A differential equation with some initial conditions is used to solve an initial value problem.
The required particular solution is given by the relation:
[tex]$4y^{(3/2)} = 9e^{(-2x/3)} + 23[/tex]
What is meant by an initial-value problem?An initial value problem in multivariable calculus is an ordinary differential equation with an initial condition that specifies the value of the unknown function at a given point in the domain. In physics or other sciences, modeling a system frequently entails solving an initial value problem.
Let the given equation be [tex]$y^{1/2} dy\ dx y^{3/2} = 1[/tex], y(0) = 9
[tex]$(\sqrt{y } ) y^{\prime}+\sqrt{(y^3\right\left) }=1[/tex] …..(1)
Divide the given equation (1) by [tex]$\sqrt{ y} $[/tex] giving
[tex]$y^{\prime}+y=y^{(-1 / 2)} \ldots(2)$[/tex], which is in Bernoulli's form.
Put [tex]$u=y^{(1+1 / 2)}=y^{(3 / 2)}$[/tex]
Then [tex]$(3 / 2) y^{(1 / 2)} \cdot y^{\prime}=u^{\prime}$[/tex].
Multiply (2) by [tex]$\sqrt{ } y$[/tex] and we get
[tex]y^{(1 / 2)} y^{\prime}+y^{(3 / 2)}=1[/tex]
(2/3) [tex]u^{\prime}+u=1$[/tex] or [tex]$u^{\prime}+(3 / 2) y=3 / 2$[/tex],
which is a first order linear equation with an integrating factor
exp[Int{(2/3)dx}] = exp(2x/3) and a general solution is
[tex]u. $e^{(2 x / 3)}=(3 / 2) \ln \[\left[e^{(2 x / 3)} d x\right]+c\right.$[/tex] or
[tex]\mathrm{y}^{(3 / 2)} \cdot \mathrm{e}^{(2x / 3)}=(9 / 4) \mathrm{e}^{(2x / 3)}+{c}[/tex]
To obtain the particular solution satisfying y(0) = 4,
put x = 0, y = 4, then
8 = (9/4) + c
c = (23/4)
Hence, the required particular solution is given by the relation:
[tex]$4y^{(3/2)} = 9e^{(-2x/3)} + 23[/tex]
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To rent a bike (r), kyre pays the flat rate of 5 pesos plus an hourly rental fee (f) of 2 pesos and 50 centavos
The cost of renting the bike will rise at a rate of (B) $2.5 per hour as the number of rent hours increases.
What is a linear function?A linear function represents a straight line on the coordinate plane.The slope of a linear function is always the same and constant.A linear function, in other words, is one that varies linearly with respect to a changing variable.To find what is the rate of change in the cost to rent the bike with respect to the number of rent hours:
The rate of change is also known as the function's slope.Because it is a linear function, the slope will be constant.Slope = difference in ys coordinate/difference in xs coordinateSlope = (30-5)/(10-0) = 2.5Therefore, the cost of renting the bike will rise at a rate of (B) $2.5 per hour as the number of rent hours increases.
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The correct question is given below:
To rent a bike, Max pays a flat rate of $5 plus an hourly rental fee. The graph shows the amount, C, in dollars, that Max pays based on the number of hours, t, that Max rents the bike. What is the rate of change in the cost to rent the bike with respect to the number of rental hours?
(A) $5 per hour
(B) $2.50 per hour
(C) $2 per hour
(D) $7.50 per hour
(7.26x10^6)-(1.3x10^4) in scientific notation
Answer: 7.247 x 10^6
Step-by-step explanation:
(7.26x10^6)-(1.3x10^4)
⇒ 7.247 x 10^6
Scientific notation of given expression = 7.247× 10⁶
What is scientific notation?Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.
For example,
650,000,000 can be written in scientific notation as 6.5 ✕ 10⁸.
Given expression
(7.26x10⁶)-(1.3x10⁴)
It can be written as
= (7.26×1000000) - (1.3 × 10000)
= 7260000 - 13000
= 7247000
= 7.247× 10⁶
Hence, 7.247× 10⁶ is the scientific notation of given expression.
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Find the midpoint given the endpoints:
(_________ , _________)
Question 2 options:
Blank # 1
Blank # 2
Answer:
- 4+23e
Step-by-step explanation:
Find, in gradient-intercept form, the equation of a line which has:
a gradient of -4/5 and which passes through (4,-2)
The gradient is -4/5, so the equation is of the form
[tex]y=-\frac{4}{5}x+c[/tex]
Substituting in the coordinates (4, -2),
[tex]-2=-\frac{4}{5}(4)+c \\ \\ c=\frac{6}{5} \\ \\ \therefore y=-\frac{4}{5}x+\frac{6}{5}[/tex]
What is the decimal number 34.567 written in expanded form?
