Answers
Answer:
Part A: [tex]\displaystyle f(x) = \frac{19}{2}x^2 + 15x + C[/tex]
Part B: [tex]\displaystyle f(x) = \frac{19}{2}x^2 + 15x - 5[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityAlgebra I
Functions
Function NotationCalculus
Differentiation
DerivativesDerivative NotationDifferential Equations
Integration
Integrals[Indefinite Integrals] Integration Constant CIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f'(x) = 19x + 15[/tex]
Step 2: Find Antiderivative
[Derivative] Integrate both sides: [tex]\displaystyle \int {f'(x)} \, dx = \int {19x + 15} \, dx[/tex][Left Integral] Simplify: [tex]\displaystyle f(x) = \int {19x + 15} \, dx[/tex][Integral] Rewrite [Integration Property - Addition/Subtraction]: [tex]\displaystyle f(x) = \int {19x} \, dx + \int {15} \, dx[/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle f(x) = 19 \int {x} \, dx + 15 \int {} \, dx[/tex][Integrals] Integration Rule [Reverse Power Rule]: [tex]\displaystyle f(x) = 19 \bigg( \frac{x^2}{2} \bigg) + 15x + C[/tex]Simplify: [tex]\displaystyle f(x) = \frac{19}{2}x^2 + 15x + C[/tex]Step 3: Find Particular Solution
Substitute in function value [Function f(x)]: [tex]\displaystyle 87 = \frac{19}{2}(-4)^2 + 15(-4) + C[/tex]Evaluate: [tex]\displaystyle 87 = 92 + C[/tex]Solve: [tex]\displaystyle C = -5[/tex]Substitute in C [General Solution]: [tex]\displaystyle f(x) = \frac{19}{2}x^2 + 15x - 5[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differential Equations
Related Questions
Determine whether the system has no one, or infinitely many solutions.
y = 2x + 6
y = -x - 3
Answers
Answer:
One solution
Step-by-step explanation:
I think its 1 solution but I could be wrong, I looked it up and it said one solution.
Answer:
one
Step-by-step explanation:
I am using substitution method:
2x+6=-x-3
subtract 6 from both sides
2x=-x-9
add x to both sides
3x=-9
divide by 3
x=-3
you can also graph this to see. I personally like using desmos.
Vrite and simplify an expression to find he total cost of x pencils , 1 poster board , and (x + 1) notebooks.
Answers
Answer:
The expression to find the total cost of x pencils, 1 poster board, and (x + 1) notebooks will be:
[tex]C=xp+b+nx+n[/tex]
Step-by-step explanation:
Consider '[tex]x[/tex]' be the number of pencils which were bought
Consider '[tex]p[/tex]' denotes the cost of [tex]1[/tex] pencil
Consider '[tex]b[/tex]' denotes the cost of [tex]1[/tex] poster board
Consider '[tex]x+1[/tex]' be the number of notbooks which were bought
Consider '[tex]n[/tex]' denotes the cost of [tex]1[/tex] notebook
As we have to find the total cost. Let 'C' denotes the total cost
so the expression becomes
[tex]C=xp+b+\left(x+1\right)n[/tex]
simplifying
[tex]C=xp+b+nx+n[/tex]
Therefore, the expression to find the total cost of x pencils, 1 poster board, and (x + 1) notebooks will be:
[tex]C=xp+b+nx+n[/tex]
Find x in the following solution: x+x+10+2x-6=180
Answers
Answer:
X = 44
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
x=44
Step-by-step explanation:
First you add the all the x's.
4x+10-6=180
Then you subtract 6 from 10
4x+4=180
Next, you add subtract 4 from both sides.
4x=176
Divide by 4 and you get 44.
176/4
x=44
(10 - 1 ) x 2 + 2 x 3 what is the value of the expression
Answers
Answer:
24
Step-by-step explanation:
(10-1) x 2 + 2 x 3
9 x 2 + 6
18 + 6
24
Write this essay for me
ftgyhujiokpjhgfrd6tyujnhbgvfcd bdyt wehdfvdfo dfvkdsfdofne gergohewrierofnerg
syke its a giveaway for 50 points
Answers
Answer:
thanks for the free points! ✌
Step-by-step explanation:
Answer:
Thank you for the giveaway, I guess?
you have your tires rotated every 6 months and you replace the windshield wiper blades every eight months. How many months will hou next rotate the tires and replace the windshield wipers on the same day?
