Thus, the vale of x for, when the graphs of f and g have parallel tangent lines, is x ≈ -0.302, which is choice D.
To find when the graphs of f and g have parallel tangent lines, we need to find when their derivatives are equal. The derivative of f(x) is f'(x) = 6e^(2x), and the derivative of g(x) is g'(x) = 18x^2.
Setting f'(x) equal to g'(x) gives us:
6e^(2x) = 18x^2
Dividing both sides by 6 gives:
e^(2x) = 3x^2
Taking the natural logarithm of both sides gives:
2x = ln(3x^2)
2x = ln(3) + 2ln(x)
Now we can use a graphing calculator to find the value of x where the graphs of f and g have parallel tangent lines. We can graph the left side of the equation (2x) and the right side of the equation (ln(3) + 2ln(x)) on the same set of axes, and find where they intersect.
Alternatively, we can use Newton's method to approximate the solution. Starting with an initial guess of x = -0.5, we can use the formula:
x_(n+1) = x_n - f(x_n)/f'(x_n)
where f(x) = e^(2x) - 3x^2 and f'(x) = 2e^(2x) - 6x.
After a few iterations, we get:
x_1 ≈ -0.288
x_2 ≈ -0.306
x_3 ≈ -0.302
So the result is approximately x ≈ -0.302, which is choice D.
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p) find the sum of the infinite geometric series:
a1 = -20 a5 = -1650 r = 3
The sum of the infinite geometric series is 10
How to solve for the infinite geometric seriesFrom the values that we have, the first term a1 = - 20, the common ratio r = 3
From the above we can get the first 5 terms of the geometric series. We do this by multiplying each number derived by 3
this would be :
-20, -60, -180, -540 , -1650 ...
The formula for the sum of the infinite geometric series is given as
S = a1 / 1 - r
from the question we have
a1 = -20
r = 3
we would put the values into the formula
S = -20 / 1 - 3
S = -20 / -2
s = 10
Hence the sum is given as 10
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URGENT!!!
In the figure [FD]=[FE] and [DM]=[NE] prove that the triangle FMN is two sided
Therefore , the solution of the given problem of congruences comes out to be [FD]=[FE] and [DM]=[NE]
What is congruency?SSS stands for “side, side, side” and means that we have two triangles with all three sides equal.
SAS stands for “side, angle, side” and means that we have two triangles where we know two sides and the included angle are equal.
SAS theorem of congruence: The SAS (side-angle-side) theorem of congruence states that if two sides and their included angle in one triangle are exactly equal to the corresponding two sides and their included angle in another triangle, then the two triangles are congruent.
Here,
SSS – side, side, and side. ...
SAS – side, angle, and side. ...
ASA – angle, side, and angle. ...
AAS – angle, angle, and side. ...
HL – hypotenuse and leg.
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The temperature is -3F at 7:00 a.m during the next 4 hours,the temperature increases to 21F.what is the temperature at 11:00 a.m?
Answer:
I believe it is 24°F
Step-by-step explanation:
I'm just cool like that
f(x) = 3(0.5)* transformation?
Answer: Vertical stretch by a factor of 3.
2 x 4 x 15 commutative property and simplified
Using the commutative property of multiplication the solution of the equation is solved to be
120What is commutative property of multiplication?The addition and multiplication arithmetic operations are covered by the commutative property.
This implies that the outcome of adding or multiplying two numbers remains unchanged if the order or position of the numbers are changed.
applying the commutative property of multiplication in the problem we have that
= (2 * 4) * 18
= 8 * 15
= 120
Also
= 2 * (4 * 15)
= 2 * 60
= 120
the answer does not change
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the festival organizers expect 10,000 people to attend the four day festival at the end they have exceeded their attendance by 2000 people determine the average number of people that attended the festival per day
Answer:
500 people came each day
Step-by-step explanation:
2000 divide by 4= 500
If A =3L(2h+pie R)find r in terms of A,L,pie and R
The value of the equation is r = ( 1/2 ) ( A / 3L - πR )
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 equation be represented as A
Now , the value of A is
A = 3L ( 2r + πR ) be equation (1)
Now , on simplifying the equation , we get
( 2r + πR ) = A / 3L
Subtracting πR on both sides of the equation , we get
2r = A / 3L - πR
Divide by 2 on both sides of the equation , we get
r = ( 1/2 ) ( A / 3L - πR )
Therefore , the value of r is ( 1/2 ) ( A / 3L - πR )
Hence , the equation is r = ( 1/2 ) ( A / 3L - πR )
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Sophie invested $26,000 in an account paying an interest rate of 6% compounded continuously. Sydney invested $26,000 in an account paying an interest rate of 5% compounded monthly. After 20 years, how much more money would Sophie have in her account than Sydney, to the nearest dollar?
Sophie would have $15,786 more than Sydney.
