Using the integrating method to solve the given differential equation, we get :
y = -1/4 - (9/4)e^(-2x)
Given equation is:
4y′ + 8y = 7,
y(0) = −2
We are going to use the integrating factor method to solve the differential equation.
Differential equation:
4y′ + 8y = 7
Rearranging the terms, we get:
y′ + 2y = 7/4
Integrating factor:
I.F. = e^(∫2dx)I.F. = e^(2x)
Multiplying I.F. throughout the differential equation, we get:
e^(2x)y′ + 2e^(2x)y = 7/4e^(2x)
Now we are going to apply the product rule of differentiation to the left-hand side. Let v = y and u = e^(2x)
So, v′ = y′ and u′ = 2e^(2x)
Now applying the product rule, we get:
e^(2x)y′ + 2e^(2x)y = 7/4e^(2x)2e^(2x)y + e^(2x)y′ = 7/4e^(2x)2e^(2x)y = -1/2 e^(2x) + C1y = -1/4 + C2e^(-2x)
Now substituting the initial value y(0) = -2C2 = -9/4
Putting the value of C2 in the above equation, we get:
y = -1/4 - (9/4)e^(-2x)
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Write a statement that correctly describes the relationship between these two sequences: 2, 4, 6, 8, 10 and 1, 2, 3, 4, 5.
(giving brainlest)
Answer:
first multiples of 2 and second multiples of 1
equivalent fractions for 2 4/5 and 2 2/3 plz help I will mark brainliest
Answer:
24/5: 48/10
22/3: 44/6
plz mark me as brainliest.
Question 6 options:
The diameter of a circle is 35.7 yards. The circle's circumference is about ___ yards.
Use 3.14 for .
Answer:
C = 112.098yds
Step-by-step explanation:
Where finding the circumference so do pi times diameter.
C = 3.14×d
C = 3.14×35.7
C = 112.098yds
(-3)=−22−3+11
EVALUATE
Answer:
− 3 = − 14
Step-by-step explanation:
Hope this helps !
factorize the equation 6x^2+13x+6
Answer:
(2x+3)(3x+2)
Step-by-step explanation:
.....
......
..............
Answer:
(2x + 3)(3x + 2)
Step-by-step explanation:
[tex]6x^2+13x+6 \\ \\ = 6x^2+9x + 4x+6 \\ \\ = 3x(2x + 3) + 2(2x + 3) \\ \\ = (2x + 3)(3x + 2)[/tex]
What is the value of this prism?
A) 56.3
B) 11.75
C) 31.5
D) 63.0
Please help :P
Answer:
The value of the prism is 56.3
On a snorkeling trip, Dave dove at least 7 times as deep as Amy did. If Dave dove below 35 feet below the oceans surface, what was the deepest that Amy dove?
Answer:
The deepest that Amy dove below the ocean's surface is 5 feet.
Step-by-step explanation:
Let the deepest that Amy dove below the ocean's surface be x.
7x = 35
x = 5 ft
A skyscraper that stands 620 feet cast of shadow that is 125 feet long. What is the ratio of the shadow to the height of the skyscraper?
what is the 3.5mi circumstances i also need help with this if you guys can help me
Don’t put no links just put a answer now can someone help me
A family drinks 2 gallons of milk in 3 days,
At that rate, how many gallons will the family
drink in 15 days?
Answer: This is what I have tried --
5 gallons : 3 weeks = x gallons : 52 weeks
5/3 = x/52 (cross multiply)
3x = 260 (divide by 3)
x = 86.6 or 87 gallons
Step-by-step explanation: hope this is right
Answer:
10 gallons of milk
Step-by-step explanation:
This question is a ration every three days the family drinks 2 gallons of milk (3:2) to find how much they would drink in 15 days all you would have to do is multiple both numbers by 5 to get 15:10. This represents how much milk they drink in 15 days.
Give some memes please
Answer:
oh no homework not done
Step-by-step explanation:
mom:
For a standard normal distribution (u=0, 0=1), the area under the curve less than 1.25 is 0.894. What is the approximate percentage of the area under the curve less than -1.25? 0.894 0.394 0.211 0.106
After considering all the given data we conclude that approximate percentage of area under the curve is 10.6%, which is approximately 0.106 as a decimal or 53/500 as a fraction
In case of standard normal distribution, the area under the curve less than 1.25 is 0.894.
Then the standard normal distribution is symmetric about the mean, the area under the curve less than -1.25 is the same as the area under the curve greater than 1.25.
Hence, the approximate percentage of the area under the curve less than -1.25 is approximately
(1 - 0.894) * 100% = 10.6%,
which is approximately 0.106 as a decimal or 53/500 as a fraction
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sorry this is probably easy but i need help
Answer:
Step-by-step explanation:
there is 1,000 total students... so divide 360 / 1000
so you have 0.36 for each student... then multiply by the freshmen,
.36 * 300 = 108 :)
1) a2 - 12a + 35
Help
Answer:
(a−5)(a−7)
Step-by-step explanation:
factor a2−12a+35
a2−12a+35
The middle number is -12 and the last number is 35.
Factoring means we want something like
(a+_)(a+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get -12
Multiply together to get 35
Can you think of the two numbers?
Try -5 and -7:
-5+-7 = -12
-5*-7 = 35
Fill in the blanks in
(a+_)(a+_)
with -5 and -7 to get...
