If y = ax + 2a², then its derivative is dy/dx = a. Substitute y and dy/dx into the given equation and check if it results in an identity:
2 (dy/dx)² + x dy/dx - y = 0
2a² + ax - (ax + 2a²) = 0
0 = 0
This is of course true, so y = ax + 2a² is indeed a solution to the given equation.
Read the word problem below.
Chan rows at a rate of eight miles per hour in still water. On Wednesday, it takes him three hours to row upstream from his house to the park. He rows back home, and it takes him two hours. What is the speed of the current?
Answer:
1 3/5 miles/hr
Step-by-step explanation:
Let C be the speed of the current
Let D be the distance between Chan's house and the park
We know that Distance, D, is = Speed x Time
-----
Chan's speed going upstream is (8 - C)mph.
That gives us:
D = (8-C)(3 hr)
Chan's speed going downstream is (8+C)mph
So we have:
D = (8+C)(2 hr)
We know that the d is the same for these two equations, so:
(8-C)(3 hr) = (8+C)(2 hr)
24 - 3C = 16 + 2C
5C = 8
C = (8/5) or 1 3/5 mph
Answer:
1.6 mph
Step-by-step explanation:
Distance, speed, and time are related by ...
distance = speed × time
We assume that the distances up and back are the same, so for a current speed of c, we have ...
3(8 -c) = 2(8 +c)
24 -3c = 16 +2c . . . eliminate parentheses
8 = 5c . . . . . . . . . . add 3c-16 to both sides
c = 8/5 = 1.6 . . . . . divide by 5
The speed of the current is 1.6 miles per hour.
f(x) = -3x – 12
g(x) = 3x2 – 2x – 14
Answer:x
=
2
3
,
−
1
Step-by-step explanation:
Help please, I could not figure this problem because the answer was -108 but I only solved it to -244. The problem is “Find coefficient of x in expansion of (x-3)^4”
Answer:
You already know the answer is -108
Step-by-step explanation:
There is probably a formula for finding the coefficient of a variable in an expansion. But (x-3) is easy to square, and that gives us
x^2 - 6x +9
Now to square that quadratic trinomial I used an area model. You can get the entire expansion. But we are just only interested in the x terms. See image. They are in yellow on the image. You can see we get -54x two times. So
-54x + -54x is the -108x term you are interested in.
15 more than the quotient of a number x and 12.
Answer:
(x/12)+15
Step-by-step explanation:
A plane travels 2047.5 miles in 3.5 hours. Find the plane's speed in miles per hour.
585m/hr
Step-by-step explanation:To find the plane's speed for 1 hour, we will need to divide 2,047.5 by 3.5:
2,047.5 / 3.5 = 585.
585 miles represents the speed of the plane for 1 hour.
Round 0.1 to the nearest whole number.
diferencia entre el bote el pase y tiro en el baloncesto
Answer:
difference between bounce, pass and shot in basketball
Solve for W if:
4w^2+9w=-2
HELP!!!!!!
Find the length of segment SV.
Answer:
how do u want the formula because there is no numbers
what is the term to term rule for 2 6 18 54 162
Answer:
It's always × by 3
Step-by-step explanation:
2×3=6
6×3=18
18×3=54
54×3=162
help please..
Select the correct image.
Given triangle A in the coordinate plane, which image shows a dilation of triangle A by a factor of 2 centered at the origin?
Answer:
C
Step-by-step explanation:
C because each point is twice as far from the origin
Answer:
c
Step-by-step explanation:
A ___ equation is a second-degree equation of the form ax^2+bx+c=0 where a ≠ 0
Answer:
A quadratic equation is second degree equation with the standard form ax^2+bx+c=0 as the highest power is 2.
__________________.
solve similar triangles (advanced)
Answer:
1
Step-by-step explanation:
They are similar triangles and ED and AD are 9 so CB and AB must be 1.
pls pls pls pls help
Evaluate this -4-12/(-4)?
Answer:
4
Step-by-step explanation:
last month nick spent $50 this month he spent 60% of last month how much did nick spend
Answer:
Nick spent $30.00.
Step-by-step explanation:
60% of $50.00
60% ÷ 100 = 0.6
0.6 x 50 = 30
Answer:
30$Step-by-step explanation:
last month nick spent $50 this month he spent 60% of last month how much did nick spend?
50 : 100 * 60 =
0.5 * 60 = 30$
Plz help with this question
Answer:
the area of the tile is 190 cm2
Please Help!!!!!! Tom says that he needs 6 rolls to obtain each possible outcome on a 6-sided die. On the fourth roll, he rolls his second "3”. Tom says that the die is loaded and that each outcome is not equally likely. Is Tom correct here? If you think Tom is incorrect, how many rolls should Tom make until he sees each number occurring about 1/6 of the time?
Answer:
I think he is correct.
Step-by-step explanation:
I think he is correct because when you roll a die, it is 10 to 1 for the die to get the number you want.
Tom says that the dices outcome is NOT equally likely. When actually the outcome is equally likely.
On dice no two number repeat twice. So in this case every time he rolls the die he has the same chance of getting 3 than he does any other number.
So Tom is incorrect.
And for how many times it will take Tom for all the numbers to occur is all by luck and chance.
But each number is equally likely to come.
KEEP GETTING BOTTED! Work out. the area of a circle of radius 7cm. Give your answer in terms of pi
Step-By-Step would be appreciated!
Answer:
49π cm²
Step-by-step explanation:
[tex]A=\pi r^2[/tex]
[tex]A=\pi (7)^2[/tex]
[tex]A=49\pi[/tex]
Therefore, the area of a circle of radius 7 is 49π cm²
Hello there! :-)
The formula for calculating the area of a circle is
A=πr²
A=π(7)²
Notice that only the radius is squared.
A=π(49)
A=154 cm
Hope this helps!
Use the comment section to clarify your doubts.
Answered by
~A teen who helps others with joy and listens to her favourite music
#LetItSnow
Good luck with your studies. :-)
4200 in the scientific notation.
Answer:
4.2*10^3
Hope This Helps!!!
Answer:
The answer is 4.2×10^3
Step-by-step explanation:
To convert 4200 into scientific notation, follow these steps:
- Move the decimal 3 times to left in the number so that the resulting number, m = 4.2, is greater than or equal to 1 but less than 10
- Since we moved the decimal to the left the exponent n is positive
n = 3
- Write in the scientific notation form, m × 10^n
= 4.2 × 10^3
Therefore, the decimal number 4200 written in scientific notation is 4.2 × 10^3 and it has 2 significant figures.
In a sale, a clothes shop reduces its prices by 30%.
A shirt usually costs $24.
How much is it in the sale?
Answer:
$16.80
Step-by-step explanation:
30% of 24 and the answer is subtracted from $24
Which statement is true about the number −5? The number −5 is not a rational number because it cannot be written as a ratio of integers. The number −5 is not rational number because it is a negative integer. The number −5 is a rational number because it can be written as the fraction −51. The number −5 is a rational number because it can be written as the fraction −50.
Answer:
The number -5 is not a rational number because it is a negative integers.
Step-by-step explanation:
Hopes This Helps :)
Elizabeth bought lemons (l) and apples (a). Each apple costs 35¢ and each lemon costs 15¢. All together, she bought 17 lemons and apples for $3.95. Which system can be used to determine how many of each she bought?
Answer:
B.
Step-by-step explanation:
Each apple costs 35¢ and each lemon costs 15¢. All together, she bought 17 lemons and apples for $3.95. Which system can be used to determine how many of each she bought?
She bought a total of 17 apples and lemons combined.
So the equation that would represent this is,
l + a = 17.
Each apple costs 35¢ and each lemon costs 15¢. All the lemons and apples cost $3.95 togther.
So the equation that would represent this is,
0.15l + 0.35a = $3.95
There are 4 juice cartons and 9 milk cartons in the school refrigerator. What is the ratio of juice cartons to total cartons
A. 4 to 9
B. 4 to 13
C. 5 to 9
D. 9 to 13
Answer:
c I took the test
Step-by-step explanation:
How many solutions do 5-2x=2x-5
Answer:
1 solution is the answer
What is 1.3742 rounded to the nearest tenth?
Answer:
1.4 that is the true answer
Step-by-step explanation:
go to the place right after the decimal and then look at the number next to it.if it is greater the 5 it goes up to 1.4 and it is
esterday 5% of the 120 sixth graders at school were late. How many sixth graders were late?
Answer:6 six graders were late. 10% would be 12, and half of that is 6. You need to divide that in half because 5 is half of 10.
Answer:
6 sixth graders at school where late
Step-by-step explanation:
5% = 0.05
0.05(120) = 6
Solve for x.
-8 =X/4
x = −32
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I don’t quite understand how to solve question 1-A.
Answer:
for every 1000 people, the maximum noise level goes up by 1.5
need help with this question please
(1/5 x 5) to the 5th power =
Answer:
1
Step-by-step explanation:
According to the rule of PEMDAS, we must perform parentheses before exponents.
1/5 x 5 = 1
1 to the power of anything is still 1, so that is the answer.