What is the compound interest?We know that the compound interest has to do with the kind of interest that we have to compound but on the principal and the the interest. In this case, we can see that we have;
A = P(1 + r/n)^nt
A = amount
P = principal
r = rate
t = time
n = Number of times compounded
Then we have For Sophie;
A = 26000(1 + 0.06/365)^20 * 365
A = $86315
For Sydney;
A =26000(1 + 0.05/12)^12 * 20
A = $70529
It then implies that; $86315 - $70529
= $15,786
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What is value of x? enter your answer in the box. X = a triangle with vertices labeled as a, b, and c. Side b c is the base. A line segment is drawn from vertex a to base b c that bisects angle b a c into two parts marked with single arcs. Side a b is labeled as 8. Side a c is labeled as 12. Side b c is divided into two equal parts labeled as x plus 4 and 2 x plus 1.
The value of x calculated by using the Pythagorean theorem is equal to 6.
This can be found by using the Pythagorean theorem to solve for the length of side bc, which is the base of the triangle. By using the two given side lengths of 8 and 12, we can find that the length of the hypotenuse (bc) is equal to the square root of 8^2 + 12^2, which is equal to 16.
Since the base is divided into two equal parts, we can divide 16 by 2 and get 8. We then subtract the given length of 2x + 1 from 8 and get 7, which means x is equal to 6.
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Tony has 8 yd fabric how many inches does he have
Answer:
Each yardn is 36 inches. Multiply the number of yards. times inches and that will be the total number of inches for 8 yards.
Step-by-step explanation:
I yd = 36 inches
you have 8 yards
36 x 8 = 288 inches
Answer:
answer is 288 inches
Step-by-step explanation:
8 yards is equal to 288 inches
n
B
2 in
6 in.
64 square inches
76 square inches
Streck Boost.
Find the total surface area of the prism.
D
48 square inches
1177 0779
88 square inches
The total surface area of the prism is 48 square inches.
What is the surface area of the prism?2 in,6 in.64 square inches
76 square inches Streck Boost.
Units are displayed for convenience only; they have no bearing on the computations. The units, such as ft, ft2, or ft3, are there to indicate the findings' order. If you start with mm and know h, l, and w in mm, for instance, your calculations will provide d in mm, S in mm2, and V in mm3.
a rectangular prism's formulas:
Rectangular prism volume: V = lwh
Rectangular prism's surface area is given by
S = 2(lw, lh, and wh).
64 square inches
76 square inches
The total surface area of the prism is 48 square inches.
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Recreational water illnesses can only be contracted in fresh water sources, not swimming pools.
Please select the best answer from the choices provided.
T
F
True, Recreational water illnesses can only be contracted in fresh water sources, not swimming pools.
What is Recreational water illnesses?
Recreational water infections (RWIs) are contracted by ingesting, inhaling mists or aerosols from, or coming into touch with contaminated recreational water and are brought on by microorganisms.
In addition to swimming pools, hot tubs, water slides, water play zones, interactive fountains, lakes, rivers, and seas are all examples of recreational water.
What exactly is a recreational water?
Incorporated into this are swimming, diving, water skiing, and surfing. Recreation involving secondary touch, where you come into direct contact with the water but are unlikely to ingest it Paddling, wading, boating, and fishing all fall under this category.
without any physical interaction with the water, passive recreation.
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Please Help ASP...... One and Two please
The triangle that has two angles measuring 17 degrees and 107 degrees is a B. Obtuse triangle.
A triangle with sides of length 5, 6, and 7 would be a C. Scalene triangle.
What are some types of triangles ?There are several types of triangles and one of them is an obtuse triangle. Such a triangle would have an angle that is larger than 90 degrees, much like the triangle mentioned that has an angle with 107 degrees.
There are also Scalene triangles where all their dimensions do not have the same measurement. This is why the triangle shown has sides of 5, 6, and 7.
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If a and b are positive integers such that [tex]a^{3b}[/tex] = x and [tex]a^{b}[/tex] = y, then [tex]\frac{x}{y^{2} }[/tex] = ?
If algebraic expressions are a³ᵇ = x and aᵇ = y, then, by algebra properties, x / y² is equal to aᵇ.
How to find the result of an algebraic expression based on two given expression by algebra properties
Herein we find the following two algebraic expressions with two positive integers a and b:
a³ᵇ = x
aᵇ = y
From these equation we need to find the result associated to algebraic expression x / y² in terms of the integers given. This can be done by means of algebra properties. First, square the second expression:
(aᵇ)² = y²
Second, divide the first expression by the given formula found in previous step:
x / y² = a³ᵇ / (aᵇ)²
Third, simplify the resulting expression to a single power:
x / y² = a³ᵇ / a²ᵇ
x / y² = a³ᵇ - ²ᵇ
x / y² = aᵇ
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This is due soon please help out????
a) The equation of line is y = 270x + 10640.
b) The annual cost value in 2013 for age 17 is $15,320.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Points (8, 12800) and (14, 14420)
So, the slope is
= (14420 - 12800)/(14-8)
= 1620/6
= 270
and, the slope intercept form
(y - 12800) = 270 (x - 8)
y- 12800 = 270 x - 2160
y = 270x + 10640
b) Now, x= 17
y= 270(17) +10640
y = 15, 320
Thus, In 2013 at age of 17 the amount is $15320.
