Answer:
[tex]\displaystyle y' = 2x + 3\sqrt{x} + 1[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsAnything to the 0th power is 1Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex] Exponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Derivatives
Derivative Notation
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = (x + \sqrt{x})^2[/tex]
Step 2: Differentiate
Chain Rule: [tex]\displaystyle y' = 2(x + \sqrt{x})^{2 - 1} \cdot \frac{d}{dx}[x + \sqrt{x}][/tex]Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle y' = 2(x + x^{\frac{1}{2}})^{2 - 1} \cdot \frac{d}{dx}[x + x^{\frac{1}{2}}][/tex]Simplify: [tex]\displaystyle y' = 2(x + x^{\frac{1}{2}}) \cdot \frac{d}{dx}[x + x^{\frac{1}{2}}][/tex]Basic Power Rule: [tex]\displaystyle y' = 2(x + x^{\frac{1}{2}}) \cdot (1 \cdot x^{1 - 1} + \frac{1}{2}x^{\frac{1}{2} - 1})[/tex]Simplify: [tex]\displaystyle y' = 2(x + x^{\frac{1}{2}}) \cdot (1 + \frac{1}{2}x^{-\frac{1}{2}})[/tex]Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle y' = 2(x + x^{\frac{1}{2}}) \cdot (1 + \frac{1}{2x^{\frac{1}{2}}})[/tex]Multiply: [tex]\displaystyle y' = 2[(x + x^{\frac{1}{2}}) + \frac{x + x^{\frac{1}{2}}}{2x^{\frac{1}{2}}}][/tex][Brackets] Add: [tex]\displaystyle y' = 2(\frac{2x + 3x^{\frac{1}{2}} + 1}{2})[/tex]Multiply: [tex]\displaystyle y' = 2x + 3x^{\frac{1}{2}} + 1[/tex]Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle y' = 2x + 3\sqrt{x} + 1[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
Which of the following expressions is equivalent to -6?
A: -9 + 15
B: 9 - (-15)
C:-9 - 15
D: 9 + (-15)
What is the volume of a cone with a diameter of 12 inches and a height of 4
inches? *
Answer:
48 cubic inches
Step-by-step explanation:
Answer:
192π
and or [tex]603in^{3}[/tex]
Step-by-step explanation:
Which points reflected of each other across both exes PLEASE HELP ASAP
Answer:
I am pretty sure it is (-2,8) and (2,-8)
Step-by-step explanation:
I think my answer is correct because it goes from Quadrant 1 into 4. Other answers are just I quadrant away.
20 points.
Round off x to the nearest tenth.
Answer:
[tex]x=15.3[/tex]
Step-by-step explanation:
In right triangles only:
The sine of an angle is equal to its opposite side divided by the hypotenuse. (o/h)
The cosine of an angle is equal to its adjacent side divided by the hypotenuse. (a/h)
The tangent of an angle is equal to its opposite side divided by its adjacent side. (o/a)
Therefore, we have the following equation:
[tex]\sin 58^{\circ}=\frac{x}{18},\\x=18\sin 58^{\circ}\approx \boxed{15.3}[/tex]
Alternative:
[tex]\cos 32^{\circ}=\frac{x}{18},\\x=18\cos32^{\circ}\approx \boxed{15.3}[/tex]
137°
X-25
Find the value of X
A Cylinder with
a volume of 27π
in 3 and a height
of 3 in. What is
the radius?
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the concept of Surface Areas and Volume.
==> Volume of Cylinder = πr^2h
==> 27π = πr^2(3)
==> 27 = r^2 (3)
==> r^2 = 9
==> r = 3 inch
hence the radius is 3 inches.
Which expression is equivalent to 14 x minus 21 over 7 ?
Answer:
-42
Step-by-step explanation:
Which expression is equivalent to 14 x minus 21 over 7 ?
Mathematically this expression is written as:
= (14 × -21)÷ 7
= (14 × -21)/7
= - 294/7
= -42
Therefore, the equivalent of the above expression is calculated as -42
I NEED HELP please if you would. HELP
Answer:
10.3699136~10
Step-by-step explanation:
First i found the area of the triangle, .5(10*7)=35
And the area of a circle formula is pi*r^2 so...
35-(pi*2.8^2)=35-24.6300864=10.3699136
:) hope that's right
Please answer this troublesome question shown in the image
Simplify the expression. Write the answer using exponents.
9^6 x 9^8
Answer:
=9¹⁴x
Step-by-step explanation:
A coke can and a monster can are each in the shape of a right circular cylinder. The cans have the same radius but the height of the monster can is 2 times the height of the coke can. What is the ratio of the volume of the coke can to the volume of the monster can
Answer:
1 : 8
Step-by-step explanation:
Given the height of 2 similar cylinders = a : b , then
ratio of volumes = a³ : b³
Here the ratio of heights = 1 : 2
ratio of volumes = 1³ : 2³ = 1 : 8
EASY BRAINLIEST PLEASE HELP!!
-if you answer correctly ill give you brainliest which will give you 100pts-
(if you put links or don't answer accordingly im reporting your account)
Answer:
A B D
Step-by-step explanation:
those are the answers
But a closer look shows that B will be the best answer.
Answer:
Since all the rhombus is parallelogram
some are trapezoid and quadrilateral.
So
B.parallelogram is a answer:
it opposite side are equal.
diagonal bisect angle equally.
.
Find the slope of the line that passes through the points (-6,6)and(4,-2).
Answer:
=-4/5
Step-by-step explanation:
To find the slope, we can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( -2 -6)/(4 - -6)
= (-2-6)/( 4+6)
= -8/10
=-4/5
if the amount of money you have matched ur phone number, how much do you have?
Answer: lma0
Step-by-step explanation:
Answer:
45 even tho my mine broke xD
have a good day :)
Step-by-step explanation:
An isosceles triangle has base length 18 cm and height 4cm what is the approximate length of the two other sides
Answer:
The approximate length of the two other sides is 10cm
Step-by-step explanation:
Given
[tex]Base\ Length = 18[/tex]
[tex]Height = 4[/tex]
Required
The length of the two other sides
Divide the triangle to 2 (See attachment)
Considering one of the triangles, we have:
[tex]l^2 = 4^2 + 9^2[/tex]
[tex]l^2 = 16 + 81[/tex]
[tex]l^2 = 97[/tex]
Take square roots
[tex]l = \sqrt{97[/tex]
[tex]l = 9.8488[/tex]
[tex]l = 10[/tex] --- approximated
If a fish is swimming 20 feet below the surface of the ocean and a bird flying directly overhead of the fish is 12 feet above the surface, how far apart are they?
Answer:
32 feet
Step-by-step explanation:
The equation would be 12 - (-20)
12 + 20 = 32
The legs of a right triangle measure 6 centimeters and 8 centimeters. How long is the hypotenuse in centimeters?
A. 10cm
B. 11cm
C. 9cm
D. 7cm
Answer:
10cm ( A )
Step-by-step explanation:
This would use the Pythagorean Theorem. That means it would be -
a^2_b^2= c^2, in this case, you have 2 of your legs already so those two values would be a&b. you would stick those two into the equation and it should look like this:
6^2+8^2=c^2
then 36+64=c
and then 100=c
after that, you would take the square root of c to get
10!
Answer:
10cm
Step-by-step explanation:
[tex]Hypotenuse^{2}[/tex] = [tex]base^{2} + altitude^{2}[/tex]
The hypotenuse can be taken as 'x'. As given in the question, the length of base is 8cm and the altitude is 6cm. So substituting these in the equation, we get:-
[tex]Hypotenuse^{2}[/tex] = [tex]8^{2} + 6^{2}[/tex]
[tex]Hypotenuse^{2}[/tex] = 64 + 36
[tex]Hypotenuse^{2}[/tex] = 100
Hypotenuse = [tex]\sqrt{100}[/tex]
Hypotenuse equals 10cm!
How to make a data set with only 5 numbers. And so the mean is 7, the median is 7, and the mode is 5?
Answer:
5,5,7,8,10
Step-by-step explanation:
mode=5 so that would appear the most so start with 5,5
median=7 that would be the middle number so 7 would be next
when you add 5+5+7=17 now just choose any number to add to 17 and I choose 10 which makes 17+10=27.
mean=7 so that means the total has to be divided by how many numbers you have, which is 5. So the total divided by 5 should equal 7. Since have 27, the number divided by 5 to get 7 is 35. So, add to 27 to get 35 which would be 8.
27+8=35 that is your total. Now divide by 5 to get the mean of 7.
