The solution of the given differential equation is;
-1/(b/a + 4) = -㏑|a| - 1/5.
What is defined as the differential equation?A differential equation is a mathematical expression that contains one or even more functions and their derivatives. The function's derivatives characterize the rate of change in a function at a given point.The given differential equation is-
(b² + 7ab + 16a²)da + a²db = 0
Take da common from both;
b² + 7ab + 16a² + a²db/da = 0
The curve passes through the point (a = 1, b = 1).
As, the given differential eq is the homogeneous eq; we can use it as;
Put, b = va
Differentiate above applying product rule.
db/da = (dv/da)a + v
Substitute the value in the main equation;
(va)² + 7a(va) + 16a² + a²( (dv/da)a + v ) = 0
Dividing whole equation by a².
v² + 7v + 16 + (dv/da)a + v = 0
Further simplifying;
(dv/da)a = -(v² + 8v + 16)
(dv/da)a = -(v + 4)²
Bring similar variable together;
dv/(v + 4)² = -da/a
Integrating the equation;
-1/(v + 4) = -㏑|a| + C ; c is the integration constant.
Substitute again the values of v;
-1/(b/a + 4) = -㏑|a| + C ........equation 1
Now use the given points; a = 1; b = 1.
-1/(1/1 + 4) = -㏑|1| + C [㏑|1| = 0]
-1/5 = C
Put the value of C in equation 1.
-1/(b/a + 4) = -㏑|a| - 1/5; is the required differential equation.
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which is the least severe from of heat illness
A.) heat cramps
B.) heat exhaustion
C.) heat fatigue
D.) heat stork
the answer is (A heat cramps)
Answer:
heat cramps
Step-by-step explanation:
1 + 1 please also explain as much as possible
Answer: 2
Step-by-step explanation:
Please open this:
1. An oil tank has a circular cross section of radius 2.1 metres. It is filled to a depth of 3.4 metres. a) Calculate x, the width in metres of the oil surface. 3-4 m b) What other depth of oil would give the same surface width? 2.1m
Answer:
Step-by-step explanation:
A) We can find half of the width of the surface by applying pythagorean theorem on the right angled triangle formed by three points which are the center of the circle, the point on the circle where the the endpoints of the width and the radius meet, and the midpoint of the width.
let radius=r, width=w
[tex]r^2=(w/2)^2+(3.4-2.1)^2\\[/tex], since the distance between the origin and the midpoint of the width is 3.4m-2.1m.
[tex]-(w/2)^2=(3.4-2.1)^2-r^2, r=2.1\\-(w/2)^2=(1.3)^2-(2.1)^2\\-(w/2)^2=1.69-4.41\\-(w/2)^2=-2.72\\w/2=\sqrt{2.72}\\w=2*\sqrt{2.72}\\w=3.3 meter[/tex]
B) we can find the other depth of oil which can give the same surface area of oil if the now empty part of the cylinder is filled with oil and the now filled part of the cylinder is empty, so the other possible depth for the same surface area of oil is the diameter of the circle minus 3.4 meters:
diameter=4.2 meter, 4.2 meter-3.4 meter:
0.8 meter depth
a. The width (x) of the oil surface is approximately 5.348 meters.
b. Another depth of oil that would give the same surface width (x ≈ 5.348 meters) is approximately 3.402417 meters.
a) Here, we have to calculate the width (x) of the oil surface, we need to find the length of the chord of the circular cross-section at the top of the oil tank.
We can use the formula for the length of a chord in a circle when the depth and radius are known.
Given that the radius (r) of the circular cross-section is 2.1 meters and the depth (d) of the oil is 3.4 meters, the width (x) can be calculated as follows:
x = 2 * √(r * d)
x = 2 * √(2.1 * 3.4)
x = 2 * √(7.14)
x ≈ 2 * 2.674
x ≈ 5.348 meters
So, the width (x) of the oil surface is approximately 5.348 meters.
b) Now, let's find the other depth of oil that would give the same surface width (x = 5.348 meters).
We can rearrange the formula to solve for the depth (d):
x = 2 * √(r * d)
Divide both sides by 2:
x/2 = √(r * d)
Square both sides:
(x/2)² = r * d
Now, plug in the given values (x = 5.348 meters and r = 2.1 meters) and solve for d:
(5.348/2)² = 2.1 * d
2.674² = 2.1 * d
7.145076 = 2.1 * d
Divide by 2.1:
d ≈ 7.145076 / 2.1
d ≈ 3.402417
So, another depth of oil that would give the same surface width (x ≈ 5.348 meters) is approximately 3.402417 meters.
