Answer:
B. y = x² + 1
General Formulas and Concepts:
Symbols
e (Euler's number) ≈ 2.7182Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
FunctionsAlgebra II
Logarithms - ln and eCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Slope Fields
Solving Differentials - Integrals
Integration Constant C
U-Substitution
ln Integration: [tex]\displaystyle \int {\frac{1}{x}} \, dx = ln|x| + C[/tex]
Step-by-step explanation:
*Note:
When solving differential equations in slope fields, disregard the integration constant C for variable y.
Step 1: Define
[tex]\displaystyle \frac{dy}{dx} = \frac{2xy}{x^2 + 1}[/tex]
Point (0, 1)
Step 2: Rewrite Differential
Rewrite Leibniz Notation using Separation of Variables.
[Separation of Variables] Isolate x's together: [tex]\displaystyle dy = \frac{2xy}{x^2 + 1}dx[/tex][Separation of Variables] Isolate y's together: [tex]\displaystyle \frac{1}{y}dy = \frac{2x}{x^2 + 1}dx[/tex]Step 3: Integrate Pt. 1
Solving general form of differential using integration.
[Differential] Integrate both sides: [tex]\displaystyle \int {\frac{1}{y}} \, dy = \int {\frac{2x}{x^2 + 1}} \, dx[/tex][Left Integral] ln Integration: [tex]\displaystyle ln|y| = \int {\frac{2x}{x^2 + 1}} \, dx[/tex]Step 4: Identify Variables
Set up u-substitution for right integral.
u = x² + 1
du = 2xdx
Step 5: Integrate Pt. 2
[Right Integral] U-Substitution: [tex]\displaystyle ln|y| = \int {\frac{1}{u}} \, du[/tex][Right Integral] ln Integration: [tex]\displaystyle ln|y| = ln|u| + C[/tex]Back-Substitute: [tex]\displaystyle ln|y| = ln|x^2 + 1| + C[/tex][Equality Property] Raise e on both sides: [tex]\displaystyle e^{ln|y|} = e^{ln|x^2 + 1| + C}[/tex]Simplify: [tex]\displaystyle |y| = C|x^2 + 1|[/tex]General Form: [tex]\displaystyle |y| = C|x^2 + 1|[/tex]
Step 6: Solve Particular Solution
Since both sides have absolute value, assume that the particular solution will be positive.
Substitute in point [General Form]: [tex]\displaystyle |1| = C|(0)^2 + 1|[/tex][Particular] |Absolute Value| Evaluate exponents: [tex]\displaystyle |1| = C|1|[/tex][Particular] Evaluate absolute values: [tex]\displaystyle 1 = C[/tex][Particular] Rewrite: [tex]\displaystyle C = 1[/tex]Substituting integration constant C into the general form:
Particular Solution: [tex]\displaystyle y = x^2 + 1[/tex]
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Differentials and Slope Fields
Book: College Calculus 10e
the cost of a ticket increases by 10% to £19.35 work out the original cost
Answer:
£17.59
Step-by-step explanation:
100 + 10 = 110% (Price of a ticket after increase)
110% = 19.35
1% = 19.35 ÷ 110 = 0.1759
100% = 0.1759 x 100 = 17.59
Solve the equation.
Equation
Value
10w = 90
W=
Step-by-step explanation:
w=9
______________________________________
Answer:
W = 9
Step-by-step explanation:
__________________________________
What is the angle of F?
R 134 degrees
L 68 degrees
Answer:
angleF=66
Step-by-step explanation:
F+L=R
F+68=134
F=134-68=66
or
360-68-(180-R)=66
Please help!!!!!
I took an picture of the question
Answer:
6
Step-by-step explanation:
Remember f(x) or g(x) in this case is like saying 'y' so when y = 0 x = 6
What is an equation of the line that passes through the points ( -8, 0) and (8,4)?
Answer:
the so and bro like its be a like chocie b
Step-by-step explanation:
Diana has available 280 yards of fencing and wishes to enclose a rectangular area.
(a) Express the area A of the rectangle as a function of the width W of the rectangle.
(b) For what value of W is the area largest?
(c) What is the maximum area?
Answer:
David has 280 yards of fencing to enclose a rectangular area. Find the demensions of the rectangle that maximize the enclosed area.What is the maximum area?
