Answer:
a(n) = 12 + 8n
a1 = 20
a2 = 28 = 20 + 8
a3 = 36 = 20 + 8.2
a4 = 44 = 20 + 8.3
.......
=> this is a arithmetic with a1 = 20
d = 8
=> an = 20 + 8(n - 1) = 12 + 8n
Use the limit definition of the derivative to find the slope of the tangent line to the curve
f(x)= 7x^2 + 7x + 3 at x= 4
Answer:
[tex]\displaystyle f'(4) = 63[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Expand by FOIL (First Outside Inside Last)FactoringFunction NotationTerms/CoefficientsCalculus
Derivatives
The definition of a derivative is the slope of the tangent line.
Limit Definition of a Derivative: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]
Step-by-step explanation:
Step 1: Define
f(x) = 7x² + 7x + 3
Slope of tangent line at x = 4
Step 2: Differentiate
Substitute in function [Limit Definition of a Derivative]: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{[7(x + h)^2 + 7(x + h) + 3]-(7x^2 + 7x + 3)}{h}[/tex][Limit - Fraction] Expand [FOIL]: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{[7(x^2 + 2xh + h^2) + 7(x + h) + 3]-(7x^2 + 7x + 3)}{h}[/tex][Limit - Fraction] Distribute: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{[7x^2 + 14xh + 7h^2 + 7x + 7h + 3] - 7x^2 - 7x - 3}{h}[/tex][Limit - Fraction] Combine like terms (x²): [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{14xh + 7h^2 + 7x + 7h + 3 - 7x - 3}{h}[/tex][Limit - Fraction] Combine like terms (x): [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{14xh + 7h^2 + 7h + 3 - 3}{h}[/tex][Limit - Fraction] Combine like terms: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{14xh + 7h^2 + 7h}{h}[/tex][Limit - Fraction] Factor: [tex]\displaystyle f'(x)= \lim_{h \to 0} \frac{h(14x + 7h + 7)}{h}[/tex][Limit - Fraction] Simplify: [tex]\displaystyle f'(x)= \lim_{h \to 0} 14x + 7h + 7[/tex][Limit] Evaluate: [tex]\displaystyle f'(x) = 14x + 7[/tex]Step 3: Find Slope
Substitute in x: [tex]\displaystyle f'(4) = 14(4) + 7[/tex]Multiply: [tex]\displaystyle f'(4) = 56 + 7[/tex]Add: [tex]\displaystyle f'(4) = 63[/tex]This means that the slope of the tangent line at x = 4 is equal to 63.
Hope this helps!
Topic: Calculus AB/1
Unit: Chapter 2 - Definition of a Derivative
(College Calculus 10e)
1.
A bucket is put under a leaking ceiling. The amount of water in the bucket doubles every minute. After 8 minutes,
the bucket is full. After how many minutes is the bucket half-full?
I
Answer:
4min
Step-by-step explanation:
half full = 4min. disregard the doubles every min.
Answer:
7 minutes
Step-by-step explanation:
(3z+1)+5+7z) Step by step explanation needed
Answer: 10z + 6
Step-by-step explanation:
this is a short problem.. sometimes you would need to distribute, but since there is no number in front of parenthesis you can just get rid of them
that gives you: 3z + 1 +5 + 7z
now from here we combined liked terms
7z + 3z = 10z
1 + 5 = 6
so that gives you: 10z + 6
A U.S. penny has a mass of 2.5 grams. A U.S. quarter has a mass of 5.67 grams. What is the total mass of the two coins?
Write and simplify an expression for the area of the rectangle. Write the SIMPLIFIED answer in the text box.
Answer:
gff
Step-by-step explanation:
rwsnuggdfvg
When Mohammed was born, the baby was 21 inches tall. at his last check up, he was 38 inches tall. what is the percent increase in his growth to the nearest percent? round it to the nearest 100th
this is math btw and im giving 5 star and 15 points.
Answer:
80.95
Step-by-step explanation:
Percentage increase = [tex]\frac{New Value - Old Value}{Old Value}[/tex] *100
=> (38-21)* 100/21 = 80.9523%
The answer round it to the nearest 100th = 80.95%
Answer! Plz plz pls pls
Answer:
201.5238
Step-by-step explanation:
201.5238
calculator
Answer:
$201.52
Step-by-step explanation:
156.95 x 0.20 = 31.39 tip
subtotal = 188.34
188.34 x 1.07 = 201.52
Solve the formula for t.
d= rt
4 batteries for 5.99
I am thinking of 2 numbers.
The sum of the two numbers is 553.
Their difference is 225.
What are the 2 numbers?
which graph represents the following system of inequalities y>1/2x-1 y>-2x-1
Answer:
I think its c on plato
Step-by-step explanation:
911÷406 con operaciones
Answer:
2.24384236453
Step-by-step explanation:
division/división
Answer:
Step-by-step explanation:
2.24384236453 divicion y divicion
whats the property
someone plz help
Answer:
The property is the water cycle
7 is 1/10 of
pls help and thank you :)
7 is 1/10 of 70. You can figure this out by multiplying 7 by 10
please help!!!!! i’ve been stuck on this question
Answer:
30
Step-by-step explanation:
The angle for BOF is going to be 180.
So if the angle for COF is 150, then COB is going to be the complement angle.
This means it's 180 - 150 = 30.
The width of a rectangle is the length minus 3 units. The area of the rectangle is 40 units. What is the width, in unit, of the rectangle?
Answer: The width is 5
Step-by-step explanation:
The equation is x*(x-3)=40 solviing for x which is 8 but since width is x-3 then 8-3=5
Evaluate the expression.
–3×(6– -6÷3)
PLEASE HELP
-24 i hope this is right
Answer:
−24
Steps for answer:
1. Simplify 6÷3 to 2.
−3×(6+2)
2. Simplify 6+2 to 8.
−3×8
3. Simplify
−24
eighteen is equal to the product of a number (n) and 9
eighteen is equal to the product of a number 9 and 9
What do you get when you plug 4 in the following function?
Answer:
567
Step-by-step explanation:
It will become:
y = 7(3)^4
y = 7 * 81
y = 576
Answer:
Y = 567
Step-by-step explanation:
Y=7(3)(3)(3)(3)
Which function has a domain of x greater-than-or-equal-to 5and a range of y less-than-or-equal-to 3?
y = StartRoot x minus 5 EndRoot + 3
y = StartRoot x + 5 EndRoot minus 3
y = negative StartRoot x minus 5 EndRoot + 3
y = negative StartRoot x + 5 EndRoot minus 3
Answer:
The function that has a domain of 'x' greater-than-or-equal-to 5 and a range of 'y' less-than-or-equal-to 3 is;
[tex]y = -\sqrt{x - 5} +3[/tex].
Step-by-step explanation:
The domain of a function are the possible 'x' values of the function
The range of a function are the possible 'y' values of the function
The given possible functions are;
1) [tex]y = \sqrt{x - 5} +3[/tex]
The range of values for the above function are;
Domain; x ≥ 5
Range; y ≥ 3
2) [tex]y = \sqrt{x + 5} -3[/tex]
The range of values for the above function are;
Domain; x ≥ -5
Range; y ≥ -3
3) [tex]y = -\sqrt{x - 5} +3[/tex]
The range of values for the above function are;
Domain; x ≥ 5
Range; y ≤ 3
4) [tex]y = -\sqrt{x + 5} -3[/tex]
The range of values for the above function are;
Domain; x ≥ -5
Range; y ≤ -3
Therefore, the required function is the third function, [tex]y = -\sqrt{x - 5} +3[/tex].
Answer:
C on Edge2021
Step-by-step explanation:
THIS ISNT HOMEWORK BUT MY FRIEND GOT ME FACEMASKS ON SUNDAY AND IVE USED IT FIVE/SIX TIMES THIS WEEK(ITS NOW WEDNESDAY) AND SHE TOLD ME THATS NOT GOOD- WHAT DO I DO TO PREVENT BAD THINGS
Answer:
eat ice cream it will make the pain go away
Step-by-step explanation:
HELP PLEASE CHECK MY ANSWER!!!
