The differential equation used to solve an equation of the amount (mass) of salt within the tank at any given time t is [tex]\frac{ds}{0.04s-0.1} = dt[/tex].
What are differential equations?A differential equation in mathematics is an equation that connects the derivatives of one or more unknown functions. Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the two.Let the amount of salt any time t is given by s kg then the rate of change of s with respect to t is given by,
[tex]\frac{ds}{dt}[/tex] = (rate of salt out) - (rate of salt in)
Rate of salt in = 0.01 kg/litre × 10 litre/min = 0.1 kg/min
Rate of salt out = s/500 kg/litre × 20 litre/min = (20s/500) kg/min
A differential equation can be made on the concept that the rate of change of salt is the difference between the rate of in and the rate of out.
That gives us when combined,
[tex]\frac{ds}{dt} = 0.04s -0.1[/tex]
Now solving this differential equation,
[tex]\frac{ds}{0.04s-0.1} = dt[/tex]
Integrating both sides,
[tex]\int\ {\frac{ds}{0.04s-0.1} } \, = \int dt[/tex]
[tex]\frac{ln(0.04s -0.1)}{0.04} = t+C_{1}[/tex]
[tex]ln(0.04s - 0.1) = 0.04t +0.04C = 0.04t +C_{2}[/tex]
[tex]0.04s - 0.1 =e^{0.04t + C_{2} } =Ae^{0.04t}[/tex]
Now at t = 0, s = 10 kg
0.04(10) - 0.1 = A
A = 0.3
So the differential equation can be written as,
[tex]0.04s - 0.1 = 0.3e^{0.04t}[/tex]
Now time at which no salt is left which means s = 0 at some time t
[tex]0.1 - 0.04(0) = -0.3e^{-20t}[/tex]
The equation is not further solvable as we can see.
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b) 150 g of syrup are needed to make 8 flapjacks.
Find the quantity of oats needed to make 16 of these flapjacks.
Based on the fact that 150g of syrup are needed when making 8 flapjacks, the quantity that is needed to make 16 flapjacks is 300 g.
How to find out quantity needed?The quantity of oats needed to make 8 flapjacks is 150 g.
Assuming direct proportion, the quantity of oats needed to make 16 flapjacks can be found by the formula:
= (Quantity of oats needed for 8 flapjacks x Number of flapjacks to be made) / Number of flapjacks made
Solving for the quantity of oats needed gives:
= (150 x 16) / 8
= 2,400 / 8
= 2,400 x 1/8
= 300 g
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Please answer this question, I need help.
Answer:3 8 10
Step-by-step explanation:
What’s the frequency?
The total frequency of the particular 5 classes (67, 68, 69, 70, and 71) will be 19.
What is the frequency?The quantity of times a specific data value occurs is known as its frequency. We use f to represent a data value's frequency. For instance, grade A is said to have a frequency of five if five students received an A in science.So, the frequency for 5 classes:
Frequency of 67: 4Frequency of 68: 6Frequency of 69: 4Frequency of 70: 4Frequency of 71: 1The total frequency of these particular 5 classes will be:
4 + 6 + 4 + 4 + 1 = 19Therefore, the total frequency of the particular 5 classes (67, 68, 69, 70, and 71) will be 19.
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The price of an item has been reduced by 30% . The original price was $90 . What is the price of the item now?
THE PRICE AT WHICH THW ITEM IS REDUCED BY IS 30% OF $90
[tex] \frac{30}{100} \times \frac{90}{1} \\ = \frac{3}{10} \times 90 = 27[/tex]
THE PRUCE U BEING REDICED BY $27
TO GET THE NEW PRICE OF THE ITEM WE SUBTRACT THE PRICE IT WAS REDUCED BY FROM THE ORIGINAL SELLING PRICE.
[tex] = 90 - 27 \\ = 63[/tex]
NOW THE NEW PRICE OF THE ITEM IS $63
Question
Solve: n- 5/11=-1/3
N=?
Answer: 26/33
Step-by-step explanation:
Step-by-step explanation:
app called maple calculator
186+2947•4194(3.486)x=?
The value of x for the given equation will be -4.3×10⁻⁶.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Arithmetic operation is used to find the value of x in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that,
186+2947•4194(3.486)x
x=-186/2947•4194(3.486)
x=-4.3×10⁻⁶.
Thus, the value of x for the given equation will be 4.3×10⁻⁶.
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A contractor completed five-ninths of a job before a second contractor completed an additional one-third. What fraction of the job is left undone?
[tex]\frac{1}{9}[/tex] fraction of the job is left undone.
What is fraction?Any number of equal parts is expressed by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, represents how many components of a suitable size there are when stated in ordinary English. fraction, A number that is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction occurs in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. a week ago.
Given Data
A contractor completed five-ninths of a job before a second contractor completed an additional one-third.
Total work done is 1.
Contractor and second contractor completed:
= [tex]\frac{5}{9}[/tex] + [tex]\frac{1}{3}[/tex]
= [tex]\frac{5+3}{9}[/tex]
= [tex]\frac{8}{9}[/tex]
Total work done = 1
Work left undone:
= 1 - [tex]\frac{8}{9}[/tex]
= [tex]\frac{1}{9}[/tex]
[tex]\frac{1}{9}[/tex] fraction of the job is left undone.
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The coordinate 3 has a weight of 1 , and the coordinate 6 has a weight of 2 .
For the coordinates and their weights, the weight average is 5
How to determine the weight average?The given parameters are:
Coordinate 3 has a weight of 1
Coordinate 6 has a weight of 2
The weight average is then calculated as:
Weight average = Sum of (Weight * Coordinate)/Sum of Weights
Substitute the known values in the above equation
So, we have the following equation
Weight average = (3 * 1 + 6 * 2)/(1 + 2)
Evaluate the product in the above equation
So, we have the following equation
Weight average = (3 + 12)/(1 + 2)
Evaluate the sum in the above equation
So, we have the following equation
Weight average = (15)/(3)
Evaluate the quotient in the above equation
So, we have the following equation
Weight average = 5
Hence, the weight average of the coordinates is 5
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Complete question
The coordinate 3 has a weight of 1 , and the coordinate 6 has a weight of 2 .
Find the weighted average.
Is trangle ABC ~ trangle XYZ ? if so , what sequence of transformation maps trangle ABC to XYZ
You have the figurew ABC with the following vertices:
A(-2,-4)
B(0,-1)
C(2,-4)
First, multiply all points by 2 (this is the first transformation)
A => A'(-4,-8)
B => B'(0,-2)
C => C'(4,-8)
Next, translate the previous points 6 units upward (which means add 6 units to each y-coordinate).
A' => X(-4,-2)
B' => Y(0,4)
C' => Z(4,-2)
as you can notice, with the previous transformation you obtain the vertices X, Y, and Z and form the figure XYZ.
Answer: a dilation by and a translation
Step-by-step explanation: just did on edge
Point A is at (-1, -9) and point B is at
(2, 4).
What is the midpoint of line segment AB?
-9-8-7 -6 -5 -4 -3 -2
The most appropriate form of midpoint of line segment will be given by-
Coordinate of midpoint of AB = ([tex]\frac{1}{2}, -\frac{5}{2}[/tex])
What is midpoint of a line segment?
At first, it is important to know about section formula. Let the coordinate of end point of a line segment is ([tex]x_1, y_1[/tex]) and ([tex]x_2, y_2[/tex]) respectively. Let another line intersects the line in the ratio m : n. Coordinate of point of intersection =[tex](\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m + n})[/tex].
If m = n =1, we get the coordinate of midpoint.
Coordinate of midpoint = [tex](\frac{x_1+y_1}{2}, \frac{x_2, y_2}{2})[/tex]
Midpoint of a line segment is that point which is equidistant from both the end points.
Here,
Coordinate of A = (-1, -9)
Coordinate of B = (2, 4)
Coordinate of midpoint of AB = ( [tex]\frac{-1 + 2}{2}, \frac{-9 + 4}{2}[/tex])
= ([tex]\frac{1}{2}, -\frac{5}{2}[/tex])
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If 4−5=−12 and y = 3, what is x ?
Substituting y=3 in 4x-5y=-12 we get:
[tex]4x-5\cdot3=-12.[/tex]Simplifying the above equation we get:
[tex]4x-15=-12.[/tex]Adding 15 to the above equation we get:
[tex]\begin{gathered} 4x-15+15=-12+15, \\ 4x=3. \end{gathered}[/tex]Finally, dividing the above equation by 4 we get:
[tex]\begin{gathered} \frac{4x}{4}=\frac{3}{4}, \\ x=\frac{3}{4}\text{.} \end{gathered}[/tex]Answer: If 4x-5y=-12 and y=3 then:
[tex]x=\frac{3}{4}\text{.}[/tex]Over the last three evenings, Karen received a total of 130 phone calls at the call center. The second evening, she received 4 times as many calls as the third evening. The first evening, she received 10 more calls than the third evening. How many phone calls did she receive each evening?
