(a)
KE = m v^2 / 2 = (1200 kg)(20 m/s)^2 / 2 = 240,000 J
(b)
The energy is entirely dissipated by the force of friction in the brake system.
(c)
W = delta KE = KEf - KEi = (0 - 240,000) J = -240,000 J
(d)
Fd = delta KE
F = (delta KE) / d = (-240,000 J) / (50 m) = -4800 N
The magnitude of the friction force is 4800 N.
mark brainliest if correct
A) Findi
Consider the curve x²y + y2x = 6
dy
in terms of x and y
B) Write the equation for the tangent line where x = 2 and y = 1.
Answer:
Part A)
[tex]\displaystyle \frac{dy}{dx}=-\frac{2xy+y^2}{x^2+2xy}[/tex]
Part B)
[tex]\displaystyle y=-\frac{5}{8}x+\frac{9}{4}[/tex]
Step-by-step explanation:
We have the equation:
[tex]\displaystyle x^2y+y^2x=6[/tex]
Part A)
We want to find the derivative of our function, dy/dx.
So, we will take the derivative of both sides with respect to x:
[tex]\displaystyle \frac{d}{dx}\Big[x^2y+y^2x\Big]=\frac{d}{dx}\big[6\big][/tex]
The derivative of a constant is 0. We can expand the left:
[tex]\displaystyle \frac{d}{dx}\Big[x^2y\Big]+\frac{d}{dx}\Big[y^2x\Big]=0[/tex]
Differentiate using the product rule:
[tex]\displaystyle \Big(\frac{d}{dx}\big[x^2\big]y+x^2\frac{d}{dx}\big[y\big]\Big)+\Big(\frac{d}{dx}\big[y^2\big]x+y^2\frac{d}{dx}\big[x\big]\Big)=0[/tex]
Implicitly differentiate:
[tex]\displaystyle (2xy+x^2\frac{dy}{dx})+(2y\frac{dy}{dx}x+y^2)=0[/tex]
Rearrange:
[tex]\displaystyle \Big(x^2\frac{dy}{dx}+2xy\frac{dy}{dx}\Big)+(2xy+y^2)=0[/tex]
Isolate the dy/dx:
[tex]\displaystyle \frac{dy}{dx}(x^2+2xy)=-(2xy+y^2)[/tex]
Hence, our derivative is:
[tex]\displaystyle \frac{dy}{dx}=-\frac{2xy+y^2}{x^2+2xy}[/tex]
Part B)
We want to find the equation of the tangent line at (2, 1).
So, let's find the slope of the tangent line using the derivative. Substitute:
[tex]\displaystyle \frac{dy}{dx}_{(2,1)}=-\frac{2(2)(1)+(1)^2}{(2)^2+2(2)(1)}[/tex]
Evaluate:
[tex]\displaystyle \frac{dy}{dx}_{(2,1)}=-\frac{4+1}{4+4}=-\frac{5}{8}[/tex]
Then by the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Yields:
[tex]\displaystyle y-1=-\frac{5}{8}(x-2)[/tex]
Distribute:
[tex]\displaystyle y-1=-\frac{5}{8}x+\frac{5}{4}[/tex]
Hence, our equation is:
[tex]\displaystyle y=-\frac{5}{8}x+\frac{9}{4}[/tex]
I WILL MARK BRAINLIEST IN 5 MINUTES!
solve this and explain
Answer:
no, it's not.
Step-by-step explanation:
300- 284 = 16
284 - 236 = 48
236 - 156 = 80
156 - 44 = 112
for every one the top line goes up, the bottom line changes too, but it's not at a constant rate. it's not constant, therefore it cannot be linear.
the rate of change formula (or slope formula, they're the same thing) is :
y2- y1/ x2 -x1 and to solve it you plug in the points. x is the same a t and y is h
284-300/ 1-0
-16 /1
-16 (this is the rate of change between the first two points)
236- 284/ 2-1
-48/ 1
-48 (rate of change between the second and third points)
since the rate of change isn't constant, it's not possible for it to be a linear relationship.
Answer:
I D K
Step-by-step explanation:
my brains not working right now
Canceling units is also called:
A: changing the value
B. unit analysis
C. multiplication
D. making connections
Please select the best answer from the choices provided
Answer: B) unit analysis
This is also called dimensional analysis.
Refer to the diagram below for an example. The diagram shows why 3 feet is equal to 36 inches. The "ft" units cancel.
Answer:
unit analysis
Step-by-step explanation:
if you times a 3 digit number by a 2 digit number what is the highest number you can get
Answer:
a 5 digit number
Step-by-step explanation:
Pick the largest three digit number (999) and the largest two digit number (99) and multiply them to get 999*99 = 98901
The result is a five digit number.
Answer: 5 digit number
What is the perimeter?
Answer:
21.3 unit
Step-by-step explanation:
[tex]side CB=\sqrt{(7^{2})+(2^{2})} =\sqrt{53}\\side CA=\sqrt{(5)^{2}+(2^{2})} =\sqrt{29} \\side AB=\sqrt{(5^{2} )+(7^{2} )} =\sqrt{74}[/tex]
[tex]Perimeter=\sqrt{53} +\sqrt{29} + \sqrt{74} =21.2676[/tex] unit
A store bought a pair of shoes for $50 and sold it for $80. What percentage was the markup?
Must show work.
(Percent change = amount of change x 100 )
original amount
Correct answer get's brainliest) Just something to post
Answer: 60%
Step-by-step explanation: theres a $30 increase between the two prices. To find the percent change just take the difference of money over the original price. In this case it would be 30/50 or 60%
PLEASE HELP WITH PART B
A line passes through the points (-4, 0) and (1, 10). What is its
equation in slope-intercept form?
Answer:
The answer is y=2x+8
Step-by-step explanation:
(-4,0)&(1,10)
m=y²-y¹/x²-x¹
m=10-0/1-(-4)
m=10÷5
m=2
y-y=m(x-x¹)
y-10=2(x-1)
y-10=2x-2
+10 +10
y=2x+8
A Hummer gets 300 miles on 20 gallons of gas, how many miles can it be driven on 50 gallons of gas?
Answer:
750 miles
Step-by-step explanation:
Step one:
Given data
we are told that the hummer gets to 300miles on 20 gallons of gas
Required
The distance that the Hummer can go on 50 gallons of gas
Step two:
if 20 gallons gets to 300miles
the 50 gallons will get to x miles
cross multiply we have
[tex]x= 50*300/20\\\\x=15000/20\\\\x=750 miles[/tex]
Mr. Garza bought paper cups for his food truck. He bought 5 cartons of blue cups and 4 cartons of green cups. He ordered a total of 1,008 cups. How many cups are in each carton?
Answer:112
Step-by-step explanation:Divide 1008 by 9
solve this: 2-2÷2×2+2
Answer:
-2 I think
Step-by-step explanation:
Answer:
4 ...................
Solve each equation. Check your solution.
7k - 3 = 32
Answer:
k = 5
Step-by-step explanation:
First, add 3 to both sides;
[tex]7k = 35[/tex]
Divide by 7:
[tex]\frac{7}{7}k = \frac{35}{7}\\k = 5[/tex]
Now, let's check our answer:
[tex]7(5) - 3 = 32\\35 - 3 = 32\\32 = 32[/tex]
I hope this helps!!
If you have any questions feel free to ask!
- Kay :)
Please help me thank you I appreciate it
Answer:
angle FDE+angle CDF=90° (given CDE=90°)
angle CDF=90-42
angle CDF=48°
283 rounds to nearest tens place
Answer: 280
Step-by-step explanation:
Remember the rounding rule -
If it is 5 or more, you round it up, if it is 4 or less, you round it down.
283 rounded to the nearest ten is 280.
pls help, I've been stuck on this for a week
Using the Pythagorean identity, sin^2C + cos^2C = 1, solve for sinC.
Answer:
[tex]\sin(C)=\pm\sqrt{1-\cos^2(C)}[/tex]
Step-by-step explanation:
Given the Pythagorean Identity:
[tex]\sin^2(C)+\cos^2(C)=1\\[/tex]
We want to solve for sin(C).
First, we will subtract cos²(C) from both sides:
[tex]\sin^2(C)=1-\cos^2(C)[/tex]
Next, we will take the square root of both sides. Since we are taking an even-root, we will need to add plus/minus. Hence:
[tex]\sin(C)=\pm\sqrt{1-\cos^2(C)}[/tex]
question in the image
Answer:
thats not a question
Step-by-step explanation:
Mr. Alcazar bakes cookies in batches of 60 and batches of 90. If he bakes 6 batches of 60 cookies,
how many cookies does he bake?
A. 60 cookies
B. 90 cookies
C. 360 cookies
D. 3,600 cookies
Answer:
360 cookies
Step-by-step explanation:
60 times 6= 360
Help me please i have be very grateful
Answer:
8,20,24
Step-by-step explanation:
these numbers they make 52
Given the line below, state the slope of the PARALLEL line. y=-8x + 10 what is the answer need help
Step-by-step explanation:
the slope if the equation will be -8
I need help on these two pls
Answer:
Much larger than 1 for both of them
Step-by-step explanation:
LOOK AT PICTURE, THEN ANWSER QUESTION, WHOEVER IS CORRECT I WILL MARK BRAINIEST:)
Answer:
c is the correct answer
PLZ HELP ME!!!!!!
if you can buy 35 trumips for $15, then how many can you buy with $3?
Answer: one with change mane I’m pretty sure? Really sorry if that’s not right
Step-by-step explanation:
Answer:
I’m pretty sure it’s 7. Just divide the 35 by 5 bc 5 times 3 is 15 and so it would be 7
Hope this helps
Meryl needs to cut down 10.5 trees for every 555 cabins she builds.
Answer:
6.3 trees.
Step-by-step explanation:
We have been given that Meryl needs to cut down 10.5 trees for every 5 cabins she builds.
Let us find the number of trees Meryl needs to cut down to build 1 cabin by dividing 10.5 by 5.
Now let us multiply 2.1 by 3 to find the number of trees Meryl needs to cut down to build 3 cabins.
Therefore, Meryl needs to cut down 6.3 trees, if she builds 3 cabins.
PLEASE HELP I GOT 5 MINUTES!!!
Put each equation in slope-intercept form (y = mx + b)
y = 2(x− 3) + 1
Answer:
y = 2x - 5
Step-by-step explanation:
[tex]y = 2(x− 3) + 1 \\ \\ y = 2x - 6 + 1 \\ \\ y = 2x - 5 \\ [/tex]
Find the slope of the line passing through the points (8,-8) and (4, -2).
Answer:
-6/4
Step-by-step explanation:
m=y2-y1/x2-x1
m=-2--8/4-8=6/-4
-6/4
Answer:
The answer m= -3/2 , hope this helps you.
What is the value of the expression?
-16+ 12
-28
O _4
4
28
Answer:
-4
Step-by-step explanation:
if you switch it you get 12-16 and you have to get a negative so 16-12 is 4 so switch it to a nrgative to get -4
which of these numbers are multiples of 6 choose all that apply
Answer:
12, 24, 36, 48, 60, 72
Step-by-step explanation:
Answer:
ok its c daddy hope it helps dad
Step-by-step explanation:
find the measure of the line segment RQ
===========================================
Work Shown:
RS*QS = (TS)^2
RS*(QR+RS) = (TS)^2
27*(5x-12+27) = (45)^2
27*(5x+15) = 2025
135x+405 = 2025
135x = 2025-405
135x = 1620
x = 1620/135
x = 12
Use this to find the length of QR, which is the same as RQ
QR = 5x-12
QR = 5*12-12
QR = 60-12
QR = 48
9514 1404 393
Answer:
RQ = 48
Step-by-step explanation:
The product of secant segment lengths to the points of intersection with the circle is the same for both secants. The tangent is a degenerate case where the two points of intersection are the same.
ST·ST = SR·SQ
SQ = ST^2/SR = 45^2/27 = 75
RQ = SQ -SR = 75 -27
RQ = 48
30 POINTS FOR CORRECT ANSWER! NO TROLLING
As the ball moves from Point 3 to Point 4, which energy conversion is taking place?
Group of answer choices
potential to kinetic
kinetic potential
thermal to kinetic
kinetic to thermal
Answer: potential to kinetic
Step-by-step explanation:
Answer:
Kinetic Energy is defined as energy that a body possesses by virtue of being in motion.
Kinetic Energy is defined as energy that a body possesses by virtue of being in motion.As you walk down stairs, as water boils, and as the planets orbit the sun, kinetic energy is being utilized.GRAVITATIONALApple falls from tree and rolls behind the trunk.
GRAVITATIONALApple falls from tree and rolls behind the trunk.An object’s relative location to a gravitational field is the gravitational potential an object has to do work. Earth’s gravity will pull a ripe apple from the branch and convert it into gravitational kinetic energy.NUCLEARElectrons circle a nucleus at the atomic level.
NUCLEARElectrons circle a nucleus at the atomic level.The mass of an atom’s nucleus is almost entirely comprised of its protons and neutrons. The force binding them together is considered potential energy because it causes them to weigh less than the sum of their parts.ELASTICSpring animation expands and compresses.
ELASTICSpring animation expands and compresses.Elastic potential energy is present when the object, such as a spring, is in a deformed state but can return to a static state. This means the spring has elastic potential energy when it is either stretched or compressed.CHEMICALBattery animation motions towards a full charge.
CHEMICALBattery animation motions towards a full charge.Every animate and inanimate object is the result of chemical reactions. Chemicals in a battery have the potential to be converted into motion, therefore they have chemical potential energy.Potential Energy is defined as the energy stored by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors.
Potential Energy is defined as the energy stored by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors.When you (or a rock) are standing at the top of a hill, you possess more potential energy than when standing at the bottom. This is because your position relative to the Earth’s center of gravity can exert potential energy upon you to bring you closer to that center.Energy can neither be created nor destroyed, this is the conservation of energy law. However, energy can be altered from one form to another.
Energy can neither be created nor destroyed, this is the conservation of energy law. However, energy can be altered from one form to another.All forms of energy are either potential or kinetic energy. Potential refers to stored energy while kinetic is energy in motion.
Energy can neither be created nor destroyed, this is the conservation of energy law. However, energy can be altered from one form to another.All forms of energy are either potential or kinetic energy. Potential refers to stored energy while kinetic is energy in motion.All energy, whether potential or kinetic, is measured in Joules (J).
What is the 100th term in the sequence 15, 22, 29, 36, 43,...
Answer
Step-by-step explanation:
i dont know child