The derivative of the function y = [tex]tan^{-1}[/tex] √[(1 - x)/(1 + x)] is given by
y' = -1/[(1 + x)²× √[(1 - x)/(1 + x)]].
To find the derivative, we use the chain rule. The derivative of the outermost function, arctan, is
1/[1 + (√[(1 - x)/(1 + x)])²], and the derivative of the innermost function, the square root, is
-1/2×(1 - x)/[[tex](1+x)^{3/2}[/tex])]. Multiplying these two derivatives together gives us the final result.
1/[1 + (√[(1 - x)/(1 + x)])²]×-1/2×(1 - x)/[[tex](1+x)^{3/2}[/tex])]
=-1/[(1 + x)²× √[(1 - x)/(1 + x)]].
When we take the derivative of a function, we are essentially finding the slope of the tangent line of a function at a given point. This derivative will tell us the rate at which y changes with respect to x. The derivative of the function y = [tex]tan^{-1}[/tex] √[(1 - x)/(1 + x)] is a negative value, which means that as x increases, y decreases. Therefore, this function has a negative slope.
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Write 4.35^5 in Standard Form
please answer. i need help, i will your you brainliest !!
Answer:
21.75
Step-by-step explanation:
-6+(-2) pls help me.
Answer:
-8
Step-by-step explanation:
-6+(-2)
-6 - 2
= -8
-8
6+2=8
Then make it negative
Therefore the answer is -8
Mark me brainliest
im 12 and struggling help me please i need my grades up
Answer:
you would multiply 17% by 228,000
Step-by-step explanation:
you would get 177840
Gene starts from home and travels 3 miles north to the
The largest angle formed during his trip IS
shopping mall From the shopping mall, he travels 2
miles west to the library. Then, from the library, he
at his home
travels about 3.6 miles to return home. The entire trip
at the mall
forms a triangle.
between the mall and the library
Library
Mall
( between his home and the library
Home
Answer:
B. at the mall
Step-by-step explanation:
The largest angle formed during his trip is at the mall.
△ABC, BD &CE are the altitude of the ide AC & AB and BD=CE. Prove that △BCD≅△CBE
We have proved that △BCD≅△CBE.
What are congruent triangles?
Congruent triangles are triangles that have the same size and shape. They have the same angles and corresponding side lengths.
By the RHS congruence condition if the hypotenuse and one side of one right triangle are equal to the hypotenuse and one side of another right triangle then both right triangles are congruent.
It is given that BD=CE and BC is the hypotenuse of small triangles CEB and BDC
So, In right triangles BCD and CBE
BC=CB=common side⋯⋯[hypotenuse]
And BD=CE=given⋯⋯[sides of right triangles]
So, by RHS condition
△BCD≅△CBE.
Hence, we have proved that △BCD≅△CBE.
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We have proved that △BCD≅△CBE.
What are congruent triangles?
Congruent triangles are triangles that have the same size and shape. They have the same angles and corresponding side lengths.
By the RHS congruence condition if the hypotenuse and one side of one right triangle are equal to the hypotenuse and one side of another right triangle then both right triangles are congruent.
It is given that BD=CE and BC is the hypotenuse of small triangles CEB and BDC
So, In right triangles BCD and CBE
BC=CB=common side⋯⋯[hypotenuse]
And BD=CE=given⋯⋯[sides of right triangles]
So, by RHS condition
△BCD≅△CBE.
Hence, we have proved that △BCD≅△CBE.
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factor the trinomial 2xsquared + 5x -42
Basic quadratic expression:
[tex]ax^2+bx+c[/tex]
[tex]2x^2+5x-42[/tex]
Factoring a quadratic expression when a ≠ 0
1. Multiply a and c values (ac=k)
[tex]2(-42) = -84[/tex]
2. Find a factor pair whose sum adds to b and has the product of k
[tex]-7,12[/tex]
[tex]-7(12)=-84[/tex] [tex]-7+12=+5[/tex]
3. Replace the middle term (bx) with newfound values
[tex]2x^2 +12x-7x-42[/tex]
4. Factor by grouping
[tex]2x(x+6) -7(x+6)[/tex]
if done correctly the expression in the parentheses will be the same5. Perform the last factorization
[tex](2x-7)(x+6)[/tex]
you can verify your answer by expanding the factors to get the same expression in the beginningHi! I need some help with this (:
Answer:
the answer is 5 lists
hope this helps
Please help!! 10 minutes left!!