***
let x=width
let y=length
2x+2y=280
x+y=140
y=140-x)
Step-by-step explanation:
Help Plz again plzzzzzzzzzzzzzzzz
The angles are adjacent because they are next to each other adding to 90 degrees.
How do we find x?
Angle 1 + Angle 2 = 90°
31° + (10x - 1)° = 90°
10x + 30 = 90°
10x = 90° - 30
10x = 60°
x = 60°/10
x = 6
Answer: Adjacent and x = 6.
Help please I will give you 30 points
Answer:
it litteraly says only 5 points lol. I would help but...
Step-by-step explanation:
Answer:
x = 4
Step-by-step explanation:
x + x + x + 5 + 5 +5 = 27
3x + 15 = 27
3x = 27 - 15
3x = 12
x = 12/3
x = 4
Find the area of the regular polygon. Give the answer to the nearest tenth
square with radius 16 ft
Answer:
440.4ft
Step-by-step explanation:
:)
While visiting the beach, Dan used a pyramid-shaped mold to create a sandcastle. The base of the mold was a rectangle measuring 11 in. By 7 in. The height of the mold was 8 in what is the volume of the sand that the mold will hold?
Answer:
616
Step-by-step explanation:
First off what you will be trying to find is volume.
V=Bh
V=11(7)8
V=77(8)
V=616
Answer:Volume = 11×7×8 = 616 inches3
not sure
Step-by-step explanation:
work out the size if angle x 130 degrees and 96 degrees
Answer:
130= x+96
130-96=x
34=x
Step-by-step explanation:
Answer:
34°
Step-by-step explanation:
130+50=180 (straight line)
50+96=146
180-146=34°
Simplify the expression 1/2(h+4) - 1/8(h+4) by combining like terms.
A. 1/6 (h+4)
B. 3h/8 + 2/10
C. 3/8 (h-4)
D. 3/8 (h+4)
WILL GIVE BRAINLIEST IF THE ANSWER IS CORRECT.
Answer:
A.1/6
Step-by-step explanation:
what is the answer to 1/2 ÷2 as a fraction
Answer:
1/4
Step-by-step explanation:
1/2 ÷ 2 = 1/4
Answer:
0.25 which is 1/4.
you're welcome(:
also please give brainliest.
Step-by-step explanation:
The owner of a bakery wanted to know what items in the store generated the most income. Based on last's month's salary, this is what she found:
5% bagels
8% brownies
12% cupcakes
15% donuts
60% bread
a. What item in the store brings in the most income?
b. What percent of the store’s income comes from selling brownies and cupcakes?
c. What percent of the store’s income comes from selling items other than bread?
d. If the store owner decided to eliminate cupcakes from her inventory, by what percent would her income be reduced?
A, Bread brings the most Income ! (60% of x = 60%x)
B, 20% of the income comes from brownies and cupcakes.
C, 40% comes from others besides bread.
D, If she let go of her 12% from cupcakes, she'd be left with 88%.
If this Is correct, brainliest would be nice. <3 hope this helps.
help me or else :`( :(((((((((((((((((((
Answer:
C is the correct answer.
Step-by-step explanation:
first look at the first "kite". You got to times 30.5 x 4 ,since all of the sides are equal to each other. If you do the you will get (122).
Now onto the next one. you got to do the same but instead you got to times 40.75 x 2, and you'll come up with (81.5). Then you need to take the other number and do the same. 20.25 x 2, and that will equal to (40.5).
When you get those numbers you need to add them. So, 81.5 + 40.5= 122.
In the end you'll end up with C.
And when they ask for "What did he do wrong?"
He didn't do anything wrong, they are just trying to throw you off.
(If I'm wrong, I'm sorry, you can blame me. )
Solve for x. Enter the solutions from least to greatest.
2x^2 – 24x + 54 = 0
lesser x =
greater x =
Answer:
3
9
Step-by-step explanation:
(2x-6)(x-9)=0
lesser x = 3
greater x = 9
what is 1 ??........?
Answer:
b
Step-by-step explanation:
Answer:
1 is 1
Step-by-step explanation:
The sum of two numbers and b is equal to c The number line below shows the values of a and c. What is the value of b?
