d^2a/db^2 +a = 4b+10sin(b)
The given equation is a second order differential equation
What is a differential equation?In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives.
Isaac Newton listed three kinds of differential equations given -
[tex]${\displaystyle {\begin{aligned}{\frac {dy}{dx}}&=f(x)\\[4pt]{\frac {dy}{dx}}&=f(x,y)\\[4pt]x_{1}{\frac {\partial y}{\partial x_{1}}}&+x_{2}{\frac {\partial y}{\partial x_{2}}}=y\end{aligned}}}[/tex]
Given is a differential equation as follows -
d²a/db² + a = 4b + 10sin(b)
The given equation is -
d²a/db² + a = 4b + 10sin(b)
Let y = a and x = b, then we can write -
d²y/dx² + y = 4x + 10sin(x)
A second order differential equation is one that expresses the second derivative of the dependent variable as a function of the variable and its first derivative. It is of the form -
d²y/dx² + P(x) dy/dx + Q(x) y = f(x)
For the equation given -
d²y/dx² + y = 4x + 10sin(x)
On comparing, we get -
P(x) = 0
Q(x) = 1
f(x) = {4x + 10sin(x)}
Therefore, the given equation is a second order differential equation.
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Solve each equation for both variables help please
Answer:
x=2 y= -1
Step-by-step explanation:
Took me 5 minutes to write steps and unfortunately it disappeared. I am so sorry. But the answer is correct
What are the dimensions of this shape in terms of the dimensions of the circle?
The diameter or radius of the circle is the dimension of a circle.
What is a circle?The circular line is drawn equidistant from the center point of a circle, which is a two-dimensional geometry object on a plane.
A geometrical rule states that the dimension of an object with n dimensions is n+1. For instance, a square is made up of line segments that are 1d and a cube is built up of squares that are 2d. The circle is therefore 2d or two-dimensional space since it is made up of 1d diameters.
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Answer:
The length of the parallelogram is half of the circumference of the circle, and its height is equal to the radius of the circle.
Step-by-step explanation:
A researcher found the average cost of one and two-bedroom apartments for different cities and graphed the data in a scatter plot, with costs of one-bedroom apartments along the x-axis. The variables have a strong linear correlation and the equation for the regression line is yˆ=1.182x+19.096 .
Based on the equation, what should the researcher expect for the average cost of a two-bedroom apartment in a city where the average cost of a one-bedroom apartment is $815?
Answer:
About $982.
Step-by-step explanation:
The average cost is:
[tex]y = 1.182x + 19.096[/tex]
When the cost of a one-bedroom apartment is 815, we have [tex]x = 815[/tex], so we should expect the cost to be:
[tex]y = 1.182(815) + 19.066 = 982.4[/tex]
So:
About $982.
the phone company charges $33 for having a smartphone plus $9.95 a month for 2gb. IF mark has only $146.43 to spend on a phone, how many months can he have the phone? inequalities
The number of months Mark can have the phone is given by the equation
A = 11.4 months
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of months be represented as = A
Now , the equation is
Now , the total amount with Mark = $ 146.43
The initial amount for the smartphone = $ 33
The amount per month for 2GB is = $ 9.95
So , the amount for A months = $ 9.95 ( A )
So , the equation will be
Initial amount for the smartphone + the amount for A months = total amount with Mark
Substituting the values in the equation , we get
33 + 9.95 ( A ) = 146.43 be equation (1)
On simplifying the equation , we get
Subtracting 33 on both sides of the equation , we get
9.95 ( A ) = 113.43
Divide by 9.95 on both sides of the equation , we get
A = 11.4 months
Therefore , the value of A is 11.4 months
Hence , the number of months is 11.4 months
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How many ounces each of a 63% acid solution and a 33% acid solution must be mixed to produce 100 ounces of a 39% acid solution?
Answer:
20 ounces of the 63% solution and 80 ounces of the 33% solution.
Step-by-step explanation:
Let x = number of ounces of 63% solution.
Let y = number of ounces of 33% solution.
