Answers
The differentiation of the function y = sin(2 sin⁻¹x) is; dy/dx = d√(1 - y²)]/(√1 - x²)
How to differentiate functions?
1) We want to differentiate the function;
[tex]\frac{\sqrt{x + 1} + \sqrt{x - 1}}{\sqrt{x + 1} - \sqrt{x - 1} }[/tex]
Differentiating this gives;
dy/dx = [tex]\frac{[(\frac{1}{2\sqrt{x + 1}} - \frac{1}{2\sqrt{x - 1}}) * \sqrt{x + 1} + \sqrt{x - 1}]}{(\sqrt{x + 1} - \sqrt{x - 1})^{2} }[/tex]
That can be simplified to get;
dy/dx = [tex]\frac{\sqrt{x + 1} + \sqrt{x - 1} }{(x - 1)\sqrt{x + 1} + (-x - 1) \sqrt{x - 1}}[/tex]
2) We want to differentiate the function;
y = sin(2 sin⁻¹x)
Differentiating the function gives;
dy/dx = [2cos(2 sin⁻¹x)]/√(1 - x²)
We know from trigonometric identity that;
cos²x = 1 - sin²x
Thus;
1 - sin²(2 sin⁻¹x) = cos²(2 sin⁻¹x)
But sin²(2 sin⁻¹x) = y²cos²(2 sin⁻¹x)
Thus; √(1 - y²) = cos(2 sin⁻¹x)
dy/dx = d√(1 - y²)]/(√1 - x²)
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Related Questions
Members of a lacrosse team raised $2412.50 to go to a tournament. They rented a bus for $1072.50 and budgeted $67 per player for meals. Determine the number of players the team can bring to the tournament. Please step by step
Answers
Answer:
20 Players
Step-by-step explanation:
Total Amount of Money: $2412.50
First the team rented us a bus for $1072.50
Subtract the bus from the total
$2412.50 - $1072.50 = $1340
Total Amount of Money after bus: $1340
From there we need to find the max number of players that can go.
The budget cost for each player is $67.
So we divide the remaining money by $67 to find the number of players that can go.
$1340/$67 = 20 Players.
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Hope this helps!
Find the missing side of each triangle. Leave your answers in simplest radical form.
2√3 m
A) √ 19 m
c) √5 m
O a
a
Ob b
Oc
√7m
C
Od d
B) √17 m
D) √√2 m
Answers
Answer:
C [tex]\sqrt{5}[/tex]
Step-by-step explanation:
Use pythagorean theorem.
[tex]x^{2}[/tex] +[tex]\sqrt{7} ^{2}[/tex] = (2[tex]\sqrt{3}) ^{2}[/tex]
[tex]x^{2}[/tex] + 7 = 12 Subtract 7 from both sides
[tex]x^{2}[/tex] = 5 Take the square root of both sides to solve
x = [tex]\sqrt{5}[/tex]
Two piecewise functions are shown below. What is the value of
6f (-2) + 3g (1)?
f(x) =
0-7
O-25
1/3
O 18
{
-3x
*+2'
if x < -2
³, if x ≥-2
(2|x-1| +3,
-5√x+3-1,
g(x) =
={
if x ≤ 1
if x > 2
Answers
Step-by-step explanation:
I am not sure what your problem here is.
you understand the inequality signs ?
anyway, to get
6×f(-2) + 3×g(1)
we can calculate every part of the expression separately, and then combine all the results into one final result.
f(-2)
we look at the definition.
into what category is -2 falling ? the one with x<-2, or the one with x>=-2 ?
is -2 < -2 ? no.
is -2 >= -2 ? yes, because -2 = -2. therefore, it is also >= -2.
so, we have to use
1/3 x³
for x = -2 that is
1/3 × (-2)³ = 1/3 × -8 = -8/3
g(1)
again, we look at the definition.
into what category is 1 falling ? the one with x > 2 ? or the one with x <= 1 ?
is 1 > 2 ? no.
is 1 <= 1 ? yes, because 1=1. therefore it is also <= 1.
so we have to use
2×|x - 1| + 3
for x = 1 we get
2×0 + 3 = 3
6×f(-2) = 6 × -8/3 = 2× -8 = -16
3×g(1) = 3× 3 = 9
and so in total we get
6×f(-2) + 3×g(1) = -16 + 9 = -7
Solve the inequality for x and identify the graph of its solution.
|x+ 2|>2
Answers
Answer:
A. x < -4 or x > 0Step-by-step explanation:
[tex]|x+2| > 2\iff x+2 > 2\ \vee\ x+2 < -2[/tex]
subtract 2 from both sides
[tex]x > 0\ \vee\ x < -4[/tex]
The coordinates of the vertices of △HIJ are H(−2,2), I(8,−2), and J(−4,−3). Identify the perimeter of △HIJ to the nearest tenth
Answers
Answer:
28.2
Step-by-step explanation:
The perimeter of a plane figure is the sum of the lengths of its sides. Those lengths and their sum can be found a number of different ways.
__
graphing aidThe values computed by the graphing program in the attachment add up to 28.2 units.
__
using algebraThe length of each side of the triangle can be computed using the distance formula or the Pythagorean theorem. For a given "rise" and "run", the length of a line segment is ...
d = √(rise^2 +run^2)
HI = √((-4)^2 +10^2) = √116 ≈ 10.770
IJ = √(1^2 +12^2) = √145 ≈ 12.042
JH = √(5^2 +2^2) = √29 ≈ 5.385
The perimeter is the total of the lengths of the sides:
P = HI +IJ +JH = 10.770 +12.042 +5.385 = 28.197
To the nearest tenth, the perimeter is 28.2 units.
Fluffy the bunny ate 1/2 of a carrot in the morning, and he ate some more at night. By the end of the day, he still had 1/3 of the carrot left to eat. How much of the carrot did Fluffy the bunny eat at night?
Answers
Answer:
1/6
Step-by-step explanation:
the total carrot is 1/1 and fluffy ate 1/2 of it . this means half has been eaten and it is left with half so now 1/2 -1/3 ( carrot left in the morning - the carrot left now ) this will be 1/6
HELP PLEASE!!!!!!!!!!!!!!!!!!!
Answers
Answer:
D.) x - 4
Step-by-step explanation:
This is a graph of an exponential/quadratic function. There general structure looks like this:
ax² + bx + c
Generally, when finding the zeros these functions, you are told to factor the equation. Once you have factored the equation, you can set the factors equal to zero to find the points where the function touches the x-intercept.
That being said, you can determine the factors without having the entire equation by identifying the zeros on the function. On this graph, there is a zero at (4,0). This means that one of the factors must have been "x - 4". You can check your work by setting the factor equal to zero.
x - 4 = 0
x = 4
Pls help!!!!!!!!!!!!!!!!
Answers
Answer:
D: 6.5, 3
C: 23.5, 9
I think
Answer:
C (23.5, 9)
D (6.5, 3)
Find the constant of variation for the relation and use it to write an equation for the statement. Then solve the equation.
If y varies inversely as the square of x, and y
7
when x = 1, find y when x = 3.
3x2 (3)=
--/12
C.
7
27
y =
b.
4x² (3) 7
36
7x2 (3) 4
63
3
y=y(3)
y=
d.
Answers
Answer:
k=7,y=2.33 and y=k/x^2
Step-by-step explanation:
y=k/x^2
7=k/1
k=7
y=k/x^2
y=7/3
y=2.33
hope it helpful
What is the branch of mathematics developed by isaac newton called today?.
Answers
Answer: Calculus.
Step-by-step explanation: He created calculus.
this is hard for me could smone help me ASAP please?
Answers
Answer:
x is 90°
y is 56°
Step-by-step explanation:
Concepts used :
The angle subtended by a diameter inside the circle is always 90° .
Sum of interior angles of a triangle is 180°.
Here x is the angle subtended by the diameter of the circle therefore ,
x is 90°.
let the end points of diameter as A , B
and the point where the it subtends the 90° angle be C
using interior angle property on the triangle ΔABC
90° + 62° + ∠A = 180°
152° + ∠A = 180°
∠A = 180° - 152°
∠A = 28°
now let he midpoint of diameter as D
as the sides DC and DA are radius of circle and therefore equal
so using isosceles triangle property which states that angle opposite to equal sides are equal
so the angle ∠ACD = 28°
now using exterior angle property on ΔADC
y = 56°
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Choose the variable expression that matches this phrase.
the sum of the number of crew members on the tour boat and the 5
passengers.
A. 5-c
B. 5c
C. 5+ c
D. 5÷c
Answers
The sum of the number of crew members (c) on the tour boat and the 5 passengers is 5 + c. Then the correct option is C.
What is an equivalent expression?The equivalent is the expressions that are in different forms but are equal to the same value.
The sum of the number of crew members (c) on the tour boat and the 5 passengers.
This can be written as in the form of the mathematical form.
⇒ 5 + c
Then the correct option is C.
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Tara has a box of 908 beads for making bracelets. She wants to put 15 beads on each bracelet she makes. What is the greatest number of bracelets Tara can make with these beads? Tara has a box of 908 beads for making bracelets . She wants to put 15 beads on each bracelet she makes . What is the greatest number of bracelets Tara can make with these beads ?
Answers
Answer:
Tara can make 60 bracelets.
Step-by-step explanation:
908 / 15 = 60.5
How would you describe the red paths pictured below? ( The picture above)
A. Perpendicular
B. None are correct
C. Parallel
D. Intersecting
Answers
Answer:
perpendicular
Step-by-step explanation:
yw
Solve the equation for x by graphing.
-2x − 3 = 3x + 2
Answers
Given log subscript 4 baseline 3 almost-equals 0.792 and log subscript 4 baseline 21 almost-equals 2.196, what is log subscript 4 baseline 7?
Answers
The value of the logarithmic function log₄7 = 1.404, when the values of the logarithmic functions log₄3 = 0.792 and log₄21 = 2.196.
We are given the logarithmic functions:
log₄3 = 0.792 ,,, (i), and log₄21 = 2.196 ... (ii),
and we are asked to find the value of the logarithmic function log₄7.
On subtracting (i) from (ii), we get:
log₄21 - log₄3 = 2.196 - 0.792.
Using the quotient law of logarithms, according to which:
logₓa - logₓb = logₓ(a/b), we can write the above equation as:
log₄(21/3) = 1.404,
or, log₄7 = 1.404.
Therefore, the value of the logarithmic function log₄7 = 1.404, when the values of the logarithmic functions log₄3 = 0.792 and log₄21 = 2.196.
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Answer:
A.
1.404
Step-by-step explanation:
Which expression is the simplest form of 2x^3 - x^2 + 3 (x^3 - 4x^2)
Answers
The simplest form of the given expression is 5x^3-5x^2.
We have given that
[tex]2x^3 - x^2 + 3 (x^3 - 4x^2)[/tex]
We have to determine the simplest form of the given expression.
What is the distributive property?
The distributive property of binary operations generalizes the distributive law, which asserts that equality is always true in algebra. elementary.
Use the distributive property we get,
[tex]2x^3 - x^2 + 3 (x^3 - 4x^2)\\=2x^3 - x^2 +3x^3-12x^2\\[/tex]
Add like terms we get,
Therefore we get,
[tex]=5x^3-5x^2[/tex]
Therefore the simplest form of the given expression is 5x^3-5x^2.
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Use the drawing tools to form the correct answer on the graph. Graph the line that represents this equation: y=-5x+2
Answers
An equation is formed of two equal expressions. The graph for the given situation can be drawn as shown below.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.
The graph for the given equation y=-5x+2 can be drawn as shown below.
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in a dilation, what is preserved and what is altered?
Answers
Answer:
A dilation preserves angle measures.
A dilation alters the length of line segments by the same proportion.
Step-by-step explanation:
A dilatation is a transformation that alters a figure's size while maintaining its shape and orientation. Each linear measure of the figure, such as a side length, is multiplied by the scale factor of a dilatation. A dilation is a transformation where all line segments' lengths are altered uniformly. While a dilatation can alter a figure's size, it cannot alter a figure's form. Dilations are not isometries as the figure's size changes.
Lightning quickly heats the air causing it to expand, which produces the sound of thunder. Sound travels approximately 1 mile in 5 seconds. Knowing D = rt, how far away is a thunderstorm when you notice a 3- second delay between the flash of lightning and the sound of thunder? Lightning quickly heats the air causing it to expand , which produces the sound of thunder . Sound travels approximately 1 mile in 5 seconds . Knowing D = rt , how far away is a thunderstorm when you notice a 3 second delay between the flash of lightning and the sound of thunder ?
Answers
Answer:
every second it travels 1/5 of a mile after 3 seconds you are 3/5 miles away
Hope This helps!
solve X/3 + 5/2 = -3/2 pls pls
Answers
Answer:
X=-12
Step-by-step explanation:
Subtract -5/2 on both sides:
X/3+5/2-5/2=-3/2-5/2
X/3=-8/2
X/3=-4
Multiply both sides by 3:
X/3*3=-4*3
X=-12
Answer:
x = -12
Step-by-step explanation:
To solve for x, we always want to isolate x {isolate = getting it by itself}
So, for the equation: X/3 + 5/2 = -3/2
we should first get x on its own side:
[tex]\frac{x}{3}+\frac{5}{2}=-\frac{3}{2}[/tex]
[tex]-\frac{5}{2}[/tex] [tex]-\frac{5}{2}[/tex] {subtract 5/2 from both sides} {-3/2 - 5/2 = -8/2}
[tex]\frac{x}{3} = -4[/tex]
×3 ×3 {multiply both sides by 3 to find "1"x}
x = -12
check:
-12/3 + 5/2 = -3/2
-4 + 5/2 = -3/2
(5/2 = 2 [tex]\frac{1}{2}[/tex] ; 2 [tex]\frac{1}{2}[/tex] - 4 = -1 [tex]\frac{1}{2}[/tex])
-1 [tex]\frac{1}{2}[/tex] = -3/2 {3/2 = 1 [tex]\frac{1}{2}[/tex]}
-1 [tex]\frac{1}{2}[/tex] = -1 [tex]\frac{1}{2}[/tex]
{TRUE}
so, x = -12
hope this helps!!
this is not the answer i was looking for
Answers
Math word problems please help
Answers
Think about the zoo meals in another way. Many different foods are prepped in the commissary for the
animals. Though each animal has a very specific combination of foods, there may be foods repeated in diets
for different animals. For example, cabbage may be used in the morning meals for 20 different animals. If
the food is the input, and the animal is the output, is this relationship a function?
Answers
Answer:
89
Step-by-step explanation:
i need help filling in the blanks
Complete the steps to solve the equation above.
2x + 5 = 4x - 1
+ +
After adding on both sides, the equation looks like this:
2x + = 4x
Now it's time to the combine like terms and .
2x + = 4x
- -
After subtracting on both sides, the equation looks like this:
=
Finally, we divide by on both sides, and we have solved the equation!
x is equal to .
Answers
The 3 steps to solve the algebra equation have each sub step as explained and written below.
How to solve algebra problems?We are given the algebraic equation;
2x + 5 = 4x - 1
Step 1; After adding 1 to both sides, we have;
2x + 5 + 1 = 4x - 1 + 1
2x + 6 = 4x
Step 2; We subtract 3x from both sides to get;
2x - 2x + 6 = 4x - 2x
2x = 6
Step 3; Divide both sides by 3 to get;
2x/2 = 6/2
x = 3
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Rectangular prism with a length, width, and height of 3/5 cm, 4/5cm, and 3/5 cm, respectively
Answers
The volume of the rectangular prism is 36/125 cm³.
What is the volume?A rectangular prism is a three-dimensional shape. It also known as a cuboid.
Volume = length x width x height
3/5 x 4/5 x 3/5 = 36/125 cm³
Here is the complete question :
Rectangular prism with a length, width, and height of 3/5 cm, 4/5cm, and 3/5 cm, respectively. Find its volume?
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Loss = 10% VAT=13% SP WITH VAT=25,425 now calculate CP
Answers
The cost price of the product will be 25000.
How to calculate the price?From the information given, the cost price is 25000. The loss is 10%. This will be:
= 25000 - (10% × 25000)
= 25000 - 2500
= 22500
The tax is 13%. This will be:
= 22500 + (13% × 22500)
= 22500 + 2925
= 25425
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Shape R is reflected in
a) What are the coordinates of C'?
Then R' is translated by (-3)
-6
R
=
-5 -4 -3 -2 -1
b) What are the coordinates of C"?
Y
5+
4-
3-
2+
1
- 1 to give R'.
-1-
-2-
--3-
-4-
--5+
1
to give R".
2
3 4
sit
5
X
Answers
The new coordinates of C is (-5,2), (-5,5) (-7,3) (-7,5)
The correct question is
Shape R is reflected in x axis and is translated by (-3, 0) , What will be the coordinates of the new figure
The figure is attached with the answer.
What happens when a figure is reflected on an axis ?When a figure is reflected along any axis , the coordinate of the axis on which it is reflected remains the same while the other coordinate vis the additive inverse of the given coordinate
It is given that the coordinate point of R
(-2 ,-2) , (-2,-5) (-4,-3) (-4,-5)
When it is reflected along x axis the new coordinates are
(-2 , 2), (-2,5) (-4,3) (-4,5)
and when translated by -3,0
(-5,2), (-5,5) (-7,3) (-7,5)
Therefore the new coordinates of C is (-5,2), (-5,5) (-7,3) (-7,5)
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Solve |2x - 6| < 10
{x|-2 < x < 8}
{x|2 < x < 8}
{x|-8 < x < 8}
Answers
What is necessary to determine the z-score for a raw score in a particular set of scores?.
Answers
Answer:
See below
Step-by-step explanation:
The mean score and the standard deviation are needed
