Answers
Answer:
[tex]y'= \frac{3x+2}{2\sqrt{x} }[/tex]
General Formulas and Concepts:
Calculus
The derivative of a constant is equal to 0
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Product Rule: [tex]\frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Chain Rule: [tex]\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
[tex]y=\sqrt{x} (x+2)[/tex]
Step 2: Rewrite
[tex]y=x^{\frac{1}{2} } (x+2)[/tex]
Step 3: Differentiate
Product Rule [Basic Power/Chain Rule]: [tex]y'= \frac{1}{2} x^{\frac{1}{2} -1}(x+2)+x^{\frac{1}{2} }(1)[/tex]Simplify: [tex]y'= \frac{1}{2} x^{\frac{-1}{2}}(x+2)+x^{\frac{1}{2}}[/tex]Rewrite: [tex]y'= \frac{x+2}{2\sqrt{x} } + \sqrt{x}[/tex]Add: [tex]y'= \frac{3x+2}{2\sqrt{x} }[/tex]Related Questions
Help please math people
Answers
Answer:
29
Step-by-step explanation:
[tex]f(x)=4x+9[/tex]
Substitute x = 5 in the equation.
[tex]f(5)=4(5)+9\\f(5)=20+9\\f(5)=29[/tex]
Therefore, the answer is 29. The third choice.
Find the missing side of this triangle, round to the nearest tenth if needed PLEASE HELP WILL MARK BRAINLIEST
Answers
Answer:
The value of x:
[tex]x\:\approx \:8[/tex] inStep-by-step explanation:
Given
[tex]b=4.8[/tex] in
[tex]c=9.3[/tex] in
a = x
we have to determine 'x'.
As the given triangle is a right-angled triangle.
Pythagorean Theorem:
For a right-angled triangle, with sides 'a' and 'b', the hypotenuse 'c' is defined as
[tex]c=\sqrt{a^2+b^2}[/tex]
so
[tex]a=\sqrt{c^2-b^2}[/tex]
as
[tex]b=4.8[/tex] in[tex]c=9.3[/tex] ina = xsubstituting the values
[tex]x=\sqrt{9.3^2-4.8^2}[/tex]
[tex]x\:\approx \:8[/tex] in
Thus, the value of x:
[tex]x\:\approx \:8[/tex] incould someone please help me with this?
Answers
what is a polygon with only 3 sides
Answers
Answer:
triangle?duh ..........
Hey, Whats The answer please explain your answer marking brainliest:D.....................................
Answers
A. 21
Bugbjyvjgbjhbghcfgdchgv
Answer:
A) 21
Step-by-step explanation:
30% of 70 is 21
pls help. polynomials solving equations
Answers
Answer:
+9or -9 is the answer ☺️ you
Answer:
y will be equal to 0, 9, or 1
(y=0, 9, 1)
A school had 45 classrooms. there are 27 in each classroom how many students are in all 45 classrooms?
Answers
Answer:
1215
Step-by-step explanation:
Answer:
1,215
Step-by-step explanation:
just multiply 27 &45
Solve for x: 3x − 2 > 5x + 10. (5 points)
1) x > 6
2) x −6
Answers
Answer:
[tex]x<-6[/tex]
Step-by-step explanation:
[tex]3x-2>5x+10[/tex]
Add 2 to both sides
[tex]3x-2+2>5x+10+2[/tex]
Simplify
[tex]3x>5x+12[/tex]
Subtract [tex]5x[/tex] from both sides
[tex]3x-5x>5x+12-5x[/tex]
Simplify
[tex]-2x>12[/tex]
Multiply both sides by [tex]-1[/tex] (reverse the inequality)
[tex](-2x)(-1)<12(-1)[/tex]
Simplify
[tex]2x<-12[/tex]
Divide both sides by [tex]2[/tex]
[tex]\frac{2x}{2} <\frac{-12}{2}[/tex]
Divide the numbers: [tex]\frac{2}{2} =1[/tex]
[tex]=x[/tex]
Divide the numbers: [tex]\frac{-12}{2}[/tex]
Apply fraction rule: [tex]\frac{-a}{b} =-\frac{a}{b}[/tex]
[tex]=\frac{12}{2}[/tex]
Divide the numbers: [tex]\frac{12}{2} =6[/tex]
[tex]=-6[/tex]
[tex]x<-6[/tex]
Answer:
x < -6
Step-by-step explanation:
I just took the test. When you are dividing by a negative variable, flip the sign.