The total solution to be made is 100 oz.
x + y = 100
x ounces of 63% solution is 0.63x ounces of acid.
y ounces of 33% solution is 0.33y ounces of acid.
100 ounces of 39% solution is 39 ounces of acid
0.63x + 0.33y = 39
The system of equations is
x + y = 100
0.63x + 0.33y = 39
Multiply the both sides of the first equation by -0.33. Then add it to the second equation.
-0.33x - 0.33y = -33
+ 0.63x + 0.33y = 39
---------------------------------
0.3x = 6
x = 6/0.3
x = 20
x + y = 100
20 + y = 100
y = 80
Answer:
20 ounces of the 63% solution and 80 ounces of the 33% solution.
Radius of 256/3π cm³
The temperature today will be 2 times lower than last year's temperature on the same day. What will today's temperature be if it was -8.2° last year?
Answer:
Two times lower than last year's temperature
Let today's Temperature be x
x/2 = -8.2°
x = -8.2°*2
x = -16.4°✓Please help me im pass due and my mom will ground me
Answer:
[tex] \frac{5}{6} * 20 = \frac{5 * 20}{6} = \frac{100}{6} = \frac{50}{3} = 16\frac{2}{3} [/tex]
Step-by-step explanation:
[tex] \frac{5}{6} * 20 [/tex]
Multiply
[tex] = \frac{5 * 20}{6} [/tex]
[tex] = \frac{100}{6} [/tex]
Simplicity by reducing the fraction. Divide the numerator and denominator by 2, respectively.
[tex] = \frac{50}{3} [/tex]
Divide 50 by 3 to get a mixed number
[tex] = 16\frac{2}{3} [/tex]
Part B
Next, rewrite the exponential expression using factors of 8 so that the base of the equation is a product of two factors, with one factor being a perfect square.
The exponential expression is (√4×√2)².
What is radical form?Radical form is the expression that involves radical signs such as square root, cube root, etc instead of using exponents to describe the same entity.
The given number is √8.
Now, 8=(√4×√2)²
=(2×√2)²
= 4×2
= 8
Therefore, the exponential expression is (√4×√2)².
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"Your question is incomplete, probably the complete question/missing part is:"
Rewrite the exponential expression using factors of √8 so that the base of the equation is a product of two factors, with one factor being a perfect square.
What is the solution to the linear equation?
+pag+
O p = 1
O p = 2
o p= 8
O p = 10
The solution of the equation will be 1. Then the correct option is A.
What is the solution to the equation?In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.
The equation is given below.
2/5 + p = 4/5p + 3/5
Simplify the equation for p, then we have
2/5 + p = 4/5p + 3/5
p - 4/5p = 3/5 - 2/5
1/5 p = 1/5
p = 1
The solution of the equation will be 1. Then the correct option is A.
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My new year's resolution using mathematics word essay 200 words
A ball is thrown upward from a tower 234 ft. high with an initial velocity of 19 ft per second. In how
many seconds will it strike the groun kod and with what velocity?
Step-by-step explanation:
Set the origin of the coordinate system at the top of the tower.
Given:
y = -234 ft (when the ball hits the ground)
v0 = +19ft/a
g = 32 ft/s^2
a) The equation of motion. for this freely-falling body is
y = v0t - (1/2)gt^2
When the ball hits the ground, t = T (time of flight)
----> -234 ft = (19 ft/s)T - (1/2)(32 ft/s^2)T^2
Rearranging the terms and dropping the units momentarily for brevity, we get
(16)T^2 - 19T - 234 = 0
This is a quadratic equation whose solution is
T = (1/32)[19 +- {(-19)^2 - 4(16)(-234)}]^(1/2)
= 4.46 s. or -2.68 s
Therefore, the time of flight T = 4.46 s
b) To find the velocity upon impact, we use
v = v0 - gt, where t = T = 4.46 s
= (19 ft/s) - (32 ft/s^2)(4.46 s)
= -123.7 ft/s
The negative sign means that its velocity is pointing down.
The diagram shows a triangle.
13.4 cm
1
7.6 cm
Work out the area of the triangle.
Answer:
50.92
Step-by-step explanation:
13.4 x 1 x 7.6=101.84
101.84÷2=50.92
I think that might be it but if I am wrong I am sorry that is just what I learned
Answer:
31.0
Step-by-step explanation:
13.4
+17.6
=====
31.0
The sum of the age of a girl and her brother is 34. The girl is 8 years older than her heather, how old is her brother
Answer:
26
Step-by-step explanation:
if she is 8 years older, then is just 34-8 which is 26
Point A is located at (2, 3) on the coordinate plane. Point A is reflected over the x-axis to form point B and over the y-axis to form point C. Then, point A is reflected over both axes to form point D. The four points become vertices of a quadrilateral. What is the most precise name for the quadrilateral formed, and how do you know? Explain her thinking.
Answer: W'' = (2, -3)Step-by-step explanation:Reflection over the x-axis negates the y-coordinate ...
Step-by-step explanation:
Roller coaster A can reach a top speed of 110 ft./s roller coaster B can reach a top speed of 85 mph which roller coaster has a greater top speed?
Roller coaster B has greater top speed than roller coaster A.
What is unit conversion?Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding. Different units of conversion are used to measure different parameters.
Given,
speed of roller coaster A = 110ft./s
speed of roller coaster B = 85mph
1 mile = 5280 feet
⇒ 85 mile = 5280 × 85 = 448800 feet
1 hour = 3600 seconds
speed of roller coaster B = 448800/3600 ft/s = 124.67 ft/s
comparing speed of both
Speed of roller coaster B > speed of roller coaster A
Hence roller coaster B has greater top speed.
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Which equation represents exponential growth?
y=(0.25)^x
y= 1/3(0.1)^x
y=(7)^x
y=(2/3)^x
Answer:
y=(7)^x represents the exponential growth
Answer:y=(7)^x exponential growth, and do you use monarch aop? cause i do and i was wondering
Step-by-step explanation:
Helpp!!! Im stuck on this question!!!
for an inequality graph, if the line is dashed, that means that the border line is not part of the shaded region, so any points on it are not a solution of it, any points inside the shaded region or "true" region are solutions to it, only if the border line is solid then the border is part of the "true" region, Check the picture below.
Find 45% of 60???????
Answer:
27
Step-by-step explanation:
To find 45% of 60, you can multiply 60 by 0.45
60 x 0.45 = 27
45% of 60 is 27.
A case of tomato cans weighs 563 dekagrams. A case of soup cans weighs 458 dekagrams. How much do the two cases weigh together in decigrams? Use the metric table to help answer the question.
Metric Table
kilo-
hecto-
deka-
unit
deci-
centi-
milli-
1,000
100
10
1
0.1
0.01
0.001
1,021 decigrams
10,210 decigrams
102,100 decigrams
1,021,000 decigrams
Answer:
102200
Step-by-step explanation:
564+458= 1022
1 decagram=100 decigram
So multiply the sum by 100
1022*100=102200
The length of 1 board is 2feet and 10 inches, length of another board is 1yard 1foot 9inches. What is the total of the boards put together. Simplify answer
The total length of the two boards put together is 5ft 11in.
What is length?Length is a measure of distance. It is typically measured in units such as inches, feet, yards, miles, millimeters, centimeters, and meters. Length can also be measured in other units, such as the amount of time it takes to travel a certain distance. Length is an important concept in mathematics and is used in many different topics and applications.
To simplify this answer in feet, we can convert the 10 inches and 9 inches to feet, giving us a total of 5 feet. Therefore, the total length of the two boards put together is 5ft.
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A quadratic polynomial which has zeros at -7 and 5. ?
Answer:
x^2 + 2x - 35
Step-by-step explanation:
Sum of zeros
= - 7 + 5
= - 2
Product of zeros
= - 7 x 5
= - 35
x^2 - ( sum of zeros )x + product of zeros
= x^2 - ( - 2 ) x + ( - 35 )
= x^2 + 2x - 35
The Quadratic polynomial is x^2 + 2x - 35.
Find the value of x
144 (x-36)
Answer:
it answer is 180
Step-by-step explanation:
plz mark me as brainlist
Answer:
[tex]\huge\boxed{\fcolorbox{green}{violet}{Answer}}[/tex]
[tex]144(x - 36) \\ = 144 \times x - 144 \times 36 \\ = 144x - 5184 \\ x = \frac{5184}{144} \\ x = 36[/tex]
Original price: $26
Sales tax: 3%
Answer:
$25.22
Step-by-step explanation:
26 x .03= 0.78
26-0.78= $25.22
i hope this helps :)
PLEASE HELP FASTT
Write the equation of the line that has a slope of -3 and passes through (2, -5)
show work if possible
Answer:
y = -3x + 1
Step-by-step explanation:
Plug in your x (2) and y (-5) values into your slope-intercept formula (y=mx+b).
-5 = -3(2) +b
Solve for b:
-5 = -3(2) + b
-5 = -6 + b
1 = b
Plug in the value of b, and the slope (-3) for the formula:
y = -3x + 1
1. Spongebob, Patrick, and Mr. Krabs are investing a total of $70,000 in the Krusty Krab at a ratio
of 12:7-16. How much money did each of them invest?
Spongebob
Patrick:
Mr. Krabs:
Answer:
Too much money
Step-by-step explanation:
Summary
Suppose a quadratic expression in standard form has a value of c = 0. Can this quadratic expression be
factored? How do you know?
Answer:
yesx is a factorStep-by-step explanation:
You want to know if the standard form quadratic equation ax² +bx +c = 0 can be factored when c=0.
C = 0When the constant is zero, the equation becomes ...
ax² +bx = 0
Factoring out x, we have a factored form as ...
x(ax +b) = 0
showing that the equation can always be factored.
How do you rewrite p(x)=-5x2+120x-315 in vertex form
Answer:
[tex]p(x)=-5(x-12)^2+405[/tex]
Step-by-step explanation:
Hi there!
Vertex form: [tex]f(x)=a(x-h)^2+k[/tex]
[tex]p(x)=-5x^2+120x-315[/tex]
Factor out -5 from the first two terms
[tex]p(x)=-5(x^2-24x)-315[/tex]
Complete the square by adding [tex](\frac{24}{2} )^2[/tex] (the square of half of the x-coefficient)
[tex]p(x)=-5(x^2-24x+(\frac{24}{2} )^2)-315-(-5)(\frac{24}{2} )^2[/tex]
We're subtracting [tex](-5)(\frac{24}{2} )^2[/tex] because we need to keep the equation balanced and we can't just add new values.
Complete the square
[tex]p(x)=-5(x-(\frac{24}{2} ))^2-315-(-5)(\frac{24}{2} )^2[/tex]
Simplify
[tex]p(x)=-5(x-12)^2-315+720\\p(x)=-5(x-12)^2+405[/tex]
Summary:
Complete the squareSimplifyI hope this helps!
Use the Power Property of Logarithms to write the logarithm as a product, and simplify if possible: lnx3√.
Answer:
[tex] ln \: {x}^{ \sqrt{3} } = \sqrt{3} \: ln(x) [/tex]
We can write by power property of logarithm that [tex]logx^{\sqrt{3}}=\sqrt{3} logx[/tex]
What are Logarithms?A logarithm is the power to which a number must be raised in order to get some other number
We need to use the Property of Logarithms to write the logarithm as a product[tex]logx^{\sqrt{3}}[/tex]
We have a power property of logarithm that [tex]loga^{b} =bloga[/tex]
So Given logx to the power of root three
Here consider x as a and b as root 3.
[tex]logx^{\sqrt{3}}=\sqrt{3} logx[/tex]
Hence, We can write by power property of logarithm that [tex]logx^{\sqrt{3}}=\sqrt{3} logx[/tex]
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