A: An expression that reads three times ten, plus one times one, plus five times one-tenth, plus seven times one-hundredth, plus four times one-thousandth
B: An expression that reads three times ten, plus three times one, plus six times one-tenth, plus seven times one-hundredth, plus five times one-thousandth
C: An expression that reads three times ten, plus four times one, plus five times one-tenth, plus six times one-hundredth, plus seven times one-thousandth
D: An expression that reads three times ten, plus seven times one, plus five times one- tenth, plus four times one-hundredth, plus six times one-thousandth
Answer:
option 3
Step-by-step explanation:
C: An expression that reads three times ten, plus four times one, plus five times one-tenth, plus six times one-hundredth, plus seven times one-thousandth
Find each product mentally using the Distributive Property. Show the steps that you used. For 6x13 in distributive property
Using Distributive Property, the product of 6x13 is 78.
What is Distributive property?
The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.
The steps of distributive property are -
6 × 13
6 × (10 + 3)
(6 × 10) + (6 × 3)
((3 + 3) × (5 +5)) + ((3 + 3) × 3)
(3 × 5 + 3 × 5 + 3 × 5 + 3 × 5 ) + ((3 × 3) + (3 × 3))
(15 + 15 +15 + 15 ) + (9 + 9)
60 + 18
= 78
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what property is illustrated by the statement 2/3 x 3/2 =1
Answer:
Multiplicative inverse or reciprocal.
Step-by-step explanation:
Multiplicative inverse or reciprocal.
Which of these choices are square roots of 100? chewhich of these choices are square roots of 100? check all that apply. ck all that apply. 100^1/2 10 -10 50 -50 -100^1/2 pleaseeeee
Halla tres enteros pares consecutivos tales que 6 veces el primer entero sea 26 más que la suma del segundo y tercer enteros.
The consecutive even integers are 8, 10 and 12.
How to calculate the value?Let the integers be x, x + 2, and x + 4.
Therefore, the equation will be:
6(x) = x + 2 + x + 4 + 26
6x = 2x + 32
Collect like term
6x - 2x = 32
4x = 32
Divide
x = 32/4.
x = 8
The numbers are 8, 10 and 12.
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The pearson correlation is calculated for a sample of n = 25 individuals. what value of df should be used to determine whether or not the correlation is significant?
The correlation is a significant non-zero value.
The number of samples is n.
n = 25
The correlation of the coefficient is r.
r = -0.40
When correlation is significant,
[tex]H _{0} : p = 0[/tex]
When correlation is non-zero,
[tex]H _{ \alpha } : p ≠0[/tex]
The test statistic is,
[tex]TS = \frac{r \times \sqrt{n - 2} }{ \sqrt{1 - r {}^{2} } } [/tex]
[tex] = \frac{0.4 \times \sqrt{25 - 2} }{ \sqrt{1 - ( - 0.4) ^{2} } } [/tex]
[tex] = \frac{ - 1.918 }{ \sqrt{0.84} } [/tex]
= -2.093
The test statistic is -2.093.
The correlation is,
[tex]H _{ \alpha } : - 2.93 ≠0[/tex]
The correlation is not equal to zero and is significant.
Therefore, the correlation is a significant non-zero value.
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Sometimes we ask you to enter an equation and not just an expression. find an equation of a line that has slope 8 and passes through the point (3, 11).
The equation of the straight line is 8x - y = 85.
It is given that the slope of the line is 8 and passes through the point (3,11).
We have to find the equation of the line.
We know that,
Equation of a line is :-
[tex]y -y_1 = m (x - x_1)[/tex]
Where,
x and y are variables
m is the slope of the line
[tex](x_1,y_1)[/tex] are the coordinates of the point that passes through the line.
Here,
[tex](x_1,y_1)[/tex] = (3,11)
m = 8
Hence,
Equation of the line = y - 3 = 8(x - 11)
y - 3 = 8x - 88
8x - y = -3 + 88
8x - y = 85
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What two mixed numbers added together equals 3 4/5. (both mixed numbers with different denominators)
1 2/5 and 2 2/5 are two mixed numbers added together equals 3 4/5.
What is a mixed fraction?
A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.What is a mixed number improper fraction?
A mixed fraction is one that has both a correct fraction and a whole number portion, and whose value is consistently greater than 1.
= 1 2/5 + 2 2/5
= 7/5 + 12/5
= 19/5
= 3 4/5
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A box of chocolates contained 12. 5% caramels. There were 5 caramels in the
box. How many pieces of chocolate are in the box?
A. There are 63 pieces of candy in the box.
B. There 8 pieces of chocolate in the box.
C. There are 40 pieces of chocolate in the box.
D. There are 4 pieces of chocolate in the box
The box of chocolates which contain 12.5% caramels has C. 40 pieces of chocolate in the box.
To solve this exercise the percentage formula and the procedure to be applied is as follows:
n= (% * nt) / 100
Where
% = percentagen= number portionnt = total of the number portionInformation about the problem:
% = 12.5%n = 5nt =?Using the percentage formulate and isolating the total of the number portion (nt), we get:
n= (% * nt) / 100
nt = (n*100) / %
nt = (5 * 100) / 12.5
nt = 40
C. There are 40 pieces of chocolate in the box.
What is a percentage?Percentage is defined as the number that represents a ratio of a total that is divided by 100 equal parts. It is represented by the symbol %.
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Chelsea is making a necklace she uses 6 blue beads for every 1 silver bead complete the table to show the ratio of blue beads to silver beads?
Answer: 12:2, 18:3, 24:4
Step-by-step explanation: You can multiply 6 by 2, 3, and 4 because the graph has 4 columns. Then multiply the top by 2, 3, and 4,
What is the domain and range of this picture?
26. Paul had 3 7/8 cups of milk. He gave 1 %4 cups of milk to his cat. How much milk did he have left?
HELP PLEASE!!! :( .
Answer: The cat has left over the milk is 3.625 cups
Step-by-step explanation:
Amount of cups of milk=3(7/8) cups
That means, 3(7/8) cups= 31/8 cups
Amount of milk cat gave=1/4 cups
The amount of left over the milk :
Subtract with this values
=(31/8) -(1/4)
=3.875-0.25
=3.625
The cat has left over the milk is 3.625 cups
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what is 1408 rounded to the nearest hundredth
Answer:
It would still be 1408
Step-by-step explanation:
There are no decimal points to round to the nearest hundreth
Answer:
1408.00
Step-by-step explanation:
1408.00 ==>the underlined digit which is 1 digit away from the decimal is the hundredth digit.
2 1/7 + 3/7(3x-5)=-4
Answer:
Answer 2 1/7 +3/7(3x-5)= -4
2 1/7 + 9/7x-15/7= -4
0+ 9/7x = -4
x= -28/9
Step-by-step explanation:
Which polynomial does not have an absolute maximum?
A. 2nd degree
B. 3rd degree
C. 4th degree
Reason:
Odd degree polynomials do not have an absolute max nor absolute min. The curve stretches forever upward and downward. The range is the set of all real numbers.
Even degree polynomials on the other hand do have a highest point or lowest point, depending on the leading coefficient. If the leading coefficient is negative, then the curve has a highest point. If the leading coefficient is positive, then the curve has a lowest point.
Example: y = x^3 does not have an absolute max, but y = -x^2 does.
Your friend took an introductory statistics class last year and learned all about density curves. she tells you that two requirements of a density curve are:______.
The required requirement of the density curve is should be equal to 1 and the ordinate should not be zero.
Given that,
Two requirements of a density curve are to be determined.
A density curve is defined as a curve on a graph that represents the distribution of values in a dataset.
Here,
The two requirements of a density curve should be,
a. The area under the density curve should be equal to 1.
b. The ordinate of the curve should not be zero i.e. they should always have the vertical height.
Thus, the required requirement of the density curve is mentioned above.
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(-0.216) - (-87.1) please solve within 5 mins
Answer: I believe the answer is 86.884
Step-by-step explanation:
solve each inequality
||x-4|-7|<5
The solution of the inequality is (x > - 8 and x < 2) or (x > 6 and x < 16).
How to find the solution set of an inequalityHerein we find an inequality that involves two absolute values. Absolute values are defined by the following piecewise functions:
|x - a| = x - a for x ≥ a|x - a| = - x + a for x < aNow we proceed to solve the inequality given:
||x - 4| - 7| < 5
- 5 < |x - 4| - 7 < 5
0 < |x - 4| - 2 < 10
|x - 4| - 2 > 0 and |x - 4| - 2 < 10
Case 1: |x - 4| - 2 > 0
|x - 4| > 2
x - 4 > 2 and x - 4 < - 2
x > 6 and x < 2
Case 2: |x - 4| - 2 < 10
|x - 4| < 12
x - 4 < 12 and x - 4 > - 12
x < 16 and x > - 8
The solution of the inequality is (x > - 8 and x < 2) or (x > 6 and x < 16).