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Solve the inequality and enter your solution as an inequality comparing the
variable to the solution.
53 + x> 73
Answer here
PLEASE HELP FAST
Answer:
x > 20
Step-by-step explanation:
53 + x > 73
-53 -53
x > 20
Type an essay response to the following prompt. Completely explain all parts of your response and use the rubric to determine what you need to include in your essay. Describe a real-world situation in which opposite quantities combine to make zero.
A real-world situation in which opposite quantities combine to make zero is that "John bought 4 oranges and gave his friend 4 oranges. How many does he have?
How to illustrate the information?It should be noted that the information is that we should real-world situation in which opposite quantities combine to make zero.
An example will be that John bought 4 oranges and gave his friend 4 oranges.
The number of oranges that he has left will be:
= 4 - 4
= 0
Therefore, the combination gives zero.
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Given a scale 2in=35 miles on map what would be 6 inches be
Answer:
105
Step-by-step explanation:
you do 35/2 to find how much 1 inch is which is 17.5 and multiply by 6
8) Which are not true.
a)
6.68> 6.8
b)
6.86 <6.88
c)
6.8 = 6.08
d)
6.6>6.08
e) 6.86> 6.8
f)
6.8<6.6
The given statement which are not true are a) , c) , and f)
we have to check whether the given statement is true or not
a) 6.68 > 6.8
6.68 can be written as 6+ 0.68 and 6.8 can be written as 6+ 0.8
then we have 6 both the sides , only need to compare 0.68 and 0.8
we know that 0.8 is greater than 0.68
that is 0.8> 0.68
so 6+0.8 > 6+0.68
hence 6.8 > 6.68
but we are given that 6.68 > 6.8 so the statement is not true
b) 6.86 < 6.88
we know 0.86 < 0.88
hence 6.86 < 6.88 statement is true
c) 6.8 = 6.08
0.8 is not equal to 0.08
therefore 6.8 is not equal to 6.08 and hence statement is not true
d) 6.6 > 6.08
true
e) 6.86 > 6.8
true
f) 6.8< 6.6
6.8 is greater than 6.6 so the statement is not true
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Tn=2[n-1]-5 find t14
habbsbzbzbzbzbbzbBbbababsbsbsbsbsbs
If sin theta= 1/4 and theta is acute, find tan
(pi/2- theta).
Answer:
3.8723
Step-by-step explanation:
[tex]sin(\theta) = \frac{1}{4}[/tex]
So [tex]\theta = sin^{-1}(\frac{1}{4}) = 0.25268[/tex] radians or [tex]14.48^{\circ \:}[/tex]
[tex]\frac{\pi}{2}} \text\;in\;radians=90 ^{\circ}[/tex]
[tex]\text{So\;} \frac{\pi}{2} - \theta = 90 - 14.48 = 75.52^{\circ}[/tex]
[tex]\tan(\frac{\pi}{2}-\theta) = \tan(75.52) = 3.8723[/tex]
Apply Servers at a snack shop use the table below to find the total cost for frozen
yogurt, but some of the numbers have worn off. The total cost is proportional to the
number of cups of frozen yogurt. Find the missing numbers in the table.
Number of Cups of Frozen Yogurt
Total Cost ($)
1
2
3
4
18.00
Answer:
totaAal cost is 18
Step-by-step explanation:
Solve w^2=36 where is a real number. Simplify your answer as much as possible.
Answer:
w = 6 (or) w = -6
Step-by-step explanation:
Let's solve the problem,
→ w² = 36
→ w = √36
→ w = + 6
→ w = 6 (or) w = -6
Thus, the answer is 6 & -6.
Find BP with endpoints
B(1,6) and P(-3,10).
