplest form.
Five thousand=5,000
Two hundred=200
Sixty=60
Seven=7
Hence:
Standard form=5,000+200+60+7
Standard form=5,267
Inconclusion five thousand two hundred sixty-seven in standard form is 5,267.
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What are the solutions to the equation 0=x squared- x-6
Answer:
Factor to this equation out, the easiest way is to solve for the two x values that add up to -1 but when multiplied is equal to -6. It should look like this: (x +- ?)(x +- ?).
The factored out form is then (x - 3)(x +2), because -3 + 2 = -1 and when multiplied together gives -6.
x - 3 = 0
x = 3
x + 2 = 0
x = -2
The two solutions are therefore, x = 3 and x = -2.
Answer 9w-4=14 show solving steps pls
Answer:
[tex]w=2[/tex]
Step-by-step explanation:
So we have the equation:
[tex]9w-4=14[/tex]
Add 4 to both sides. The left cancels:
[tex](9w-4)+4=(14)+4\\9w=18[/tex]
Divide both sides by 9.The left cancels:
[tex](9w)/9=(18)/9\\w=2[/tex]
So, the value of w is 2.
And we're done :)
If x=4 what is the value of 2x+18
Answer:
26
Step-by-step explanation:
2x + 18
2(4) + 18
8 + 18
26
Answer:
26
Step-by-step explanation:
We just substitute the value of X and find the answer
Please explain your work still don’t understand
Answer:
The radius is 5√2.The center is (-3, 4).Step-by-step explanation:
It can be helpful to understand what the square of a binomial looks like:
(a +b)² = a² +2ab +b²
The middle term on the right is twice the product of the terms in the original binomial on the left.
Here, we want to use this relationship to find "b" when we're given "2ab". We recognize that "b" is half the coefficient of "a" in 2ab.
Choosing a value for b² to turn the sum (a² +2ab) into the trinomial (a² +2ab +b²) is called "completing the square" because that trinomial can now be written as the square (a+b)².
__
The standard form equation of a circle with center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
In order to find the center and radius of the circle from the given equation, you're expected to rewrite the equation in this form. You do that by "completing the square" for both x-terms and y-terms.
__
Given
x² +y² +6x -8y -25 = 0
Regrouping, we have ...
(x² +6x) +(y² -8y) = 25
Adding the squares of half of 6 and half of -8, we can write this as ...
(x² +6x +3²) +(y² -8y +(-4)²) = 25 +3² +(-4)²
And writing the trinomials as squares gives us ...
(x +3)² +(y -4)² = 50 = (5√2)²
Comparing this to the standard form equation above, we see that ...
(h, k) = (-3, 4)
r = 5√2
__
The radius is 5√2.
The center is (-3, 4).
__
The attachment shows that the original equation draws a circle with center (-3, 4) and through points that are 5 units horizontally and vertically from the center, such as the point (2, -1). That is, the radius is 5√2.
Given the sets
A
and
B
expressed in interval notation, find
A
∩
B
.
A
=
(
−
∞
,
−
42
)
∪
(
−
25
,
+
∞
)
B
=
(
−
54
,
70
)
Answer:
Step-by-step explanation:
A∩B=[-54,-42]∪[-25,70]
( 7m + 1 )( 5m 2 + 4m - 6 ) simplified
Answer:
35m³ + 33m² - 38m - 6
Step-by-step explanation:
simplify ( 7m + 1 )( 5m^2 + 4m - 6 )
= 7m * 5m² + 7m * 4m - 7m * 6 + 5m² + 4m - 6
=7 * 5mm² + 7 * 4mm - 7 * 6m + 5m² + 4m
= 35m³ + 33m² - 38m - 6
2. Find the distance between A (-1, 4) and B (1.-1)
5.39
5.19
5.29
5.09
=====================================================
Explanation:
Apply the distance formula.
[tex]d = \sqrt{ (x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{ (-1-1)^2+(4-(-1))^2}\\\\d = \sqrt{ (-1-1)^2+(4+1)^2}\\\\d = \sqrt{ (-2)^2+(5)^2}\\\\d = \sqrt{ 4+25}\\\\d = \sqrt{ 29}\\\\d \approx 5.38516\\\\d \approx 5.39\\\\[/tex]
You could also use the pythagorean theorem which is what the distance formula is based off of.
Suppose a deep sea diver dives from the surface to 202 feet below the surface. He then dives down 12 more feet. Use integers to represent this situation. Then find
the diver's present depth.
Which expression best represents the diver's situation.
