Answer:
[tex]{ \tt{ \frac{dy}{dx} + 2x + 1 = 2 }} \\ \\ { \tt{ \frac{dy}{dx} = - 2x + 1 }} \\ \\ { \tt{dy = ( - 2x + 1) \: dx}} \\ \\ { \tt{ \int dy = \int( - 2x + 1) \: dx}} \\ \\ { \tt{y = - {x}^{2} + x + c}} \\ \\ { \tt{y = - x(x + 1) + c}}[/tex]
Answer:
[tex]y=-x^2+x+\text{C}[/tex]
Step-by-step explanation:
Given equation:
[tex]\dfrac{\text{d}y}{\text{d}x}+2x+1=2[/tex]
[tex]\text{Isolate $\dfrac{\text{d}y}{\text{d}x}$}:[/tex]
[tex]\implies \dfrac{\text{d}y}{\text{d}x}+2x+1-2x-1=2-2x-1[/tex]
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=-2x+1[/tex]
Multiply both sides by dx to get all the terms containing y on the left side, and all the terms containing x on the right side:
[tex]\implies \text{d}y=(-2x+1)\;\text{d}x[/tex]
Integrate both sides:
[tex]\implies \displaystyle \int 1\;\text{d}y=\int(-2x+1)\;\text{d}x[/tex]
Fundamental Theorem of Calculus
[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
Integrate each term separately:
[tex]\implies \displaystyle \int 1\;\text{d}y=\int -2x\;\text{d}x+\int 1\;\text{d}x[/tex]
Take the constant outside the integral:
[tex]\implies \displaystyle \int 1\;\text{d}y=-2\int x\;\text{d}x+\int 1\;\text{d}x[/tex]
Integrate, using the rules given below:
[tex]\implies y=-2 \cdot \dfrac{1}{1+1}x^{(1+1)}+x+\text{C}[/tex]
[tex]\implies y=-x^2+x+\text{C}[/tex]
Integration rules:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Integrating a constant}\\\\$\displaystyle \int n\:\text{d}x=nx+\text{C}$\\(where $n$ is any constant value)\end{minipage}}[/tex]
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Find the equation (in terms of x ) of the line through the points (-2,-2) and (3,-1)
Answer:
Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.
First find the gradient.
Formula of gradient is given as (y2-y1)÷(x2-x1) or (y1-y2)÷(x1-x2)
Gradient = (-1-(-2))÷(3-(-2))
= (-1+2)÷(3+2)
= 1/5
Equation is y = 1/5 + c
Substitute either one of the points into the equation to find c.
-2 = 1/5(-2) + c
c = -8/5
Hence equation of the line is y = 1/5x - 8/5
Simplify.
7a²+ 3b +6a-2a²
A.a² + 3b-2
B. 5a² + 3b + 6a
C.9a² + 3b + 6a
D. 11a²+ 3b +6
Answer:
B. 5a² + 3b + 6a
Step-By-Step Explanation:
First, see what has like terms. 7a² and -2a² both have the exponent 2 and the letter a, so you can combine those to get 5a². 3b and 6a cannot be combined because they have a different letter. So, 5a² + 3b + 6a is your answer.
What quantity of water should be added to reduce 9 liters of 50% acidic liquid to 30% acidic liquid ?
Answer:
6 liters
Step-by-step explanation:
Given:
The 9 litre of 50% acidic liquid.
Required:
What quantity of water should be added to reduce 9 liters of 50% acidic liquid to 30% acidic liquid ?
Explanation:
The solution steps are:
Acidic liquid in 9 liters lotion = (50/100) * 9 = 4.5 liters
Then water = 9 - 4.5 = 4.5 liters
Let 'x' liters be the required quantity of water.
Then :-
[tex]\frac{4.5}{9+x} = \frac{30}{100} = \frac{3}{10}[/tex]
That leads to :-
[tex]3(9+x) = 45 == > 3x = 18[/tex]
Which gives us :-
[tex]x=6[/tex]
Thus required quantity of water = 6 liters
Final answer:
6 liters
(Hi fyi this answer took a lot of time & effort to make sure it was accurate, precise and to the point to be produced, so if you could opt this answer as the brainliest it would mean the world to me,)
Stay positive and Take care,
A fellow mate,
Cheers !
Christopher decides that another road to be named Saturn Avenue will go past the cleaners and be perpendicular to planet drive. Determine the equation of the line that represents Saturn Avenue.
The equation of the line that represents Saturn Avenue is; y = 4.
