Consider the differential equation dy/dx= e^x-1/2y. If y = 4 when x = 0 what is a value of y when x = 1?
Answers
Answer:
A. √(e + 14)
Step-by-step explanation:
[tex]\frac{dy}{dx} = \frac{e^{x} - 1}{2y}[/tex]
separating the variables, we have
2ydy = ([tex]e^{x}[/tex] - 1)dx
integrating, we have
∫ydy = ∫([tex]e^{x}[/tex] - 1)dx
∫ydy = ∫[tex]e^{x}[/tex]dx - ∫1dx + C
2y²/2 = [tex]e^{x}[/tex] - x + C
y² = [tex]e^{x}[/tex] - x + C
when x = 0, y = 4
So,
y² = [tex]e^{x}[/tex] - x + C
4² = [tex]e^{0}[/tex] - 0 + C
16 = 1 + C
16 = 1 + C
C = 16 - 1
C = 15
So,
y² = [tex]e^{x}[/tex] - x + 15
when x = 1, we find y
y² = [tex]e^{1}[/tex] - 1 + 15
y² = e + 14
y = √(e + 14)
Related Questions
What is the area of this triangle?
A=bh/2
Answers
Answer:
b=5 h=12 so therefore the equation is (5x12)/2
Step-by-step explanation:
the answer is 30 m
pls mark brainliest (it is the crown)
What is the value of the expression below when m = 9 and n = 3?
m2 ÷ (n + 6)
Answers
Answer:
Step-by-step explanation:
m2 ÷ (n + 6)
Putting values of m = 9 and n = 3 in the equation
(9)^2 ÷ (3 + 6)
81 ÷ 9
= 9
A table measures 3.6 feet long.
How long does the table measure in inches and in yards?
Answers
Answer:
43.2 inches is 3.6ft
1.2 yards is 3.6ft
Ayuda por favor es para ahorita doy 10 puntos y Coronita please contesten bien
Answers
Answer:
x = 15, y = 10
Step-by-step explanation:
x + y = 25
y = 25 - x
4x + 2y = 80
4x + 2(25 - x) = 80
4x + 50 - 2x = 80
2x + 50 = 80
2x = 30
x = 15
x + y = 25
15 + y = 25
y = 10
What are the angles below in order from left to right? *
1 point
620
90°
1350
Right angle, Obtuse angle, Acute angle
Obtuse angle, Right angle, Acute angle
Acute angle, Obtuse angle, Right angle
Acute angle. Right anglé, Obtuse angle
What are the angles from left to right
Answers
Answer:
Acute angle, Right angle, Obtuse angle
Step-by-step explanation:
Acute angles always measure less than 90 degrees, so the 1st is an Acute Angle.
Right angles measure 90 degrees, so 2nd is a Right Angle.
Obtuse angles measure more than 90 degrees, so the third one is an Obtuse angle.
Hope it helps :)
In terms of c, y, and a , what is the value of x in the equation
2ax + 2y = c?
Answers
Answer:
Step-by-step explanation:
Simplifying
2ax + 2y = c
Solving
2ax + 2y = c
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-2y' to each side of the equation.
2ax + 2y + -2y = c + -2y
Combine like terms: 2y + -2y = 0
2ax + 0 = c + -2y
2ax = c + -2y
Divide each side by '2x'.
a = 0.5cx-1 + -1x-1y
Simplifying
a = 0.5cx-1 + -1x-1y
The value of the equation in terms of c, y, and a is (x - 2y)/2a so option (D) will be correct.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
More than one variable may be present inside a linear equation. An equation is said to be linear if the maximum power of the variable is consistently unity.
In another word, the equation must be constrained with some constraints.
Given the equation,
2ax + 2y = c where x and y are variable and c is constant.
Now,
2ax + 2y = c
2ax = x - 2y
Divide by 2a into both sides
x = (x - 2y)/2a
Hence "The value of the equation in terms of c, y, and a is (x - 2y)/2a".
For more about the equation,
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LC)Which of the following algebraic expressions can be used to express the statement "three less than a squared?"
z²-3
3-22
3-22
27-3
Answers
Answer:
A
Step-by-step explanation:
mark me brainliest pls
Answer:
algebraic expressions can be used to express the statement "three less than a squared"
is
3-z²
if z≠0,&1.
Anna divided a sheet of paper into 5 equal sections and colored 3 of the sections blue. What percent of the paper did she color?
