Answer:
dx/dt = - 18,79 mph
Step-by-step explanation:
The two cars with the intersection point and the straight-line distance between the cars make up a right triangle. In that right triangle, the legs are the distance between each car and the intersection point, and the distance between cars is the hypothenuse
If we call x and y distances between blue car and red car respectively and L the hypothenuse by Pythagoras theorem we have:
L² = x² + y² (1)
Tacking derivatives on both sides of the equation
2*L*dL/dt = 2*x*dx/dt + 2*y*dy/dt
And from equation (1)
L² = (0,5)² + (0,5)² ⇒ L = √(0,5)² + (0,5)² ⇒ L = 0,5*√2
By subtitution in equation (2)
2*(0,5*√2)*15 = 2*0,5*dx/dt + 2*0,5*40
(15*√2 - 40 ) / 1 = dx/dt [mph]
dx/dt = - 18,79 mph
Note the( - ) sign is equivalent to say that the car is driving away from the intersection point
Chris bought c tickets to a movie for $8 each. Michele bought m tickets to a movie for $8 each. Which expression can be used to find the total amount Chris and Michele spent for these tickets?
Answer:
8c+8m
Step-by-step explanation:
c tickets are $8 a piece and m tickets are also $8 a piece. as an expression, the equation is not completed and cannot be completed until we know the value of the missing variables. to find the total, you must add the total amount of tickets Chris bought for 8 dollars and add that to the total of tickets Michele bought for 8 dollars
An exponential function in the form y = ab^x goes through the points (3, 10.125) and (6, 34.2). Find a to the
nearest integer and b to the nearest tenth, then find f (10) to the nearest integer.
Answer:
[tex]f(10) = 173[/tex]
Step-by-step explanation:
Given
Exponential Function
[tex](x_1,y_1) = (3,10.125)[/tex]
[tex](x_2,y_2) = (6,34.2)[/tex]
Required
Determine f(10)
We have that
[tex]y = ab^x[/tex]
First, we need to solve for the values of a and b
For [tex](x_1,y_1) = (3,10.125)[/tex]
[tex]10.125 = ab^3[/tex] --- (1)
For [tex](x_2,y_2) = (6,34.2)[/tex]
[tex]34.2 = ab^6[/tex] ---- (2)
Divide (2) by (1)
[tex]\frac{34.2}{10.125} = \frac{ab^6}{ab^3}[/tex]
[tex]\frac{34.2}{10.125} = \frac{b^6}{b^3}[/tex]
[tex]3.38= b^{6-3}[/tex]
[tex]3.38= b^{3}[/tex]
Take cube root of both sides
[tex]b = \sqrt[3]{3.38}[/tex]
[tex]b = 1.5[/tex]
Substitute 1.5 for b in [tex]10.125 = ab^3[/tex]
[tex]10.125 = a * 1.5^3[/tex]
[tex]10.125 = a * 3.375[/tex]
Solve for a
[tex]a = \frac{10.125}{3.375}[/tex]
[tex]a = 3[/tex]
To solve for f(10).
This implies that x = 10
So, we have:
[tex]y = ab^x[/tex] which becomes
[tex]y = 3 * 1.5^{10[/tex]
[tex]y = 3 * 57.6650390625[/tex]
[tex]y = 172.995117188[/tex]
[tex]y = 173[/tex] -- approximated
Hence:
[tex]f(10) = 173[/tex]
Let y 00 + by0 + 2y = 0 be the equation of a damped vibrating spring with mass m = 1, damping coefficient b > 0, and spring constant k = 2. (a) Convert this second order equation into a system of two first order equations. (b) Express the eigenvalues for this system in terms of b. (c) Describe the stability of the equilibrium solution ~0 for b > 2 √ 2. Justify your claim with information about the eigenvalues of the matrix for the system. (d) Connect the behavior of solutions near an equilibrium of this type with the spring mass system with damping coefficient b > 2 √ 2 and explain why your answer for part (c) is (or is not) what one should expect.
