Compute the derivatives of the following functions using the chain rule. (a) f(x) = (4x² + 2x + 3)⁹ b) f(x) = sin(x³ + 2) c) f(x)=tan(√x) d, f(x) = sec(5x)
Answer:
Answer to a)
f'(x) = 9 • (4x² + 2x + 3) ^8 • (4x + 2)
https://www.1728.org/chainrul.htm
(scroll to the bottom of that page.)
Step-by-step explanation:
The following table shows the world record times for the 200m race for flying start machines (a kind of bicycle). Find the line of best fit model, R(t) , that represents the world record times , t, since 1970. Before determining the equation , we need to convert all years to years since 1970. The first two rows are completed for you . Complete the rest of the table with the correct years since 1970 . After completing the table , use Excel to create a linear regression equation using only the second two columns . Do not use any spaces in your submission .
Using a calculator, the linear regression equation is given by:
R(t) = -0.22552t + 10.89293.
What is the missing information?The table of values is missing, and the values are as follows:
Years since 1970: 4, 5, 6, 7, 9, 15, 16, 22.Record time: 10.4, 10, 9.4, 9.1, 8.8, 7.2, 6.8, 6.5.How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
For this problem, inserting the points (Years since 1970, Record Time), the regression line is given as follows:
R(t) = -0.22552t + 10.89293.
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Select all the triangle that have and area of 45 square units.
A
B
C
D
E
The value of x that makes x2 + 6x + 13 maximum is equal to
A. 6
B. -3
C. 13
D. 3
The given equation (x²+6x+13) gives maximum value when the value of x is 13. The correct option will be C.
What is Substitution?Substitution is the replacement of a given variable with the numerical values. Substitute all the given values of x in the equation x²+6x+13:
A. x = 6
Substitute the value of x = 6,
x²+6x+13 = (6)²+6×6+13 = 36+36+13 = 85
B. x = -3
Substitute the value of x = -3,
x²+6x+13 = (-3)²+6×(-3)+13 = 9+(-18)+13 = 4
C. x = 13
Substitute the value of x = 13,
x²+6x+13 = (13)²+6×13+13 = 169+78+13 = 260
D. x = 3
Substitute the value of x = 3,
x²+6x+13 = (3)²+6×3+13 = 9+18+13 = 40
260 is greater than all the three other options. Therefore, C is the correct option.
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One day the temperature started at -8° F and dropped 18° by the end of the day. What
was the temperature at the end of the day?
At the
Answer:
at the end of the day the temperature would be -26° F
Which is a counterexample of the following conditional?
"If a number is divisible by five, then it is even."
O 30
O 25
O 20
O 18
Answer: 20
Step-by-step explanation:
its divisible by 5 and it is not even
I will mark brainliest
Answer: Quadrant I
Step-by-step explanation:
what is the answer to the equation of x^2 + 2x
9. A large pool, containing 1400 liters of water, is being drained at a rate of
7 liters per minute.
a. How many liters of water remain in the pool after 1 hour?
b. How long until the pool contains 350 liters of water?
Answer:
Step-by-step explanation:
b
4^4 x 8^2 = [?]
Will pick brainliest to the most detailed answers, so try your hardest!
Answer:
16,384
Step-by-step explanation:
4^4 = 4×4×4×4=256
8^2 = 8×8=64
256×64=16,384
Answer:
16384 or [tex]2^{14}[/tex]
Step-by-step explanation:
This is easiest done by creating identical bases (the number being raised by the exponent, 4 and 8 here).
How do we do that? Well let’s start with [tex]4^{4}[/tex].
For both 8 and 4 the bases can be rooted to 2
[tex]\sqrt[3]{8} = 2 \\ \sqrt{4} = 2[/tex]
Because the root of 4 is 2, that means [tex]2^{2} =4[/tex].
Therefore, we can substitute [tex]2^{2}[/tex] for 4 in [tex]4^{4}[/tex], which looks like this:
[tex]2^{2^{4} }[/tex]
And, we should know that an exponent raised to an exponent is the same as multiplying those exponents together. This means [tex]2^{2^{4}} =2^{8}[/tex].
We can repeat the process with [tex]8^{2}[/tex]
[tex]8 = 2^{3} \\8^{2} =2^{3^{2} } \\2^{3^{2} } =2^{6}\\8^{2}=2^{6}[/tex]
Now that we have [tex]2^{8}\ and\ 2^{6}[/tex] we can continue. Given that the bases are the same we can simply add the exponents together when we multiply.