Answers
Answer:
3/5 or 60%
Step-by-step explanation:
if the paper is split into 5ths and she colors three sections its 3/5
Answer:
3/5 of the paper or 60/100 or 60%
Step-by-step explanation:
A cone has a height of 18 millimeters and a radius of 17 millimeters. What is it's volume.
Answers
Answer:
5447.52 mm.cubed
Step-by-step explanation:
V=πr^2h/3
π·172·18/3 =5447.52
Have a good day :)
In May 2019 the average price of a liter of milk in France was 1.09 euros. Given that a liter is equivalent to 0.264172 US gallons, and that the exchange rate at that time was $1 equals 0.89 euros, find the equivalent of US dollar price for a gallon of French milk.
Answers
9514 1404 393
Answer:
$4.64/gal
Step-by-step explanation:
€1.09/(1 L) × $1/(€0.89) × (1 L)/(0.264172 gal) ≈ $4.64/gal
__
To convert units, multiply by a fraction that has numerator and denominator equal, but with different units. The units you don't want should be placed in the fraction so they cancel the units in the measure you're converting.
Here, we want dollars per gallon. So, we start with the currency value and quantity we're given: euros per liter.
Since euros is in the numerator and we want dollars there, we multiply by a fraction that has dollars in the numerator and euros in the denominator: $1/€0.89.
We have liters in the denominator and we want gallons there. We can cancel the liters unit by putting it in the numerator of our conversion factor: (1 L)/(0.264172 gal).
Multiplying euros per liter by these two conversion factors give us the equivalent in dollars per gallon.
Cameron's family traveled
3/8
of the distance to his aunt’s house on Saturday. They traveled
3/5
of the remaining distance on Sunday. What fraction of the total distance to his aunt’s house was traveled on Sunday?
Answers
Answer:
[tex]\frac{3}{8}[/tex]
Step-by-step explanation:
After Saturday, there was [tex]\frac{5}{8}[/tex] of the journey left. [tex]\frac{3}{5}[/tex] of that would be:
[tex]\frac{5}{8}[/tex] * [tex]\frac{3}{5}[/tex] = [tex]\frac{15}{40}[/tex] = [tex]\frac{3}{8}[/tex] of the journey.
Thus, the answer is 3/8
This week, Jamyra spent a total of 100 minutes studying. This total was 20 more than four times the amount of
minutes she studied last week. How many minutes did Jamyra spend studying last week?
Answers
Answer:
20
Step-by-step explanation:
100-20 = 80
80/4 = 20
Plz HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
[tex] \boxed{ \boxed{\huge{ \mathrm{ \underline{ Answer } ✓ }}}}[/tex]
Figure - 1 :
Let the missing side as " n "
[tex] \mathrm{ \triangle DEF \sim \triangle DRQ}[/tex]
Therefore the sides will be proportional,
[tex] \dfrac{n}{9} = \dfrac{4}{12} [/tex][tex]n = \dfrac{1}{3} \times 9[/tex][tex]n = 3 \: \: units[/tex]_____________________________
Figure - 2 :
Let the missing side as " m "
The Triangles are similar, therefore their sides will be proportional.
[tex] \dfrac{m}{8} = \dfrac{9}{6} [/tex][tex]m = \dfrac{3}{2} \times 8[/tex][tex]m = 3 \times 4[/tex][tex]m = 12 \: \: units[/tex]_____________________________
[tex]\mathrm{ ☠ \: TeeNForeveR \: ☠}[/tex]
Answer:
I hope it helps
have a great day
#Captainpower
Charles worked for 12 hours on Wednesday. This was 3 times as long as he worked on Tuesday. How many hours did Charles work on Tuesday?
Answers
Ans:12*3=36 the answer is D
Step-by-step explanation
Andy has $123in his checking account. if andy has $7 less than 4 times the amount that rachel has in her account, what is the amount of money in rachels account?
Answers
Answer:
Balance in Rachel account = $37.75
Step-by-step explanation:
Given:
Balance in Andy checking account = $123
Balance in Andy checking account = 4[Balance in Rachel account - 7]
Find:
Balance in Rachel account
Computation:
Assume;
Balance in Rachel account = a
So,
Balance in Andy checking account = 4[a - 7]
123 = 4[a - 7]
123 = 4a - 28
4a = 151
a = 37.75
Balance in Rachel account = $37.75
PLEASE HELP DUE TODAY
Evaluate
3^ square root5 square root5
divided by 3^ square root 5 5^
Answers
Answer:
It's the last option: 5^-5/6.