The answer of the sum is BP = 4√2
To solve this particular sum we need to know about distance formula. IT is basically nothing but gives the length of the line segment . There are various types of distance formula:
Distance between two points in a 2D planeDistance between two points in a 3D planeDistance from a point to to a line in 2D Distance from a point to to a line in 3D Distance between 2 parallel planesThe formula we are going to use in the sum is :
√{(x₂-x₁)² + (y₂-y₁)² } [ the root is over full expression ]
Here in the given sum
(x₁,y₁)=(1,6)
(x₂,y₂)=(-3,10)
If we put the values of x₁ , x₂, y₁, y₂ in the above formula we get :
BP = √{(-3-1)² + (10-6)²}
√{(-4)²+4²}
√(16+16 )
√32
4√2
So the value of BP is 4√2
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A wooden board is attached by a carpenter on a metal sheet that was 0.125 inches thick, and the wooden board was 1.5 inches thick. Find the combined thickness of the board and the metal sheet. son
Answer:
1.625
Step-by-step explanation:
1.5+0.125=1.625
A train makes a trip at 65mph. A plane traveling at 130mph makes the same trip in 3 fewer hours. Find the distance of the trip.
65mph
130mph 3 fewer hours
130-65=65
3 hours 65mph difference
plane takes 6 hours to get there.
6*130=780
780 miles
Compete the pattern
5, 7, 4, 6, 3, 5, _
Answer:
its 2
Step-by-step explanation:
it goes as 5, 7, 4, 6, 3, 5, so the next number should be 2
because 5 6 7 is a pair
and 3 4 5 is a pair
so if you look at it like counting numbers then you'll see how i got the answer.
Y = mx + b solve for m
The equation solved for b gives b = Y - mx
What is subject of formula?A subject of formula can be defined as the the variable that is written in terms of other variables in an equation or expression.
It is also known as the variable that is being sorted out in a given expression or equation.
Example;
To make a the subject from the equation;
ab + c = 1
Take the variable 'c' to the other side
ab = 1 - c
Divide both sides by b, we have;
a = 1 - c/b
Given the expression;
Y = mx + b
Take 'mx' over the equality sign
Y - mx = b
This is also written as;
b = Y - mx
Thus, the equation solved for b gives b = Y - mx
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transistors are used to build computer chips. The size of the earliest transistors
The number of times that the old transistor is bigger than the new ones in the computer is 1 × 10^6.
How to illustrate the information?It should be noted that the the side of the earliest form of transistors for computer was 1 × 10⁴.
Now, the size of the transistor today was illustrated as 1 × 10^-².
Therefore, the difference in size will be about:
= 1 × 10⁴ / 1 × 10^-²
= 1 × 10^6
Therefore, the number of times that the old transistor is bigger than the new ones in the computer is 1 × 10^6.
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If it takes 37 hours and 4 minutes to complete 185 assignments, how long would it take to complete 45 assignments? (Explain your answer).
Answer: I believe it would take 9 13/800 (9.01625) hours.
Step-by-step explanation:
If you divide the 37 hours and 4 minutes by 185 assignments, you would get how many hours or minutes it would take to complete 1 assignment, then you multiply it by the 45 assignments, and there's your answer. :) Hope this helps.
Solve the following equation. Then place the correct number in the box provided. 8 + x = 13 + 2x
Answer:
-5
Step-by-step explanation:
8 + x - 8 = 13 + 2x - 8
The 8 cancels on the left
x - 2x = 13 + 2x - 8 - 2x
The 2x cancels on the right
x - 2x = 13 - 8
Do the calculation to find
- x = 5
- x . (-1) = 5 . (-1)
Times by -1 to cancel the negative sign because you arises to find x and not -x
You finally get x = -5
Answer: You must have typed it wrong cause they can not equal each other
Step-by-step explanation:
8 + 1 does not equal 13 + 2
nor with two, three, four, and so on.
simplify.
−x2+2y−3x2+10
Answer:
(2 (y - 2 x^2 + 5))
Step-by-step explanation:
Simplify the following:
2 y - x^2 - 3 x^2 + 10
Grouping like terms, 2 y - x^2 - 3 x^2 + 10 = 2 y + (-x^2 - 3 x^2) + 10:
2 y + (-x^2 - 3 x^2) + 10
-x^2 - 3 x^2 = -4 x^2:
2 y + -4 x^2 + 10
Factor 2 out of 2 y - 4 x^2 + 10:
Answer: (2 (y - 2 x^2 + 5))
Answer:
(2 (y - 2 x^2 + 5))
21. Cindy is longboarding 6 mi ahead of Tamira. Cindy is traveling at an average rate of 2 mph Tamira is traveling at a rate of 4 mph. Let represent the number of hours since Tamira started longboarding . When will Tamira be ahead of Cindy ? Write an inequality to represent this situation.