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9. (6x +12) -2(x-7)= 19
Answer: x=-1.75
Step-by-step explanation:
(6x +12) -2(x-7)= 19
6x+12-2x-(-14)=19
6x+12-2x+14=19
6x-2x+12+14=19
4x+26=19
4x+26-26=19-26
4x=-7
x=-7/4
x=-1.75
express
the speed
10m
per second as
km per hour
10 m/s can be expressed as 36km/h.
Here, we are given an expression for speed, that is: 10 meter per second.
Now, as per the rules of mathematics,
1 kilometer = 1000 meters
⇒ 1 meter = 1/1000 kilometers
or 1 meter = 0.001 kilometers
and also, 1 hour = 60 mins
and 1 min = 60 seconds
⇒ 60 mins = 60 × 60 seconds
= 3600 seconds
Thus, 1 hour = 60 mins = 3600 seconds
⇒ 1 second = 1/3600 hours
Now, we need to convert meter per second into kilometer per hour,
1 meter/ 1 second = [tex]\frac{0.001}{\frac{1}{3600} }[/tex]
= (0.001 × 3600)/ 1
= 3.6
This 1 meter per second = 3.6 kilometer per hour
⇒ 10 meter per second = 3.6 × 10 = 36 kilometers per hour
Thus, 10 m/s is 36km/h.
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Ms. longora has two bags of wid- bird seed. the first bag has 20 ounces of wild- bird sod, and the second bag has 3; times as much wid-bird seed as the first. ms. longoria uses ; of the wild-bird seed from the larger bag to feed the birds in her backyard. how many ounces of wild-bird seed did she use?
Answer:
2
Step-by-step explanation:
Express 15 km as a percentage of 120 km
The expression of 15km as a percentage of 120km as required in the task content is; 12.5%
What percentage representation is 15km of 120km as required in the task content?Since it follows from convention that a percentage is a representation of an entity as a fraction of a hundred partitions.
On this note, the percentage representation is such that;
15km of 120km is;
(15/120) × 100%
0.125 × 100%
= 12.5%.
Ultimately, 15km is 12.5% of 120km.
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Which equation can be used to find the answer to 30 divided by 5
Answer:
[tex]30 \div 5[/tex]
Way A
• 5 divided by 0 is 0.
• 5 divided by 3 is 0.6, flip the number, and you get 6.
Way B
• Divide 30 by 5 to get 6.
In the figure below, m1= 35° and m/2 = 27°.
Find mTSW.
62°
A line is a simple, one-dimensional shape that can go on forever in the opposing directions. A line may be vertical or horizontal. It can be drawn either top to bottom or left to right.
When the ends of two rays collide at a single location, an angle is the geometry that results. They are measured in degrees (°) or radians. A 360-degree angle is the same as a whole rotation. It is symbolized by the character "∠"
∠1+∠2 = 35° +27°
=62°
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If mQOS, mPOR, and mPOQ, what is mROS?
Applying the angle addition postulate, the measure of angle ROS is: 16°
How to Apply the Angle Addition Postulate?Given the following angle measures:
m<QOS = 49°
m<POR = 56°
m<POQ = 23°
Find the measure of angle QOR:
m<QOR = m<POR - m<POQ [angle addition postulate]
Substitute the values into the equation
m<QOR = 56 - 23
m<QOR = 33°
Find the measure of angle ROS:
m<ROS = m<QOS - m<QOR [angle addition postulate]
Substitute the values into the equation
m<ROS = 49 - 33
m<ROS = 16°
Therefore, applying the angle addition postulate, the measure of angle ROS is: 16°
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A startup sports public relations company is looking to grow. They currently represent 2 clients and plan on representing 3 additional clients each year. The following graph can be used to help determine the number of clients, y, the company will have after x years.
ased on the context, what is the range of the function?
[0, ∞)
[2, ∞)
[−7, 7]
ℝ
Based on the context, the range of this function is given by: C. [−7, 7]
What is a range?A range can be defined as the set of all real numbers that connects with the elements of a domain. This ultimately implies that, a range refers to the set of all possible output numerical values, which are shown on the y-axis of a graph.
How to identify the range of this graph?The vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph of function f(x) shown, we can infer and logically deduce the following:
Range = [−7, 7]
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