Linear approximation to g(x) at x=0:
For this, we will require to compute g(0), g'(0), and use the formula g(x) ≈ g(0) + g'(0)x.
Let's first find g(0):
g(0) = 3(0) + 4cos(1/2(0)) = 4
Next, let's find g'(x):
g(x) = 3x + 4cos(1/2 x)
g'(x) = 3 - 2sin(1/2 x)
Evaluate g'(0):
g'(0) = 3 - 2sin(1/2(0)) = 3
So we have the linear approximation around x=0:
g(x) ≈ 4 + 3x.
Approximating 3(0.2) + 4cos(0.1) using linear approximation:
We will use the result from the first part:
g(x) ≈ 4 + 3x, so that g(0.2) ≈ 4 + 3(0.2) = 4.6
Now we will approximate 4cos(0.1) by using the linear approximation of cos(x) at x=0, which is:
cos(x) ≈ 1 - x
So that cos(0.1) ≈ 1 - 0.1 = 0.9
Now we use these approximations to approximate 3(0.2) + 4cos(0.1):
3(0.2) + 4cos(0.1) ≈ 3(0.2) + 4(0.9) = 1.8 + 3.6 = 5.4
The approximation is 5.4.
A particle moves in such a way that at times t, its velocity is given by v(t) = 4e^(t/4) - 4 (cm/s). What is the displacement of the particle during the first 2 seconds?
The velocity is given by v(t) = 4e^(t/4) - 4. This is a continuous function, so we can calculate the displacement by finding the antiderivative of the velocity function and evaluating it between the limits of 0 and 2.
We can also notice that the velocity function is the derivative of the displacement function, so the displacement function is simply the antiderivative of the velocity function: s(t) = ∫v(t) dt.
Let's compute the displacement for the first 2 seconds by evaluating the antiderivative between 0 and 2. We can use the formula for the antiderivative of an exponential function ∫e^x dx = e^x + C.
s(t) = ∫v(t) dt = 4e^(t/4) - 4t + C
The constant of integration is arbitrary and we will determine it by using the initial condition that s(0) = 0:
s(0) = 4e^(0/4) - 4(0) + C = 4 - 0 + C = 4 => C = 0
Now we have:
s(t) = 4e^(t/4) - 4t
The displacement for the first 2 seconds is:
s(2) - s(0) = (4e^(2/4) - 4(2)) - (4e^(0/4) - 4(0)) = (4e^(1/2) - 8) - 4 = 4
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Find the equation of the line shown.
y
10
655521 LEO
O
1 2 3 4 5 6 7 8 9 10
X
The equation of the line shown is y = 1x + 9.
What is the equation?An equation is a statement of equality between two expressions. It is typically expressed in mathematical notation, with the left side of the equation equal to the right side. Equations are used to describe how two values are related, and can be used to solve problems or predict outcomes. Equations can be used in any field of study, from physics to economics.
The equation of the line shown can be found by using the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is m = (10 - 9)/(10 - 0) = 1.
The y-intercept is b = 9, as this is the point at which the line crosses the y-axis. Therefore, the equation of the line shown is y = 1x + 9.
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Complete questions as follows-
this is happening do proper format and calculation
Find the equation of the line shown.
y
10
S87654321
9
0 1 2 3 4 5 6 7 8 9 10
X
Reed's number cube numbered (1, 2, 3, 4, 5, 6) is rolled and a spinner with 4 sections (A, B, C, D) is spun. P(1 and A)
The probability of rolling a 1 and spinning section A on the spinner is 1/24.
To find the probability of rolling a 1 and spinning section A on the spinner, we need to first determine the total number of possible outcomes for the experiment. The number cube has 6 possible outcomes, and the spinner has 4 possible outcomes. Therefore, the total number of possible outcomes for the experiment is 6 x 4 = 24.
Next, we need to determine the number of outcomes that meet the criteria of rolling a 1 and spinning section A. Rolling a 1 has a probability of 1/6, and spinning section A has a probability of 1/4.
