Answer:
E
Step-by-step explanation:
y’’ + 9y = sin(3x)
The characteristics equation is;
m^2 + 9 = 0
solving this we have 2 complex roots
m= -3i, 3i
Thus;
yh = Ccos(3x)+ Dsin(3x)
let yp = Axcos(3x) + Bxsin(3x)
Now, because we have sin(3x) and cos(3x) with constant coefficient in yh, option E is our answer
Perform the indicated operation and simplify the result.
Answer:
7/ (3a-1)
Step-by-step explanation:
3a^2 -13a +4 28+7a
------------------ * --------------------
9a^2 -6a+1 a^2 -16
Factor
(3a-1)(a-4) 7(4+a)
------------------ * --------------------
(3a-1) (3a-1) (a-4)(a+4)
Cancel like terms
1 7
------------------ * --------------------
(3a-1) 1
Leaving
7/ (3a-1)
5x + 7y = -29 y = x + 1
Answer:
(x, y) = (-3, -2)
Step-by-step explanation:
Perhaps this is a system of equations you want the solution for.
Since you have an expression for y, substitution is a viable approach.
5x +7(x+1) = -29 . . . . . . substitute for y
12x = -36 . . . . . . subtract 7 and simplify
x = -3 . . . . . . . . . divide by 12
y = (-3) +1 = -2 . . . use the expression for y
The solution is (x, y) = (-3, -2).
Define f(0,0) in a way that extends f(x,y)=x^2 - y^2/x^2 + y^2 to be continuous at the origin.
Answer:
It cannot be extended.
Step-by-step explanation:
Consider the function [tex]f(x,y) = \frac{x^2-y^2}{x^2+y^2}[/tex]. To extend this functions so it is continous at (0,0) we must define [tex] f(0,0) = \lim_{(x,y)\to(0,0)\frac{x^2-y^2}{x^2+y^2}[/tex]. However, this implies that the limit exists. So, we should find if the limit exists or not.
In this case, consider the case in which y =0. When y=0 then
[tex]\lim_{(x,y)\to(0,0) \frac{x^2-0^2}{x^2+0^2} = \lim_{x\to 0}\frac{x^2}{x^2}= 1[/tex]
But, when x=0, we get
[tex]\lim_{(x,y)\to(0,0) \frac{0^2-y^2}{0^2+y^2} = \lim_{y\to 0}\frac{-y^2}{y^2}=-1[/tex].
So, since the limit depends on how we approach to the point (0,0) the limit does not exist. So we can't extend f(x,y) so it is continous.
slope of line passes through (7/20, 8/3) and (3/8, 7/9)
Answer:
[tex]slope = \dfrac{-680}{9}[/tex]
Step-by-step explanation:
We are given coordinates of two points:
Let the points be A and B respectively:
[tex]A(\dfrac{7}{20}, \dfrac{8}{3})\\B(\dfrac{3}{8}, \dfrac{7}{9})[/tex]
To find the slope of line AB.
Formula for slope of a line passing through two points with coordinates [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] is given as:
[tex]m = \dfrac{y_2- y_1}{x_2- x_1}[/tex]
Here, we have:
[tex]x_2 = \dfrac{3}{8}\\x_1 = \dfrac{7}{20}\\y_2 = \dfrac{7}{9}\\y_1 = \dfrac{8}{3}\\[/tex]
Putting the values in formula:
[tex]m = \dfrac{\dfrac{7}{9}- \dfrac{8}{3}}{\dfrac{3}{8}- \dfrac{7}{20}}\\\Rightarrow m = \dfrac{\dfrac{7-24}{9}}{\dfrac{15-14}{40}}\\\Rightarrow m = \dfrac{\dfrac{-17}{9}}{\dfrac{1}{40}}\\\Rightarrow m = \dfrac{-17\times 40}{9}\\\Rightarrow m = \dfrac{-680}{9}[/tex]
So, the slope of line AB passing through the given coordinates is:
[tex]m = \dfrac{-680}{9}[/tex]
A large mixing tank initially contains 1000 gallons of water in which 30 pounds of salt have been dissolved. Another brine solution is pumped into the tank at the rate of 4 gallons per minute, and the resulting mixture is pumped out at the same rate. The concentration of the incoming brine solution is 2 pounds of salt per gallon. If represents the amount of salt in the tank at time t, the correct differential equation for A is:__________.A.) dA/dt = 4 - .08AB.) dA/dt = 8 -.04AC.) dA/dt = 4-.04AD.) dA/dt = 2-.04AE.) dA/dt = 8-.02A
Answer:
(B)[tex]\dfrac{dA}{dt}=8-0.004A[/tex]
Step-by-step explanation:
Volume of fluid in the tank =1000 gallons
Initial Amount of Salt in the tank, A(0)= 30 pounds
Incoming brine solution of concentration 2 pounds of salt per gallon is pumped in at a rate of 4 gallons per minute.