Answer:
its almost correct but its just a little bit off
Step-by-step explanation:
1. on the left its on the two bring it closer to the 4 than the 2 so its gonna be right before the four ill insert a picture so u can see as well.
2. on the left side its going to be right before -2.
3. on the bottom its going to be moved down to -18 and a little bit out going to the right.
the picture is right there hope it helped
Hannah invested $540 in an account paying an interest rate of 4.7% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 18 years?
Answer:
1300
Step-by-step explanation:
did it on usatestprep
I need fast help help help me
Answer:
d
Step-by-step explanation:
Answer:
it is d
Step-by-step explanation:
can you please give me brainliest? thanks!
hope this helps!
HELP ME PLZ !!! IT'S ALGEBRA
Answer:
x = - 8/23
y = 40/23
Step-by-step explanation:
-5x- y = 0
and
-8x+3y = 8
The first step to solve this would be to get what one of the two variables equal. The easiest in this case is y from the first equation.
-5x-y = 0
-y = 5x
y = - 5x
Now you can take this y value and plug it into the section equation.
-8x + 3(-5x) = 8
-8x - 15x = 8
-23x = 8
x = - (8/23)
Once you get the x value you can plug it back into equation one to get y's value
-5*-(8/23) - y = 0
40/23 - y = 0
y = 40/23
15 pints because 2 questions
Answer:
1.its B
2.G
Step-by-step explanation:
Find the area of the triangle
19cm
15cm
12cm
Answer:
Step-by-step explanation:
HELP!!! What mistake did I make? And what would u suggest to help me???
Answer:
All the dots need to be on the line, and maybe dont add so many dots
Step-by-step explanation:
Choose the graph that represents the following system of inequalities: y ≤ −3x + 1 y ≤ 1 over 2x + 3 In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and labeled B, and the area where they have shading in common is labeled AB. Graph of two intersecting lines. Both lines are solid. One line f of x passes through points negative 2, 2 and 0, 3 and is shaded above the line. The other line g of x passes through points 0, 1 and 1, negative 2 and is shaded above the line. Graph of two lines intersecting lines. Both lines are solid. One line g of x passes through points negative 2, 2 and 0, 3 and is shaded below the line. The other line f of x passes through points 0, 1 and 1, negative 2 and is shaded above the line. Graph of two intersecting lines. Both lines are solid. One line passes g of x through points negative 2, 2 and 0, 3 and is shaded below the line. The other line f of x passes through points 0, 1 and 1, negative 2 and is shaded below the line. Graph of two intersecting lines. Both lines are solid. One line f of x passes through points negative 2, 2 and 0, 3 and is shaded above the line. The other line f of x passes through points 0, 1 and 1, negative 2 and is shaded below the line.
We want to find the graph of a system of inequalities. We want to select the correct option, but sadly is really hard to interpret the given text, so I will add a graph of the system at the end.
The system is:
y ≤ -3x + 1y ≤ (1/2)*x+ 3To graph these we first need to graph the two lines:
y =-3x + 1
Is a line with a negative slope that passes through the y-axis at y = 1.
Because here we have y ≤ -3x + 1 we know that y must be equal or smaller than the line, thus we need to shade below the line, and because y can be equal to any value in the line we need to use a solid line.
For the other equation:
y = (1/2)*x+ 3
We have a positive slope and this line intercepts the y-axis at y = 3.
Similar as before, here we have y ≤ (1/2)*x+ 3 so the shaded area will be below the line and the line must be solid.
With this in mind, we can graph the system, and you can see it below:
If you want to learn more, you can read:
https://brainly.com/question/19526736
1. What do you remember about the slope of a line? 2. A ramp may not be steeper than 1:12. Draw a right triangle whose "rise" is 1 unit, and whose "run" is 12 units. 3. Set up a trig ratio and use it to solve for the maximum angle of elevation of the ramp. Round to the nearest hundred 4. The height of the door on your restaurant is 9.5 inches from the ground. Using the maximum angle of elevation possi what would the length of the ramp be (x)? What would the horizontal distance be (y)
I remember every thing it was so good j set ramp