A.4 Simplity radical expressions SC5
Subtract. Write your answer in simplest form.
-9. 5 - 10/5
Answer:
your answer should be -11.5
Step-by-step explanation:
all you do is divide 10/5 which will give you 2 then you do -9.5-2 which gives you -11.5
AREA OF A CIRCLE HELP PLS
Answer:
201.06
Step-by-step explanation:
pi × 8²
Does the location of the first aid station actually fall in the middle of the park? Provide mathematical calculations to support your answer.
Answer:
The first aid station is at the middle of the park.
Step-by-step explanation:
Given
[tex](0,0) \to[/tex] Origin of Fun
[tex](-7, 6) \to[/tex] Quadratics in Motion
[tex](-2, 14) \to[/tex]Towers of Trigonometry
[tex](5,8) \to[/tex] The Food Equation
[tex](-1,7)\to[/tex] First aid station
Solving (a): Plot the above points
See attachment for plot
Solving (b): Determine if the first aid station is at the center of the park
From the plot, we have the opposite points to be:
(1) [tex](0,0)[/tex] and [tex](-2, 14)[/tex]
(2) [tex](5,8)[/tex] and [tex](-7, 6)[/tex]
Calculate midpoint using:
[tex]M = \frac{1}{2}(x_1 + x_2, y_1 + y_2)[/tex]
For (1):
[tex]M = \frac{1}{2}(0 -2, 0 + 14)[/tex]
[tex]M = \frac{1}{2}(-2,14)[/tex]
[tex]M = (-1,7)[/tex]
For (2):
[tex]M = \frac{1}{2}(5 -7, 8 + 6)[/tex]
[tex]M = \frac{1}{2}(-2,14)[/tex]
[tex]M = (-1,7)[/tex]
From the above computation, we have midpoint to be:
[tex]M = (-1,7)[/tex]
Given that:
[tex](-1,7)\to[/tex] First aid station
We can conclude that the first aid station is at the middle of the park.
it takes 0.75 cups of sugar to make a batch of lemon cookies i have 5.5 cups of sugar how mant batches can i make
Answer:
7.3
Step-by-step explanation:
The county park wants to install a circular fence around the sandpit. How much fencing will they need if the diameter of the sandpit is 10 ft?
Answer:
157.07963
Step-by-step explanation:
2πr²
2π(5)²
2π(25)
50π
157.07963
Solve for x.
..................................
Answer: For 7x-11 is There are no like terms.
I don’t know if you want me to solve because I did “Answer: There are no like terms.” or how you want it because the picture you show it confusing
For 4x-2 is Factor 4x−2
4x−2
=2(2x−1)
Answer:2(2x−1)
Step-by-step explanation: Hope this help :D
Amy bakes x cakes.
Barry bakes four times as many cakes as Amy.
Ceri bakes 12 more cakes than Amy.
They bake a total of T cakes.
Find a formula, in terms of x, for the total number of cakes.
Give your formula in its simplest form
Answer:
6x+12=T
Step-by-step explanation:
Amy bakes x cakes.
Barry bakes 4x.
Ceri bakes x+12
So the total is 6x+12=T
can somebody please help (no websites)
Answer:
x y
0 .75
3 3.75
9 9.75
Step-by-step explanation:
You add .75 to whatever number x equals, to get y.
Hope that this helps!
What is the volume of the Cube?
132 cubic inches
726 cubic inches
1331 cubic inches
33 cubic inches
Answer:
1331 cubic inches
Step-by-step explanation:
volume = 11×11×11 = 1,331 in³
Help please!
Thanks.
Answer:
6a is the answer I believe.
If i'm wrong correct me in comments.
a car uses 32 L of gas to travel 450 KM. how many liters would be required to drive 800 km (to the nearest tenth)?
Answer: 56.88 L
Explanation:
Let L represents number of liters
A Car uses 32 L of gas to travel 450 km.
Write a proportion for the problem using rates.
450/32 = 800/L
Cross product is 450*L = 800*32
450L = 25600
Divide each side by 450.
450L/450 = 25600/450
L = 56.88
Solve the inequality and describe the solution set.
y–6≥12
Answer:
y ≥ 18
All numbers greater than or equal to 18
Step-by-step explanation:
y – 6≥ 12
Add 6 to both sides
y ≥ 18
All numbers greater than or equal to 18