Rate In=(concentration of salt in inflow)(input rate of brine)
[tex]=(2\frac{lbs}{gal})( 4\frac{gal}{min})=8\frac{lbs}{min}[/tex]
The resulting mixture is pumped out at the same rate, therefore:
Rate Out =(concentration of salt in outflow)(output rate of brine)
[tex]=(\frac{A(t)}{1000})( 4\frac{gal}{min})=\frac{A}{250}[/tex]
Therefore:
The rate of change of amount of salt in the tank,
[tex]\dfrac{dA}{dt}=$Rate In-Rate out\\\dfrac{dA}{dt}=8-\dfrac{A}{250}\\\dfrac{dA}{dt}=8-0.004A[/tex]
Does anyone know the slope of this line?
Answer:
3/4
Step-by-step explanation:
Use [tex]\frac{rise}{run}[/tex]. From the bottom red point, you have to go up 3 and left 4 to get to the top point. That's your answer.
To decide whether two different types of steel have the same true average fracture toughness values, n specimens of each type are tested, yielding the following results.
Type Sample Average Sample SD
1 60.7 1.0
2 60.5 1.0
Required:
a. Calculate the P-value for the appropriate two-sample z test, assuming that the data was based on n = 100. (Round your answer to four decimal places.)
b. Calculate the P-value for the appropriate two-sample z test, assuming that the data was based on n = 500. (Round your answer to four decimal places.)
c. Is the small P-value for n = 500 indicative of a difference that has practical significance
Answer:
a. P-value = 0.1589
b. P-value = 0.0016
Step-by-step explanation:
a. This is a hypothesis test for the difference between populations means.
The claim is that the two types of steel have different true average fracture toughness values.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]
The significance level is α=0.05.
The sample 1, of size n1=100 has a mean of 60.7 and a standard deviation of 1. The sample 2, of size n2=100 has a mean of 60.5 and a standard deviation of 1.
The difference between sample means is Md=0.2.
[tex]M_d=M_1-M_2=60.7-60.5=0.2[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2+\sigma_2^2}{n}}=\sqrt{\dfrac{1^2+1^2}{100}}\\\\\\s_{M_d}=\sqrt{\dfrac{2}{100}}=\sqrt{0.02}=0.1414[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.2-0}{0.1414}=\dfrac{0.2}{0.1414}=1.4142[/tex]
The degrees of freedom for this test are:
[tex]df=n_1+n_2-2=100+100-2=198[/tex]
This test is a two-tailed test, with 198 degrees of freedom and t=1.4142, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=2\cdot P(t>1.4142)=0.1589[/tex]
As the P-value (0.1589) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the two types of steel have different true average fracture toughness values.
b. As the sample size changes, the standard error and the degress of freedom change.
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2+\sigma_2^2}{n}}=\sqrt{\dfrac{1^2+1^2}{500}}\\\\\\s_{M_d}=\sqrt{\dfrac{2}{500}}=\sqrt{0.004}=0.0632[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.2-0}{0.0632}=\dfrac{0.2}{0.0632}=3.1623[/tex]
The degrees of freedom for this test are:
[tex]df=n_1+n_2-2=500+500-2=998[/tex]
This test is a two-tailed test, with 998 degrees of freedom and t=3.1623, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=2\cdot P(t>3.1623)=0.0016[/tex]
As the P-value (0.0016) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the two types of steel have different true average fracture toughness values.
Jaleel and Lisa are simplifying the expression 2 (x minus 2) + 2 as shown. Jaleel’s Method 2 (x minus 2) + 2 = 2 x minus 4 + 2 = 2 x minus 2 Lisa’s Method 2 (x minus 2) + 2 = 2 x minus 2 + 2 = 2 x Whose method is correct and why? Lisa’s method is correct because 2 (x minus 2) equals 2 x minus 2. Lisa’s method is correct because 2 (x minus 2) equals 2 x. Jaleel is correct because 2 (x minus 2) equals 2 x minus 2. Jaleel is correct because 2 (x minus 2) equals 2 x minus 4.
Answer:
(D)Jaleel's method is correct because 2(x-2)=2x-4.