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Question 6 of 22
Question 6
An air-conditioning and heating company has a fixed monthly cost of $3000. Furthermore, each service call costs the company $20.
Write an equation in slope-intercept form to represent the total cost for 1 month, y, if x service calls are made during the month.
y=
Answer:
For each service call cost of 20$ will be added to fixed cost of 3000$.
Step-by-step explanation:
The total cost for 1 month is the sum of the fixed monthly cost and the cost of all the service calls, so we can write the equation as:
y = 3000 + 20x
This equation is already in slope-intercept form, where "y" is the dependent variable, "x" is the independent variable, 3000 is the y-intercept (the point where the line crosses the y-axis, when x=0), and 20 is the slope of the line.
This equation can be interpreted as
For each service call cost of 20$ will be added to fixed cost of 3000$.
Erisa collected quarters. After a year he had quite a few of them. In fact, when he counted them in groups of two, three, four, and so on, up to groups of 16, there was always one left over. What is the smallest number of quarters Erisa could have collected
Erisa collected quarters. After a year he had quite a few of them. The smallest number of quarters that Erisa could have collected is 17.
What is the smallest number?Generally, Erisa collected quarters. After a year he had quite a few of them.
The smallest number of quarters that Erisa could have collected is 17.
This is because 17 is a prime number, and when it is divided into groups of 2, 3, 4, and so on, up to 16, there will always be one left over.
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Please help me with my work
In algebra, fractions can be added, subtracted, multiplied, and divided just like in basic arithmetic.
In algebra, what does a fraction mean?The components of a whole or group of objects are represented by fractions. A fraction consists of two parts. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the whole or collection. The denominator is the figure that appears below the line.
What are the Algebra Fundamentals?Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the fundamentals of algebra. Additionally, the algebraic expressions contain the fundamental arithmetic operations of addition, subtraction, multiplication, and division.
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Please help don't understand
Answer:
Step-by-step explanation:
what do you not understand
Which expression is equivalent to the given expression?
A.
B.
C.
D.
Answer:
c
Step-by-step explanation:
Answer:Answer: c ( 8m^9n^3)
Step-by-step explanation:
(see image)
someone help please thank you
Answer:
distance = (62t) + 22
Step-by-step explanation:
Distance = speed * time
distance = (62*t) + 22
Hope this helps!
Classifying Triangles Card
The triangle problem's solution is given by the relationship amongst x,y and z, which is z²= x²+y² .
Explain the triangle.Due to its three vertices and three sections, a triangles is a polygon. It has a simple geometric form. Triangle ABC refers to a triangular with the points A, B, and C. When three factors are not collinear, a singular plane and triangle are found. Triangles are regarded as polygons since they have three corners and a right side. The points where a triangle's three sides intersect are known as the triangle's corners. By summing three triangle angles, one gets 180 degrees.
Here,
Given: In this situation, triangle XYZ is a right triangle.
Thus,
We discover:
Z, X, and Y components
They are linked in the following ways:
It being a right triangle,
So,
According to the Pythagoras Theorem,
=>z²= x²+y²
The triangle problem's solution can be found by using the relationship among z, x, and y, which is given by z2=x2+y2.
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. The points (–5, 26) and (3, 26) are located on the same parabola. What is the equation for the axis of symmetry for this parabola?
The equation for given two points of parabola will be (x+1)^2=y-10.
What is parabola?
A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line which is known as the directrix.
In general, if the directrix is parallel to the y-axis in the standard equation of a parabola is given as:
y^2 = 4ax
If the parabola is sideways i.e., the directrix is parallel to x-axis, the standard equation of a parabola becomes,
x^2 = 4ay
Apart from these two, the equation of a parabola can also be y2 = -4ax and x2 = -4ay if the parabola is in the negative quadrants.
Now,
the parabola having points (–5, 26) and (3, 26) is given in graph
and the equation will be (x+1)^2=y-10
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What are the 2 formulas for distance?
We have many distance formulas in a coordinate system that can be used to find the distance between two points, the distance between a point to a line, the distance between two parallel lines, and the distance between two parallel planes.
The Distance Formula is a useful tool for calculating the distance between two points that can be arbitrarily represented as points:
A (x1,y1) and B (x2,y2) are on the coordinate plane.
