The pair x(t) = e^3t, y(t) = e^t is a solution to the given system.
Is the given pair (x(t), y(t)) a solution?The given system consists of two differential equations: dx/dt = 3y^3 and dy/dt = y. We are given the pair x(t) = e^3t and y(t) = e^t. To verify if this pair is a solution, we need to substitute these values into the differential equations and check if they hold true.
Substituting x(t) = e^3t and y(t) = e^t into the first equation, we have dx/dt = 3(e^t)^3. Simplifying, we get dx/dt = 3e^(3t).
Similarly, substituting x(t) = e^3t and y(t) = e^t into the second equation, we have dy/dt = e^t.
We can see that both sides of the differential equations match the given pair (x(t), y(t)). Hence, x(t) = e^3t and y(t) = e^t satisfy the given system of differential equations.
To sketch the trajectory of the given solution in the phase plane, we can plot the points (x(t), y(t)) for different values of t. The trajectory would represent the path traced by the solution in the phase plane.
Learn more about the phase planes
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14. A right cone has a height of 14 in and a base diameter of 17 in.
a Sketch and label a diagram of the cone
b. Determine the area of the lateral surface of the cone, to the nearest square inch
Given:
The height of a right cone = 14 in
Base diameter = 17 in
To find:
The diagram of the cone and its lateral surface area.
Solution:
(a)
The diagram of a right cone with height 14 in and base diameter of 17 in is shown below.
Diagram is not to scale.
(b)
We know that lateral surface of the cone is
[tex]A=\pi rl[/tex]
[tex]A=\pi r\sqrt{r^2+h^2}[/tex] ...(i)
Where, r is the base radius, h is vertical height and l is the slant height of the cone.
Base radius of the cone = [tex]\dfrac{\text{Base diameter}}{2}[/tex]
[tex]r=\dfrac{17}{2}[/tex]
[tex]r=8.5[/tex]
Now,
Putting r=8.5, h=14 and π=3.14 in (i), we get
[tex]A=(3.14)(8.5)\sqrt{(8.5)^2+(14)^2}[/tex]
[tex]A=26.69\sqrt{72.25+196}[/tex]
[tex]A=26.69\sqrt{268.25}[/tex]
[tex]A=437.1379[/tex]
[tex]A\approx 437[/tex]
Therefore, the lateral surface area of the cone is 437 sq. inches.
Which of the following coordinate pairs make the equation x-9y=12 true? A (3,-1) B (0,-4/3) C (0,12) D (12,0) (There are multible answers.)
Answer:
Burun yardımı lazım ders programlı
Step-by-step explanation:
Lise pitirdim üventisiyi bitirdim
A cuboid with a square base of side length 6 cm and height 10 cm then its volume equal what in Sixth grade of primary school
Answer:
360
Step-by-step explanation:
Volume of cube is s^3
Volume of a rectangular prism is BH, OR LWH
Since the base is a SQUARE, and it has a side length of 6 cm, the other side length is also 6 cm. 6 x 6 x 10 = 360 cm cubed.
16/5 where is that on the number line?
(x + 7)^2 – 11 = 0
lesser =
greater =
Answer:
Lesser = -[tex]\sqrt{11}[/tex] - 7 = -10.317
Greater = +[tex]\sqrt{11}[/tex] - 7 = -3.683
Step-by-step explanation:
I am assuming you are asking for the lesser x solution and greater x solution.
(x + 7)^2 – 11 = 0
(x + 7)^2 = 11
x+7 = ±[tex]\sqrt{11}[/tex]
x = ±[tex]\sqrt{11}[/tex] - 7
Lesser = -[tex]\sqrt{11}[/tex] - 7 = -10.317
Greater = +[tex]\sqrt{11}[/tex] - 7 = -3.683
Answer:
lesser= -14
greater= 0 (:
Find the slope please!!
Answer:
Slope = 2
Step-by-step explanation:
Do rise/run, this one rises up 2 and the run is 1 and 2/1 is 1. Rise/run is usually only necessary for small numbers.