Step-by-step explanation:
Jaleel and Lisa are simplifying the expression 2(x-2)+2 as shown.
[tex]J$aleel's Method: \left\{\begin{array}{ccc}2 (x -2) + 2 \\= 2 x - 4 + 2 \\= 2 x - 2\end{array}\right[/tex]
[tex]L$isa's Method: \left\{\begin{array}{ccc}2 (x-2) + 2 \\= 2 x -2 + 2 \\= 2 x\end{array}\right[/tex]
We can see that Jaleel's method is correct because:
2(x-2)=2x-4.
When you expand, you must multiply the term outside by all the terms inside the bracket.
The correct option is D.
Answer:
Jaleel is correct because 2 (x minus 2) equals 2 x minus 4.
D is correct
Step-by-step explanation:
i just took the quiz.
Determine the absolute maximum and minimum of f(x)= 2 cosx+ sin 2x
Answer:
2.598 and -2.598.
Step-by-step explanation:
f(x) = 2 cos x + sin 2x
f'(x) = -2 sin x + 2 cos 2x = 0 for turning points.
cos 2x = 1 - 2 sin^2 x so we have
-2 sin x + 2 - 4 sin^2 x = 0
4sin^2 x + 2 sin x - 2 = 0
2(2 sin^2 x + sin x - 1) = 0
2(2sinx - 1)(sinx + 1) = 0
sin x = 0.5, -1 when f(x) is at a turning point.
x = π/6, -π/2, 5pi/6
The second derivative is 2 cos x + 2 * -2 sin 2x
= 2 cos x - 4 sin 2x
When x = π/6, this is negative , when x = -π/2 it is positive
so x = π/6 gives a maximum f(x) and x = -π/2 gives 0 so this is a point of inflection
When x = π/6 , f(x) = 2.598
When x = 5pi/6, f(x) = -2.598.
what is the slope of a line of duty hat is parallel to the line whose equation is 5y+2x=12
Answer:
-2/5
Step-by-step explanation:
The slope of two parallel lines will be the same.
Here, our equation is 5y + 2x = 12. Let's find the slope by isolating y:
5y + 2x = 12
5y = -2x + 12
y = (-2/5)x + 12/5
So, the slope is -2/5.
Thus, the slope of the line parallel to the given one will be -2/5.
~ an aesthetics lover
Answer:
-2/5
Step-by-step explanation:
5y+2x=12
Solve for y
Subtract 2x
5y = -2x+12
Divide by 5
5y/5 = -2/5 x +12/5
y = -2/5x +12/5
The slope is -2/5
Parallel lines have the same slope
Recall the equation that modeled the volume of the raised flower bed, y, in terms of the width of the box, y = x3 + 11x2 − 312x. Now, open the graphing tool and graph the equation. Remember, this equation represents the volume of a flower box, so neither the width nor the volume can be negative. Using the pointer, determine the x-intercept where the width is positive and the volume will change to positive as x increases.
Answer:
x = 17.349
Step-by-step explanation:
The right-most x-intercept is 17.349, where the curve continues upward to the right.
The U.S. Department of Agriculture (USDA) uses sample surveys to obtain important economic estimates. One USDA pilot study estimated the price received by farmers for corn sold in January from a sample of 20 farms. The mean price was reported as $3.64 per bushel with a standard deviation of $0.0835 per bushel. Give a 95% confidence interval for the mean price received by farmers for corn sold in January.
Answer:
{$3.60; $3.68}
Step-by-step explanation:
The confidence interval for a sample of size 'n', with mean price 'X' and standard deviation 's' is determined by:
[tex]X\pm z*\frac{s}{\sqrt n}[/tex]
The z-score for a 95% confidence interval is 1.96.
Applying the given data, the lower and upper bounds of the confidence interval are:
[tex]3.64\pm 1.96*\frac{0.0835}{\sqrt 20} \\L=\$3.60\\U=\$3.68[/tex]
The confidence interval for the mean price received by farmers for corn sold in January is:
CI : {$3.60; $3.68}
A smart phone manufacturer is interested in constructing a 99% confidence interval for the proportion of smart phones that break before the warranty expires. 97 of the 1750 randomly selected smart phones broke before the warranty expired. Round your answers to three decimal places. A. With 99% confidence the proportion of all smart phones that break before the warranty expires is between and .
Answer:
With 99% confidence the proportion of all smart phones that break before the warranty expires is between 0.041 and 0.069.
Step-by-step explanation:
We have to calculate a 99% confidence interval for the proportion.
The sample proportion is p=0.055.
[tex]p=X/n=97/1750=0.055[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.055*0.945}{1750}}\\\\\\ \sigma_p=\sqrt{0.00003}=0.005[/tex]
The critical z-value for a 99% confidence interval is z=2.576.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=2.576 \cdot 0.005=0.014[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.055-0.014=0.041\\\\UL=p+z \cdot \sigma_p = 0.055+0.014=0.069[/tex]
The 99% confidence interval for the population proportion is (0.041, 0.069).
Identify the statement as true or false.
New Jersey is a state if and only if Florida is not a state.
Is the statement true or false?
O true
O false
Which best compares the volumes of the two cylinders? Geometry
Answer:
The correct answer would be C
Step-by-step explanation:
please mark brainliest
The choice which best compares the volume of the cylinders is; Choice B; The volume of cylinder B is the same as that of cylinder A.
Which best compares the volumes of the two cylinders?From geometry, It can be concluded that the volume of a solid shape is the product of its cross sectional area and the height over which the area spans. On this note, since the volume of a cylinder is dependent on the radius and height of the cylinder, both cylinders have equal volumes.
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A population of monkeys' tail lengths is normally distributed with a mean of 25 cm with a standard deviation of 8 cm. I am preparing to take a sample of size 256 from this population, and record the tail length of each monkey in my sample. What is the probability that the mean of my sample will be between 24 and 25 cm?
Answer:
The probability that the mean of my sample will be between 24 and 25 cm
P(24 ≤X⁻≤25) = 0.4772
Step-by-step explanation:
Step(i):-
Given mean of the Population 'μ'= 25c.m
Given standard deviation of the Population 'σ' = 8c.m
Given sample size 'n' = 256
Let X₁ = 24
[tex]Z_{1} = \frac{x_{1}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{24-25}{\frac{8}{\sqrt{256} } } = -2[/tex]
Let X₂ = 25
[tex]Z_{2} = \frac{x_{2}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{25-25}{\frac{8}{\sqrt{256} } } = 0[/tex]
Step(ii):-
The probability that the mean of my sample will be between 24 and 25 cm
P(24 ≤X⁻≤25) = P(-2≤ Z ≤0)
= P( Z≤0) - P(Z≤-2)
= 0.5 + A(0) - (0.5- A(-2))
= A(0) + A(2) ( ∵A(-2) =A(2)
= 0.000+ 0.4772
= 0.4772
Final answer:-
The probability that the mean of my sample will be between 24 and 25 cm
P(24 ≤X⁻≤25) = 0.4772
Find the slope through each pair of two points. Report answers in simplest form.
(0,0) and (0.5,0.25)
m =
Answer: m=0.5 or m=1/2
Step-by-step explanation:
To find the slope, you use the formula [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. Since we are given the coordinate points, we can directly plug them in.
[tex]m=\frac{0.25-0}{0.5-0} =\frac{0.25}{0.5} =0.5[/tex]
Help pls urgent!!!!!!!!!!
Answer:
d
Step-by-step explanation:
A composition of reflections over parallel lines is the same as a __________. A. translation B. rotation C. glide reflection D. double rotation
Answer: A
Step-by-step explanation:
Answer: A.
Step-by-step explanation:
A composition of reflections over two parallel lines is equivalent to a translation.
Let x be a variable, and let n be an arbitrary constant. What is the derivative of x^n?
Answer:
nx^(n-1)
Step-by-step explanation:
What is the value of p?
Answer:
Step-by-step explanation:
The angle next to 90 degrees is also 90 degrees and it's supplementary
the angle next to 133 degrees is 47 degrees and it's also supplementary
p + 90 + 47 = 180
p + 137 = 180
p = 43 degrees
the solution is d
NEED UGANT HELP really stuck xx
Answer:
0.6
Step-by-step explanation:
3+2=5
P (white) = 3/5 = 0.6
(Hopefully this works, if not, on hearty maths you can go back to your assigned tasks page and go back onto the task to get a new question if that makes sense)
Two planes travel toward each other from cities that are about 1725 km apart at rates of 360 km/hr and 330 kr/hr. They started at the same time. In how many hours
will they meet?
hours.
The two planes will meet after
(Simplify your answer.)
Answer: 2 1/2 or 2.5 hours
Step-by-step explanation:
Add 360 and 330
360 + 330 = 690
Divide 1,725 by 690
1,725 / 690 = 2.5
The two planes will meet in 2.5 hours
The speed is the distance covered by an object at a particular time. The time it will take for the two planes to meet is 2.5 hours.