Show Your Work Find the area of the sector
Answer:
look at the picture I sent
A pet store has 15 puppies, 6 kittens, and 8 hamsters. Alice, Bob, and Charlie each want to buy a pet. For variety, they each want a different kind of pet. How many ways can Alice, Bob, and Charlie buy pets and leave the store satisfied
There are 24 ways for Alice, Bob, and Charlie to buy pets and leave the store satisfied. They could each buy a puppy, a kitten, and a hamster, or they could each buy a different combination of the three types of pets.
How many different pet options can Alice, Bob, and Charlie choose from before feeling satisfied?Alice, Bob, and Charlie can leave the pet store satisfied in 12 different ways.This can be shown using a combination equation, where n = the number of items (in this case, pets) and r = the number of selections (in this case, 3): C(n,r) = n! / (r! × (n - r)!). In this equation, n = 29 (15 puppies + 6 kittens + 8 hamsters) and r = 3 because Alice, Bob, and Charlie each have to select one pet.When plugging these numbers into the equation, the result is C(29,3) = 29! / (3! × (29 - 3)!) = 29! / (3! × 26!) = 8649 / 514880 = 12 different ways. Alice, Bob, and Charlie can each select a puppy, a kitten, and a hamster and leave the store satisfied in 12 different ways.Alice, Bob, and Charlie can buy pets and leave the store satisfied in 6 ways. Step 1: Alice can buy a puppy, Bob can buy a kitten, and Charlie can buy a hamster. This would leave the store with 14 puppies, 5 kittens, and 7 hamsters. Step 2: Alice can buy a kitten, Bob can buy a hamster, and Charlie can buy a puppy. This would leave the store with 14 puppies, 5 kittens, and 7 hamsters. Step 3: Alice can buy a hamster, Bob can buy a puppy, and Charlie can buy a kitten. This would leave the store with 14 puppies, 5 kittens, and 7 hamsters. Step 4: Alice can buy a puppy, Bob can buy a hamster, and Charlie can buy a kitten. This would leave the store with 14 puppies, 5 kittens, and 7 hamsters. Step 5: Alice can buy a kitten, Bob can buy a puppy, and Charlie can buy a hamster. This would leave the store with 14 puppies, 5 kittens, and 7 hamsters. Step 6: Alice can buy a hamster, Bob can buy a kitten, and Charlie can buy a puppy. This would leave the store with 14 puppies, 5 kittens, and 7 hamsters. In sum, Alice, Bob, and Charlie can buy pets and leave the store satisfied in 6 ways. Each person can buy a different kind of pet and the store will still have the same number of pets afterwards.To learn more about the combination theory refer to:
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find the difference between point A (3,2) & point B (5,9) , then round the answer to re nearest tenth please help asap
Answer:
The answer is the square root of 53, or about 7.28.
Step-by-step explanation:
To find the distance between two points, you use the formula [tex]\frac{y_{2} -x_{2}}{y_{1} -x_{1} }[/tex]. When we insert the coordinates given, you get the square root of 53, or 7.28.
Please help:)
The table summarizes data about the median debt for graduating students from a sample of universities in California and New York.
median debt less than $9,000
median debt at least $9,000
total
California universities
130
445
575
New York universities
72
271
343
total
202
716
918
Is there an association between the state and the amount of median debt for graduates? Explain your reasoning
Yes, there is an association between the state and the amount of median debt for graduates.
What is median debt?Median debt is the midpoint of a range of debt levels for a specific group of people or organizations. This debt is usually reported as the sum of all loans and credit card balances owed by the group, divided by the total number of people or organizations in the group. Median debt is different from average debt, as it is not affected by extreme values. Median debt is a good measure of the financial health of a group because it provides an indication of the typical amount of debt held by an individual or organization.
In California, the median debt for graduates is significantly lower than in New York, with 130 graduates having median debt less than $9,000 and 445 graduates having median debt at least $9,000. In New York, 72 graduates have median debt less than $9,000 and 271 graduates have median debt at least $9,000. This indicates that graduates from California universities are more likely to have lower median debt than graduates from New York universities.
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please help lollllllllllllllll
Answer:
AB=6
Step-by-step explanation:
Answer:
AB = 6
Step-by-step explanation:
12 / 2 = 6
please help i need it by tomarrow
Answer:
2-6
3-9
5-15
6-18
2-6
4-12
5-15
8-24
Step-by-step explanation:
Multiply by 3
Im a little stuck on this one yall
The pairs of alternate interior angles are <5<4 and <6<3
What is alternate interior angles ? Alternate interior angles are the pair of angles that are formed on the inner side of the two parallel lines but on the opposite side of the transversal.When two parallel lines are crossed by a transversal, the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are called alternate interior angles. These angles are always equalAlternate interior angles are the angles formed when a transversal intersects two coplanar lines. They lie on the inner side of the parallel lines but on the opposite sides of the transversal. The transversal crosses through the two lines which are Coplanar at separate points.To learn more about alternate interior angles refers to:
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A certain library charges a late fee of $0.05 for each day that a book is
late. Last month, 158 people returned books that were 7 days late.
This month, 40 less people than last month will return books that are 7
days late. How much will the library collect in late fees this month for
returned books that are overdue by 7 days?
Answer: $41.3
Step-by-step explanation:
this month late = 158 - 40 = 118
7× $0.05 = $0.35
118 × $0.35 = $41.3
please help !!!!:!:):):$:)
Answer: B. 9(−7+10x^2)
Step-by-step explanation: 9(−7+10x^2)
=(9)(−7+10x^2)
=(9)(−7)+(9)(10x^2)
=−63+90x^2
what is square root
[tex]what is \: square \: root \: of \sqrt{81} [/tex]
Answer:
9 :)
Step-by-step explanation:
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
Answer:
D (4.34,3.22)
Step-by-step explanation:
Line Y (2,4), (-4,6)
**y=mx+b slope-intercept form
m=slope; b=y-intercept
[tex]m_Y=(6-4)/(-4-2)=2/-6=(-1/3)\\y=-1/3x+b[/tex]
plug in 1 point
[tex]4=-1/3(2)+b; b=14/3[/tex]
Line Z (8,8) (-5,9)
[tex]m_Z=(8-(-9))/(8-(-5))=17/3\\y=(17/3)x+b\\8=17/3(8)+b; b=-32/13\\[/tex]
Substitution
[tex]-\frac{1}{3} x +\frac{14}{3}=\frac{17}{13}x-\frac{32}{13} : x=139/32\\y=-\frac{1}{3}(\frac{139}{32})+\frac{14}{3}\\ : y=103/32[/tex]
Sector of a circle has arc length 11cm and central angle. Find its radius and area.
Answer:
s = 11.cm
Θ = 2.2.radians
Step-by-step explanation:
A quadratic function y=f(x) is plotted on a graph and the vertex of the resulting parabola is (−5,−3). What is the vertex of the function defined as g(x)=−f(x)+3?
Answer:
(-5 , 6)
Step-by-step explanation:
f(x) = (x - (-5))² - 3 ... vertex (h , k) : (-5 , -3) y = (x-h)² + k
g(x) = -f(x) + 3 = -((x+5)² - 3) + 3 = -(x + 5)² + 6
vertex of g(x) is : (-5 , 6)
1) (0,-3) (-2,-4) find the slope
Therefore , the solution of the given problem of slope comes out to be
M = 1/2.
What is a slope?What determines a line's steepness is its slope. Gradient overflow is a mathematical expression for the gradient. The slant is the proportion of both the vertical difference (rise) over the distance between two locations to the lateral change (run) over the same distance. Hill form of an equation is used to express a straight line's equation, which is written as y = mx + b. A point on the line where the slope is m, b equals a, and the y-intercept is placed is (0, b). An illustration would be the slope and y-intercept of the formula y = 3x - 7 (0, 7). At the location of the y-intercept, the line has a slope of m, b, and c.
Here,
Given : (0,-3) and (-2,-4)
Thus,
To calculate the slope ,
We use formula:
=> M = y2 -y1 /x2-x1
=> M = -4 -(-3) / -2 - 0
=> M = -1 /-2
=> M = 1/2
Therefore , the solution of the given problem of slope comes out to be
M = 1/2.
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Help.
Cannot figure out fractions
Answer:
62 [tex]\frac{5}{12}[/tex]
Step-by-step explanation:
Manish and Ravi are reading the same series of books. As of today, Manish has read a total of 544 pages. If he reads at the same pace, after 8 days he will read a total of 928 pages.
The total number of pages that Ravi has read is modeled by the equation y=51x+594, where x is the number of days after today, and y is the total number of pages read.
Who will finish the series first? Why?
Select the response that correctly answers both questions.
Responses
Ravi will finish first, because he has already read more than Manish as of today, and he reads more than Manish each day.
Ravi will finish first, because he has already read more than Manish as of today, and he reads more than Manish each day.
Ravi will finish first, because even though Manish has read more as of today, Ravi reads faster overall.
Ravi will finish first, because even though Manish has read more as of today, Ravi reads faster overall.
Manish, because even though Ravi has read more as of today, Manish reads faster overall.
Manish, because even though Ravi has read more as of today, Manish reads faster overall.
Manish will finish first because he has already read more than Ravi as of today, and he reads more than Ravi each day.
The person that will finish the series first is;
Ravi will finish first, because even though Manish has read more as of today, Ravi reads faster overall.
How to interpret Linear Equation Problems?The general equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Total pages manish has read as at today = 544 pages
He reads at the same pace and after 8 days he has read 928 pages. Thus, the equation that represents the number of pages that Manish has read is; 928 = 8m + 544
922 - 544 = 8m
m = 378/8
m = 47.25
Thus, his rate is 47.25 pages per day
The equation for Ravi is y = 51x + 594
This shows a rate of 51 pages per day
Thus, Ravi will finish first
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PLISSSS HELP IS FOR A TEST!!!!
The vertices of quadrilateral MNPQ are M(28, 1), N(3, 4), P(7, 21), and Q(24, 24).
a. The coordinates of M' are (16,4) after a translation. State the translation rule.
b. Use GeoGebra to complete a 90° rotation around the origin
Answer:
56=78b
Step-by-step explanation:
The vertices of quadrilateral MNPQ are M(28, 1), N(3, 4), P(7, 21), and Q(24, 24).
a. The coordinates of M' are (16,4) after a translation. State the translation rule.
b. Use GeoGebra to complete a 90° rotation around the origin
Hugo began his science experiment with 22 grams of sugar crystals. During the experiment, the change in the mass of the sugar crystals was
6 grams.
What is the final mass of the sugar crystals?
Answer:
I don't think there's enough information here to answer your question
Nilda has 40 points on a game show. She answers the next question incorrectly and loses 50 points. Sketch a number line to find the new score.
Improper fraction for 4 1/5
Find the area. The figure is not drawn to scale. Please show work
Answer:
I believe it is 27.6
Step-by-step explanation:
I'm not really sure, I just multiplied. Hope this helps.
Simplify (12x3 - 8x2) - (3x3 + 9x2 + x - 7).
Answer:
9x^3-17x^2-x+7
Step-by-step explanation:
Distribute the negative you'll get
(12x^3-8x^2)+(-3x^3-9x^2-x+7)
Combine like terms
12x^3-3x^3=9x^3 , -8x^2-9x^2=-17x^2 , -x , +7
Putting it all together:
9x^3-17x^2-x+7