Answer:
8x/5
Step-by-step explanation:
What is the slope of the line tangent to the curve square root (x) +square root (y) = 2 at the point ( 9/4, 1/4 )? (photo attached of answer choices)
Answer:
B. [tex]\displaystyle -\frac{1}{3}[/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
Terms/CoefficientsExponential 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
Derivative of a constant is 0
The definition of a derivative is the slope of the tangent line
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Implicit Differentiation
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \sqrt{x} + \sqrt{y} = 2[/tex]
[tex]\displaystyle (\frac{9}{4}, \frac{1}{4})[/tex]
Step 2: Differentiate
Implicit Differentiation
[Function] Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle x^{\frac{1}{2}} + y^{\frac{1}{2}} = 2[/tex][Function] Basic Power Rule: [tex]\displaystyle \frac{1}{2}x^{\frac{1}{2} - 1} + \frac{1}{2}y^{\frac{1}{2} - 1}\frac{dy}{dx} = 0[/tex][Derivative] Simplify: [tex]\displaystyle \frac{1}{2}x^{\frac{-1}{2}} + \frac{1}{2}y^{\frac{-1}{2}}\frac{dy}{dx} = 0[/tex][Derivative] Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle \frac{1}{2x^{\frac{1}{2}}} + \frac{1}{2y^{\frac{1}{2}}}\frac{dy}{dx} = 0[/tex][Derivative] Isolate [tex]\displaystyle \frac{dy}{dx}[/tex] term [Subtraction Property of Equality]: [tex]\displaystyle \frac{1}{2y^{\frac{1}{2}}}\frac{dy}{dx} = -\frac{1}{2x^{\frac{1}{2}}}[/tex][Derivative] Isolate [tex]\displaystyle \frac{dy}{dx}[/tex] [Multiplication Property of Equality]: [tex]\displaystyle \frac{dy}{dx} = -\frac{2y^{\frac{1}{2}}}{2x^{\frac{1}{2}}}[/tex][Derivative] Simplify: [tex]\displaystyle \frac{dy}{dx} = -\frac{y^{\frac{1}{2}}}{x^{\frac{1}{2}}}[/tex]Step 3: Evaluate
Find slope of tangent line
Substitute in point [Derivative]: [tex]\displaystyle \frac{dy}{dx} \bigg| \limit_{(\frac{9}{4}, \frac{1}{4})} = -\frac{(\frac{1}{4})^{\frac{1}{2}}}{(\frac{9}{4})^{\frac{1}{2}}}[/tex][Slope] Exponents: [tex]\displaystyle \frac{dy}{dx} \bigg| \limit_{(\frac{9}{4}, \frac{1}{4})} = -\frac{\frac{1}{2}}{\frac{3}{2}}[/tex][Slope] Simplify: [tex]\displaystyle \frac{dy}{dx} \bigg| \limit_{(\frac{9}{4}, \frac{1}{4})} = -\frac{1}{3}[/tex]Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Differentiation - Implicit Differentiation
Book: College Calculus 10e
The circumcenter is the center of the __________ circle.
Question 2 options:
A)
obtuse
B)
circumscribed
C)
inscribed
D)
congruent
a bottle of soft drinks costs $2. the commission paid on one bottle is 2% of the cost price.find the commission on 24 bottles of soft drinks
Answer:
$0.96
Step-by-step explanation:
First, find the cost of the 24 bottles, by multiplying 24 by 2
24(2)
= 48
Find the commission by finding 2% of 48
48(0.02)
= 0.96
So, the commission will be $0.96
The commission on 24 bottles of soft drinks is $0.96.
How to find the commission on 24 bottles of soft drinks?Given:
a bottle of soft drinks costs $2. the commission paid on one bottle stands at 2% of the cost price.
First, we want to estimate the cost of the 24 bottles, by multiplying 24
by 2
[tex]= 24*(2)[/tex]
= 48
To find the commission by estimating 2% of 48
commission = 48*(0.02)
commission = 0.96
So, the commission will be $0.96.
Therefore, the commission on 24 bottles of soft drinks is $0.96.
To learn more about algebra
https://brainly.com/question/17201233
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- If A = 2x + 4 and B = 5x – 10 what is the value of
B-A?
Answer:
3x - 14Step-by-step explanation:
5x-10 - (2x+4)
= 5x - 10 -2x - 4
=3x-14express -17/8 in decimal form
Answer:
-2.125
Step-by-step explanation:
Find the surface area of the Triangular prism.