Step-by-step explanation:
Converting to fractional exponents:
= 5^1/3 * 5^1/2 / 5^(5*1/3)
= 5^5/6 / 5^5/3
= 5^(5/6 - 5/3)
= 5(5/6 - 10/6)
= 5^-5/6
If you can please help thank you
Answers
Answer:
d) 2x^2 + 2x -59
Step-by-step explanation:
(x-8)(x+4) + (x-3)(x+9) *multiply each term (...)(...)*
x^2 - 4x - 32 + x^2 + 6x -27 *combine like terms*
2x^2 +2x - 59
The base of a ladder is placed 5 feet away from a 10-foot-high wall, so that
the top of the ladder meets the top of the wall. What is the measure of the
angle formed by the ladder and the ground? Round nearest degree
A
10 ft
63 degrees
O 79 degrees
O 73 degrees
68 degrees
Answers
Answer:a i belive not 100% sure
Step-by-step explanation:
Extend numeric patterns with constant ratio 1;3;9;27
Calculate the constant ratio
Answers
someone please help me
Answers
What is CBAD similar to in the image above
Answers
Harry owes the bank money. To repay his debt, he paid $150 back to the bank each month. After 10 months, his
remaining debt was $6900.
Answers
Answer:
HIS DEBT WAS __
Step-by-step explanation:
his original debt was 8400 as after 10 months of repeatedly paying the bank 150 bucks the total amount came to 1500 bucks and the remaining debt was 6900 so 6900 + 1500 = 8400 bucks
Answer:
Step-by-step explanation:
6900 + 150 * 10 = 8400
8400 / 150 = 56 months = 4 years 8 months
A person invests 6500 dollars in a bank. The bank pays 7% interest compounded quarterly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 20100 dollars?
Answers
Answer:
16.2 years
Step-by-step explanation:
Is a straight line an angle? Please respond ASAP! Thanks!
Answers
Answer:
a straight line is a angle also called as flat angle
Step-by-step explanation:
No, a straight line is a straight angle and not a reflex angle.
Hope it helps!
Cheese Block
10 inches
4 inches
6 inches
What is the volume of the block of cheese?
A 120 cubic inches
В.
46 cubic inches
С.
240 cubic inches
D
64 cubic inches
Answers
10*4*6=240
Helpfjfififofof help number 6
Answers
Answer:
6
Step-by-step explanation:
The circumference of a circle is 2*pi*radius. You can multiply 2 by pi and then divide the circumference by that number to get the radius.
2 * 3.14 = 6.28
37.7/6.28 = 6.00318471, which rounds down to 6 in.
Triangle PQR is shown. Use the ruler provided to measure the dimensions
of the triangle to the nearest ? inch.
1
0
Inches
0
Inches
Which measurement is closest to the area of triangle PQR in square
inches?
PLS HELLPP
Answers
Answer:
maybe 6 1/2
Step-by-step explanation:
5 square inches is the area of triangle PQR in square inches.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given a triangle PQR.
We need to find the measurement is closest to the area of triangle PQR in square inches.
The PR is 2.6 inches in height and RQ is 4.1 inches.
We know that area of triangle is 1/2 times base and height.
By using ruler we calculated the height of triangle is 2.6 inches and base is 4.1 inches
The formula for area is
Area=1/2(Base×Height)
Plug in the values of base and height
=1/2(4.1×2.6)
=1/2(10.66)
=5.33
=5 square inches
Hence, 5 square inches is the area of triangle PQR in square inches.
To learn more on Triangles click:
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please help i’ll give brainliest!!! thanks
Answers
Answer:
Lack of order
Step-by-step explanation:
help lolololololol um
Answers
Answer:
The correct answer is B. m = 1.1
Step-by-step explanation:
Every time x is increases by 1, y increases by 1.1.
Answer:
m = 1.1
Step-by-step explanation:
The function equation is y = 1.1x because every increase in x produces an additional output of 1.1, therefore the slope equals 1.1.
Find the measure of the label angles below note: you must find y first
13
124
6.8
68.2
Answers
Answer:
124°
Step-by-step explanation:
since they are vertical angles, then put them equal to eachother
9y + 7 = 2y + 98
7y = 91
y = 13
9(7)+7= 124
2(13)+98= 124