The inequality to represent the equation is 4x>2x ₊ 6
Given,
Cindy is longboarding 6 miles ahead of Tamira.
Cindy is traveling at an average rate of 2 mph
cindy = 2x ₊ 6
Tamira is traveling at a rate of 4 mph.
Tamira = 4x
Tamira will be ahead of cindy so,
4x > 2x ₊ 6
hence we get the inequality as 4x > 2x ₊ 6
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643=4 x 160 + n write what n represents in the related division problem
Answer: n is 3
Step-by-step explanation: As you multiply 4 and 160 you'll end up with 640 then add n which then adds to 643. This indicates that n is 3.
Sohan and his sister ate 2/5 of 25 chocolates. How many chocolates they didn't eat?
HELPPPPPPPP!!!!! 50 POINTS!
Answer:
a, b, a/2, b/2
Step-by-step explanation:
The coordinates of C are (a,b).
You find the midpoint by taking the averages of the coordinates.
The third blank is a/2.
The fourth blank is b/2.
Answer:
a, b, a/2, b/2
Step-by-step explanation:
ASAP not that hard for 15 points
Answer:
24
Step-by-step explanation:
When 2 gallons of gasoline is added the tank goes from 1/6 full to 1/4 full. So the equation is:
2 = (1/4 - 1/6)x
2 = (1/12)x
x = 24
Total capacity of the tank is 24 gallons.
(-4,1), (-7,-8) find the distance between these pairs round go the nearest tenth
Answer: 9.4
Step-by-step explanation:
Everett, Miguel, and Ramona are partners, sharing income 1:2:3. After selling all of the assets for cash, dividing losses on realization, and paying liabilities, the balances in the capital accounts are as follows: Everett, $53,600 Cr.; Miguel, $45,500 Dr.; and Ramona, $37,900 Cr. How much cash is available for distribution to the partners?
The amount of cash available for distribution to the partners is $46,000.
How is the amount of cash determined?The amount of cash available for distribution to the partners is computed by summing the partners' capital balances.
From the scenario, Miguel owes the partnership $45,500. Since Miguel has not brought in this amount, the cash available for now is $46,000.
If Miguel cannot bring in $45,500, it implies that the other two partners will share the loss in their income-sharing ratio before distributing the remaining cash.
Data and Calculations:Partners = Everett, Miguel, and Ramona
Income-sharing ratio = 1:2:3
Capital account balances:
Everett, $53,600 Cr.
Miguel, $45,500 Dr.
Ramona, $37,900 Cr.
Total = $46,000 CR
Thus, the amount of cash available for distribution to the partners is $46,000.
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True or false: An equation in the form of A x + B y = C , where A ≥ 0 , A and B are not both zero, and A, B, and C are integers with a greatest common factor of 1 can represent either a linear or nonlinear function.
Answer:
True
Step-by-step explanation:
This will always be the equation of a line, which represents a linear function.
Assume 6,000 children go to Disneyland today. How much additional revenue will Disneyland receive if it raises the cost of admission
from $31 to $41?
The additional revenue that Disneyland will get if admission is raised from $31 to $41.
= $60000.
What is additional revenue ?An additional revenue stream is exactly what it sounds like – another option for you and your company to make money. It is supplemental income that you earn in addition to the main revenue stream that defines and mostly sustains your firm.
Is revenue profit or income?Revenue denotes income generated by business operations, whereas profit denotes net income after deducting expenses from earnings. Sales, fee income, and property income are all examples of revenue.
According to the given data:6,000 children
first cost = 31
second cost = 41
The cost was raised from 31 to 41 so the Disneyland will make 10 profit per children.
The additional revenue will Disneyland receive if it raises the cost of admission from $31 to $41:
6000 x 10
= $60000
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K
Order the numbers below from least to greatest.
1
2-3√6, -7,34
Choose the correct answer below.
O A.
2₁
7
OB. 7
O C. -3,
OD. -3,
7
4'
-
3.4, √6,-3
3.4, √6
7 1
42 √6,3.4
7 1
42.3.4, √6
Answer:
the anwser is B
Step-by-step explanation:
B is the best option choice given
Answer:
1. -7, -3, square root of 6, 2, 34
Step-by-step explanation: