The expression for the rate of change of A with respect to t is dA/dt = 4h * dh/dt in²/s. Option D
How to determine the valueThe formula for calculating the area of a rectangle is expressed as:
A = wh
Given that;
h represents the variable for the heightw represents the variable for the widthFrom the information given, we have that;
If the width is twice the height
This is represented as;
w = 2h
Then, substitute the values into the formula for area of a rectangle
A = (2h)h
A = 2h²
Then, the rate of change of area will be expressed as;
dA/dt
Take the differentiation
dA/dt = dA/dh × dh/dt
dA/dt = 4h * dh/dt in²/s
Hence, the rate is dA/dt = 4h * dh/dt in²/s
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The complete question:
A rectangle has width w inches and height h inches, where the width is twice the height. Both w and h are functions of time t, measured in seconds. If A represents the area of the rectangle, which of the following gives the rate of change of A with respect to t ?
A. dA/dt=4h in/sec
B. dA/dt=3h dh/dt in^2/sec
C. dA/dt=4h dh/dt in/sec
D. dA/dt=4h dh/dt in^2/sec
for the following problems do at least one problem using unit form and at least one problem using fraction form 3.2 x 1.4=
If Jamal currently has 2000 in saving, he will need to Save________each month
Calculus helpppppppppppppppp
Answer:
[tex]\displaystyle y' = \frac{5x^2 + 3}{3(1 + x^2)^\bigg{\frac{2}{3}}}[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
FunctionsFunction NotationExponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Algebra II
Logarithms and Natural LogsLogarithmic Property [Multiplying]: [tex]\displaystyle log(ab) = log(a) + log(b)[/tex]Logarithmic Property [Exponential]: [tex]\displaystyle log(a^b) = b \cdot log(a)[/tex]Calculus
Derivatives
Derivative Notation
Derivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
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]
Logarithmic Derivative: [tex]\displaystyle \frac{d}{dx} [lnu] = \frac{u'}{u}[/tex]
Implicit Differentiation
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = x\sqrt[3]{1 + x^2}[/tex]
Step 2: Rewrite
[Equality Property] ln both sides: [tex]\displaystyle lny = ln(x\sqrt[3]{1 + x^2})[/tex]Logarithmic Property [Multiplying]: [tex]\displaystyle lny = ln(x) + ln(\sqrt[3]{1 + x^2})[/tex]Exponential Rule [Root Rewrite]: [tex]\displaystyle lny = ln(x) + ln \bigg[ (1 + x^2)^\bigg{\frac{1}{3}} \bigg][/tex]Logarithmic Property [Exponential]: [tex]\displaystyle lny = ln(x) + \frac{1}{3}ln(1 + x^2)[/tex]Step 3: Differentiate
ln Derivative [Implicit Differentiation]: [tex]\displaystyle \frac{d}{dx}[lny] = \frac{d}{dx} \bigg[ ln(x) + \frac{1}{3}ln(1 + x^2) \bigg][/tex]Rewrite [Derivative Property - Addition]: [tex]\displaystyle \frac{d}{dx}[lny] = \frac{d}{dx}[ln(x)] + \frac{d}{dx} \bigg[ \frac{1}{3}ln(1 + x^2) \bigg][/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle \frac{d}{dx}[lny] = \frac{d}{dx}[ln(x)] + \frac{1}{3}\frac{d}{dx}[ln(1 + x^2)][/tex]ln Derivative [Chain Rule]: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot \frac{d}{dx}[(1 + x^2)][/tex]Rewrite [Derivative Property - Addition]: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot \bigg( \frac{d}{dx}[1] + \frac{d}{dx}[x^2] \bigg)[/tex]Basic Power Rule]: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot (2x^{2 - 1})[/tex]Simplify: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{1}{3} \bigg( \frac{1}{1 + x^2} \bigg) \cdot 2x[/tex]Multiply: [tex]\displaystyle \frac{y'}{y} = \frac{1}{x} + \frac{2x}{3(1 + x^2)}[/tex][Multiplication Property of Equality] Isolate y': [tex]\displaystyle y' = y \bigg[ \frac{1}{x} + \frac{2x}{3(1 + x^2)} \bigg][/tex]Substitute in y: [tex]\displaystyle y' = x\sqrt[3]{1 + x^2} \bigg[ \frac{1}{x} + \frac{2x}{3(1 + x^2)} \bigg][/tex][Brackets] Add: [tex]\displaystyle y' = x\sqrt[3]{1 + x^2} \bigg[ \frac{5x^2 + 3}{3x(1 + x^2)} \bigg][/tex]Multiply: [tex]\displaystyle y' = \frac{(5x^2 + 3)\sqrt[3]{1 + x^2}}{3(1 + x^2)}[/tex]Simplify [Exponential Rule - Root Rewrite]: [tex]\displaystyle y' = \frac{5x^2 + 3}{3(1 + x^2)^\bigg{\frac{2}{3}}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Implicit Differentiation
Book: College Calculus 10e
In a survey at a shoe store, 200 customers were asked whether they have
running shoes or basketball shoes. The results are in the relative frequency
table.
Total
Have running shoes
0.23
Have basketball shoes
No basketball shoes
Total
No running shoes
0.31
0.32
0.14
What percentage of the people surveyed have basketball shoes?
A. 37%
B. 54%
O C. 46%
O D. 63%
Find the slope of the line that passes through the given points.
Answer: -1/6
Step-by-step explanation:
slope= change of y over change of x
3-4/ 5--1=
-1/6
Hope this helps!
Answer:
-1/6
Step-by-step explanation:
(-1, 4) and (5, 3)
y2 - y1 / x2 - x1
y2 = 3
y1 = 4
x2 = 5
x1 = -1
(3 - 4) / (5 - -1)
-1 / 6
slope = -1/6
Which algebraic expression represents the phrase "the quotient of negative eight and the sum of a number and three"
-8
Og+3
8
9+3
-8+g
3
+3
Answer:
[tex]\dfrac{-8}{x+3}[/tex]
Step-by-step explanation:
We need to find an algebraic expression for the given statement i.e. "the quotient of negative eight and the sum of a number and three".
Let the number be x. Quotient means to divide. It means we need to divide -8 and the sum of x and 3.
So, we can write it as follows :
[tex]\dfrac{-8}{x+3}[/tex]
Hence, this is the required solution.
243 to the 1/5 power
Answer:
-3
Step-by-step explanation:
Help asap
Find the value of x. Round to the
nearest tenth.
3
4
X =
= [?]
Answer:
36.9°
Step-by-step explanation:
→ Identify the triangle required by seeing which side is not given
Hypotenuse is not given so we need to use Tan⁻¹ = Opposite / Adjacent
→ Substitute values in
Tan⁻¹ = ( 3 ÷ 4 )
→ Simplify
36.9°
Jonas has 16 carnations and 12 roses. He wants to make identical bouquets for a party. How many bouquets can he make?
Answer:
Jonas can make 4 bouquets, each containing 4 carnations and 3 roses.
Step-by-step explanation:
Given that Jonas has 16 carnations and 12 roses, and he wants to make identical bouquets for a party, to determine how many bouquets can he make the following calculation must be performed, obtaining the largest common divisor between both numbers:
12 = Divisible by 2, 3, 4, 6 and 12
16 = Divisible by 2, 4, 8 and 16
Thus, the common greatest divisor between the two numbers is 4.
12/4 = 3
16/4 = 4
So, Jonas can make 4 bouquets, each containing 4 carnations and 3 roses.
What is the y-intercept for this function?
y = x2 - 2x - 3
Answer:
-3
Step-by-step explanation:
Find the surface area or i will kiII myseIf (I give brainliest! :D)
Answer:
I'll cya in h.e.l.l
ima k.i.l.l. myself as well if they don't give us the answer
Step-by-step explanation:
Answer:
I believe its 122
Step-by-step explanation:
122 total surface area
Solve x2 + 6x = 7 by completing the square. Which is the solution set of the equation?
If you apply the changes below to the quadratic parent function, f(x) = x?,
what is the equation of the new function?
• Shift 1 unit right.
• Vertically stretch by a factor of 5.
• Reflect over the x-axis.
O A. g(x) = (-5x + 1)2
O B. g(x) = -5(x + 1)2
O C. g(x) = 5x2 - 1
O D. g(x) = -5(x - 1)2
Answer:
The answer is A
Step-by-step explanation:
(D) g(x) = -5(x-1)² is the correct answer for the given changes in function.
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
The starting parent function is f(x) = x².
To shift 1 unit right, we need to replace x with (x-1).
To vertically stretch by a factor of 5, we need to multiply the function by 5.
To reflect over the x-axis, we need to multiply the function by -1.
So the new function g(x) can be written as:
g(x) = -5(x-1)²
Therefore, the correct answer is (D) g(x) = -5(x-1)².
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Hakima and Joshua both opened savings accounts. Both started with a balance of zero dollars. For every $3 that Hakima saves in her account, Joshua saves $5. If they have saved a total of $336, how much did Hakima save?
help plese i beg of you
9514 1404 393
Answer:
k = 45 . . . miles per hourk = 1/45 . . . hours per mileStep-by-step explanation:
One way we can relate distance and time is ...
time = k × distance
Then the value of k (the constant of proportionality) is ...
k = time/distance = 4 hours/(180 miles)
k = (1/45) hours/mile
__
Another way we can relate the variables is ...
distance = k × time
Then the value of k (the constant of proportionality) is ...
k = distance/time = (180 miles)/(4 hours)
k = 45 miles/hour
What is the perimeter of a square with side length: 3 cm Do not include units (cm) in your answer. I also will be reporting any links as answers
Answer:
perimeter of a square is 3 + 3 + 3 + 3 = 12 (cm)
Step-by-step explanation:
Or use the formula P = 4a = 4(3) = 12 (cm)
PLZ needed now plz URGENT!
Answer:
Realtionship B
Step-by-step explanation:
Relationship A doesn't pass the line test
The area of a rectangular living room is 264 square feet. The length of the room is 2 feet less than twice the width.
What is the width of the living room in feet?
9514 1404 393
Answer:
12 ft
Step-by-step explanation:
Let the width of the room be represented by w. Then the length is (2w-2), and the area is ...
A = LW
264 = (2w-2)w
132 = w² -w . . . . . . . divide by 2, eliminate parentheses
132.25 = w² -w +.25 . . . . . add (-1/2)² to complete the square
√132.25 = w -0.5 . . . . . take the square root
0.5 +11.5 = w = 12 . . . . . add 0.5; use the positive root
The width of the living room is 12 feet.
HELP PLEASEEEE!!! SOMEONE HELP ME FOR ONCE, NO ONE IS ANSWERING MY QUESTIONS AND IM SO FREAKING STRESSED OUT. OH MY GOD SOMEONE PLS IM BEGGING YOU EXPLAIN YOUR ANSWER STEP BY STEP FOR ONCE
In 1985 an antique automobile club had 23,000 members. Since then its membership has grown at an average rate of 5% per year. Assuming this trend continues, how many members will there be in 2020? Round to the nearest thousand.
a) 112,000 members
b) 78,000 members
c) 151,000 members
d) 127,000 members
Answer:
I have come to the conclusion that it is A. 112,000
Answer:
d) 127,000 members
Step-by-step explanation:
In this problem we have an exponential function of the form
where a is the initial value
b is the base
The base is equal to b=1+r
r is the average rate
In this problem we have a=23,000 members
r=5%=5/100=0.05
b=1+0.05=1.05
substitute
x ----> is the number of years since 1985
How many members will there be in 2020?
x=2020-1985=35 years
substitute in the function
Round to the nearest thousand
90:(3+6)-20.(60-55) propiedad
Answer:
https://www.commoncoresheets.com/Math/Properties/Applying%20Properties%20of%20Operations/Spanish/2.pdf
Step-by-step explanation:
This will help you:) not a spam link its a pdf that brings you straight to the worksheet <3
Need the answer for x and y
Answer:
x = 7°
y = 10°
Step-by-step explanation:
7x = 49
x = 7°
180 = 13y + 1 + 49
combine like terms:
13y = 130
y = 10°
Answer:
X equals to 7 & y equals to 10 'cause ;
7X=49
X=7
50 + 13 y + 1 = 180
13y = 130
y=10
Step-by-step explanation:
Good luck.
hope it was helpful for u .