The local newspaper has letters to the editor from 30 people. If this nunber represents 5% of all of the
newspaper's readers, how many readers does the newspaper have?
The newspaper has___readers.
Answers
Answer:
600 readers
Step-by-step explanation:
just do 100/5=20
and then 30x20=600 readers
Write in slope intercept form . y+4=−12(x−2)
Answers
Answer:
20
Step-by-step explanation:
y+4=−12(x−2)
Step 1: Add -4 to both sides.
y+4+−4=−12x+24+−4
y=−12x+20
how many lines of symmetry does the Eiffel Tower have?
Answers
Answer:
it has 2 lines of symmetry 1 going across it diagonally and 1 going straight through the middle.
Step-by-step explanation:
Help ASAP I’ll give brainliest
Answers
Answer:
B
Step-by-step explanation:
—Math–x/4 < 7
–x < 28
x > –28
follow my account^^
Answer:
B. x > -28
Step-by-step explanation:
-x/4 < 7 =
Multiply both sides by 4
-x < 28
x > -28
At a carnival game, the chance of winning a prize is 0.45. Kylee plays the game 3 times. Using the table, what is the probability that she wins at most 2 prizes?
0.09
0.33
0.58
0.91
Answers
The probability of winning one prize in 3 attempts is P = 0.41.
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
Given that, the chance of winning a prize is 0.45, Kyle plays the game 3 times. we need to find the probability that she wins at most 2 prizes
Out of 3 attempts, the probability of winning one prize is:
P(1) = (0.45)x(0.55)²p
where p is the number of permutations, you can win on the first attempt, second attempt, or third attempt, so there are 3 permutations.
Then the probability is:
P(1) = (0.45)x(0.55)²x3 = 0.41
Hence, the probability of winning one prize in 3 attempts is P = 0.41,
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Answer: D 0.91
Step-by-step explanation:
Add 0.17 + 0.41 + 0.33 = 0.91
To get 0.17:
0.41 + 0.33 + 0.09 = 0.83
1 - 0.83 = 0.17
:)
nth term (math) asap please.
Answers
Answer:
Just do minus two, and you will get 27-100=-73
Step-by-step explanation:
The distribution of random variable r has mean 10 and standard deviation 4. The distribution of random variable s has mean 7 and standard deviation 3. If r and s are independent, what are the mean and standard deviation of the distribution of r−s ?.
Answers
The random variable r has a mean μ = 10 and σ = 4. For the variable s, the μ = 7 and σ = 3. The mean of r-s will be obtained by arithmetic subtraction of the μ for r and a. The standard deviation isn't independent since it's obtained by square root of the variance of a distribution. The standard deviation will be obtained by obtained through the square root of the squared sum of σ.
μ (r-s) = μ(r) -μ(s)
μ (r-s) = 10 -7 = 3
σ (r) -σ(s) = √(σ (r))²+ (σ (s))²
σ (r) -σ(s) = √(4²+ 3²)
σ (r) -σ(s) = √(16+ 9)
σ (r) -σ(s) = √25 = 5
thus, the mean is 3 and the standard deviation is 5.
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Help me with this it’s for geometry
Answers
Answer:
x = 4
Step-by-step explanation:
The transversal line is perpendicular to both the parallel lines. So ,
[tex]21x+6=90\\=>21x=90-6=84\\=>x = \frac{84}{21} = 4[/tex]
1.) A tower casts a shadow that is 60 feet long when the angle
of elevation of the sun is 65". How tall is the tower?
Answers
Answer:
128.67 ft
Step-by-step explanation:
Let the height of the tower be x feet.
[tex] \tan \: 65 \degree = \frac{x}{60} \\ \\ 2.1445069205 = \frac{x}{60} \\ \\ x = 2.1445069205 \times 60 \\ \\ x = 128.670415 \\ \\ x = 128.67 \: ft[/tex]
Ill make you brainlist write in y=mx+b form
Answers
Answer:
y = [tex]\frac{2}{5}[/tex] x + 2
Step-by-step explanation:
Graph below.
Answer:
y = 2/5x + 2
Step-by-step explanation:
y = mx + b
First, we find out the slope. The slope is the change in y over the change in x.
The change in y is the second y-value subtracted from the first. The first y-value is 0 and the second is 2.
0 - 2 = -2
The change in x is the second x-value subtracted from the first. The first x-value is -5 and the second is 0.
-5 - 0 = -5
The slope is the change in y over the change in x.
-2/-5 = 2/5
y = 2/5x + b
b is the y-intercept, which is the value of y when x = 0.
When x = 0, y = 2 (0,2), so b = 2.
y = 2/5x + 2
Hope this helps!
4(x - 6) + 2 = 6x -2
solve the equation
Answers
Answer:
x=−10
Step-by-step explanation:
Let's solve your equation step-by-step.
4(x−6)+2=6x−2
Step 1: Simplify both sides of the equation.
4(x−6)+2=6x−2
(4)(x)+(4)(−6)+2=6x+−2(Distribute)
4x+−24+2=6x+−2
(4x)+(−24+2)=6x−2(Combine Like Terms)
4x+−22=6x−2
4x−22=6x−2
Step 2: Subtract 6x from both sides.
4x−22−6x=6x−2−6x
−2x−22=−2
Step 3: Add 22 to both sides.
−2x−22+22=−2+22
−2x=20
Step 4: Divide both sides by -2.
−2x
−2
=
20
−2
x=−10
Answer:x=-10
Step-by-step explanation:4x-24+2=6x-2 -22+4x=6x-2 , 2x=-20 , x=-10
I’m not sure how to do this can anyone help!!!!!
Answers
9514 1404 393
Answer:
22/44
Step-by-step explanation:
The probability of black is the ratio of black cards to all cards. If the Ace and 2 are removed from each suit, there will be 11 of the 13 cards remaining. 2 suits are black, for a total of 2×11 = 22 black cards. Of course there are 4 suits altogether, for a total of 4×11 = 44 total cards. Then you have ...
P(black) = (black cards)/(total cards)
P(black) = 22/44
_____
You are expected to be familiar with the fact that a deck of 52 playing cards consists of 4 suits: diamonds, clubs, hearts, spades. Each suit has 13 cards, identified as Ace, 2, 3, ..., 10, Jack, Queen, King. The clubs and spades are black; the diamonds and hearts are red.
Until the scale was changed in 1995, sat scores were based on a scale set many years ago. For math scores, the mean under the old scale in the early 1990s was 470 and the standard deviation was 110. In 2016, the mean was 510 and the standard deviation was 103. Gina took the sat in 1994 and scored 500. Her cousin colleen took the sat in 2016 and scored 530. Who did better on the exam, and how can you tell?.
Answers
Gina—her standardized score is higher than Colleen’s. The person who did better relative to their peers is Gina and this is because her standardized score is higher than Colleen
z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.
For Gina
Gina took the SAT in 1994 and scored 500 on the Math test.
For Math scores, the mean under the old scale in the 1990s was 470 and the standard deviation was 110.
x = 500
μ = 470
σ = 110
Hence, the z score is given as:
z = 500 - 470/110
z = 0.27273
Gina's z or standardized score is 0.27273
For Colleen
Her cousin Colleen took the SAT in 2016 and scored 530 on the Math test.