O A. O + (-202) + 12
OB. 0 + (-202)+(-12)
OC. 0+202 +(-12)
OD. 0+202 + 12
The diver is presently feet below the surface.
(Simplify your answer.)
Answer:
B.) (-202)+(-12)
Step-by-step explanation:
The undersea level is negative then going under again will produce a completely negative answer.
How do you solve this equation by using the quadratic formula 8x^2+3x-45=0
The 8 is a, the 3 is b and -45 is c
Plug them into the quadratic formula
Limes are on sale. That sale price is 8 limes for $2.00. Why could the unit rate be 4 or 0.25?
Answer:
C.No, because each lime will cost a bit more than 30¢, so 4 limes will cost a bit more than $1.20.Step-by-step explanation:
The unit price of the 8 limes is $0.25 per lime.
The given expression:
The selling price for 8 limes = $2.00
To find:
if the unit price is $4 or $0.25The unit price of the lime is calculated by dividing the total selling price by the total number of limes purchased.
[tex]unit \ price = \frac{total \ amount \ paid \ for \ 8 \ limes }{8 \ limes } \\\\unit \ price =\frac{\$ \ 2}{8 \ limes } \\\\unit \ price = (\frac{1}{4} ) \frac{\$}{lime} \\\\unit \ price = \$0.25 \ per \ lime[/tex]
Thus, the unit price of the 8 limes is $0.25 per lime.
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Find the value of x in the triangle shown below.
12
Answer:
The answer is option CStep-by-step explanation:
Since the triangle is a right angled triangle we can use Pythagoras theorem to find the missing side x
Using Pythagoras theorem we have
c² = a² + b²
where
c is the hypotenuse
From the question x is the hypotenuse
So we have
[tex] {x}^{2} = {5}^{2} + {12}^{2} \\ x = \sqrt{25 + 144} \\ x = \sqrt{169} [/tex]We have the final answer as
x = 13Hope this helps you
If you randomly select a letter from the phrase "Sean wants to eat at Olive Garden," what is the probability that you select a vowel
Answer:100%
Step-by-step explanation: Think about it for a second S-ea-n w-a-nts t-o e-a-t a-t o-liv-e g-a-rd-e-n their are vowels in every word
Answer:12/27
Step-by-step explanation:there are 12 vowels in the phrase so the probability is 12:27 or 4:9 (you can write these as fractions too, numerators are on the left)
One-half of the sum of 3 times v and twenty-eight
Need help writing this in expression form please
Answer:
(1/2)(3v+28)
Step-by-step explanation:
of= multiply
sum= add
Could it be (3v +28)/2
After being arranged and simplified which of the following equations could be solved using the quadratic formula?
Answer:
B. 2x² + x² + x = 30
D. 9x + 3x² = 14 + x - 1
Step-by-step explanation:
2x² + x² + x = 30
simplify
3x² + x - 30 = 0
x can be solve using quadratic equations
x = 3 and x = -10/3
so the answer is B
9x + 3x² = 14 + x - 1
simplify
3x² + 8x - 13 =0
x can be solve using quadratic equations
so the answer is D
Note: options A and C do not qualify for quadratic equation
The solution is Option B , Option D.
The set of quadratic equations are 2x² + x² + x = 30 and 9x + 3x² = 14 + x -1
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
a)
2x² + x² + x = 30 be equation (1)
On simplifying the equation , we get
3x² + x = 30
Subtracting 30 on both sides of the equation , we get
3x² + x - 30 = 0
Now , on factorizing the equation , we get
x = 3 and x = -10/3
b)
9x + 3x² = 14 + x -1 be equation (1)
On simplifying the equation , we get
Subtracting x on both sides of the equation , we get
3x² + 8x = 13
Subtracting 13 on both sides of the equation , we get
3x² + 8x - 13 = 0
Now , on factorizing the equation , we get
x = ( -4/3 ) ± ( √55/3 )
Hence ,
The quadratic equations are 2x² + x² + x = 30 and 9x + 3x² = 14 + x -1
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How many whole tens are in 3,200
Answer:
320
Step-by-step explanation:
There are 320 tens in 3,200.
320 x 10 = 3200
Answer:
320
Step-by-step explanation:
3200/10=320
12.) When rounding to the nearest 10, what is the largest number that will
round to 30?
a.) 31
b.) 34
c.) 21
d.) 25
what is the sum of 8.7 + 5.22=
Answer:
8.7+5.22=13.92
Hope it helps you...
Answer:
13.92
Step-by-step explanation: