Answers
The derivative of the function f(x) = Sin⁻¹(3x) is f'(x) = 3/√(1-9x²) , the correct option is (c) .
In the question ,
a function is given as
f(x) = Sin⁻¹(3x) , we need to find the derivative .
we know that the derivative of Sin⁻¹(x) is equal to 1/√(1 - x²) .
So , on differentiating both sides with respect to "x" .
we get
f'(x) = d/dx (Sin⁻¹(3x))
= 1/√1-(3x)² × d/dx (3x)
= 1/√(1 - 9x²) × 3
On simplifying further ,
we get
= 3/√(1 - 9x²)
Therefore ,the derivative of the function is 3/√(1-9x²) , the correct option is (c) .
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Related Questions
Aim: How can you earn money with a Savings Account?
Exit Ticket #5 Simple Interest
Find the simple interest on a $2,350 principal
deposited for 6 years at a rate of 2.77%
I =
P =
t =
I = prt
I=( )( )( )
Answers
Answer:
I = (2350)(0.0277)(6)
Step-by-step explanation:
We're told the principal, rate, and time so we just plug in.
We must convert the 2.77% to a decimal by moving the period two places to the left to get the rate 0.0277
F(x)=3x^4-4x^3+x^2+6x-2
Answers
The rational zeros for f(x) = 3x^4 - 4x^3 + x^2 + 6x - 2 are x = -1 and x = 1/3 whereas the linear factors of f(x) are (x + 1) and (3x - 1).
We will use the synthetic division method to determine the rational zeros and linear factors of given polynomials.
Polynomials are divided via synthetic division.
The procedure entails of synthetic division:
Step 1: Create a synthetic divide.
Step 2: Bring the leading coefficient down to the bottom row.
Step 3: Divide this by the value stated in the bottom row.
Step 4: Finally, add the column you defined in step 3.
This can proceed as:
Given: f(x) = 3x⁴- 4x³ + x² + 6x - 2
3x⁴ - 4x³ + x² + 6x - 2 = 0
We will put x = -1 in f(x). In this case, replace x with -1. This will be:
f(-1) = 3 * 1⁴ - 4 * 1³ + 1² + 6 * 1 - 2 = 0
Since f(-1) = 0, so (x + 1) is a factor of f(x).
Using synthetic division:
-1)....3....-4....1....6....-2
.........3.....-7...8....-2..|..0
Remainder = 0
Quotient = 3x³ - 7x² + 8x - 2
For 3x³ - 7x² + 8x - 2, f(1/3) = 0, so (x - 1/3) is a factor.
1/3)....3....-7....8....-2
..........3.....-6...6...|..0
Remainder = 0
Quotient = 3x² - 6x + 6 = 3(x² - 2x + 2)
Because x² - 2x + 2 has no more rational zeros or linear components. The rational zeros are hence x = -1 and x = 1/3.
Thus, the rational zeros for f(x) = 3x^4 - 4x^3 + x^2 + 6x - 2 are x = -1 and x = 1/3 whereas the linear factors of f(x) are (x + 1) and (3x - 1).
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A 2-column table with 9 rows. The first column is labeled year with entries 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013. The second column is labeled precipitation with entries 5.98, 6.05, 7.59, 5.27, 3.11, 7.18, 2.95, 7.22, 2.61. The table shows the precipitation in December, in inches, for Washington state from 2005 to 2013. What was the mean amount of precipitation during this time? Round to the nearest hundredth. 1.97 inches 2.61 inches 5.33 inches 5.98 inches
Answers
Answer:
5.33 inches
Step-by-step explanation:
Mean is another term for average. Therefore, we add up all precipitation items from Column B and divide by the total number of items (9):
[tex]5.98+6.05+7.59+5.27+3.11+7.18+2.95+7.22+2.61=47.96[/tex]
[tex]47.96\div{9}\approx{5.33}[/tex]
Population: The Henry family has 5 children: Abby (age 15), Brian (age 10), Colin (age 9), Deena (age 7), and
Elise (age 5).
Sample
n = 2
Ages
Sample
range
A, B
15, 10
5
A, C
15,9
6
A, D
15,7
8
Α, Ε
15, 5
10
B, C
10,9
1
B, D B, E
00000000
10,7
3
10, 5
The last sample range in this table is missing. What is the missing value? 2
C, D
9,7
5 2
C, E
9,5
4
D, E
7,5
Answers
The last sample range in this table is missing,the missing value is 2.
Given:
The Henry family has 5 children: Abby (age 15), Brian (age 10), Colin (age 9), Deena (age 7), and Elise (age 5).
Sample(n = 2) A, B A, C A, D Α, Ε B, C ........ D,E
Ages 15, 10 15,9 15,7 15, 5 10,9 ....... 7,5
Sample range 5 6 8 10 1 ...........
Let x be the sample range missing.
sample range = ages difference
= Age of D - Age of E
= 7 - 5
= 2
Therefore The last sample range in this table is missing,the missing value is 2.
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Answer:
answer is 2 i did it and got it right
Step-by-step explanation:
the sum of two numbers is 33. the sum of 3 times the larger and 4 times the smaller is 107
Answers
The value of the larger number and the smaller number are 25 and 8 respectively.
What is Simultaneous Equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y.
They are called simultaneous equations because the equations are solved at the same time.
If the bigger value is represented by x and the smaller value is represented by then
x+y= 33 equation 1
3x+ 4y= 107 equation 2
using Elimination method,
we multiply the coefficients of x by opposite equation
3x+3y=99 equation 3
3x+4y= 107 equation4
subtracting equation 3 from 4
y=107- 99
y= 8
substituting 8 for y in equation 1
x+8= 33
x= 33-8=25
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What is the y-intercept of this line?
Answers
Answer:
The Y intercept of this line is -3.
Step-by-step explanation:
The X intercept of the crossing line is about -1.4.
On finding the Y intercept:
Step 1: look at the vertical black line (Y Axis)
Step 2: Locate where the blue line crosses on this line.
Step 3: graph Y function of the point as your answer.
Hope this helped a bunch!
Have a great day!
- Kit-Kat~
0°F; drops 15° what’s the new temperature
Answers
The new temperature is given as -15°F.
What is a Measurement unit?A measurement unit is a unit to measure certain quantities.
For example, the mass can be measured in kilograms, length can be measured in meter and time can be measured in seconds.
To find the measurement of a new quantity known units can be used in operation. As to find the unit for speed we use m/s as a unit, where, m is the unit of distance and s is the unit of time.
Given that,
The present temperature is 0°F.
And, the drop in the temperature is 15°.
The new temperature after the drop can be found by subtracting the amount of drop from the initial temperature as follows,
0 - 15°F
= -15°F
Hence, the new temperature after the drop is -15°F.
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Completely factor the expression -4/5yn6 - 5/6y4n8
Answers
Answer:
See below
Step-by-step explanation:
You can pull one y and 6 n's out to start
then 4/5 = 24/30 and 5 / 6 = 25/30
and you can factor out a -1
- y n^6 /30 ( 24 + 25 y^3n^2 )
Help! I’m so confused
Answers
The measure of ∠5 is 62 degrees if the value of ∠2 is 48 degrees and ∠3 is 62 degrees. Option B is correct.
First, let us understand the types of angles formed by parallel and transversal lines:
Corresponding Angles — Corresponding angles are angles on the same side of a transversal that are either above or below the lines.
Alternate Interior Angles - Alternate interior angles are the pairs of interior angles on opposing sides of the transversal.
Alternate Exterior Angles - Alternate exterior angles are the pairs of exterior angles on opposing sides of the transversal.
Consecutive interior angles - Internal angles on the same side of a transversal are also known as consecutive interior angles, related angles, or co-interior angles.
We are given:
∠2 is 48 degrees and ∠3 is 62 degrees.
We need to find the ∠5.
From the given figure we can see that;
∠3 and ∠5 are alternate interior angles.
So, ∠3 = ∠5 = 62 degrees.
So, the measure of ∠5 is 62 degrees.
Thus, the measure of ∠5 is 62 degrees if the value of ∠2 is 48 degrees and ∠3 is 62 degrees. Option B is correct.
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Which expression has the same value as 3 ÷ 5/9? A. 3 × 5/9 B. 1/3 ÷ 5/9 C. 3 ÷ 9/5 D. 3 × 9/5
Answers
Answer:
D: 3x9/5
Step-by-step explanation:
the formula for dividing fractions is skip flip multiply where we keep the first term the same and then flip the second to multiply
Hopes this helps please mark brainliest
Write and solve an inequality to find the values of x for which the perimeter of the rectangle is less than 122.
A rectangle has a width of x and a length of x plus 4.
Answers
The inequality to find the value of x for the rectangle is 2(2x+4) < 122 and the value of x should be less than 28.5.
According to the question,
We have the following information:
The perimeter of the rectangle is less than 122.
A rectangle has a width of x and a length of x plus 4.
Now, the expressions for the width and length of the rectangle are given below:
Width = x units
Length = (x+4) units
We know that the following formula is used to find the perimeter of rectangle:
2(length+width) < 122
2(x+4+x) < 122
2(2x+4) < 122
Dividing by 2 on both sides:
2x+4 < 122/2
2x+4 < 61
Subtracting 4 from both sides:
2x < 61-4
2x < 57
Dividing by 2 on both sides:
x < 57/2
x < 28.6
Hence, the inequality to find the value of x for the rectangle is 2(2x+4) < 122 and the value of x should be less than 28.5.
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Find the exact solutions of the given equation in the interval .
sin 4x= –2sin 2x
Answers
The exact solutions of the given equation in the interval are;
A: x = 0, π/2, π, ³/₂π
How to find the exact solutions of trigonometric equations?
We are given the equation as;
sin 4x = –2sin 2x
Writing the equation in standard form gives;
sin 4x + 2sin 2x = 0
Using trigonometric Identity, substitute (sin 4x) with (2sin 2x.cos 2x) to get;
2sin 2x cos 2x + 2sin 2x = 0
Factorize to get;
2sin 2x(cos 2x + 1) = 0
A. sin 2x = 0
The unit circle will give us 3 solutions for 2x as follows;
2x = 0
Thus; x = 0
2x = π
Thus; x = π/2
2x = 2π
Thus; x = π
B. cos 2x = - 1
The unit circle gives 2 solutions for 2x as;
2x = π
Thus; x = π/2
2x = 3π
Thus; x = ³/₂π
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Complete question is;
How do you find the exact solutions of the equation sin4x = −2sin2x in the interval [0, 2π)?
Represent the following expressions as a power of the number a where a ≠ 0: (a^3)^-2. PLEASE ANSWER I WILL GIVE BRAINLYEST
Answers
Answer:
a^-6 or 1/a^6
Step-by-step explanation:
(a³)-²
=a^-6
=1/a^6
what is 5\sqrt(3ft *3\sqrt(12))
Answers
The solution of 5√3 × 3√12 = 30√3.
What is square root?Square root of a number is defined as the number in which the multiplication by itself gives the original number. That is the square root of 9 would be = 3 in which when multiplied by itself gives the original number being 9.
Other examples include √ 4 = 2, √ 25 = 5, √100 = 10.
To simplify the give expression;
5√3 × 3√12= 5√3 × 3√4×3
= 5√3 × 3×2√3
= 5√3 × 6 √3
= 30√3.
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When Nathaniel moved into a new house, he planted two trees in his backyard. At the time of planting, Tree A was 38 inches tall and Tree B was 20 inches tall. Each year thereafter, Tree A grew by 6 inches per year and Tree B grew by 9 inches per year. Let AA represent the height of Tree A tt years after being planted and let BB represent the height of Tree B tt years after being planted. Write an equation for each situation, in terms of t,t, and determine the interval of time, t,t, when Tree A is taller than Tree B.
Answers
The equations of both trees are Tree A = 38 + 6t and Tree B = 20 + 9t and the growth interval of tree A is t < 6
The equations of the growth of both treesFrom the question, we have the following parameters that can be used in our computation:
Tree A
Initial height = 38 inchesRate = 6 inches each yearTree B
Initial height = 20 inchesRate = 9 inches each yearThe height after t years is
Tree = Initial height + rate * t
So, we have
Tree A = 38 + 6t
Tree B = 20 + 9t
The interval of timeRecall that
Tree A = 38 + 6t
Tree B = 20 + 9t
When Tree A is taller than Tree B, we have
38 + 6t > 20 + 9t
Evaluate the like terms
-3t > -18
Divide
t < 6
Hence, the interval is t < 6
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What is the slope of this line?
O 3/2
O 2:3
0 −3/2
O I don't know.
Answers
Answer:
3/2
Step-by-step explanation:
the answer is 3/2 because you take the slope by using the equation y/x. I did this problem by starting prop the point (0,-6). I then counted for how many points I went up, how many did I go to the right or left. If it went to the right it’s positive, to the left it is negative. In this case it went to the right 2 times every time it went up 3. Meaning 3/2
Gayle Miller works 43 hours every week. Her weekly salary is $397.75. How much overtime does Gayle make each week?
Answers
Answer:
$9.25
Step-by-step explanation:
$397.75÷43=$9.25
Weekly salary divided by hours of work = hourly pay
Find the rate if a principal of $1,100 earned $1,089 interest in 12 years.
Answers
Answer:
8.25
Step-by-step explanation:
there are 32 steps in one floor of a tower max lives .he climbs 6 floors of his building. if he clims 6 floor every day , how many steps does he climb every week
Answers
Answer:
1,344
Step-by-step explanation:
First, find how many steps he climbs every day
32*6=192
Now, multiply that by 7 to see how many he climbs in a week
192*7=1,344
If the nth term of a number sequence n2-3 find the first 3 terms
Answers
Answer:
-1,-2,0
Step-by-step explanation:
n(2-3)
1st term=n(2-3)
substitute value
1(2-3)=-1
2nd term=2(2-3)=-2
3rd term=3(3-3)=0
Write an equation of the line that is PARALLEL to 12x - 4y = 4 and through the point (-9,-2).
Answers
Answer:
y=3x+25
Step-by-step explanation:
we need start by making slope intercept form
lets move the 12x after moving it we get
-4y=-12x+4 we need to remove the - 4 from the y so we need to divide the whole equation by - 4
we get y=3x-1
now we can create an equation to get the parallel line
y+2=3(x+9) now distribute
y+2=3x+27 and subtract the two
y=3x+25
Find two vectors that are orthogonal to u = -2i +5j -3k and w = 3i +2j + k
Show work, please
Answers
After solving the equation of vector, the value obtained is equal to one, which shows that vectors are orthogonal.
What are vector?A vector is a quantity with both magnitude and bin physics. It is often depicted by an arrow with the same direction as the amount and a length proportionate to the size of the quantity. A vector has magnitude and the direction, but no position. As soon as a vector's length remains unchanged, it is consequently untouched by movement perpendicular to itself.
In contrast to vectors, scalars are normal variables having a magnitude but no direction. Displacement, velocity, and acceleration are all vector quantities, unlike speed, time, or weight, which are scalar variables.
uw = -6 + 10- 3
uw = 1.
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The ages of people visiting a senior center one afternoon are recorded in the line plot
Does the data contain an outlier? If so, explain its meaning in this situation.
A: No, there is no outlier. This means that the data was not collected correctly, as there would be lots of age ranges at the center.
B: No, there is no outlier. This means that the people at the center were all seniors around the same age.
C: Yes, there is an outlier of 85. This means that one person was age 85, which is 15 years older than the next closest age.
D: Yes, there is an outlier of 105. This means that someone at the center is 105 years old.
Answers
Answer:
b
Step-by-step explanation:
The correct option is (b) The data does not contain an outlier. This means that the people at the center were all seniors around the same age.
What is an Outlier in a Dataset?Outlier in a data set is simply the extremely low data point or an extremely high data point compared to other points in the dataset.
It will stand out from the other values in the dataset.
The line plot shows the ages of people visiting a senior center one afternoon.
The data points are,
70, 70, 70, 75, 75, 80, 80, 85, 90, 90, 95, 95, 95, 100.
If there is an outlier in the set, it would be extremely low or high compared to other points.
But there are no such points.
So there are no outliers.
This means that people visited at the center were all seniors around the same age.
Hence the correct option is (b).
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00
Which could be the base shape of the cylinder?
Oline
O non-square rectangle
O circle
O square
Answers
Answer:
The answer is a D. a circle
The base shape of the cylinder can only be a circle.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
A cylinder is a three-dimensional shape that has two congruent parallel circular bases connected by a curved surface.
The shape of the base determines the shape of the cylinder. If the base is circular, then the cylinder is called a circular cylinder.
A non-square rectangle and a square are not circular, and thus cannot be the base shape of a cylinder.
Hence, the base shape of the cylinder can only be a circle.
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Randy is 8 years old. His brother is twice as old as randy. Randys sister is three years younger than randy. Write a expression to represent the age of randys brother
Answers
The expression that represents the age of randy's brother is
2x.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Randy age = 8 years old
Randy's brother age = 2 x 8 = 16
Randy's sister age = 8 - 3 = 5
The expression that represents the age of randy's brother.
Let the age of Randy = x.
= 2x
= 2x
= 2 x 8
= 16 years old.
Thus,
The expression that represents the age of randy's brother is
2x.
Where x is the age of Randy.
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Determine whether the percent of change is a percent of increase or a
percent of decrease. Then find the percent of change.
%
original: 20
new: 18
by
Answers
Answer:
the change is in %age of decrease of 10%
Step-by-step explanation:
original value = 20
new value = 18
decrease = 2
%age decrease = decrease/original value * 100
= 2/20 * 100
= 10%
The animals at a safari park include camels,
kangaroos and meerkats.
There are 12 more kangaroos than there are
camels.
There are 3 times as many meerkats as there
are camels.
There are the same number of kangaroos as
there are meerkats.
How many camels are there at the safari park?
Answers
m = 3c
k = m
Equating the RHS of the first two equations gives
3c = c + 12
2c = 12
c = 6
There are 6 camels
How can I find the scale factor of the two similar triangles and how can I use similarity and scale factor to find the length?
Answers
Answer:
i think, x equal 12 and y equal 20
On Saturday, 120 hotel guests used the valet service, and 280 hotel guests did
not use the valet services. What percentage of the guests at this hotel used the
valet service on Saturday?
Answers
Answer: 42.86%
Step-by-step explanation: 120/280*100 = 42.86%
How many times greater is 5.96 × 10^4 then 2.98 × 10^3?
Answers
Answer: 2.5>9.5
Step-by-step explanation: maybe we should both pay attention to math