Answer:
Step-by-step explanation:
Given that:
The equation of the damped vibrating spring is y" + by' +2y = 0
(a) To convert this 2nd order equation to a system of two first-order equations;
let y₁ = y
y'₁ = y' = y₂
So;
y'₂ = y"₁ = -2y₁ -by₂
Thus; the system of the two first-order equation is:
y₁' = y₂
y₂' = -2y₁ - by₂
(b)
The eigenvalue of the system in terms of b is:
[tex]\left|\begin{array}{cc}- \lambda &1&-2\ & -b- \lambda \end{array}\right|=0[/tex]
[tex]-\lambda(-b - \lambda) + 2 = 0 \ \\ \\\lambda^2 +\lambda b + 2 = 0[/tex]
[tex]\lambda = \dfrac{-b \pm \sqrt{b^2 - 8}}{2}[/tex]
[tex]\lambda_1 = \dfrac{-b + \sqrt{b^2 -8}}{2} ; \ \lambda _2 = \dfrac{-b - \sqrt{b^2 -8}}{2}[/tex]
(c)
Suppose [tex]b > 2\sqrt{2}[/tex], then λ₂ < 0 and λ₁ < 0. Thus, the node is stable at equilibrium.
(d)
From λ² + λb + 2 = 0
If b = 3; we get
[tex]\lambda^2 + 3\lambda + 2 = 0 \\ \\ (\lambda + 1) ( \lambda + 2 ) = 0\\ \\ \lambda = -1 \ or \ \lambda = -2 \\ \\[/tex]
Now, the eigenvector relating to λ = -1 be:
[tex]v = \left[\begin{array}{ccc}+1&1\\-2&-2\\\end{array}\right] \left[\begin{array}{c}v_1\\v_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right][/tex]
[tex]\sim v = \left[\begin{array}{ccc}1&1\\0&0\\\end{array}\right] \left[\begin{array}{c}v_1\\v_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right][/tex]
Let v₂ = 1, v₁ = -1
[tex]v = \left[\begin{array}{c}-1\\1\\\end{array}\right][/tex]
Let Eigenvector relating to λ = -2 be:
[tex]m = \left[\begin{array}{ccc}2&1\\-2&-1\\\end{array}\right] \left[\begin{array}{c}m_1\\m_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right][/tex]
[tex]\sim v = \left[\begin{array}{ccc}2&1\\0&0\\\end{array}\right] \left[\begin{array}{c}m_1\\m_2\\\end{array}\right] = \left[\begin{array}{c}0\\0\\\end{array}\right][/tex]
Let m₂ = 1, m₁ = -1/2
[tex]m = \left[\begin{array}{c}-1/2 \\1\\\end{array}\right][/tex]
∴
[tex]\left[\begin{array}{c}y_1\\y_2\\\end{array}\right]= C_1 e^{-t} \left[\begin{array}{c}-1\\1\\\end{array}\right] + C_2e^{-2t} \left[\begin{array}{c}-1/2\\1\\\end{array}\right][/tex]
So as t → ∞
[tex]\mathbf{ \left[\begin{array}{c}y_1\\y_2\\\end{array}\right]= \left[\begin{array}{c}0\\0\\\end{array}\right] \ \ so \ stable \ at \ node \ \infty }[/tex]
A family went to a restaurant. The total cost of the meal was $48.30. The family had a coupon for 20% off the total. What was the final cost?
Answer:
$38.64
Step-by-step explanation:
to find the percent off of the original price, multiply 48.30 to 20. then, move the decimal over twice.
48.30
x 20
----------
966 ---------> $9.66 off
then subtract that from 48.30.
$38.64 is you answer.
give me brainliest
Sam got a job mowing lawns earning $20 for every lawn he mows, m Represents this situation by filing in the table below, creating a graph, and writing an expression. Then determine how much Sam will earn for mowing 22 lawns, justifying/showing how much you got your answer
You would multiply each number by 20
Step-by-step explanation:
It says that right there
Anju's office uses paper cups shaped like cones to serve water. Each cup has a maximum diameter of 8 cm and a height of 10 cm. Anju fills the cup to of its height to prevent spills.
What is the approximate volume of water in Anju's cup?
Answer:
V = 167.55
Step-by-step explanation:
V = pir^2 h/3
V = pi(4)^2 (10/3)
The approximate volume of water in Anuj's cup is 42 cubic cm.
What is volume?Volume is a measure of capacity that an object holds.
Formula for finding the volume of cone
volume of cone = [tex]\frac{1}{3} \pi r^{2} h[/tex]
where,
r is the radius of cone
h is the height of cone
π = 3.14
According to the given question
paper cups are of the shape of cone.
and,
diameter = 8cm
⇒ radius = [tex]\frac{8}{2}[/tex] = 4cm
the approximate volume of water in cup = [tex]\frac{1}{3} \pi r^{2} h[/tex]
=[tex]\frac{1}{3}[/tex]×[tex]2^{2}[/tex]×π×10
=[tex]\frac{1}{3}[/tex]×4×3.14×10
= 41.86 = 42 cubic cm.
Hence, the approximate volume of water in Anuj's cup is 42 cubic cm.
Learn more about the volume of cone here:
https://brainly.com/question/1984638
#SPJ2
solve for x and y :
9 + 12i = 3x + 4yi
Answer:
27
Step-by-step explanation:
about 99.7 of sixth grade students will have heights between inches and inches
51.1 and 64.9
Step-by-step explanation:
Answer: 55.1 and 64.9
On edge.
Step-by-step explanation:
At a football match, 10 men bought either a pie or a cup of
coffee. A pie costs 60p and a coffee costs 50p. The total
amount spent on pies and cups of coffee was £5.80. How many
of each must have been bought? (show all your working)
Answer:
8 pies and 2 coffees
Step-by-step explanation:
10 men bought pie or a cup of coffee.
x=pie
y=coffee
x+y=10
0.6x+0.5y=5.8
0.6x+0.6y=6
0.1y=0.2
y=2
x=8
Hope this helps plz hit the crown :D
You have 15 marbles in a bag; 5 are red. If you pull out five marbles in a row and don't put
them back in, what are your chances of pulling all 5 red marbles? Decimal answer please.
Step-by-step explanation:
0.33 so says my mother bc she divide
Answer:
The probability of drawing a different marble is 0.25. The probability of drawing a red marble = 0.5
I do not know if this is correct please forgive me if I am wrong.
If I am right hope this helps!
Find the slope of the line that passes through the points given in the table.
х у
-3 | 0
2 | 2
7 | 4
12 | 6
Answer:
2/5
Step-by-step explanation:
(2,2) and (7,4) 4-2/7-2=2/5
plees 555+555 and 6 541,5-5 410,6
Answer:
what is this......................
Pls help with the math!! It would mean a lot if you could print it out and do it! Tyyyyyy WILL MARK BRAINLIST!
Answer:
Step-by-step explanation:
Answer:
mark the answer below as brainliest x
Step-by-step explanation:
Which one of the statements below is FALSE?
O Graphing is a method for solving a System of Equations.
Substitution is a method for solving a System of Equations.
Simplification is a method for solving a System of Equations.
Elimination is a method for solving a System of Equations.
Answer:
Simplification is a method for solving a system of equations
Step-by-step explanation:
-Graphing is a real way to solve a System of Equations
-Substitution is a real way to Solve Systems of Equations
-Elimination is a real way to solve Systems of Equations
so, Simplifcation can't be one
Take 2x-4y=6 and 4x+2y=17 for example.
They are both in standard form, so you could change them to y=mx+b and graph it. The intersection is the correct answer.
You can also solve one of the equations for y or x, and substitute that into the other equation, and solve for both x and y
or, you could add the two equations together and solve for x and y.
You can't simplify them.
can u pls help me with this question
Answer:
Please check the explanation.
Step-by-step explanation:
We know that when 'y' varies directly with 'x', the equation becomes
y ∝ x
y = kx
where 'k' is called the constant of proportionality.
From the table, it is clear that 'y' varies directly with 'x'
Let us check the value of k for all the points
k = y/x
For the point (130, 9.10)
k = 9.10 / 130 = 0.07For the point (145, 10.15)
k = y/x = 10.15 / 145 = 0.07For the point (150, 10.50)
k = y/x = 10.50 / 150 = 0.07For the point (185, 12.95)
k = y/x = 12.95 / 185 = 0.07Thus, the value of proportionality constant is same.
i.e. k = 0.07
Determining the cost of 21 feet of the wire
And need 21 feet of the wire.21 feet = 252 inch
Using the equation
y = kx
where y represents the cost and x represents the length in inchesThus, the cost of 252-inch wire will be:
y = kx
substituting k = 0.07, and x = 252
y = 0.07 × 252
y = 17.64 Dollars
Thus, the cost of 21 feet wire will be: 17.64 Dollars
Determining the cost of 15 yards of the wire
Emily needs 15 yards of the wire.15 yards = 540 inches
Using the equation
y = kx
where y represents the cost and x represents the length in inchesThus, the cost of 15 yards of wire will be:
y = kx
substituting k = 0.07, and x = 540
y = 0.07 × 540
y = 37.8 Dollars
Thus, the cost of 15 yards of wire will be: 37.8 Dollars
If P is the circumcenter of triangle ABC, find each measure.
Find AP.
B
11x – 14
D
E
А
F
С
6x + 1
Answer:
Step-by-step explanation:
Hhhh
Answer: 19
Step-by-step explanation:
Did it
A parabola has the focus at (4, 6) and the directrix y = –6. Which equation represents this parabola?
(x – 4)2 = 24y
(x – 4)2 = StartFraction 1 Over 24 EndFractiony
(x – 4)2 = –24y
(x – 4)2 = Negative StartFraction 1 Over 24 EndFractiony
Answer:
Step-by-step explanation:
If you graph both the focus and the directrix you will see that the directrix is below the focus...12 units below to be exact. The focus is on the vertical line x = 4, so the vertex also has an x coordinate (which is actually h since h and k represent the vertex) of 4. The vertex is exactly halfway between the focus and the directrix, so that means that the vertex is at (4, 0). h = 4, k = 0. The standard form for this parabola (we know it opens upwards since the parabola ALWAYS wraps itself around the focus and is directed away from the directrix) is:
[tex](x-h)^2=4p(y-k)[/tex]
p is the number of units between the focus and the vertex, or the vertex and the directrix (which is the same number of units since the vertex is smack dab in the middle of them!). That means that p = 6. Filling in 6 for p, 4 for h, and 0 for k we have:
[tex](x-4)^2=4(6)(y-0)[/tex] and simplify to
[tex](x-4)^2=24y[/tex] which is the first choice you're given.
The equation that shows the parabola when parabola has the focus at (4, 6) and the directrix y = –6 should be considered as the (x – 4)2 = 24y.
What is a parabola?In terms of mathematics, a parabola represent the plane curve in which there is the mirror-symmetrical and should be made of U-shaped.
Since there has the focus at (4, 6) and the directrix y = –6
So the first equation should be considered.
Learn more about parabola here: https://brainly.com/question/8063993
Type the correct answer in each box. Use numerals instead of words.
Renee and David plan to file taxes as married filing jointly. They have a combined taxable income of $51,325. Use the table to determine the amount of tax due, and calculate their effective tax rate, rounding to the nearest tenth.
Answer:
the answer is 6766 and the percent is 13.2
Step-by-step explanation:
100 on the plato test
Georgette has purchased award plaques for her company’s conference. Each plaque
costs $7.50, and Georgette paid a one-time shipping fee of $40 for the order. Calculate the total cost for the order based upon the number of plaques purchased.
i need the slope
Answer:
y=1/7.50x+40
Step-by-step explanation:
I doubled checked myself on desmos and it worked. You start at 40$ because you pay that no matter what. For each one they buy the price goes up by 7.50$.
A department store is having a holiday sale. Mr. Smith bought a couch
that had a regular price of $500. He received a $150 discount. What was
the percentage of the discount that Mr. Smith received?
Answer:
Step-by-step explanation:
500×30=15000
Select the statement that indicates that the triangles in each pair are congruent.
50 points
Answer:
D. ∆XVW ≅ ∆XBC
Step-by-step explanation:
Angle X = Angle X (vertical angles are congruent)
Angle V = angle B (corresponding angles are congruent)
Angle W = angle C (corresponding angles are congruent)
The three angels in ∆XVW are congruent to the three corresponding angles in ∆XBC.
Therefore, the statement that indicates both triangles are congruent is:
∆XVW ≅ ∆XBC
Tim has 39 pairs of headphones and 13 music players. Tim wants to sell all of the headphones and music players in identical packages.
What is the greatest number of packages Tim can make?
Answer:
he can make 4 packages hope this helps
i will give brainliest<3
The length of a rectangle is twice its width. Find its area, if its perimeter is 7 1/3 cm.
Answer:
241/81 cm^2
Step-by-step explanation:
[tex]2\: lenghts = wide\\\\lenght=x\\\\2x=wide\\\\Perimeter = 2(wide+lenght)\\\\P=2(2x+x)\\\\P=2(3x)\\\\P=7\frac{1}{3}\\\\\frac{22}{3}=6x\\\\x=\frac{22}{3*6}\\\\x=\frac{11}{9}\\\\width = 2x=2(\frac{11}{9})=\frac{22}{9}[/tex]
[tex]Area = lenght\times width\\\\Area = \frac{11}{9}\times\frac{22}{9}\\\\A=\frac{11*22}{9*9}\\\\A=\frac{242}{81}cm^2[/tex]
Answer:
[tex]2\frac{80}{81}[/tex] cm²
Step-by-step explanation:
A = lw
P = 2(l + w)
~~~~~~~~~~~
l = 2w
2(2w + w) = [tex]7\frac{1}{3}[/tex]
2(3w) = [tex]\frac{22}{3}[/tex]
3w = [tex]\frac{11}{3}[/tex]
w = [tex]\frac{11}{9}[/tex]
l = [tex]\frac{22}{9}[/tex]
A = [tex]\frac{22}{9}[/tex] × [tex]\frac{11}{9}[/tex] = [tex]\frac{242}{81}[/tex] = [tex]2\frac{80}{81}[/tex] cm²
what’s the slope?
a line has the given equation 8x-6y=24
Answer:
-1.333333
Step-by-step explanation:
:)
have a very nice day
1) There are about 20 million people in New York State, with a total land area of about 47,000 square miles.
What is the population density of New York State?
A. 0.0004 people per sq. mile
B. 426 people per sq. mile
C. 2,350 people per sq. mile
D. 940,000 people per sq. mile
Step-by-step explanation:
B. 426 people per square. mile
Mal runs around a track at a constant speed of 750 meters in 30 minutes how many meters per minute is that?
Answer:
25 meters per second
Step-by-step explanation:
Divide to find m/s.
750 / 30 = 25
Check in necessary.
25 * 30 = 750
Answer:
25 per sec
Step-by-step explanation:
Your friend finds the measure of the exterior angle shown. Is your friend correct?
Answer:
will i think that's true
Step-by-step explanation:
I hope this helps you
Answer:
I think that it is yes
Step-by-step explanation:
Hope this helped have an amazing day!
(5 + 3i) + (2 - 81)
(Plz help)
Answer:
-74+3i
Step-by-step explanation:
Answer:
Step-by-step explanation:
(5 + 3i) + (2 - 81)
5 + 3i + 2 - 81
74 + 3i
Distribute 2(-3x + 5)
Answer:
= −6x+10
Step-by-step explanation:
Answer:
-6x+10
Step-by-step explanation:
Multiply the 2 by each figure in the parenthesis. So, it becomes the sum of (2)-3x and 2(5), which is -6x+10.