Answer: If a parallelogram has diagonals that are perpendicular, it is a rhombus. … This definition can also be stated as: A square is a quadrilateral that is also a rectangle and a rhombus.
Step-by-step explanation:
Mona has a bag containing 4 red marbles, 12 green marbles, and 8 black marbles. Without looking, she pulls out one marble from the bag and places it in an empty jar. She then pulls a second marble from the bag and places it in the jar. WHat is the probability that she will have 2 green marbles in the jar?
A. 12/24 x 11/23
B. 12/24 x 12/24
C. 1/12 x 1/11
D. 12/24 x 12/23
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]
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
Type the integer in the box.
Solve:: t/2 + 10 =-40
Answer:
t = -100
Step-by-step explanation:
Simplify to isolate t:
[tex]\frac{t}{2}+10-10=-40-10[/tex]
[tex]\frac{t}{2} * \frac{2}{1} = -50 * 2[/tex]
[tex]t = -100[/tex]
The times that a cashier spends processing individual customers' orders are independent random variables with mean 3.5 minutes and standard deviation 3 minutes. Find the number of customers n such that the probability that the orders of all n customers can be processed in less than 2 hours, is approximately 0.1. (Round your answer to the nearest integer.)
Answer:
26 customers
Step-by-step explanation:
First: determine the z score from standard normal probability table with an indicative area of 0.1
Z-score from probability table = - 1.28
mean = 3.5 minutes
std = 3 minutes
next determine the Z-score based on the information given in the question
Z = ( std - mean ) / processing time
= ( 3 - 3.5 ) / 2 = -0.25
Finally determine the number of customers
N = [tex](\frac{-1.28}{-0.25} )^2[/tex] = 1.6384 / 0.0625 = 26.21 ≈ 26 customers
Caroline has a rock stuck in her Jeep’s tire
Answer:
oh no
Step-by-step explanation:
sorry about that I guess
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.
What is the volume of a sphere with a radius of 3.1 cm, rounded to the nearest tenth
of a cubic centimeter?
can someone help me :(
Answer:
A is the correct answer
.......................
Answer:
A. y+116+30=180
Step-by-step explanation:
A straight angle is 180°.
all the given angles make up a straight angle, so they add to 180°.
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.
PLSSSSSSSSSSS ASAP!!!!! Find the area of the figure shown below.
Answer:
54 square ft
Step-by-step explanation:
Find missing sides:
8+6 = 14
9-6 = 3
Find area of full rectangle:
9×8 = 72
Find the area of the missing part of the full rectangle
3×6 = 18
Find the area of the actual shape:
72-18 = 54
Area = 54 square ft
Which statement describes whether the function is continuous at x = 2?
O The function is continuous at x = 2 because f(2) exists.
O The function is continuous at x = 2 because lim f(x) exists.
X-2
The function is not continuous at x = 2 because f(2) does not exist.
The function is not continuous at x = 2 because lim f(x) does not equal f(2).
X-2
Answer: (b)
Step-by-step explanation:
Given
The function is given as
[tex]f(x)=\dfrac{x^2-12x+20}{x-2}[/tex]
Solving the function
[tex]f(x)=\dfrac{x^2-2x-10x+20}{x-2}\\\\f(x)=\dfrac{(x-2)(x-10)}{(x-2)}\\\\f(x)=x-10[/tex]
for [tex]x=2[/tex]
[tex]f(2)=2-10\\f(2)=-8[/tex]
The function is continuous at [tex]x=2[/tex] because [tex]\lim_{x \to 2} f(x)[/tex] exists.
If the limit exists at a point, then the function is continuous.
Answer:
on edge its fs not b or c
Step-by-step explanation:
Identify a second of transformations that maps triangle ABC onto triangle A"B"C in the image below.
Answer: The answer is B because the triangle rotated a 90 degrees counterclockwise then got a reduction.
Step-by-step explanation:
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
Is the line a good fit for the data points plotted in the scatter plot below?
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]
Find the perimeter of a rectangle with a base of 12 ft and a height of 5 ft.
Answer:
P=34ft
Step-by-step explanation:
Solution
P=2(l+w)=2·(12+5)=34ft
a cylinder has a diameter of 12 and height of 12. the volume of the cylinder is:
A. 1728π cubic units
B. 288π cubic units
C. 144π cubic units
D. 432π cubic units
A. 35
B. 96
C. 51
D. 80
Answer:
Its D
Step-by-step explanation:
Hank wants to rent a bike. Bike rentals cost $1.25 per hour plus a one-time
fee of $3. Which equation represents the relationship between the number
of hours h Hank rents the bike and the total cost c?
Answer:
c = 3 + (1.25 x h)
PLEASE HELP FAST WILL MARK BRAINLIEST PLEASEEE
Answer:
[tex]\frac{8x^{18} }{y^{2} }[/tex]
Step-by-step explanation:
pls help me loves :((
Answer:
609 m²
Step-by-step explanation:
Area of unshaded:
(6 x 18) + ((13-6) x 7) = 157
Area of overall rectangle:
36 x 28 = 1008
Area of the chunck of rectangle not included:
11 x 22 = 242
Area of shaded:
1008 - 157 - 242 = 609
I need this please help me
Answer:
A. Right 6, Down 5
Step-by-step explanation:
I don't know how to explain this
Does anybody know the answer please.
Answer:
The sign of each y-coordinate changed.
Step-by-step explanation:
This was a reflection over the x-axis.
If you look at point F, it is (-5, -1) the corresponding point F' is (-5,1). Notice the numerical values of x and y are the same, but the sign of y flipped from negative to positive. The other four points all follow the same pattern.
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.
If Bill hiked 6.5 miles at a rate of 10.4 mph, how long did it take him to complete his hike?
Answer:
I think it depends how far bill wants to hike..
Step-by-step explanation:
The scatter chart below displays the residuals verses the dependent variable, x. Which of the following conclusions can be drawn based upon this scatter chart? a. The residuals are normally distributed. b. The model over predicts the value of the dependent variable for small values and large values of the independent variable. c. The model fails to capture the relationship between the variables accurately, and there may exist nonlinear relationship. d. The residuals have a constant variance.
Answer: Hello the scatter plot related to your question is missing attached below is the scatter plot
answer : The model fails to capture the relationship between the variables accurately, and there may exist nonlinear relationship ( C )
Step-by-step explanation:
The conclusion that can be drawn based upon the scatter chart is that The model fails to capture the relationship between the variables accurately, and there may exist nonlinear relationship
A scatter plot helps in observing the relationship within different numeric variables but the scatter plot attached fails in the showing the actual relationship
1+1 why does my dog not love me?
Answer:
2
Step-by-step explanation:
your dog doesn't love you because it saw what you did. it knows. be cautious around your dog from now on. it knows more than you think and sees all. I'm warning you
What is the expanded form of 8,609?
A 8,000+600+ 90
8,000+60+9
8,000 +900+ 6
8,000+600 +9
The last one 8,000 + 600 + 9
Please help soon- The weight of oranges growing in an orchard is normally distributed with a mean
weight of 6 oz. and a standard deviation of 1 oz. From a batch of 2500 oranges, how
many would be expected to weight less than 4 oz., to the nearest whole number?