[tex]2^{8}[/tex] x [tex]2^{6}[/tex] = [tex]2^{14}[/tex] (or 16384).
a. A square classroom has a perimeter
of 120 yards. What is the length of
each side of the classroom?
Answer:
the answer is 30 yd
Step-by-step explanation:
The formula for surface area of sphere is A = 4πr2, Where r is the length of the radius. find the surface area of a sphere with a radius of 14 feet. use 22/7 for π
The surface area of the sphere is 1232² feet.
What is a sphere?A sphere is a three-dimensional analog of a two-dimensional circle. A sphere is a collection of points in three-dimensional space that are all the same distance r from a given point. The given point is the sphere's center, and r is the radius of the sphere.The formula for the surface area of the sphere: 4πr²
Now, substitute the values in the formula as follows:
The formula for the surface area of the sphere = 4πr²The formula for the surface area of the sphere = 4 × 22/7 × 14²The formula for the surface area of the sphere = 4 × 22/7 × 14 × 14The formula for the surface area of the sphere = 4 × 22 × 14The formula for the surface area of the sphere = 1232² feetTherefore, 1232² feet is the surface area of the sphere.
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write the expression in terms of sine and cosine, then simplify : [tex]\frac{sinx}{cscx - cotx}[/tex]
Answer:
[tex]1+\cos x[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4cm}\underline{Trigonometric Identities}\\\\$\csc \theta=\dfrac{1}{\sin \theta}\\\\\\\cot \theta=\dfrac{\cos \theta}{\sin\theta}\\\\\\\cos^2 \theta + \sin^2 \theta = 1$\\\end{minipage}}[/tex]
[tex]\begin{aligned}\implies \dfrac{ \sin x}{ \csc x - \cot x} & = \dfrac{ \sin x}{\dfrac{1}{\sin x} - \dfrac{\cos x}{ \sin x}}\\\\& = \dfrac{ \sin x}{\dfrac{1 - \cos x}{\sin x}}\\\\& = \sin x \times \dfrac{\sin x}{1 - \cos x}\\\\& = \dfrac{\sin^2 x}{1-\cos x}\\\\& = \dfrac{1-\cos^2x}{1-\cos x}\\\\& = \dfrac{(1-\cos x)(1+ \cos x)}{1-\cos x}\\\\& = 1 + \cos x\end{aligned}[/tex]
If BM = 15 inches and BV = 10 inches, what is MV?
Answer: 25 inches
Step-by-step explanation:
MB=BM
MB=15
MV=MB+BV
MV=15+10
MV=25 inches
Convert 41°C to degrees Fahrenheit.
If necessary, round your answer to the nearest tenth of a degree.
Here are the formulas.
C=-=-(F-32)
F=C+32
F
The required measure of 41°C in Fahrenheit is given as 105.8°F.
What is temperature?Temperature is defined as the degree of measure of heat in an object.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Conversion from Celsius to Fahrenheit is given as,
F = (41°C × 9/5) + 32
F = 105.8°F
Thus, the required measure of 41°C in Fahrenheit is given as 105.8°F.
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2) Solve for f
3d+2f=21
Answer:
[tex]2f = 21 - 3d \\ f = \frac{21}{2} - \frac{3}{2} d \\ f = - \frac{3}{2} d + \frac{21}{2} [/tex]
a store sells candy for $6.14 per pound The piece you want weighs 0.29 how much will it cost to the nearest cent
Answer:
$1.78
Step-by-step explanation:
You need to multiply!
Do this: $6.14 x 0.29 = 1.7806 (using a calculator.)
Round to the nearest whole number/cent, which will give you $1.78. That is your answer!
A bowl contains four candies-red, brown, yellow, and green. Draw two candies at random, one for you to eat, and one for
a friend. (Assume you eat the first candy drawn.)
List the simple events in the sample space. (Enter your answers as a comma-separated list. Enter each simple event in the
format (C₁, C₂) where C, is the color of the ith candy. Use R for red, B for brown, Y for yellow, and G for green.)
By using the given notation and format, we see that the sample space for the experiment is:
( {R, B}, {R, G}, {R, Y}, {B, R}, {B, G}, {B, Y}, {Y, R}, {Y, G}, {Y, G}, {G, R}, {G, B}, {G, Y})
How to get the sample space?The sample space is the set of the total possible events or outcomes in a given experiment.
Here we have 4 candies and you select two, such that the events have the format:
(C₁, C₂)
For example, if the first candy you draw is red and the second is blue, then the event will be:
(R, B)
Which is different to the event when you first draw blue and then red, which is:
(B, R).
So we just need to write all the possible events, it will give use the sample space:
( {R, B}, {R, G}, {R, Y}, {B, R}, {B, G}, {B, Y}, {Y, R}, {Y, G}, {Y, G}, {G, R}, {G, B}, {G, Y})
Where the notation used is the given one:
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What is 617 rounded to the nearest ten
Answer:
620
Step-by-step explanation:
617 rounded to the nearest ten = 620.
The number 617 when rounded to the nearest ten will be 620.
We examine the digit in the position of the one and decide whether it is closer to the previous ten or the next ten to round a number to the closest ten.
The digit in the ones place for the number 617 is 7. We round up to the next ten since 7 is bigger than or equal to 5, so we do.
The tens digit is raised by one and all the digits to its right are set to zero in order to round up to the following ten.
So, when we round 617 to the nearest tenth, we get 620.
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Solve the equation for v.
v over 6 minus 3 equals negative 11
v = 24
v = 63
v = −48
v = −84
The solution for v in the equation is v = -48
How to solve the equation for v?The equation is given as:
v over 6 minus 3 equals negative 11
Rewrite properly as
v/6 - 3 = -11
Add 3 to both sides
v/6 = -8
Multiply both sides by 6
v = -48
Hence, the solution for v in the equation is v = -48
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Answer: the answer is v=48 hope this helps!!
-6 + 13 show all work
Each function in parts (a)-(c) is a translation (horizontal/vertical/or both) of f(x). In each case the function can be written in the form y=f(x+h)+k, where h and k denote the corresponding horizontal and vertical shifts. For each of the tables below find a possible formula by applying transformations to f(x).
For the values like (0.-4) and (1,3.5),the function is h(x)=9x-4.
Given a table which contain values of the function h(x) and the respective values of x.
We are required to form the function.
Function is basically the relationship between two or more variables that are expressed in equal to form. The values that we enter in the function are known as part of domain and the values that we get from the function is known as part of range of the function.
We have to just take two points like (0.-4) and (1,3.5).
We have to just form the equation.
y-(-4)={5-(-4)}/{1-0}(x-0)
y+4=9x
y=9x-4
h(x)=9x-4
Hence for the values like (0.-4) and (1,3.5),the function is h(x)=9x-4.
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Question is incomplete as it should include the attached figure.
Given the graph of the function f(x) below, estimate the slope of the tangent line to the curve at x=−2. Select the answer that is closest.
The slope of the tangent line of the given graph of f(x) is found by the ratio of the rise to the run of the tangent line at x = -2, which gives;
The slope of the tangent line at x = -2 is 1/2How can the slope of a line, tangent to the curve of the graph be found?The tangent to a curved graph at a point is given by a line that is perpendicular to the radius of the curve at that point.
The formula that gives the tangent is expressed as follows;
[tex]tan( \theta) = \frac{d f(x)}{dx} = \frac{dy}{dx} [/tex]Examination of the graph gives;
The slope at the point x = -2 is positive
The maximum slope from x = -6.5 to x = -1.5 is approximately 3/2 = 1.5
Therefore;
The option that gives the estimate for the slope of the tangent line at x = -2 is therefore;
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After it snows it takes Maria and her little sister Anita 1/2 of an hour to shovel the snow off of the sidewalks on their street. This is 2/3 of the time it takes Maria to do the same job by herself. How long does it take Maria to do this job by herself?
3/4 of the time it takes Maria to do the same job by herself.
A time interval that is equivalent to 60 minutes and one-fourth of a mean solar or civil day.
(a)The situation from 3 to 9 on clock the hour hand turns through 1/2 gives 2/1 of revolution , clockwise.
(b)The situation 4 to 7 on the clock, the hour hand turns through 1/4 gives 4/1 of revolution, clockwise.
(c)The situation from 7 to 10 on the clock, the hour hand turns 1/4 gives 4/1 of revolution, clockwise.
(d) The situation from 12 to 9 on the clock, the hour hand turns 3/4 gives 4/3 of revolution, clockwise.
(e)The situation from 1 to 10 on the clock, the hour hand turns 3/4 gives 4/3 of revolution, clockwise.
(f)The situation from 6 to 3 on clock, the hour hand turns 1/4 gives 4/1 of revolution, clockwise.
1/2*3/2 = 3/4
use keep, flip, change.
Time is the series of events that take place over time, from the past through the present and into the future. The duration of events or the gaps between them can be measured, compared, or even ordered using time.
Hence, 3/4 of the time it takes Maria to do the same job by herself.
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Answer: 3/4 is the correct answer because when you solve they give you 3/4
Find the sum of the first n terms of the sum that corresponds to the succession
Answer:
a
Step-by-step explanation:
This is a geometric series with first term 7 and common ratio -2/5.
Four players are to be selected from a 25-player baseball team to visit schools to support a summer reading program. In how many ways can this selection be made?
The total number of possible ways in which the selection can be made is 12650.
We have a baseball team.
We have to determine in how many ways can the selection be made from 25 students to form a group of 4 students.
What is Combination ?A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
According to the question -
Total number of players in team = 25
Number of players to be selected = 4
The total number of possible ways in which this selection can be made is-
[tex][25]C_{4}[/tex] = [tex]$\frac{25!}{(25-5)!5!}[/tex] = 12650
Hence, the total number of possible ways in which the selection can be made is 12650.
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solve 4n-6(n+1)>12 (first blank is the inequality sign, second blank is the value) n
The solution to the inequality expression is n < -9
How to solve the inequality expression?The inequality expression is given as
4n - 6(n + 1) > 12
Open the bracket in the above inequality expression
4n - 6n - 6 > 12
Evaluate the like terms
-2n > 18
Divide both sides by -2
n < -9
Hence, the solution to the inequality expression is n < -9
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A circle has a diameter with endpoints
at A (-3, -12) and B(-7, 4). The point
M(-5, -4) lies on the diameter
What is the distance from A to M (Round to 2 decimal place
What is the distance from B to M (Round to 2 decimal places)
By using the Pythagorean theorem, both the distance from A to M and the distance from B to M are approximately equal to 8.25 units.
How to calculate distances in line segmentsDiameters are line segments whose endpoints lie on the same circumference and whose midpoint is the center of the circle associated to that circumference. In this problem we know the locations of the endpoints (points A and B) and a third point (point M) inside the diameter, and based on all this information we must determine the distances between points A and M and points B and M.
Each case can be found by using the Pythagorean theorem in the following form:
Points A and M
AM = √[[- 5 - (- 3)]² + [- 4 - (- 12)]²]
AM = 2√17
AM ≈ 8.25
Points B and M
BM = √[[- 7 - (- 5)]² + [4 - (- 4)]²]
BM = 2√17
BM ≈ 8.25
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The circle's center is on the x-axis.
Three units make up the circle's radius.
The radius of this circle corresponds to the radius of the circle whose equation is x2 + y2 = 9.
What is the x-axis?In accordance with the previous sentence, a Cartesian coordinate system in a plane is a coordinate system that uniquely identifies each point by a pair of numerical coordinates, which are the signed distances between two fixed perpendicular oriented lines to the point, measured in the same unit of length;
according to given statement;
Circle's standard equation is written as:
Centre is (-g, -f)
radius = √g²+f²-C
Given a circle whose equation is
Get the center of the circle
2gx = -2x
2g = -2
g = -1
Similarly, 2fy = 0
f = 0
Centre = (-(-1), 0) = (1, 0)
This shows that the center of the circle lies on the x-axis
r = radius = √g²+f²-C
radius = √1²+0²-(-8)
radius =√9 = 3 units
The radius of the circle is 3 units.
For the circle x² + y² = 9, the radius is expressed as:
r² = 9
r = 3 units
Hence the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
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Can someone help me with this :))))))))))))
The values of the variables in the linear equations are almost constant values.
According to the statement
We have to find that the values of the variables.
So, For this purpose, we know that the
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.
From the given information:
The given equations are:
1) r = -29+11
r = -18
2) x =20-16
x = 4
3) n = 7-1
n = 6
4) r = -153/9
r = -17
5) m = -20/2
m = -10
6) m = 12+1
m = 13
7) x = -13*4
x = -52
8) k = -30+18
k = -12
9) n = 32-15
n = 17
10) x = -30+15
x = -15.
So, The values of the variables in the linear equations are almost constant values.
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