The probability of both events occurring simultaneously is the product of the two probabilities, which is (1/6) x (1/4) = 1/24.
This means that out of the 24 possible outcomes, only one outcome will result in rolling a 1 and spinning section A on the spinner.
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Complete Question:
A number cube numbered (1, 2, 3, 4, 5, 6) is rolled and a spinner with 4 sections (A, B, C, D) is spun. Find the probability of P(1 and A).
A(-1, 2) and C(3, 4) are opposite vertices of a rhombus ABCD. Find the coordinates of the points where the diagonals intersect
Since M and N have the same coordinates, we know that AC and BD intersect at the point (1,3). The coordinates of the intersection point are (1,3).
What is rhombus?
A rhombus is a special type of parallelogram in which all four sides are of equal length. Equivalently, a rhombus is a quadrilateral with four sides of equal length.
Since ABCD is a rhombus, its diagonals AC and BD are perpendicular bisectors of each other, and they intersect at their mutual midpoint M.
The midpoint M of AC is the average of the coordinates of A and C, namely:
M = ((-1+3)/2, (2+4)/2) = (1, 3)
Similarly, the midpoint of BD is the average of the coordinates of B and D. Since we don't know the coordinates of B and D, we need to find them first.
The other two vertices of the rhombus are obtained by reflecting A and C about the midpoint M, since opposite sides of a rhombus are parallel and equal in length. To do this, we subtract the coordinates of M from those of A and C, and then add them to M:
B = 2M - A = 2(1,3) - (-1,2) = (3,4)
D = 2M - C = 2(1,3) - (3,4) = (-1,2)
Now we can find the midpoint of BD:
N = ((3-1)/2, (4+2)/2) = (1, 3)
Since M and N have the same coordinates, we know that AC and BD intersect at the point (1,3). Therefore, the coordinates of the intersection point are (1,3).
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Nrite equations of the lines through the given point parallel to and perpendicular to the given li x+y=3,(-3,2)
Answer:
vfejwbjelkn
Step-by-step explanation:
You are designing an icon for a mobile app. Use the provided ruler to answer the following questions.
a. Find the perimeter and area of the icon in the scale drawing. Round the measurements for the length and the width to the nearest half centimeter to calculate your answers.
The perimeter in the scale is ___ centimeters
The area in the scale drawing is __ square centimeters.
b. Find the actual perimeter and area of the icon.
The actual perimeter is ___ millimeters.
The actual area is ___ square millimeters.
a. The perimeter in the scale is 36 centimeters
The area in the scale drawing is 80 square centimeters.
b. The actual perimeter is 40 millimeters.
The actual area is 937.5 square millimeters.
To find the perimeter of the icon in the scale drawing, you need to add up the length of all its sides. Using the ruler provided, measure the length and width of the icon and round them to the nearest half centimeter. Then, add up the length and width and multiply by 2 to get the perimeter.
a. Assuming the scale of the drawing is 1 cm : 2 units, the length of the icon in the drawing would be 2 x 5 = 10 units and the width would be 2 x 4 = 8 centimeters.
The perimeter in the scale drawing would be 2 x (length + width) = 2 x (10 + 8) = 36 cm (rounded to the nearest half-centimeter).
The area in the scale drawing would be length x width = 10 x 8 = 80 square cm.
b. Assuming the scale of the drawing is 1 cm : 2 units, the actual length of the icon would be 2.5 cm / 2 = 1.25 units and the actual width would be 1.5 cm / 2 = 0.75 units.
The actual perimeter would be 2 x (length + width) = 2 x (1.25 + 0.75) = 4 cm = 40 mm.
The actual area would be length x width = 1.25 x 0.75 = 0.9375 square cm = 937.5 square mm.
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help plsss its due today
The equation of line is y = -3x + 2
Define equation of variable?An equation for two variables is a mathematical statement that relates two variables, typically represented by x and y, using mathematical symbols and operations such as addition, subtraction, multiplication, and division.
To find the equation of the line that passes through the given points (2, -4), (3, -7), (4, -10), and (5, -13), we can use the slope-intercept form of the equation of a line:
y = mx + b, where slope of the line is m and y-intercept is b.
First, let's find the slope of the line using two of the points, say (2, -4) and (3, -7). The slope, m, is given by:
m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
= (-7 - (-4)) / (3 - 2)
= -3
we know the slope, we can use one of the points, say (2, -4), and the slope to find the y-intercept, b. Use the slope intercept to form the equation of a line:
y = mx + b, and substitute in the slope and coordinates of one of the points:
-4 = (-3)(2) + b
Simplifying this equation, we get:
b = -4 + 6
= 2
Therefore, the equation of the line that passes through the given points (2, -4), (3, -7), (4, -10), and (5, -13) is: y = -3x + 2
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The graph is a translation of one of the basic functions , , , . Find the equation that defines the function.
Watch help video Given f(x)=x^(3)+kx+9, and the remainder when f(x) is divided by x-3 is 27 , then what is the value of k ?
When f(x) is divided by x-3 is 27 , then what is the value of k is -3
What is remainder theοrem?Remainder Theοrem is an apprοach οf Euclidean divisiοn οf pοlynοmials. Accοrding tο this theοrem, if we divide a pοlynοmial P (x) by a factοr ( x – a); that isn’t essentially an element οf the pοlynοmial; yοu will find a smaller pοlynοmial alοng with a remainder.
When f(x) is divided by x - 3, the remainder is 27, which means that
f(3) = 27.
We can use this fact tο sοlve fοr k as fοllοws:
f(x) = x³ + kx + 9
f(3) = 27
Substituting x = 3 intο the expressiοn fοr f(x), we get:
f(3) = 3³ + k(3) + 9 = 27
Simplifying the left side, we get:
27 + 3k + 9 = 27
Cοmbining like terms, we get:
3k + 36 = 27
Subtracting 36 frοm bοth sides, we get:
3k = -9
Dividing bοth sides by 3, we get:
k = -3
Therefοre, the value οf k is -3.
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Solve the system of equations.
x + y = 8
y = x2 – 4
a. (3, 5) and (–4, 12)
b. (–3, 11) and (4, 4)
c. (4, 4) and (5, 3)
d. (12, –4) and (7, 1)
The solution of the system of equation is (3, 5) and (–4, 12) [option A]
The given system of equations is:
x + y = 8
y = x² – 4
To solve for x and y, we can substitute the second equation into the first equation for y:
x + (x² - 4) = 8
Simplifying, we get:
x² + x - 12 = 0
Now we can use the quadratic formula to solve for x:
x = (-b ± √(b² - 4ac)) / 2a
where a = 1, b = 1, and c = -12
x = (-1 ± √(1² - 4(1)(-12))) / 2(1)
x = (-1 ± √(1 + 48)) / 2
x = (-1 ± 7) / 2
Solving for x gives us two possible values: x = 3 or x = -4.
To find the corresponding values of y for each value of x, we can substitute them into either of the original equations. Using y = x² - 4:
When x = 3, y = 3² - 4 = 5
When x = -4, y = (-4)² - 4 = 12
Therefore, the solution to the system of equations is (3, 5) and (-4, 12), which is answer choice (a).
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Help plsss
Determine if it’s linear
If point X (-4,5) was rotated 180 Degrees counterclockwise around the origin, what would the coordinates of X' be?
Answer:
(4,-5)
Step-by-step explanation:
(x,y) → (-x, -y)
(-4,5) → (4,-5)
Helping in the name of Jesus.
At which point do the lines y=4x+1 and y=2x-1 intersect
The lines having linear equation y=4x+1 and y=2x-1 intersect at the point (-1, -3).
What is a linear equation, exactly?
A linear equation is an algebraic equation of the first degree that describes a line in a two-dimensional plane. It is an equation of the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept. The slope represents the rate of change of y with respect to x, while the y-intercept represents the point at which the line crosses the y-axis
Now,
To find the point of intersection between the lines y=4x+1 and y=2x-1, we can set the two equations equal to each other or we can graph these and find the intersection point.
1.
4x+1 = 2x-1
Simplifying this equation, we get:
2x = -2
x = -1
Now, we can substitute this value of x into either equation to find the corresponding value of y:
y = 4x+1 = 4(-1)+1 = -3
Therefore,
the lines y=4x+1 and y=2x-1 intersect at the point (-1, -3).
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1. Before you took this course, you probably heard many stories about Statistics courses. Oftentimes
parents of students have had bad experiences with Statistics courses and pass on their anxieties to their
children. To test whether actually taking AP Statistics decreases students' anxieties about Statistics, an
AP Statistics instructor gave a test to rate student anxiety at the beginning and end of his course.
Anxiety levels were measured on a scale of 0-10. Here are the data for 16 randomly chosen students
from a class of 180 students:
paired
t
SU
Pre-course anxiety level
Post-course anxiety level
Difference (Post - Pre)
7 6 9 5
4 3 7 3
-3 -3 -2 -2
6 7
4 5
-2 -2
5
4
-1
7 6 4
6 5 3
-1 -1 -1
3
2
-1
2 1
2 1
0 0
3
3
0
4
4
0
2
3
1
The assumptions include:
1. The observations are normally distributed.
2 The observertions are independent.
What are the test hypothesis?Test hypotheses include the null hypothesis that the anxiety level is same before after the course and the alternative hypothesis that the anxiety level derveases after taking the course.
The standard deviation is 1.1475. The value of to will be:
= -1.125 / (1.1475 / √16)
= 3.9212
Based on the p value, it should be noted that the null hypothesis is rejected.
In conclusion, the anxiety level decrease after the students take the course.
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Before you took this course, you probably heard many stories about Statistics courses. Oftentimes parents of students have had bad experiences with Statistics courses and pass on their anxieties to their children. To test whether actually taking AP Statistics decreases students' anxieties about Statistics, an AP Statistics instructor gave a test to rate student anxiety at the beginning and end of his course.
Anxiety levels were measured on a scale of 0-10. Here are the data for 16 randomly chosen students from a class of 180 students:
Do the data indicate that anxiety levels about Statistics decreases after students take AP Statistics? Test an appropriate hypothesis and state your conclusion.
Solve 7u²-56=0, where u is a real number.
Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
If there is no solution, click on "No solution".
Therefore, the solutions to the equation 7u² - 56 = 0 are u = 2.83 and u = -2.83 (rounded to the nearest hundredth).
Answer: u = 2.83, -2.83.
What is equation?An equation is a mathematical statement that asserts the equality of two expressions. It typically consists of two sides separated by an equals sign (=). The expressions on both sides of the equals sign are called the left-hand side (LHS) and the right-hand side (RHS) of the equation. The goal in solving an equation is to find the value or values of the variable(s) that make the equation true.
What is real numbers?The real numbers are a set of numbers that includes all rational and irrational numbers. Real numbers can be represented on the number line, where every point corresponds to a unique real number. The real number system is denoted by the symbol R.
In the given question,
To solve the equation 7u² - 56 = 0, we can start by isolating the variable u by adding 56 to both sides of the equation:
7u² - 56 + 56 = 0 + 56
Simplifying the left side, we get: 7u² = 56
Dividing both sides by 7, we get: u² = 8
Taking the square root of both sides, we get: u = ±√8
Simplifying the square root, we get: u = ±2.83
Therefore, the solutions to the equation 7u² - 56 = 0 are u = 2.83 and u = -2.83 (rounded to the nearest hundredth).
Answer: u = 2.83, -2.83.
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What is the length of the hypotenuse?
Answer:
41
Step-by-step explanation:
a^2+b^2=c^2
So...
40^2+9^2=1681
√1681=41
Tina make 480 sandwiches she only makes tuna sandwiches beef sandwiches and ham sandwiches amd cheese sandwiches 3/8 of the sandwiches are tuna 35% of the sandwiches are beef the ratio of the number of ham sandwhiches to the number of cheese sanwiches is 5:6 work out the number of ham sandwhiches that tina makes
= 5x = 5(12) = 60 sandwiches, the number of ham sandwiches. Tina makes 60 ham sandwiches.
First, we need to find the total number of each type of sandwich that Tina makes:
3/8 of the sandwiches are tuna, so the number of tuna sandwiches
= 3/8 x 480
= 180 sandwiches
35% of the sandwiches are beef, so the number of beef sandwiches
= 35% x 480
= 0.35 x 480
= 168 sandwiches
The remaining sandwiches must be ham and cheese sandwiches. Let's call the number of ham sandwiches "h" and the number of cheese sandwiches "c". We know that h:c = 5:6, which means that h = 5x and c = 6x for some common factor x. The total number of sandwiches is 480, so:
h + c = 480 - 180 - 168
h + c = 132
Substituting h = 5x and c = 6x, we get:
5x + 6x = 132
11x = 132
x = 12
Therefore, the number of ham sandwiches = 5x = 5(12) = 60 sandwiches. Tina makes 60 ham sandwiches.
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1. Use properties of logarithms with the given approximations to evaluate the expression. Use logb2=0.693 and/or logb6=1.792 to find logb12.2. Complete parts (a) and (b). a. Write the inverse of y=8x in logarithmic form. b. Graph y=8x and its inverse and discuss the symmetry of their graphs.3. 2log2^15 EVALUATEUse properties of logarithms with the given approximations to evaluate the expression.loga3≈0.477andloga5≈0.699.Use one or both of these values to evaluate loga27.Write as a single logarithm. Assume that variables represent positive numbers.5log2x+2log2zOn the basis of data for the years 1918 through1997, the expected life span of people in a country can be described by the functionf(x)=12.576ln x+17.088 years, where x is the number of years from1905 to the person's birth year. What does this model estimate the life span to be for people born in 1941?This model estimates that the life span for people born in1941 is
1. Use properties of logarithms with the given approximations to evaluate the expression. Use log2=0.693 and/or log6=1.792 to find log12.
Answer: log12 = log6 + log2 = 1.792 + 0.693 = 2.485.
2. Complete parts (a) and (b).
a. Write the inverse of y=8x in logarithmic form.
Answer: log8(y) = x.
b. Graph y=8x and its inverse and discuss the symmetry of their graphs.
Answer: The graph of y=8x and its inverse will have the same shape, but it will be flipped across the line y = x. This is known as the symmetry of their graphs.
3. 2log215 EVALUATE Use properties of logarithms with the given approximations to evaluate the expression. log3≈0.477 and log5≈0.699. Use one or both of these values to evaluate log27. Write as a single logarithm. Assume that variables represent positive numbers. 5log2x+2log2z
Answer: log27 = log5 + log3 = 0.477 + 0.699 = 1.176.
4. On the basis of data for the years 1918 through 1997, the expected life span of people in a country can be described by the function f(x) = 12.576ln x + 17.088 years, where x is the number of years from 1905 to the person's birth year. What does this model estimate the life span to be for people born in 1941?
Answer: This model estimates that the life span for people born in 1941 is 70.698 years.
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Solve for y. Then find the values of y that correspond
to the given values of x for the linear equation.
y + 8x = -2 forx = 0, 1, 2
Answer:
no one can solve that because how you spelled it but good luck
Answer:
y= -2 when x is 0,y= -10 where x is 1 and y= -18 where x is 2
Step-by-step explanation:
when you equate x to 0 then you substitute to the equation give which is y+8x= -2, the same thing applies to the next numbers which is 1 and 2. to show it will look like is suppose to be in the form like when x is 0 it will be y+8(0)= -2
which will solve to get y+0=-2
which is the same as y=-2
part B observe the graph at what point do the lines appear to insersect
Answer:
Step-by-step explanation:
A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model:
E(y) = ?0 + ?1x,
where y = appraised value of the house (in thousands of dollars) and x = number of rooms. Using data collected for a sample of n = 74 houses in East Meadow, the following results were obtained:
? = 74.80 + 19.72x
What are the properties of the least squares line, ? = 74.80 + 19.72x?
For each additional room in the house, we estimate the appraised value to increase $74,800.
We estimate the base appraised value for any house to be $74,800.
For each additional room in the house, we estimate the appraised value to increase $19,720.
There is no practical interpretation, since a house with 0 rooms is nonsensical.
The properties of the least squares line are that the intercept represents the estimated base appraised value for any house in East Meadow, and the slope represents the estimated increase in appraised value for each additional room in the house.
The properties of the least squares line, ? = 74.80 + 19.72x, are as follows:
1. The intercept, ?0, is 74.80. This represents the estimated base appraised value for any house in East Meadow, regardless of the number of rooms. However, there is no practical interpretation for this value, since a house with 0 rooms is nonsensical.
2. The slope, ?1, is 19.72. This represents the estimated increase in appraised value for each additional room in the house. For each additional room in the house, we estimate the appraised value to increase $19,720.
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The border of a susan b. Anthony dollar is in the shape of a regular polygon. How many sides does the polygon have what is the measure of each angle of the border round your answer to the nearest degree
The polygon has 12 sides and each angle has a measure of 30°.
The border of a Susan B. Anthony dollar is in the shape of a regular polygon. A regular polygon is a polygon with equal sides and equal angles. To calculate the number of sides and measure of the angles, the formula for finding the measure of the interior angles of a regular polygon is used. The formula is (n-2)180/n where n is the number of sides. For the Susan B. Anthony dollar, the number of sides is 12, so the measure of the interior angles is (12-2)180/12 = 30°. Therefore, the polygon has 12 sides and each angle has a measure of 30°, rounded to the nearest degree.
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I tried it two times and got it wrong, please help!
Answer:
[tex]\dfrac{dy}{dx}=-\dfrac{52x\left(3x^{37}y-1\right) }{4x^{39}+9y^8}[/tex]
Step-by-step explanation:
Note: I will provide links with descriptions/steps to each of the rules used in this differential equation at the bottom of this answer.
Given
[tex]-26x^2+4x^{39} y+y^9=-21[/tex]
Find [tex]\dfrac{dy}{dx}[/tex]
Differentiate the left side of the equation.
[tex]\dfrac{d}{dx}\left(-26x^2+4x^{39}y+y^9\right)= \dfrac{d}{dx}\left(-21\right)[/tex]
Focus the left side of the equation. Apply the Sum Rule for derivatives.
[tex]\dfrac{d}{dx} \left[-26x^2\right]+\dfrac{d}{dx} \left[4x^{39}y\right]+\dfrac{d}{dx} \left[y^9\right][/tex]
Lets evaluate each derivative.
1. Evaluate [tex]\frac{d}{dx} \left[-26x^2\right][/tex]
Differentiate using the Power Rule for derivatives.
[tex]\dfrac{d}{dx} \left[-26x^2\right]=2*26x^{2-1}[/tex]
Simplify.
[tex]2*-26x^{2-1}\\-52x^{2-1}\\-52x[/tex]
2. Evaluate [tex]\frac{d}{dx} \left[4x^{39}y \right][/tex]
Differentiate using the Product Rule for derivatives.
[tex]4\left(x^{39}\dfrac{d}{dx}\left[y\right]+y\dfrac{d}{dx}\left[x^{39}\right]\right)[/tex]
Rewrite [tex]\dfrac{d}{dx}\left[y\right][/tex] as [tex]y'[/tex]
[tex]4\left(x^{39}y'+y\dfrac{d}{dx}\left[x^{39}\right]\right)[/tex]
Differentiate using the Power Rule for derivatives.
[tex]4\left(x^{39}y'+y\left(39x^{39-1} \right)\right)[/tex]
Simplify.
[tex]4\left(x^{39}y'+39yx^{38} \right)[/tex]
3. Evaluate [tex]\frac{d}{dx} \left[y^9\right][/tex]
Differentiate using the Chain Rule for derivatives.
[tex]9y^8\dfrac{d}{dx} \left[y\right][/tex]
Rewrite [tex]\dfrac{d}{dx}\left[y\right][/tex] as [tex]y'[/tex]
[tex]9y^8y'[/tex]
Add up all of the derivatives then simplify.
[tex]-52x+4\left(x^{39}y'+39yx^{38} \right)+9y^8y'[/tex]
[tex]-52x+4\left(x^{39}y'\right)+4\left(39yx^{38} \right)+9y^8y'[/tex]
[tex]-52x+4x^{39}y'+156yx^{38}+9y^8y'[/tex]
[tex]4x^{39}y'+156x^{38}y+9y^8y'-52x[/tex]
Focus the right side of the equation.
[tex]\dfrac{d}{dx}\left(-21\right)[/tex]
Since [tex]-21[/tex] is constant with respect to [tex]x[/tex] , the derivative of [tex]-21[/tex] with respect to [tex]x[/tex] is 0 .
Now we have
[tex]4x^{39}y'+156x^{38}y+9y^8y'-52x=0[/tex]
Finally lets solve for [tex]y'[/tex].
Subtract [tex]156x^{38}y[/tex] from both sides of the equation.
[tex]4x^{39}y'+9y^8y'-52x=-156x^{38}y[/tex]
Add [tex]52x[/tex] to both sides of the equation.
[tex]4x^{39}y'+9y^8y'=-156x^{38}y+52x[/tex]
Factor [tex]y'[/tex] out of [tex]4x^{39}y'[/tex]
[tex]y'\left(4x^{39}\right) +9y^8y'=-156x^{38}y+52x[/tex]
Factor [tex]y'[/tex] out of [tex]9y^8y'[/tex]
[tex]y'\left(4x^{39}\right)+y'\left(9y^8\right)=-156x^{38}y+52x[/tex]
Factor [tex]y'[/tex] out of [tex]y'\left(4x^{39}\right)+y'\left(9y^8\right)[/tex]
[tex]y'\left(4x^{39}+9y^8\right)+=-156x^{38}y+52x[/tex]
Divide each term by [tex]4x^{39}+9y^8[/tex]
[tex]\dfrac{y'\left(4x^{39}+9y^8\right)}{4x^{39}+9y^8} =\dfrac{-156x^{38}y}{4x^{39}+9y^8} +\dfrac{52x}{4x^{39}+9y^8}[/tex]
Cancel the common factor of [tex]4x^{39}+9y^8[/tex] on the left side of the equation.
[tex]y'=\dfrac{-156x^{38}y}{4x^{39}+9y^8} +\dfrac{52x}{4x^{39}+9y^8}[/tex]
Combine the numerators over the common denominator.
[tex]y'=\dfrac{-156x^{38}y+52x}{4x^{39}+9y^8}[/tex]
Factor [tex]52x[/tex] out of [tex]-156x^{38}y+52x[/tex] and simplify.
[tex]y'=\dfrac{52x\left(-3x^{37}y\right)+52x}{4x^{39}+9y^8}[/tex]
[tex]y'=\dfrac{52x\left(-3x^{37}y\right)+52x(1)}{4x^{39}+9y^8}[/tex]
[tex]y'=\dfrac{52x\left(-3x^{37}y+1\right) }{4x^{39}+9y^8}[/tex]
[tex]y'=-\dfrac{52x\left(3x^{37}y-1\right) }{4x^{39}+9y^8}[/tex]
Rewrite [tex]y'[/tex] as [tex]\dfrac{dy}{dx}[/tex].
[tex]\dfrac{dy}{dx}=-\dfrac{52x\left(3x^{37}y-1\right) }{4x^{39}+9y^8}[/tex]
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What’s the answer to this
Answer: 45 ml/h
Step-by-step explanation: that is s/t graph
read in any point on the part of graph distance , and divide
it with time .
95:2 hours,
The temperature in Australia one morning was -5°C at 08:00 and increased by 2°C every hour until 12:00. What will the temperature be at 11:00
Answer:
3*C
Step-by-step explanation:
We can Frame an equation, taking the previous temperature as "x" and adding 2 by every hour.
Previous Temprature + 2 = New Temprature
Therefore by this equation:
at 8AM , the Temperature is -5 + 2 = -3*c
at 9AM , the Temperature is -3 + 2 = -1*c
at 10 AM, the Temperature is -1 + 2 = 1*c
Therefore at 11AM , the Temperature will be 1 + 2 = 3*c
Hope it helps.
4x-2+3x+14=180
Solve for x.
Answer: x = 24
Step-by-step explanation:
To solve for x, we need to simplify the left side of the equation first by combining like terms:
4x - 2 + 3x + 14 = 180
7x + 12 = 180
Next, we will isolate the variable by subtracting 12 from both sides:
7x + 12 - 12 = 180 - 12
7x = 168
Finally, we will solve for x by dividing both sides by 7:
7x/7 = 168/7
x = 24
Therefore, the solution to the equation 4x-2+3x+14=180 is x = 24.
The trinomial 2x2 + 13x + 6 has a linear factor of x + 6.
2x2 + 13x + 6 = (x + 6)(?)
What is the other linear factor?
pls tell me how to do the table thing
The trinomial( consists three different terms), 2x² + 13x + 6, has a linear factor of (x + 6) and the linear factor of (x+6) is equals to a (2x+1).
We have, a trinomial 2x² + 13x + 6 has a linear factor of x + 6 and we have to determine that linear factor of (x + 6). To determine the linear factor of (x + 6) either dividing the trinomial by (x+6) or factorization of this trinomial. Factoring a trinomial means expanding an equation into the product of two or more binomials. Here, middle term of trinomial, b = 13
last term, c = 6
Using spliting middle term method for factorization, 2x²+ 13x + 6 = 2x² + 12x + x + 6
=> 2x² + 13x + 6 = 2x( x + 6) + 1(x + 6 )
Common factor from binomials,
=> 2x² + 13x + 6 = (x + 6)(2x + 1)
Thus, the linear factor of (x+6) is (2x +1).
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2(-3x+5)+2(x+4) when x=2
Answer:
12
Step-by-step explanation:
p(x) = 2(-3x+5)+2(x+4)
Substitution :
p(2) = 2(-3(2) +5) + 2(2+5)
= 2(-6 + 5) + 2 (7)
= 2(-1) + 2(7)
= -2 + 14
= 12
I really need help with this math problem
Step-by-step explanation:
The area with the highest inches receives most rainfall 1¼
The area with the lowest inches received lowest rainfall 1/8
1¼ location will have highest frequency using the ⅛line plot. There are 10 of ⅛ in 1¼
Add all the inches
1/8 + 3/8 +1/8 + 1/8 + 3/4+ 3/4 + 1/4 + 1¼ + 1/4 +1
6/8 + 2¼ + 1
6/8 + 3¼
6/8 + 13/4 = 32/8
Total rain = 4inches
11 + x = 7 - 4x what is x
Answer:
x = 6
Step-by-step explanation:
Solve for x
[tex]11+x=7-4x[/tex]
Add 7 on both sides
[tex]18+x=4x[/tex]
Subtract x on both sides (same as 1x)
[tex]18=3x[/tex]
Divide by 3
[tex]6=x[/tex]
Kohli scored 10 runs less than Rohit in innings. Rahul scored 5 runs more than Rohit. In total they scored 442 runs. What was the score of kohli
Throughout his innings, Kohli scored 432 runs in total.. Rohit scored 422 runs and Rahul scored 427 runs. In total, they scored 442 runs.
Kohli, Rohit and Rahul are three of the greatest batsmen in Indian cricket. In a match, they scored 442 runs in total.Rohit scored the most runs (422 total),. Kohli scored 10 runs less than Rohit, making his total score 432 runs. Rahul was the third highest scorer, with 5 runs more than Rohit, making his total score 427 runs. This shows the great batting prowess of the three batsmen and how they were able to score a combined 442 runs between them. This goes to show the great talent and skill that the three players possess and how they are able to make such a great contribution to their team's total score.
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