WILL MARK BRAINLYEST
A street sign is 8 feet tall and casts a shadow that is 28 feet long. At the same time, a nearby tree casts a shadow that is 210 feet long. How tall is the tree?
A.60
B.70
C.80
D.90
At a school health fair, individual pieces of fruit are placed in paper bags and distributed to students randomly. There are 20 apples, 15 apricots, 25 bananas, 25 pears, and 30 peaches. Write the answer as a fraction in simplest form. Find the probability of NOT getting an apple.
Answer:
Around 82%
Step-by-step explanation:
95/115
Last year 5200 people entered a contest to win free swimming lessons at the rec center. This year there was a 14% increase in the number of entrees. How many entries were there this year?
Answer:
There were 5928 entries
Step-by-step explanation:
You multiply 14% by 5200, which is 0.14 in decimal form, and you get 728. Then you add 5200 and 728 together, since 14% of 5200 is 728
17. An equation is shown.
3x7=+7
What number makes the number sentence true?
A 3
B, 14
C. 21
D. 28
Help me please it’s for math class
Answer:
No solution
Step-by-step explanation:
To start, a solution requires the lines to intersect
However both lines share a slope of -3 and are thus parallel
Since parallel lines dont intersect, there is no solution
Answer:
Hi! The answer to your question is A. No solution, i also have a picture to help you if u need it.
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☆Brainliest is greatly appreciated!☆
Hope this helps!!
- Brooklynn Deka
Need the answer for x and y
Answer:
See below
Step-by-step explanation:
There is no 'y' in your question but I will answer the Q in the pic:
the two sides are equal so
10x-1 = 8x+11
2x = 12
x = 6 then CD = 8x+11 = 8(6)+ 11 = 59 units
PLEASE HELP!!!!!!!!!! BRAINLIEST
Add the following fractions. Simplify and reduce to the lowest terms.
9/16 + 3/16
Answer:
3/4
Step-by-step explanation:
12/16
divided by 4
3/4
Answer: /34
Step-by-step explanation:
9/16 + 3/16
=(9+3)/16 ⇔ Fractions with the same denominator can subtract or add
=12/16 ⇔ Simplify
=(3×4)/(4×4) ⇔ Factor each number
=3/4 ⇔ Divide 4 on both numerator and denominator
Hope this helps!! :)
Please let me know if you have any questions
6 friends are going to a bowling alley. They have to pay a fee per game and $2 to
rent shoes. If they plan on only playing one game, the cost is $48.
Answer:
3
Step-by-step explanation:
Let x be the number of games they bowled.
Then, we know that each shoe rental was $2.50. So, the total cost for shoes was 3 * $2.50 = $7.50
The total number of games they bowled was 3 * x (since there were 3 persons).
Now, the cost per game was $5.30. So, the total cost for games bowled (minus shoes) was:
3x($5.30) = $15.90x
Now, add the cost of the shoes ($7.50) and you have the total cost ($55.20):
$15.90x + $7.50 = $55.20
Subtract $7.50 from both sides:
$15.90x = $47.70
Divide both sides by $15.90:
x = 3 (the number of games they bowled)
6(5 - 8n) + 12 = -54
please step my step
Answer:
Look Below
Step-by-step explanation:
6(5 - 8N) + 12 = -54
-48N + 30 + 12 = -54
-48N + 42 = -54
(-48N + 42) + (-42) = -54 + (-42)
-48N = -96
-48N / 48 = N
-96 / 48 = 2
N = 2
Hope This Helps! If you find any fault in my answer please let me know. Thanks! Have a good day!