Answer:
1
Look how a and c is spaced out. The, find the middle. Then, just like that, you see the middle. It's 1!
The population of a city in 2000 was 18,500 people. Since then the population has increased 4.8% every year. Determine the correct equation that would represent what the population would be in the year 2028.
Answer:
see below
Step-by-step explanation:
Consider the year 2000 to be year 0. This would make year 2028 year 8.
Population growth or decay function: [tex]A = Pe^{rt}[/tex]
where A is the final amount, P is the principal amount, r is the rate, and t is time.
[tex]A = 18,500e^{(0.048)(8)}[/tex]
This can be simplified to
[tex]A = 18,500e^{0.384}[/tex]
Hopefully this is what the question is asking!
What is the sum of 43 and z is equal to 72.98.
Answer:
x + 43 = 72.98
- 43 - 43
x = 29.98
Step-by-step explanation:
0.4x + 2.9 = 1.5
what is x
Answer:
x= −3.5
youre welcome
Answer:
x= -3.5
Step-by-step explanation:
Step 1: Subtract 2.9 from both sides.
Step 2: Divide both sides by 0.4.
Three gallons of gasoline cost $3.36. How much does 5 gallon cost?
Answer:
Step-by-step explanation:
5gal($3.36/3gal)=$5.60
Answer:
$5.68 i think
Step-by-step explanation:
I GOT THE POWER OF GOD AND ANIME ON MY SIDE
What is the probability that a point chosen inside the rectangle is in the shaded triangle?
write as reduced fraction.
Answer:
wait what
Step-by-step explanation:
While making soup, Jenna added 5 fluid ounces of broth. About how many milliliters of broth does she add to her soup?
please help as fast as posible this is 100 pints
Answer:
148
Step-by-step explanation:
5 times 29.6
x-8/6 = 1/3 what is X
Answer:
x = 10
Step-by-step explanation:
Answer:
i got the answer 10
x-8/6 =1/3
or, x-8 = 6/3
or, x=8+2 =10
4x + 2 (3x + 7) - 7x
Answer:
3x + 14
Step-by-step explanation:
2 x 3x = 6x 2 x 7 = 14, 6x + 4x = 10x - 7x = 3x + 14
therefore its:
3x + 14
Answer:
3x+14
Step-by-step explanation:
4x+2(3x+7)-7x
4x-7x+2(3x+7)
-3x+2(3x+7)
-3x+(2*3x+2*7)
-3x+(6x+14)
-3x+6x+14
answer: 3x+14
what is an equivalent ratio to 1:3
Answer:
5:15
Step-by-step explanation:
Just times both by a random number, I chose 5
So it would be 1x5=5 and 3x5=15
So take those and boom 5:15
Hope this helps :)
2(x+y) =
I need the answer and how’d you get it.
Answer:
2x + 2y
Step-by-step explanation:
2 (x+y)
You distribute the properties and you get:
2x + 2y
Answer:
2x + 2y
Step-by-step explanation: you had to to simplify
hat is the surface area of a cylinder that has a volume if 785.4in3 and a radius of 5 in?
A 471.2in2
B 10in2
C 150in2
D 4712.3in2
Answer:
A. 471.2 in²Step-by-step explanation:
Cylinder volume:
V = πr²hCylinder surface area:
A = 2πr(r + h)Find h from the first equation:
h = V/(πr²) = 785.4/(3.14*5²) = 10 inFind surface area:
A = 2π(5)(5 + 10) = 471.23 in²Correct choice is A
Answer:
volume of cylinder=πr²h
785.4=22/7×5²×h
h=785.4×7/(22×25)=9.99=10in
Step-by-step explanation:
surface area of cylinder =2πr(r+h)=2π×5(5+10)=
471.238898038in²
A 471.2in2 is your answer.
20 points :D
Point A is located at (1,13). Point B is located at (5,8).
Draw parallelogram ABCD in the coordinate grid such that side BC is 7 units long and lies entirely in the first quadrant.
Answer:
Step-by-step explanation:
A(1,13), B(5,8)
Let C be 7 units to the right of B: C(5+7,8) = C(12,8)
Let D be 7 units to the right of A: A(1+7,13) = A(8,13)