Answers
Answer:
28 : 40
Step-by-step explanation:
6 8
12 16
18 24
24 32
28 40
Both of these months will be on March
May I have brainliest please? :)
Function 1: Sam is 150 feet below sea level in a cave and trying to climb back out to safety at zero elevation. He climbs at a rate of 4 feet per
minute. This situation can be modeled with a function where C(m) represents the number of feet he has left to climb in order to reach
zer elevation
Function 2: The function below shows the number of feet that Sam's friend, Arthur, has left to climb
to reach zero elevation from a different cave as a function of time x in minutes). Assume that the domain is represented by all real numbers for
0 < 30
X
f(x)
5
-125
10
-100
15
-75
20
-50
25
-25
30
0
Who climbs at a faster rate? Make sure to explain your answer and how you know
Answers
Answer:
Start at -150, then add 3(-5), then add 122.2. -150 + 3(-5) + 122.2 = -45.3.
The answer is -45.3 feet depth. while minus sign shows the descend under the water with water surface as starting point.
Step-by-step explanation:
Initial depth of diver under the water =-150feet=−150feet
Diver descends 5 feet per minute for 3.5 minutes =3.5*(-5)=3.5∗(−5)
=-17.5=−17.5
Note: minus sign shows that the diver is under the water.
Diver ascends =122.2feet=122.2feet
Now adding all the terms a below as a numerical expression.
Current Depth of Diver after he descends 5 feet for 3.5 minutes and ascend 122.2 feet after =-150-17.5+122.2=−150−17.5+122.2
=45.3feet=45.3feet
By taking the initial depth of diver from which we add or subtract the changes made when he ascends or descends in the water to get the current depth.
PLEASE MARK ME AS BRAINLIEST
-k +3 Can u help, please
Answers
Answer:
-k3 is the answer or somebody help me also
5. $120 for 15 books A. $8−−−−1 book B. 1 book−−−−$8 C. $15−−−−1 book D. 1 book−−−−$15
Answers
Answer:
it should be A and if it is not a then b but I think A
Answer:
B. 1 book-––$8 that should be the answer
Use the figure and given angle to find the measure of each angle below (tell me how many degrees it is).
Answers
9514 1404 393
Answer:
∠6 = ∠4 = 84°
∠5 = ∠3 = 96°
Step-by-step explanation:
Angle 4 and the marked angle (84°) are corresponding angles, so are congruent. Angles 4 and 6 are vertical angles, so are congruent.
∠6 = ∠4 = 84°
Angle 3 and the marked angle are a linear pair, so angle 3 is the supplement of 84°:
∠3 = 180° -84° = 96°
Angle 3 and angle 5 are alternate interior angles, so are congruent.
∠5 = ∠3 = 96°
Deshane for one day there was a bit of $19.99, and there was an additional charge of 98 cents for each mile driven. Deshaun had to pay 140.53 when he returned the truck. For how many miles did he drive the truck.
Answers
Answer:
1.23
Step-by-step explanation:
Find the value of the variable, x
Group of answer choices
6
102
27
17
Answers
Answer:
17
Step-by-step explanation:
Let's solve your equation step-by-step.
6x+78=180
Step 1: Subtract 78 from both sides.
6x+78−78=180−78
6x=102
Step 2: Divide both sides by 6
6x/6=102/6
x=17
Answer:
x = 17
Step-by-step explanation:
If you subsitute x in "2x" you get 34. If you subsitute x for "4x - 4" you get 64.
After subtracting 180 from 98 you get 82. Add up 34, 64, and 82 then you get 180.
Select the statement that correctly describes a Type I error.
Answers
Answer:
can you add the answers?
Step-by-step explanation:
Find f(9) if f(x) = 2x+6
Answers
Answer:
24
Step-by-step explanation:
To do this all you need to do is replace x with 9
F(9) = 2(9) + 6
2 x 9 = 18
18 + 6 = 24
The answer is 24
Hope this helps
Simplify this expression.
1 + 4.25n + 32p – 3 + (–2p) + 54n
Answers
Answer:
58.25 n +30p-3
step explanation:
Answer:
30p - 2 + 58.25n
Step-by-step explanation:
54n + 4.25n = 58.25n
1 - 3 = -2
(since the 2 is in parenthasis you will be subtracting instead of adding)
32p - 2p = 30p
hope this helps :)
What is the solution to this system of equations? 4x + 5y = 7 3x – 2y = –12 The solution is .