Which equation shows exponential GROWTH?
A) y=.5^x
B) y=.25^x
C) y= 25^x
D) y= .2^x
c) y = 25^x
explanation
because y increase as x increases
Dan drives 23 miles to work every day. He works 5 days a week. How many miles does he travel to and from work over 52 weeks?
Answer:
Step-by-step explanation:
They make it sound like it is 23 miles one way.
2(23)5(52)
11960 miles
If you give me the correct answer I will give you brainliest plz help
what is the precent of change from 12 to 19
Answer:
158%
Step-by-step explanation:
19/12 = 1.58
Based on the side lengths alone, could the triangles be similar? 16.0 cm R 6.4 cm 3.0 cm 15.0 cm S T 6.0 cm X 7.5 cm U
No, the side are not proportional.
Yes, the sides are in the ratio 2:5.
yes, the sides are in the ratio 4:5.
Yes, the sides are in the ratio 1:5.
Answer:
Yes, the sides are in the ration 2:5!
Step-by-step explanation:
Hope this helps.
Answer:
The correct answer is B. Yes, the sides are in the ratio 2:5.
Step-by-step explanation:
Hope this helps, and have a wonderful day! :)
Lawrence knows his race car can accelerate from 0 miles per hour to 100 miles per hour in 60 seconds. He assumed the acceleration was constant and created the graph below. If his graph is accurate, what point on the graph would give him the speed of the race car after 30 seconds of accelerating
Answer:
50 miles at 30 seconds
Step-by-step explanation:
It is that half way point of both the x and the y axis for the first minute of driving
Answer:
Lawrence knows his race car can accelerate from 0 miles per hour to 100 miles per hour in 60 seconds
I really need help really fast!!!
Answer:
-3 sqrt 2 or -4.242640687
Step-by-step explanation:
Find the values of the variables in the parallelogram. The diagram is not to scale.
Step-by-step explanation:
option B is the correct answer of this question.
x = 29, y = 49 and z = 102 .
plz mark my answer as brainlist plzzzz vote me also .
hope this will be helpful to you.
Answer:
B
Step-by-step explanation:
x is 29 because the inverse opposite of angles are the same.
z is 102 because opposite parallelogram angles are the same.
y is 49 through process of elimination.
Amy buys 8 sandwiches and 12 waters.her total cost is 8s+12 how much did she pay
[tex]\frac{5}{6}x - 8=\frac{1}{3}(3x-15)[/tex]
Answer:
x= -18
Step-by-step explanation:
Solve for
x
by simplifying both sides of the equation, then isolating the variable.
if 6n = 0, what does n equal?
Answer:
6n=0
n=0/6
n=0
hope it helps.
Answer:
n=0
Step-by-step explanation:
6n is the same of 6×n
∴ 6×0 = 0
Hello! It would help a lot if I had assistance with this question:
Answer:
Simplest form
Someone help:
Decrease 120 by 60%
Answer:
48
Step-by-step explanation:
if increase⇒100%+the percentage given in the question
e.g ⇒ increase N (number) by 50%
so 150/100×N
if decrease⇒100% - the percentage given in the question
e.g ⇒ decrease N (number) by 70%
so 30/100×N
the answer of this question by steps is:
100%-60%=40%
40/100×120=48
5. I NEED HELP ASAP!! PLEASE PUT AND ANSWER AND STEP BY STEP EQUATION!! IF YOU DON'T KNOW THE ANSWER DON'T PUT ANYTHING!!
Write a rule for the linear function in the table.
X F(x)
0 3
3 15
6 27
9 39
A. f (x) = 1/4x + 3
B. f (x) = 4x + 3
C. f (x) = x + 3
D. f (x) = -4x - 3
Answer:
i can't find the answer
Step-by-step explanation:
Find the area of the semicircle. 10
Exact Area = 25pi square units
Approximate Area = 78.5 square units
The approximate value is found using pi = 3.14
====================================================
Explanation:
I think you meant to say "quarter circle" instead of "semicircle".