(a-5)(a-7)
Find mzw.
X
po
w
(x + 12°
Need help
Answer:
∠ W = 51°
Step-by-step explanation:
Since WX is the diameter , then
∠ WYX = 90° ( angle in a semicircle )
The sum of the 3 angles in a triangle = 180° , then
x + x + 12 + 90 = 180
2x + 102 = 180 ( subtract 102 from both sides )
2x = 78 ( divide both sides by 2 )
x = 39
Then
∠ W = x + 12 = 39 + 12 = 51°
An operator at the top of a lighthouse sights a sailboat. The point from which the sighting is made is 25 m above sea level. The angle of depression of the sighting is 10 degrees. How far is the boat from the base of the lighthouse?
Answer:
141.78 m
Step-by-step explanation:
Let d = distance of boat from the base of the lighthouse
Tan 10 = 25/d
d tan 10 = 25
d = 25/tan 10
d = 141.78 m
PLEASE HELP QUESTION IN PHOTO WILL GIVE BRAINLIST!
Answer:
13x degrees
Step-by-step explanation:
brainliest????!!!
The two pentagons are similar. Find the missing side lengths.
X
12 ft
y
15 ft
21 ft
3
21 ft
N
18 ft
24 ft
What is the solution of 3x + 5 = 2x - 7?
Answer:
[tex]x=-12[/tex]
Step-by-step explanation:
[tex]3x+5=2x-7[/tex]
Subtract 2x from each side,
[tex]x+5=-7[/tex]
Subtract 5 from each side to find x,
[tex]x=-12[/tex]
Attempt in Progress The table shown below gives seven pairs of x and y values. X Y 12 18 9 35 14 12 8 40 10 31 4 33 18 10 Using the regression of y on x, the predicted value of y for x = 15, rounded to two decimal places, is:
The predicted value of y when x = 15 is given as follows:
15.8.
How to find the equation of linear regression?To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.
The points in this problem are given as follows:
(12, 18), (9, 35), (14, 12), (8, 40), (10, 31), (4, 33), (18,10).
Inserting these points into the calculator, the line of best fit is given as follows:
y = -2.28x + 50.
When the value of y when x = 15 is given as follows:
y = -2.28(15) + 50
y = 15.8.
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The complex number z = -1 -i is given.
a) Write down this number in the trigonometric form.
b) Calculate all the roots of √z and plot them all on the complex plane.
The trigonometric form of the complex number z = -1 - i is z = √2cis(3π/4) and the roots of √z are √2/2cis(3π/8) and √2/2cis(11π/8).
a) Trigonometric form of the complex number z = -1 - i is given by:
r = |z| = √(1²+1²) = √2θ = arctan(-1/-1) + π = 3π/4
Therefore, z = √2cis(3π/4)b)
Since, √z = (√2cis(3π/4))/2
= (√2/2)(cis(3π/4)/2), the roots of √z are given by:
√2/2cis(3π/4 + 2nπ)/2, where n = 0, 1.
Therefore, the roots are √2/2cis(3π/8) and √2/2cis(11π/8) and they are plotted as shown below:
In summary, the trigonometric form of the complex number z = -1 - i is z = √2cis(3π/4) and the roots of √z are √2/2cis(3π/8) and √2/2cis(11π/8).
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7 x 10 + 3 x 1 + 8 x
+ 5 x
100
1,000
Answer:
8x+5005073
Step-by-step explanation:
The weights of four puppies are shown in pounds
9.5
9 3/8
9.125
9 3/4
Which list shows these weights in order from greatest to least?
9 3/4 9.5 9 3/8 9.125
9.5 9 3/8 9 3/4
9.125 9.125 9 3/8 9.5 9 3/4 9 3/4 9 3/8 9.5 9.125
Choose the monetary amount that is equivalent to 2 . $2.03 $0.30 $ 0.03 $ 2.30
PLEASE HELP!! This is due today!
Answer:
$20.4
Step-by-step explanation:
20% of 17= 3.4
Add it to the initial $17 and you get $20.4
Answer: $20.40
Step-by-step explanation:
Since you're giving a 20% tip, your total will be 120% the price of the shampoo and cut.
17 * 120%
= 17 * 1.2
= 20.4
The total amount of money you spent at the salon and barbershop is $20.40
Your answer is correct :)
Write an equation of the line perpendicular to the given line that contains P.
Step-by-step explanation:
As the required line is perpendicular to y = (1/2)x + 5, product of slope of y = (1/2)x + 5 and required line should be - 1.
=> (1/2)m = - 1
=> m = - 2
Thus, required line is
=> y - (-8) = (-2)(x - 3)
=> y + 8 = -2(x - 3)
On her coffee table, Anita has a pile of 9 magazines. She plans to get through 2 of them over
the weekend. How many sequences of 2 magazines are possible?
sequences
Answer:
either of the 2 is read so the answer is 2/9
Which system of inequalities has this graph as its solution?
y 10
-10
- म
5
10
-10
OA. y < 21 - 3
y
OB.y > 2 - 3
y> : +4
Ocy > 21 - 3
y < = + 4
advance pile up trigonometry
Answer:
x = 6.9168 or x = 7
Step-by-step explanation:
Hope that helps :)