CORRECT ANSWERS ONly
Answer first evening she received 130 second evening she received 520 third evening she received 1300
Step-by-step explanation: that's the right one for shure i worked it out
find the exact perimeter of hexagon ABCDEF plotted below
Perimeter Hexagon = 31.99
perimeter Hexagon = AB+BC+CD+DE+EF+FA
AB= [tex]\sqrt{58[/tex] =7.61
BC = 5
CD = 6
DE = [tex]\sqrt{29}[/tex] =5.38
EF =7
FA= 1
∴ perimeter Hexagon = 31.99
What is hexagon?Hexagons are six-sided polygons in geometry. A hexagon is said to be a regular hexagon if all of its sides and angles have identical lengths. To put it another way, a regular hexagon's sides are congruent.The area of a hexagon is calculated using the formula Area = (33 s2)/2, where s is the length of one of the regular hexagon's sides. The area of a hexagon can also be calculated using the apothem by using the formula Area of hexagon = (1/2) a P, where an is the apothem's length and P is the hexagon's perimeter.To learn more about : Hexagon
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Hi dear! Can you help me to solve exercise #18 please!!!
Hello there. To solve this question, we'll have to remember some properties about dividing polynomials.
Given the polynomials, we want to evaluate the division:
[tex](1+3x+x^4)\div(3-2x+x^2)[/tex]Rewriting it the way we perform long division:
We start with the higher degree terms, namely x^4 and x².
Dividing x^4 by x², we get x². Now we multiply every term from the division by this factor and subtract from the term being divided.
Now, we have a 2x³ as the higher degree term from the term being divided. Dividing it by x², we get 2x. Multiply each term of the divisor and subtract from it.
Finally, the highest degree term from the term being divided is x². Dividing it by x², we get 1. Multiply each term of the divisor and subtract it from the dividend.
Now, the highest degree term from the dividend is -x, when the highest degree term from the divisor is x². We cannot proceed with the long division anymore.
It means that we have a quotient:
[tex]x^2+2x+1[/tex]And a remainder:
[tex]-x-2[/tex]Notice if we rewrite it as:
[tex]x^4+3x^2+1=(x^2-2x+3)\cdot(x^2+2x+1)-x-2[/tex]We have the division P(x)/D(x) written in the form:
[tex]P(x)=D(x)\cdot Q(x)+R(x)[/tex]Where Q(x) and R(x) are the quotient and remainder polynomials.
If a triangle’s original dimensions are 24 cm by 40 cm, which triangle would be an enlargement of the original by a scale factor of 2.2?
The triangle’s enlargement dimensions will be 52.8 cm by 80 cm.
What is scale factor?The size by which the shape is enlarged or reduced is called as its scale factor.
Scale factor is defined as the number or the conversion factor which is used to change the size of a figure without changing its shape.
It is used to increase or decrease the size of an object.
The scale factor can be calculated if the dimensions of the original figure and the dimensions of the dilated (increased or decreased) figure are known.
For example, a rectangle has a length of 5 units and a width of 2 units. Now, if we increase the size of this rectangle by a scale factor of 2, the sides will become 10 units and 4 units, respectively. Hence, we can use the scale factor to get the dimensions of the changed figures.
Given:
A triangle’s original dimensions are 24 cm by 40 cm
scale factor=2.2
Thus,
enlarged dimensions= scale factor x original dimensions
[2.2] x 24 = 52.8 cm
[2.2] x 40 = 80 cm
Hence, the triangle’s enlargement dimensions will be 52.8 cm by 80 cm.
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Find the recursive formula. 2, 32, 62, 92, ...
Answer:
122
Step-by-step explanation:
2+30 =32
32+30=62
62+30=92
Answer:
Use the formula
Step-by-step explanation:
I hope it helps
what is -5 x (- 3/9)
Answer:
Step-by-step explanation:
−5(−3/9)
Divide
-5x(-1/3)
Multiply
−5x(−1/3)
x 5/3
combine multiple terms into single fraction
5x/3
The revenue, R(x), of producing and selling x Awesome Hearing Aids is modeled by the function
R(x) = -3x² + 56x
How many hearing aids need to be produced and sold in order to maximize the revenue? (Round to
the nearest whole number.)
The revenue is at a maximum after
- -
The maximum revenue is $
hearing aids are produced and sold.
What is the revenue? (Round answer to the nearest cent.)
The revenue is at a maximum after x = 9
The maximum is $ 261
9 hearing aids are produced and sold.
The revenue, R(x), of producing and selling 'x' Awesome Hearing Aids is modeled by the function,
R(x) = -3x² + 56x
We need to find the number of hearing aids produced and sold in order to maximize the revenue.
We use the differentiation method to find the maximum of the function R(x).
Differentiate R(x) with respect to x and equate it with 0,
R'(x) = -6x + 56
Then, -6x + 56 = 0
⇒ 6x = 56
⇒ x = 56/6 = 9.33 ≈ 9 [since x is the number of hearing aids]
Now we find the second derivative of R(x) at x = 9.
R''(x) = -6
⇒ R''(9) = -6 < 0
Since R''(9) < 0, the revenue R(x) is maximum at x = 9.
So the maximum revenue is obtained after x = 9.
Therefore maximum revenue = R(9) = -3 x 9²+56 x 9 = $ 261
Hearing aids produced and sold in order to maximize the revenue = 9
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Find the greatest common factor of thefollowing monomials:10x^3y^3 32xy^2
The greatest common factor between the monomials can be determined as,
[tex]\text{GCF}(10x^3y^3,32xy^2)=2xy^2[/tex]Thus, the above expression gives the required greatest common factor.
The height of Debbie is 85 centimetres. The height of Leo is 90 centimetres. Write the height of Debbie as a fraction of the height of Leo. Give your answer in its simplest form.
To write the height of Debbie as a fraction of the height of Leo in its simplest form is this: 17/18.
What does it mean to write a figure as a fraction of another?Writing one figure as a fraction of another can be done by representing the figures as numerators and denominators. In this case, what we will have is 85/90. That is the height of Debbie divided by the height of Leo.
To express this fraction in its simplest form will mean dividing the figures until they can no longer be divided. Using 5 as a common factor for dividing, we can conclude that the simplest form of the answer is 17/18.
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12. Check for Reasonableness Which of the quotients are equivalent to 2.5? Select all that apply.
10/-4
10/4
-10/-4
-5/-2
-5/2
5/2
A coin is weighted so that there is a 58% chance that it will come up "heads" when flipped. The coin is flipped four times. Find the probability of getting two "heads" and two "tails". Round your answer to four decimal places.
P(A) =Probability of heads
P(B) = Probability of tails
P(B)= 1 - P(A) = 1 - 58 = 42%
The events are independent, so, let's assume that we flip the coin and the first two results are heads, so:
P(A) =0.58
Now, let's assume the last two results are tails so:
P(B) = 0.42
Therefore:
[tex]\begin{gathered} P(A\cap A\cup B\cap B)=P(A)\cdot P(A)\cdot P(A)+P(B)\cdot P(B) \\ P(A\cap A\cup B\cap B)=0.58\cdot0.58+0.42\cdot0.42=0.3364+0.1764=0.5128 \end{gathered}[/tex]Find the value of x that makes line u parallel to line v
Answer:
x = 10
Step-by-step explanation:
the angles shown are corresponding angles
corresponding angles are equal
12x - 4 = 10x + 16
subtract 10x from both sides
2x - 4 = 16
add 4 to both sides
2x = 20
divide both sides by 2
x = 10
the equation of a line is y=mx+b. if we know the line passes through (7,8), what does that tell us
The equation of the line is given as y = -2x + 22. This means that when x is equal to zero, y = 22. M also shows how steep the line is, being the gradient.
What is the calculation that justified the above?In order to arrive at a logical solution, we must assume the value of the slope as this is not given.
Assuming the slope of the line is -2, we thus can say:
The equation of a line that passes through a point (x₁,y₁) and a slope m is given by
(y - y1) = m (x - x1)
Recall that the slope, m = -2
While
Point (x1, y1) = (7, 8)
Hence, the equation of the line is:
y-8 = (-2) (x-7)
y-8 = -2x + 14
y = -2x+ 14 + 8
Hence,
y = -2x + 22
Thus, the equation of the line is:
y = -2x + 22
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h, the points A(−5, 6), B(2, 6), C(2, -1) and D(-5, -1) are the vert of a square. what is the area of the square?
Answer:
so find dots, then count how many sections are beetween them, so you will find lenght of every side and use formula to find area(S=a²+b²).
The standard form for a parabola with vertex (h,k) and an axis of symmetry of y=k is:(y-k)^2=4p(x-h)The description below is for a parabola. Write it in standard form. When answering the questions type coordinates with parentheses and separated by a comma like this (x,y). If a value is a non-integer then type is a decimal rounded to the nearest hundredth.Vertex is (2,2); directrix is x=2-\sqrt[]{2}, focus is (2+\sqrt[]{2},2)The value for p is: AnswerThe value for h is: AnswerThe value for k is: Answer
Given that a parabola has
[tex]\begin{gathered} Vertexis(2,2) \\ directrix\text{ }is\text{ }x=2-\sqrt[]{2} \\ focus\text{ }is\text{ }(2+\sqrt[]{2},2) \end{gathered}[/tex]And that the standard form of a parabola can be expressed as
[tex]\mleft(y-k\mright)^2=4p\mleft(x-h\mright)[/tex]We are asked to find the value of p, h and k. This can be seen below.
Explanation
Recall, If a parabola has a horizontal axis, the standard form of the equation of the parabola is this
[tex](y-k)^2=4p(x-h)[/tex]where p≠ 0. The vertex of this parabola is at (h, k). The focus is at (h + p, k). The directrix is the line x = h - p. The axis is the line y = k. If p > 0, the parabola opens to the right, and if p < 0, the parabola opens to the left.
Value of h and k
By comparison
[tex]\begin{gathered} \text{Vetex = (h,k) = (2,2)} \\ \therefore h=2;k=2 \end{gathered}[/tex]Answer: h = 2 and k =2
Value of p
Also, by comparison
[tex]\begin{gathered} focus=(h+p,k)=(2+\sqrt[]{2},2) \\ \therefore p=\sqrt[]{2}=1.41 \\ \end{gathered}[/tex]Answer : p =1.41
Writing the equation of the parabola in standard form
We can then use the given data to express the parabola in standard form as;
Answer
[tex](y-2)^2=4\sqrt[]{2}(x-2)[/tex]Find the circumference of a circular swimming pool with a radius of 8.5 yards. Use 3.14 as an approximation for pie. Round your answer to the nearest whole yard. Enter only the number.
Answer:
53 yards
Step-by-step explanation:
Hello!
The circumference formula of a circle is [tex]C = 2\pi r[/tex], where C is the circumference, and r is the radius.
Given that pi is 3.14, solve for the circumference.
Solve for C[tex]C = 2\pi r[/tex][tex]C = 2(3.14)(8.5)[/tex][tex]C = 53.38[/tex]The circumference of the circle is 53.38, but rounded to the nearest whole yard would be 53 yards.
Please help me out, I need to turn it in in 15 mins
What is their rate of change (speed) in Section D (Hours 7-10)? Remember to include units.
Step-by-step explanation:
I assume the hours are also in units of 2.
that means in D the distance is -20 miles in 10 hours or
-20 miles / 10 hours = -2 miles / hour
What equation would you set up to solve for X?
Sales of SUVs (sport utility vehicles) in the United States (in millions) for the years 1990-1999 can be modeled by the quadratic equation shown below.y = 0.016x^2 +0.124x +0.787Here x = 0 represents 1990, x = 1 represents 1991, and so on. Use the model to approximate sales in 1995, Sales in 1995 were approximately ____ million SUVs.(Round to the nearest tenth as needed.)
The sales in 1995 were approximately 1.8 millions.
Explanation:
Since x = 0 is 1995, x = 1 is 1991 and so on, if we want to find the approximate amount of sales, we need to evaluate the expression for x = 5:
[tex]y=0.016x^2+0.124x+0.787[/tex][tex]\begin{gathered} y=0.016\cdot5^2+0.124\cdot5+0.787 \\ y=0.016\cdot25+0.62+0.787 \\ y=0.4+0.62+0.787 \\ y=0.4+0.62+0.787 \\ y=1.807 \end{gathered}[/tex]To the nearest tenth, the sales of SUV were approximately 1.8 millions