Distance between two points:
(x₁,y₁),(x₂,y₂)
d=√(x₂-,y₂)²,(x₁-y₁)²
Distance between three points:
(x₁,y₁,z₁),(x₂,y₂,z₂)
d=√(x₂-,y₂)²,(x₁-y₁)²+(z₂-z₁)²
At point (x₁,y₁) and a line ax+by+c=0 is
d=|ax₁+by₁+c|/√a²+b²
Two parallel lines ax+by+c₁=0 and ax+by+c₂=0
d=|c₂-c₁|/√a²+b².
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The table shows the length and width of proportional rectangles. Length (in inches) 4 6 12 16 width (in inches) 10 15 30 40 using the table, find the width of a rectangle that has a length of 24.
The width of a rectangle that has a length of 24 inches would be 60 inches.
According to the data, we can assume that all the rectangles in the table have the same ratio of measurement.
To find unknown width of the rectangle, we can use this equation:
A/B = C/D
Where:
A represents the length of the first rectangle
B represents the width of the first rectangle
C represents the length of the second rectangle
D represents the width of the second rectangle
In this case, we are going to use 12 as the length of the first rectangle, and 30 as its width.
12/30 = 24/D
12D = (30 x 24)
12D = 720
D = 60
Thus, the width of the rectangle that has a length of 24 inches is 60 inches.
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21 500 ml + 31 650 ml
Answer:
53,150 ML
Simply add both of the numbers and you have your answer.
On the third grid, create a graph of the set of points (2+5t, 3-4t) for -2 ≤ t ≤ 7 pm the xy-plane
The graph of the set of the points has the constraints -8≤2+5t≤37 & -25≤3-4t≤11
What is an inequality?An inequality is an inequation separated by <,>≥,≤
Given here: The set of points (2+5t,3-4t) in the xy-plane
when -2≤t≤7 set of points (2+5t,3-4t)
then 2+5×-2≤2+5t≤2+5×7
-8≤2+5t≤37
Again, 3-4×-2≤3-4t≤3-4×7
-25≤3-4t≤11
We can construct a graph using the above accordingly
Hence, The graph of the set of the points has the constraints -8≤2+5t≤37 & -25≤3-4t≤11
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A tunnel is constructed with a semielliptical arch. The width of the tunnel is 70 feet, and the maximum height at the center of the tunnel is 20 feet. What is the height of the tunnel 10 feet from the edge? round your answer to the hundredths place.
Considering the equation of an ellipse, it is found that the height of the tunnel 10 feet from the edge is of 14 feet.
The following is the equation for a horizontal ellipse of center with coordinates (h,k):
(x - h)²/a² + (y - k)²/b² = 1.
In relation to this issue, we have that:
The origin is where the center is.
Since the major axis is 70, 2a = 70 and a = 35.
The maximum height is 20, therefore b is equal to 20.
As a result, the ellipse's equation is as follows:
x²/35² + y²/20² = 1.
It is determined that x = 25 when the tunnel is 10 feet from the edge since 35 – 10 = 25; therefore, the height y is calculated as follows:
25²/35² + y²/20² = 1
0.51 + y²/20² = 1
y²/20² = 0.49
y² = 20² x 0.49
y =√(20² x 0.49)
y = 14 feet.
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Bella recorded data and used her graphing calculator to find the equation for the line of best fit. She then used the.correlation coefficient to determine the strength of the linear fit. Which correlation coefficient represents the strongest linear relationship?
0.9 -0.3
0.5 -0.8
Answer: The correlation coefficient (also known as Pearson's correlation coefficient or r) is a measure of the strength of the linear relationship between two variables. The value of the correlation coefficient ranges between -1 and 1, with a value of 1 indicating a perfect positive linear relationship, a value of -1 indicating a perfect negative linear relationship, and a value of 0 indicating no linear relationship.
In this case, the correlation coefficient that represents the strongest linear relationship is
0.9
The absolute value of the correlation coefficient measures the strength of the linear relationship, regardless of whether it is positive or negative. So, the absolute value of 0.9 and -0.3 are both 0.9. but as we are looking for the strongest linear relationship, the value of 0.9 is closer to 1 than -0.3 is and it indicates stronger positive relationship.
In summary, the closer the correlation coefficient is to 1 or -1, the stronger the linear relationship between the variables is. In this case, 0.9 has the strongest linear relationship of the given options.
Step-by-step explanation:
Find the additive inverse of the linear expression. −2x+5 __
The answer is 2x-5
What are like and unlike terms in an expression?In Algebra, the like terms are defined as the terms that contain the same variable which is raised to the same power. In algebraic like terms, only the numerical coefficients can vary. We can combine the like terms to simplify the algebraic expressions.
Given here: linear expression. −2x+5
Thus the additive inverse is -2x+5+2x-5=0
Hence, the additive inverse is 2x-5
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