A = bh
A = 1/2(bh)
Answer:
Surface area of triangular prism =1/2(bh)
=1/2(3*4)
=6
PLEASE ANSWER ASAP !!! 90 POINTS AND BRAINLIEST!!!!!!!
( -5) + (+8) =
(+5) + (+4) =
( -3) + (+1) =
( -8) + ( -7) =
( -6) + (+3) =
Answer:
-5+8=-3
5+4=9
-3+1=-2
-8+-7=-15
-6+3=-3
Answer:
( -5) + (+8) = 3
(+5) + (+4) = 9
( -3) + (+1) = - 2
( -8) + ( -7) = - 15
( -6) + (+3) = 7
y-step explanation:
hope this helps!! and is it right? and make me brainliest pleaseee
Find the value of x.
6
14
3x-12
21
x = [?]
Charlie made hamburgers
for his family and they
each had a diameter of 7
cm. If he made 12
hamburgers. What is the
total area for all 12?
Answer:
461.58
Step-by-step explanation:
How much is 1/3 cup of butter equivalent measurement?
Answer: equal 5 tablespoons plus 1 teaspoon butter.
Step-by-step explanation:
Answer:
1/3 cup would equal 5 tablespoons plus 1 teaspoon butter
Step-by-step explanation:
i Hope this was the answer you was looking for. If not just go to one of my questions and take the points that you need to gain back!!!
what is photosynthesis
Answer:
writing m thoda problem h lakin samagh lena
Answer:
Photosynthesis is the process by which plants make there own food.
Step-by-step explanation:
Hope this will help you!
It takes 3 hour 15 minutes to fly from city a to city b at constant speed. Find how long the journey takes if
A) the speed is 1×1÷2 times of the original speed and
B) if the speed is three-quarters of the original speed.
Answer:
a) t= 2hours and 10 minutes
b) t=4hours and 20 minutes
v1t1=v2t2
Answer:
Step-by-step explanation:
rate = distance / time distance is constant (a-b) so call it D
time = distance / rate rate = speed (ie miles per hour = mph)
time = distance / speed
A) if the new speed is 1.5 of the original speed
original time = 3.25 hours or 195 minutes
3.25 = D / 1 new time = D/1.5 find new time
3.25 is to D as new time is to D/1.5
3.25/D = new time / D/1.5 multiple D/1.5 on both sides
(3.25/D) ( D/1.5) = new time the distance D cancels
3.25 (D / D) / 1.5 = new time
3.25 / 1.5 = 2.167 hours or 2 hours and 10 minutes
B) if the speed is 3/4 the original speed
original time = 3.25 hours or 195 minutes
3.25 = D / 1 new time = D/(3/4) find new time
3.25 is to D as new time is to D/0.75
3.25/D = new time / D/0.75 multiple D/0.75 on both sides
(3.25/D) ( D/0.75) = new time
3.25 (D / D) / 0.75 = new time
3.25 / 0.75 = 4.333 hours or 4 hours and 20 minutes
A number between 0 and 1, expressed as one number over another, is called a
Answer:
its called a frcaction
Step-by-step explanation:
What is the slope of the line?
Answer:
1
Step-by-step explanation:
g(x) = 3x2 – 2x + 7 2x + 5 Find g(-1)
Answer:
2x+5= g(−1)=12
Step-by-step explanation:
Simplify is simple
Directions: Find the area of a circle with given radius. Round off your answer to the nearest hundredths.
1. r= 3.2 m
2. r = 17 mm
3. r = 36.5 mm
4. r = 83 cm
5. r = 5.8 m
A. Find the volume of the following:
Formula: V = e x e x e
6. e = 45.25 cm
7. e = 29 cm
Formula: V = L x W x H
8. l = 23 cm
w= 14 cm
h = 11 cm
9. l = 41 cm
w= 28 cm
h = 17 cm
10. l = 20 cm
w= 18 cm
h = 14 cm
Answer:
Part A:
1. 32.17
2. 907.92
3. 4185.39
4. 21642.43
5. 105.68
Part B:
6. 92652.203125 or 92652.20
(not sure if you wanted rounded or exact number)
7. 24389
Part C:
8. 3542
9. 22848
10. 5040
Step-by-step explanation:
Part A:
To find the area of the circle, use the following formula:π × r²"r" is the radius of the circle, or the distance between the center and the edge of the circle.Example:Radius - 10π × r²π × 10²π × 100≈314.16Part B:
To find the volume of a cube, multiply e × e × eExample:e = 5 cme × e × e5 × 5 × 5 = 125 cm³Part C:
To find the volume of a figure, multiply length × width × heightExample:L = 5cm, W = 2cm, H = 6cm5 × 2 × 6 = 60 cm³
If you bought a lunch for $4.60 and the tax rate was 6%,
How much is the total owed?
Answer: It would be $4.88
CAN SOMEONE PLEASE HELP ME
Answer:
isosceles
Step-by-step explanation:
16. Under the Christmas tree at my house, there are five presents for my wife, three presents for me, and 8
presents for my son. (Hint: How many packages are under the tree in total?)
a) What percentage of the presents are for my wife?
b) What percent of the presents are for my son?
c) What percent of the presents are for me?
Answer:
a) 31.25%
b) 50%
c) 18.75%
pls help me i’ll give u brainlest if correct
Answer:
0%
Step-by-step explanation:
there is only one card with a 6; if you select the 6 card and do not replace it there is zero possibility of selecting another 6 card
The state government claims that the average earnings for a high school student who works during the summer is $1,500. A survey of 200 local high school students determined that the average amount of money earned at a summer job in the area was $1,100 and a 90% confidence interval was found to be ($975, $1,225). The confidence level is interpreted to mean that:
Answer:
B. if we repeat our survey many times. then about 90% of our confidence intervals will contain the true amount earned at a summer job.
Step-by-step explanation:
What is the answer to this question
Matthew rakes leaves to earn money. The points in this graph represent the total amount of money Matthew earns based on the number of hours he rakes leaves. Matthew wants to purchase sneakers that costs $48. How many hours does Matthew need to rake leaves to earn enough money to buy the sneakers?\
Answer:
it will take him 6 hours to earn enough money to buy the sneakers
Step-by-step explanation:
I took the test
Answer:
The answer should be 6
Step-by-step explanation:
I took the test too
URGENT HELP NEEDED ASAP
PHOTO ATTACHED
CALCULUS
Answer:
Option A
Step-by-step explanation:
From the piecewise function given in the picture,
f(x) = k³ + x If x < 3
= [tex]\frac{16}{k^2-x}[/tex] If x ≥ 3
Here, function is discontinuous at x = 3
If the function is continuous at x = 3 then,
k³ + 3 = [tex]\frac{16}{k^2-3}[/tex]
(k³ + 3)(k² - 3) = 16
k⁵ - 3k³ + 3k² - 9 = 16
k⁵ - 3k³ +3k² - 25 = 0
By using a graphing tool we can get the point where k = 2.081.
Option A is the answer.
Find the slope of a line that contains the two points 0, 1 and 1, 3
Answer:
The slope is 2.
Step-by-step explanation:
Use the slope formula:
m = y2 - y1 / x2 - x1
Plug in the numbers from the ordered pairs:
m = 3 - 1 / 1 - 0
m = 2/1
Simplify:
m = 2
3 1/4 pints =____ fl oz?
Answer:
52
Step-by-step explanation:
Answer:52
Step-by-step explanation:
Allison and Sean were splitting nachos. If Allison ate 5/12 of the nachos and Sean ate 1/5 of the nachos, what fraction of the nachos did they eat together?
Answer:
thank for points
Step-by-step explanation:
Answer:
37/60
Step-by-step explanation:
Because 5/12+1/5=37/60
Helpp click on picture
Find the 97th of the arithmetic sequence 25, 29, 33, ...
Answer:
If im not wrong is 409
Step-by-step explanation:
have a nice day :)
What is the equation of the exponential function??
Anthony's mom bought a new Prius in 2018 that cost
$28,000. She looked up the current value and saw that
it was only $22,000 after two years! She is worried
about how much her car will be worth in 3 more years.
What is the exponential equation?
1
How much will the car be worth in 3 years?
Submit
Answer:
$19500Step-by-step explanation:
Let the depreciation rate is x per year, then we have:
28000*x² = 22000x² = 22000/28000x² = 0.7857x = √0.7857 x = 0.8864Exponential function for this case is:
V(t) = 28000*0.8864^t, where V(t) - future value, t- number of yearsValue of the car after 3 years:
V(3) = 28000*0.8864^3 V(3) = 19500