In 2016 the mean was 510 and the standard deviation was 103.
x = 530
μ = 510
σ = 103
Hence, the z score is given as:
z = 530 - 510/103
z = 0.19417
Colleen's z or standardized score is 0.19147
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Jordan is starting to save $150 to buy a new cell phone. In December, he saved $5. In January, he plans twice as much as he did in December, for a total savings of $15 ($5 + $10). If Jordan continues to save twice as much he saved from the previous month, in which month will his total savings will be enough to buy the phone.
Answers
9514 1404 393
Answer:
April
Step-by-step explanation:
The sequence of amounts saved is a geometric sequence. The sum of those amounts is given by the formula ...
Sn = a1·(r^n -1)/(r -1)
where a1 is the amount saved in month 1, r is the common ratio, and n is the number of months. We want to find n such that ...
150 ≤ 5(2^n -1)/(2 -1)
30 ≤ 2^n -1
31 ≤ 2^n
We can solve this using logarithms, or we can make use of our knowledge of powers of 2: 2^5 = 32. That is, n = 5 will be the first month when Jordan's total savings exceeds $150.
The fifth month will be April. Jordan's total savings will be enough in April.
__
The attached shows a spreadsheet that computes Jordan's amount of savings each month, and his running total. Once the formulas are written, they can be copied down as far as required to see where the total savings is enough.
Please help me, inequalities...............................
Answers
Answer:
x is greater than or equal to 1
Step-by-step explanation:
simplify 5n+11n=16n PLEASE
Answers
Answer:
16n=16n or n=1
Step-by-step explanation:
5n + 11n = 16n add like terms
16n = 16n divide both sides by 16
n = 1
Answer:
16n = 16n ⇒ True
Explanation:
Add to simplify:
5n + 11n ⇒ equals 16n
So, the final answer is:
16n = 16n ⇒ True (16n does equal 16n)
Hope this helps! :)
Solve for y: 20x + 4y = 28
Answers
Answer:
y = 7 - 5x
Step-by-step explanation:
20x + 4y = 28
4y = 28 - 20x
y = 28/4 - 20x/4
y = 7 - 5x
-TheUnknownScientist
Manuel created a factor tree and wrote the prime factorization of 60 shown below.
A factor tree of 60. 60 branches to 4 and 15. 15 branches to 3 and 5. The equation is 60 = 3 times 4 times 5.
What is Manuel’s error?
He did not include 15 in the prime factorization.
He did not find the prime factors of 4.
He should have started the factor tree with 2 times 30.
He should not have found the factors of 15.
Answers
Answer:
The second one or B- "He did not find the prime factors of 4."
Step-by-step explanation:
I got it right on Edge2020
Answer:
B
Step-by-step explanation:
what is the value of the fourth term in a geometric sequence for which a1 = 3- amd r = 1/2
Answers
The value of the fourth term in a geometric sequence is 3/8.
How to calculate the sequence?We are meant to find the value of the fourth term in a geometric sequence for which a1 = 3- and r = 1/2.
It should be noted that the formula will be:
ar^n-1
where n = 4
r = 1/2
a = 3
Therefore, ar^n-1 = ar^(4-1) = ar³
= ar³.
= 3(1/2)³
= 3 × 1/8
= 3/8
Thw 4th term is 3/8.
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50 POINTS AND BRAINLIEST
Answers
out to one or greater than one.
Find the gradient of the line segment between the points (-3,3) and (2,5).
Give your answer in its simplest form.
Answers
Answer:
2/5
Step-by-step explanation:
5-3/2-(-3)=2/5
what is 11 = 12 - q ?
Answers
Answer:
1
Step-by-step explanation:
12 - 1 = 11
to solve for q all you had to do was 12-11=1 (switch 11 and one)
Hey there!
11 = 12 - q
-q + 12 = 11
SUBTRACT 12 to BOTH SIDES
-q + 12 - 12 = 11 - 12
SIMPLIFY IT!
-q = 11 - 12
-q = -1
-1q = -1
DIVIDE -1 to BOTH SIDES
-1q/-1 = -1/-1
SIMPLIFY IT!
q = -1/-1
q = 1
Therefore, your answer should be:
q = 1
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)