Determine the line's equation?The equation of a line can be ascertained using the formula,
y = mx + c
where m is the line's slope and c is just the y - intercept.
m = vertical change/ horizontal change
m = Δy/Δx
m = (y₂ - y₁)/(x₂ - x₁)
In this question, draw a line through the cleaners as well as perpendicular to Planet Drive.
The point at which x = 0 is known as (0, 4).This means that the y - intercept is four.We can discover the slope of the equation by contemplating two points just on line.
Consider the following points: (8, 4) and (16, 4).
Put the value sin slope.
m = (4 - 4)/(16 - 8)
m = 0/8
m = 0
So we got that,
y - intercept = 4
slope = 0
Put back the values in equation of line.
y = mx + c
y = (0)x + 4
y = 4
As a result, y = 4 is the equation of the line which represents Saturn Avenue, given that Christopher decides that another road named Saturn Avenue, which will run past this same cleaners and be perpendicular to Planet Drive, is required.
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Find the slope of the line graphed below.
Answer:
The slope is -5/2
Step-by-step explanation
I tried to show how I solved this problem in the image, but its not too great, so I hope this helps. :)
Given the diagram below, find the measure of each missing angle.
The scale factor of model of Eiffel tower is 3:1640.
The scale factor is the ratio of measure of small length to large length. The base of both actual tower and scale down model is mentioned in question. Keep the values in ratio to find the scale factor.
Scale factor = 0.75 : 410
Removing decimal to get the whole number
Scale factor = 75:41000
Dividing the both parts of ratio by 25 to find the scale factor of mentioned model
Scale factor = 3:1640
As the Eiffel tower is scaled down in the model, the scale factor is 3:1640.
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where is ( -3 1/2, -1 1/4 ) on the coordinate plane?
The point ([tex]-3\frac{1}{2}[/tex], [tex]-1\frac{1}{4}[/tex] ) on the coordinate plane is shown in the figure .
The Coordinate plane can be defined as a 2 D plane formed by the intersection of two line ,
where the horizontal line is called x axis and
the vertical line is called y axis .
In the question ,
the point is given
the point is ([tex]-3\frac{1}{2}[/tex] , [tex]-1\frac{1}{4}[/tex] )
writing the mixed fraction in decimal form , we get
x coordinate = [tex]-3\frac{1}{2}[/tex] ⇒ -(3*2+1)/2 = -7/2 = -3.5
y coordinate = [tex]-1\frac{1}{4}[/tex] ⇒ -(1*4+1)/4 = -5/4 = -1.25
So, the point to be plotted on the coordinate plane becomes (-3.5,-1.25)
the points plotted are shown in the figure below .
Therefore , the point ( [tex]-3\frac{1}{2}[/tex], [tex]-1\frac{1}{4}[/tex] ) on the coordinate plane is shown in the figure .
The given question is incomplete , the complete question is
Where is ([tex]-3\frac{1}{2}[/tex] , [tex]-1\frac{1}{4}[/tex] ) on the coordinate plane?
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The Maybe Pay Life Insurance Company is trying to sell you an investment policy that will pay you and your heirs $37,000 per year forever. Assume the required return on this investment is 6.2 percent. How much will you pay for the policy?
Percentage - The amount to pay for the policy $596,774.19
What is Percent ?
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a measurement system.
Given that,
Investment policy pay
PV = $37,000 year;
investment return: 6.2%
r = 6.2%
r = 6.2/100
r = 0.062
We must use one year as the number of periods even if we just need to calculate the value for one year. We employ: to determine the FV of a lump sum.
FV=PV/r
FV=37,000/0.062
FV= $596774.1935
to 2 decimal point
FV=$596,774.19
Hence, $596,774.19 is to pay for the policy
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Please help I’ll mark you as brainliest if correct!!
Answer:
a) 27 b) 5 c) 16 d) 7
Step-by-step explanation:
There are 3030 stuffed animals in a gift gallery.
Seven more stuffed animals added to the collection.
Find the total number of animals.
Answer:
Answer:
3037 trttthdhsbdhwhsshs
A soccer ball is kicked from the ground by the goalie and lands 40 meters from where it waskicked. The ball's path is that of a parabola, and the ball reaches a maximum height of 3 meters,How far from where the ball was kicked will it have a height of 2 meters? (Round your answer tothe nearest tenth.)
Given:
The distance travelled by the ball is, d = 40 m.
The maximum height the ball reached is, h = 3 m.
The objective is to find the distance travelled by the ball at a height of h' = 2 m.
. (vertex)
n, the
The value of x can be calculated using the general form of the equation of parabola,
[tex]y=a(x-p)^2+q[/tex]Here, (p,q) stands for the vertex of the parabola (20,3).
To find the value of a, consider a coordinate (0,0) and substitute the obtained values in the general equation of parabola.
[tex]\begin{gathered} 0=a(0-20)^2+3 \\ 0=a(400)+3 \\ -400a=3 \\ a=-\frac{3}{400} \end{gathered}[/tex]Now, consider the coordinate of the required distance x of the ball, (x,2).
Substitute the above coordinate, the value of a and the vertex in the equation of parabola.
[tex]\begin{gathered} y=a(x-p)^2+q \\ 2=-\frac{3}{400}(x-20)^2+3^{} \\ 2=-\frac{3}{400}(x-20)^2+3 \\ 2-3=-\frac{3}{400}(x-20)^2 \\ -1=-\frac{3}{400}(x-20)^2 \\ (\frac{400}{3})=(x-20)^2 \end{gathered}[/tex]To solve the square on RHS, take square root on both sides of the equation.
[tex]\begin{gathered} \sqrt[]{\frac{400}{3}}=\sqrt[]{(x-20)^2} \\ 11.5=(x-20) \\ x=11.5+20 \\ x=31.5\text{ m} \end{gathered}[/tex]Since, the height of 2 m of ball can be obtained at either side of the vertex.
So the distance between the vertex and the required position is
[tex]\begin{gathered} c=31.5-20 \\ c=11.5 \end{gathered}[/tex]Then, the other possible position of the ball is,
[tex]\begin{gathered} x^{\prime}=20-c \\ x^{\prime}=20-11.5 \\ x^{\prime}=8.5 \end{gathered}[/tex]Hence, the height of the ball will be 2m, either at a distance of 8.5m from origin or 31.5m from the origin.
Please help I don’t know how to solve this
(a) 291/2020
Divide the total for the 10-14 year column by the total.
(b) 77/465
There are 465 people from the east, 77 of which were loyal for 10 to 14 years
(c) 437/1010
There are 291+583=874 people who were loyal for at least 10 years. Divide this by the total of 2020 people.
(d) 145/376
376 people are from the West, (45+100)=145 of which are at least 10.
(e) 32/157
157 people were loyal for less than a year, 32 of which were from the East.
(f) 53/157
157 people were loyal for less than a year, 53 of which were from the South.
(g) 433/465
465-32=433 people were loyal for at least 1 year out of the 465 people from the East.
(h) 335/376
376-41=355 people were loyal for at least 1 year out of the 376 people from the West.
The U.S. Energy Information Administration (US EIA) reported that the average price for a gallon of regular gasoline is $3.91. The US EIA updates its estimates of average gas prices on a weekly basis. Assume the standard deviation is $.24 for the price of a gallon of regular gasoline and recommend the appropriate sample size for the US EIA to use if they wish to report each of the following margins of error at 95% confidence. Round up to the next whole number.
a. The desired margin of error is $0.11 The appropriate sample size is
.
b. The desired margin of error is $0.07 The appropriate sample size is
.
c. The desired margin of error is $0.04 The appropriate sample size is
.
How many peanuts would Eric need to make 5 batches of trail mix?
hello! it would help if you gave more information so we could better answer the question ^^
i need help with this question please
Answer:
espiritu satninon
Step-by-step explanation:
The first three terms of an arithmetic sequence are x, 2x + 4, 5x. Find the value of x.
P
Answer:
x = 4
Step-by-step explanation:
You want to know the value of x in the arithmetic sequence x, 2x+4, 5x.
Arithmetic sequenceTerms of an arithmetic sequence have a common difference. This means ...
(2x+4) -x = 5x -(2x+4)
x +4 = 3x -4 . . . . . . . . . . simplify
8 = 2x . . . . . . . . add 4-x
4 = x . . . . . . divide by 2
The value of x is 4.
__
Additional comment
The common difference is x+4 = 8. The sequence is ...
4, 12, 20, ...
Bertha and Vernon are competing in a diving competition. Bertha's dive ended -25 m from the starting platform. Vernon's dive ended -5 m from the starting platform. How many times farther was the end of Bertha's dive than the end of Vernon's dive?
Bertha's dive is 5 times farther than the end of Vernon's dive
What is ratio?A ratio can defined mathematical as an ordered pair of numbers, like variables b and c, when written form b / c with the denominator greater than the value zero.
It explains how many times a particular number is composed of another number in a given proportion.
It is also seen as the comparison of two quantities, elements or numbers having the same unit measure. It goes further to explain how much of one of the element or quantity contains another.
This is done on the basis of their magnitude or sizes.
Given that;
Bertha's dive ended = -25 m
Vernon's dive ended = -5 m
Divide the values
= -25/-5
= 5 times
Hence, the value is 5 times
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Consider the integral - tan(0) · ln(3 cos(0)) dė:
.
This can be transformed into a basic integral by letting
In (3 cos (0))✓ O O and
U=
du = -tan (0)✓o de
After perfroming the substitution, you obtain the integral
du
[tex]\displaystyle \int -\tan(\theta )\cdot \ln(3\cos(\theta )) ~~ d\theta \\\\[-0.35em] ~\dotfill\\\\ u=\ln(3\cos(\theta ))\implies \cfrac{du}{d\theta }=\cfrac{1}{3\cos(\theta )}\cdot -3\sin(\theta ) \\\\\\ \cfrac{du}{d\theta }=-\tan(\theta )\implies \cfrac{du}{-\tan(\theta )}=d\theta \\\\[-0.35em] ~\dotfill\\\\ \displaystyle \int -\tan(\theta )\cdot u\cdot \cfrac{du}{-\tan(\theta )}\implies \int u\cdot du[/tex]
Which of the following is an equivalent expression of 15x2 +12x + 8?
27x3 + 8
15x2(12x + 8)
12x + 15x2 + 8
8(15x2 + 12x)
The option that is an equivalent expression of 15x² +12x + 8 is C. 12x + 15x² + 8.
What is an equivalent expression?Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same values for the variable, two algebraic expressions that are equivalent have the same values.
If two systems of equations have the same solution, they are equivalents. In algebra, 2(2x - 3y + 6) is equal to 4x -6y + 12 as an example of an equivalent expression.
In this case, it should be noted that 15x² +12x + 8 is the same as 12x + 15x² + 8. Therefore, the correct option is C.
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Evaluate Piecewise Functions. (Everything you need to know is in the photo. You can also use the word "undefined" next to the answer only if necessary).
Answer:
f(-1) = 6
Explanation:
Looking at the piecewise function given, we see that
f(x) = -3x -5
for x different from -1
And
f(x) = 6
for x = -1
So, we choose the suitable one, since x = -1
Find the GCF of 10, 30, 50
The GCF of 10, 30, and 50 is 10.
What is GCF?The GCF (Greatest Common Factor) of two or more numbers is the biggest number among all the common factors of the given numbers.The GCF is the largest integer that can be utilized to divide the two natural integers x and y without leaving any remainders.Given numbers are 10, 30, and 50.
To calculate the Greatest Common Factor of the numbers, list the prime factors of each number.
10 = 2 × 5
30 = 3 × 2 × 5
50 = 2 × 5²
GCF is the result of the factors that each of the given numbers has in common.
So, GCF = 2 × 5 = 10
Therefore, 10 is the greatest positive integer that divides 10, 30, and 50 without leaving any remainder.
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Please help, hurry due today
Which relation is a function?
Answer:
c
Step-by-step explanation:
Help!!! Giving 25 points!
The system of linear equations and their solutions are:
1. (51, 26): x - y = 25; 2x + 3y = 180
2. (-17, -36): x - y = 19; -2x + y/6 = 28
3. (47, 33): 2x - 3y = -5; x + y/11 = 50
4. (-31, -56): 2x - y = -6; x - 305/3 = 2y.
How to Solve a System of Equations?We can solve a system using the substitution method by finding the value of one of the variables, followed by substitution.
1. x - y = 25 -- eqn. 1
2x + 3y = 180 -- eqn. 2
Rewrite eqn. 1:
x = 25 + y
Substitute x = 25 + y into eqn. 2:
2(25 + y) + 3y = 180
50 + 2y + 3y = 180
5y = 180 - 50
5y = 130
y = 26
Substitute y = 26 into eqn. 1:
x - 26 = 25
x = 25 + 26
x = 51
The solution is: (51, 26).
2. x - y = 19 -- eqn. 1
-2x + y/6 = 28 -- eqn. 2
Rewrite eqn. 1:
x - y = 19
x = 19 + y
Substitute x = 19 + y into eqn. 2:
-2(19 + y) + y/6 = 28
-38 - 2y + y/6 = 28
-11y/6 = 28 + 38
-11y/6 = 66
-11y/6 (-6/11)= 66(-6/11)
y = -36
Substitute y = 36 into eqn. 1:
x - y = 19
x - (-36) = 19
x + 36 = 19
x = 19 - 36
x = -17
The solution is: (-17, -36).
3. 2x - 3y = -5 -- eqn. 1
x + y/11 = 50 -- eqn. 2
x + y/11 = 50
x = 50 - y/11
Substitute x = 50 - y/11 into eqn. 1
2(50 - y/11) - 3y = -5
100 - 2y/11 - 3y = -5
-35y/11 = -5 - 100
-35y/11 = -105
-35y/11(-11/35) = -105(-11/35) (multiplication property)
y = 33
Substitute y = 33 into eqn. 2:
x + 33/11 = 50
x + 3 = 50
x + 3 - 3 = 50 - 3
x = 47
The solution is (47, 33).
4. Solving the last one, we will definitely have the solution, (-31, -56).
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TRUE OR FALSE NEED NOW
Answer:
False
Step-by-step explanation:
No data points pass through 2 or more vertical lines
QUESTION DOWN BELOW! PLEASE HELP WILL GET 100 POINTS IM STUCK PLEASE HELP EXPLAIN ITS DUE SOON!!
many thanks!!!
1) given
2) base angles theorem
3) PN=QN
4) [tex]\angle 3=\angle 4[/tex]
5) MP=OQ
7) PQ, QP
8) MQ=PO
9) ASA
Due to traffic congestion the bus took 20% more timeto travel and took 180 minutes to travel between twocitiies. What could have the time of travel, if therewas no traffic congestion?
Solution:
First of all, we must find the 20% of 180 minutes:
180 x 0.20 = 36 minutes.
That means that the bus takes an extra 36 minutes in traffic. So that, if there
was no traffic congestion the total time is:
180-36 = 144 minutes.
So that, we can conclude that the correct answer is:
144 minutes.
What is the scale of triangle AJV TO TRIANGLE A’J’V ?
Answer:
Explanations:
Dilation is a transformation technique that changes the size of an object in a xy-plane.
From the given figure, there was an enlargement from AJV to A'J'V'. This shows that the scale factor is greater than 1:
Using one of the coordinates V and V'
V = (0, 1)
V' = (0, 4)
Determine the scale factor
Scale factor = V'/V
Scale factor = 4/1
Scale factor = 4
Hence the scale factor of triangle AJV till A'J'V' is 4
Vince wants to make a square patio in his yard. He has enough concrete to pave an area of 378 square feet. How long can a side of his patio be? Use radical equation to solve. Round answer to the nearest tenth.
The side length of his patio will be 3·√42 ft long.
What is the area of a square?The area of a square can be calculated as the square of the sides of a given figure.
The area of a square = side x side
Given that Vince wants to make a square patio in his yard and has enough concrete to pave an area of 378 square feet
The parameters given are;
The Area of the square patio = 378 square feet
Lets 's' be the side of the square;
Therefore, the dimensions of the sides of a patio that has an area of 378 ft.² is ;
s² = 378
Take square root on both sides
Therefore, s = √378
s = √(9 × 42)
s = 3·√42 ft
Hence, The side length of his patio will be 3·√42 ft long.
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The diagram shows a prism placed on a horizontal floor
The prism has height 3 m
The volume of the prism is 18m³
The pressure on the floor due to the prism is 75 newtons/m²
Work out the force exerted by the prism on the floor.
The force exerted by the prism on the floor = 450N
Given: height = 3m, volume = 10m³
Pressure = 75 N/m², prism
To find force
Solution:
Volume of prism = Area of base x height
= Аrеа х 3
Area = 18 = 6m²
Now,
Pressure: force / Area ⇒ 75 = force 6
force= 75×6 = 450N.
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How do I solve this?
The average rate of change from
3 to 5 is -16.
0 to 2 is -4
-3 to 0 is -6.
What is average rate of change?It represents the typical amount by which the function changed for each unit over that time. On the function graph, it is calculated using the slope of the line connecting the interval's ends.
Given Data
Equation = 4 -2x²
Formula-
[tex]\frac{f(a)-f(b)}{a-b}[/tex]
a)To find the average rate of change from 3 to 5
a = 5, b = 3
Equating values in the formula
[tex]\frac{4-2(5^{2} )-(4-(3)}{5-3}[/tex]²
[tex]\frac{-46+14}{2}[/tex]
-[tex]\frac{32}{2}[/tex]
-16
The average ROC 3 to 5 is -16.
b) The average ROC from 0 to 2
a = 2 b=0
Equating values in the formula
[tex]\frac{4-2(2^{2})-(4-2(0) }{2-0}[/tex]
[tex]\frac{-4-4}{2}[/tex]
[tex]\frac{-8}{2}[/tex]
-4
The average ROC from 0 to 2 is -4
c)The average ROC from -3 to 0
a= 0 b = -3
Equating values in the formula
[tex]\frac{4-2(0)-(4-2(3^{2} )}{-3-0}[/tex]
[tex]\frac{4+14}{-3}[/tex]
-[tex]\frac{18}{3}[/tex]
-6
The average ROC from -3 to 0 is -6.
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