The area of a full circle with radius r = 10 is
A = pi*r^2
A = pi*10^2
A = pi*100
A = 100pi
But we only want one quarter of this. So we divide the full area by 4
(100pi)/4 = (100/4)pi = 25pi
The exact area in terms of pi is 25pi square units
If we used the approximation pi = 3.14, then we can say 25*pi = 25*3.14 = 78.5 is the approximate area
To get a better approximation, use more decimal digits in pi.
You have 59 total coins in a jar on your nightstand at home. The total amount of money is $12.05. You only have quarters and dimes. How many of each type of coin do you have? (hint - use a different method to write and solve the system).
9514 1404 393
Answer:
41 quarters18 dimesStep-by-step explanation:
When there are two contributors to the mix, it usually works well to let a variable represent the quantity of the larger contributor. Here, that larger contributor is the quarter.
Let q represent the number of quarters. Then 59-q is the number of dimes. The value of the coins, in cents, is ...
25q +10(59 -q) = 1205
15q +590 = 1205 . . . . . . . . eliminate parentheses, collect terms
15q = 615 . . . . . . . . . . . subtract 590
q = 41 . . . . . . . . . . divide by 15
59-q = 59 -41 = 18 . . . . . number of dimes
You have 41 quarters and 18 dimes.
PLS HELP!!
Solve for an angle in right triangles
B = ???
round your answer to the nearest hundredth
Answer:
100
Step-by-step explanation:
The school that Billy Bob goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.
What is the ordered pair of your intersection?
Make sure you use parenthesis and no spaces! example: (5,9)
Answer:
if your looking for the ordered pair its 8,14....But if you looking for the answer for the prices it
for grandpa 8 dollars
For children 14 dollars
write
S8,C14
Step-by-step explanation:
Litterally the answer is the ordered pair and the answer is on the graph shown in the problem.
Please help! Will give brainliest!
Options
1/9
1/6
1/4
1/2
A community builds a sandbox section and a playground section at one of the local parks. The area of the playground
section is 1,675 square feet. It is 100 square feet more than 4.5 times the area of the sandbox section.
• Write an equation that can be used to determine the area, A. of the sandbox section.
. What is the area of the sandbox section? Show all work.
Enter your equation, answer, and work in the box
Please help worth 25 points
9514 1404 393
Answer:
A + (100 +4.5A) = 1675A ≈ 286.4 square feetStep-by-step explanation:
The problem statement tells us that the area of the sandbox and playground together is 1675 square feet. Using A as the area of the sandbox section, the playground section is said to be (100 +4.5A). Then the total area is ...
A + (100 +4.5A) = 1675 . . . . . . an equation to determine A
5.5A = 1575 . . . . . . . . . . . . . . . subtract 100, collect terms
A = 1575/5.5 = 286 4/11 . . . . . divide by 5.5
The area of the sandbox section is about 286.4 square feet.
HELP I NEED HELP ASAP
A. 5%
B. 0.5%
C. 50%
D. 0.05%
Answer:
the answer is A.5%
Step-by-step explanation:
PLEASE HELP! ANSWER FOR 20 POINTS PLS PLS
Answer:
5³ = 125
Step-by-step explanation:
5³ = 5 × 5 × 5 = 25 × 5 = 125
Answer:
5³ = 15 because the ³ mean 3 left over 5's like if i had 2² the ² = 2 so 2²=4
5+5+5=15
Answer : 15
What is the slope of the line that passes through the points (−6,−4) and (-12, -4) ?
Answer:
0
Step-by-step explanation:
The formula for slope is [ y2-y1/x2-x1 ].
-4-(-4)/-12-(-6)
0/-6
Since the numerator is 0, the slope is 0.
Best of Luck!
(5×100)+(6×110)+(7×1100)
What is this number in standard form?
(5×100)+(6×110)+(7×1100)=500+660+7700=8860