Answers
Answer:
(-2,3)
Step-by-step explanation:
Answer:
(-2,3)
Step-by-step explanation:
got none
Two pounds of grapes cost $6.
Complete the table showing the price of different amounts of grapes at this rate.
What number belongs in the leftmost empty cell?
What number belongs in the rightmost cell?
Answers
Answer:
leftmost empty cell: ⅓
rightmost empty cell: 3
Step-by-step explanation:
✔️If 2 pounds grapes cost $6, then x pounds of grapes cost $1.
Thus;
2 : 6 = x : 1
2/6 = x/1
Multiply both sides by
²/6 × 1 = x/1 × 1
²/6 = x
¹/3 = x
x = ⅓
✔️If 2 pounds grapes cost $6, then 1 pound of grapes cost $x.
Thus;
2 : 6 = 1 : x
²/6 = ¹/x
Cross multiply
2x = 6
Divide both sides by 2
2x/2 = ⁶/2
x = 3
When preparing to cook, Joanna can chop 7.5 pounds of carrots in 16 minutes. How many ounces can she chop per second?
Answers
8 ounces per second I’m pretty sure
ThAnks for the help pls
Answers
I think the answer is D
what is g(h(10))? on edge2020
Answers
Answer:
2√2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
g(x) = √(x - 4)
h(x) = 2x - 8
Step 2: Evaluate
h(10)
Substitute: h(10) = 2(10) - 8Multiply: h(10) = 20 - 8Subtract: h(10) = 12g(h(10))
Substitute: g(h(10)) = √(12 - 4)Subtract: g(h(10)) = √8Simplify: g(h(10)) = 2√2Answer: A
Step-by-step explanation:
The larger the two numbers is one more than four times the small number. if the sum of the numbers is 106,find the two numbers
Answers
Answer:
Smaller no. = 21
Larger no. = 85
Step-by-step explanation:
Smaller no. = y
Larger no. = 4y + 1
y + (4y + 1) = 106
y + 4y + 1 = 106
5y + 1 = 106
5y = 106 - 1
5y = 105
y = 105/5
y = 21
Smaller no. = y = 21
Larger no. = 4y + 1 = 4×21 + 1 = 84 + 1 = 85
Describe your results. If you had to express this relation as a verbal statement, how would you describe it?
Forearm (Input) Foot(Output)
9 inches 9 inches
8 inches 9 inches
8 inches 8 inches
5 inches 4 inches
10 inches 9 inches
Answers
Answer:
this is the answer
Step-by-step explanation:
A E
The verbal statement that would describe it is
An input of 9will result to a 9 and an 10and an input of 4will result to an 9and 5
Selena is 6 years younger than Paul. in 15 years, Paul will be 4 times the age that Selena is now. find their present ages
Answers
please help me bro I’ll give u wtv
Answers
Answer:
slope(m)=-3
Step-by-step explanation:
guuys heeelppp asaaaaaap
Answers
Answer:
-3/5
Step-by-step explanation:
see the details in the attachment.
What is the value of x when solving the equation Negative 2 x + (negative 8) = 2 x + 8 using algebra tiles?
Answers
Answer:
x= -4
Step-by-step explanation:
-2x-8=2x+8 or, -2x-8-2x-8=0 or,-4x-16=0 or,-4(x+4)=0 or,x+4=0 or,x= -4Answer:
your answer -4
Step-by-step explanation:
PLEASE HELP!!
Does this circle have a radius or a diameter?
Answers
Answer:
Just remember to divide the diameter by two to get the radius.
Step-by-step explanation:
So, no?
Find the slope of the line through the
given points: (2,6) & (5, 6)
Answers
Answer:
Zero Slope
Step-by-step explanation:
rise over run or y2 - y1 / x2 - x1
6-6/5-2 = 0/3
PLZ HELP ME WITH THIS!!! I WILL MARK BRAINLIEST!!!
Answers
Answer:
-4
Step-by-step explanation:
Hope this helps! Consider Brainiest!
Answer:
-8
Step-by-step explanation:
1
What is the inverse operation that would need to be done in order to isolate the variable?
-15 = -0.2x *
(1 Point)
Answers
Answer: Division
Step-by-step explanation: Because since 0.2x is multiplication (0.2 * x [or 1x]), then it would be division, and obviously do that on both sides