What is speed?The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.
[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]
Given that the speed of the two planes is 360 km/hr and 330 km/hr. Therefore, the relative speed of the two planes with respect to each other is,
Relative speed = 360 km/hr + 330 km/hr
= 690 km/hr
Now, since the total distance between the two cities is 1725 km. Therefore, the time it will take for two planes to meet is,
Time = Distance /Speed
= 1725 km / 690 km/hr
= 2.5 hour
Hence, the time it will take for the two planes to meet is 2.5 hours.
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Plz solve this question, it's very urgent.
i think it is ur required ans..
Please answer this question now in two minutes
Answer:
the slope equation is y2 - y1 divided by x2 - x1
Step-by-step explanation:
so the answer would be 3 over 2 because of this method
Answer:
3/2
Step-by-step explanation:
Use the easy rise over run method.
start at the point (50,20) then go up 3 units and 2 units to the right to get the next point.
3/2 should be the slope.
Hope I helped you!
The population of a town is 9,000, and it grows at a rate of 7% per year. What will the population be in 6 years?
Answer:
12,780
Step-by-step explanation:
Initial population = 9000
grows 7% of 9000= 630 people in a year
after 6 yrs, number of added people = 630× 6=3780 ...... totally, population = 9000+ 3780
= 12,780
The population of the town after 6 years will be 13506.
Concept:As the population grows at r% per year and if the Current population is P, then After 'x' years, the population will be [tex]P_x = P(1 + \frac{r}{100} )^x[/tex]How to solve the given question?Initial Population, P = 9000Rate of increase in population, r = 7% per yearPeriod , x = 6 years∴ The population after 6 years,[tex]P_x = P(1 + \frac{r}{100} )^x[/tex]Thus, the population of the town after 6 years will be 13506.
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7. Look at the figure below.
Which theorem can be used to show that triangles QSN and LEJ are congruent?
A. HL
B. ASA
C. SAS
D. SSA
I'm pretty sure that ' HL ' stands for "hypotenuse and leg". That's the one.
-- We see the little boxes in the lower left corners, so we know that these are right triangles, and we can use the rules we know about for right triangles.
-- The hypotenuses of both triangles are marked with the same length.
-- The base legs of both triangles are marked with the same length.
-- So we have (the hypotenuse and one leg of one right triangle) equal to (the hypotenuse and corresponding leg of another right triangle). That's exactly the description of the HL conguence theorem, so we know that these two triangles are congruent.
Find the length of ST to the nearest meter.
Answer:
42 m
Step-by-step explanation:
First, find <S
<S = 180 - (41+113) [ sum of angles in a triangle)
<S = 180 - 154 = 26°
Next is to find length of ST, using the law of sines: a/sin A = b/sinc B = c/sin C
Let a = RT = 28m
A = <S = 26°
b = ST
B = <R = 41°
Thus, we have:
28/sin(26°) = b/sin(41°)
Cross multiply
28*sin(41°) = b*sin(26°)
28*0.6561 = b*0.4384
18.3708 = b*0.4384
Divide both sides by 0.4384 to make b the subject of formula
18.3708/0.4384 = b
41.9041971 = b
b ≈ 42m (rounded to nearest meter)
Length of ST to nearest meter = 42 meters
Find the slope through each pair of two points. Report answers in simplest form.
(0,0) and (0.5,0.25)
m =
Answer:
m = 0.5
Step-by-step explanation:
m = (y2 - y1) / (x2 - x1)
= (0.25 - 0) / (0.5 - 0)
= 0.25/0.5
= 0.5
Please find the missing side of the triangle and round the answer to the nearest tenth. Thanks.
Answer:
x = 74.3
Step-by-step explanation:
Using the trigonometric ratio formula, the missing side, x, of the right angled triangle, can be found as follows:
Ѳ = 22°,
adjacent side length = x
Opposite side length = 30
Thus, we would apply the formula:
tan Ѳ = opposite length/adjacent length
[tex] tan 22 = \frac{30}{x} [/tex]
Multiply both sides by x
[tex] tan 22*x = \frac{30}{x}*x [/tex]
[tex] tan 22*x = 30 [/tex]
[tex] 0.4040*x = 30 [/tex]
Divide both sides by 0.4040 to make x the subject of the formula
[tex] \frac{0.4040*x}{0.4040} = \frac{30}{0.4040} [/tex]
[tex] x = \frac{30}{0.4040} [/tex]
[tex] x = 74.26 [/tex]
x ≈ 74.3 (to the nearest tenth)