Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
x^2/3 + y^2/3 = 4
(-3√3, 1)
(astroid)
Differentiate both sides of
[tex]x^{2/3} + y^{2/3} = 4[/tex]
implicite with respect to x :
[tex]\dfrac23 x^{-1/3} + \dfrac23 y^{-1/3} \dfrac{\mathrm dy}{\mathrm dx} = 0[/tex]
Solve for the derivative dy/dx :
[tex]x^{-1/3} + y^{-1/3} \dfrac{\mathrm dy}{\mathrm dx} = 0 \\\\ y^{-1/3} \dfrac{\mathrm dy}{\mathrm dx} = - x^{-1/3} \\\\ \dfrac{\mathrm dy}{\mathrm dx} = -\dfrac{x^{-1/3}}{y^{-1/3}} \\\\ \dfrac{\mathrm dy}{\mathrm dx} = -\left(\dfrac yx\right)^{1/3}[/tex]
Get the slope at the given point (-3√3, 1) :
[tex]\dfrac{\mathrm dy}{\mathrm dx}(-3\sqrt3,1) = -\left(\dfrac{1}{-3\sqrt3}\right)^{1/3} = \dfrac1{(3\sqrt3)^{1/3}} = \dfrac1{\sqrt3}[/tex]
Then the equation of the tangent line to the curve through (-3√3, 1) is
[tex]y - 1 = \dfrac1{\sqrt3}(x+3\sqrt3) \\\\ \boxed{y = \dfrac1{\sqrt3}x + 4}[/tex]
6 + blank = 4 what is the blank part
Answer:
-10 also I POSTED A MATH PROBLEM PLS HELP IF U CAN!! :)
1. translation 6 units left and 3 units down
Image
A'
Preimage
A (1,7)
B (7,7)
C (7,4)
D (1,4)
B'
C
D
Answer:
A’(-5,4)
B’ (1, 4)
c’ (1,1)
d’ (-5, 1)
Step-by-step explanation:
5 A triangle has a base length of 2x cm and a height of (x - 3) cm. If its area
is 18 cm², calculate its height and base length.
Answer:
base = 12; height = 3
Step-by-step explanation:
Area: ( b x h ) / 2
base: 2x
height: (x - 3)
---------------------------------
( ( 2x )*( x - 3 ) )/ 2 = 18
( 2x ^2 - 6x ) = 36
2x ^2 - 6x - 36 = 0
(quadratic formula)
x = 6
x = -3
---------------------------------
taking the positive value : x = 6
---------------------------------
base: 2x = 2(6) = 12
height: x - 3 = 6 - 3 = 3
round 45,621 to the nearest 10
Answer:
45621.0
Step-by-step explanation:
Already rounded to the nearest tenth.
Answer
the answer to this question is 45620.
3x-47=180 solve for x
Answer:
x=75.66
Step-by-step explanation:
+47 180+47
3x=227
divide 3 on each side
x=75.66
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Write the fraction in simplest form.
6/22=?
Answer:
3/11
Step-by-step explanation:
Divide both the numerator and denominator by 2.
[tex]\dfrac{6}{22}=\dfrac{2*3}{2*11}=\dfrac{3}{11}[/tex]
You roll two fair dice. If they land with a sum of 7, you get a $10. If they land with a sum of 6 or 8, you get $5. Everything else earns $0. Which of the following would be the highest value you could set the price and the player would still win?
$8
$5
$2
$10
Using the expected value, it is found that the highest value you could set the price is: $5.
-----------------------------
A game is fair, that is, the player would still win, if the expected value is 0.The expected value is the sum of each outcome multiplied by it's probability.A probability is the number of desired outcomes divided by the number of total outcomes.For two fair dice, there are 36 total outcomes, as [tex]6^2 = 36[/tex].
The charge is x.
6 outcomes result in a sum of 7, which are (1,6), (2,5), (3,4), (4,3), (5,2) and (6,1), thus, [tex]\frac{6}{36}[/tex] probability of getting 10.
10 outcomes result in a sum of 6 or 8, which are (1,5), (2,4), (2,6), (3,3), (3,5), (4,2), (4,4), (5,1), (5,3) and (6,2), thus, [tex]\frac{8}{36}[/tex] probability of getting x.
36 - 14 = 22, thus [tex]\frac{22}{36}[/tex] probability of losing x.
Since we want the expected value to be 0:
[tex]\frac{6}{36}(10) + \frac{8}{36}(5) - \frac{22}{36}x = 0[/tex]
[tex]\frac{60 + 50 - 22x}{36} = 0[/tex]
[tex]22x = 110[/tex]
[tex]x = \frac{110}{22}[/tex]
[tex]x = 5[/tex]
The highest value you could set the price is: $5.
A similar problem is given at https://brainly.com/question/24905256
Find three consecutive multiples of 6 with a sum that is four times the least of the numbers.
Answer:
18 , 24, 30
Step-by-step explanation:
6x + (6x+6) + (6x+6+6) = 4*6x
18x + 18 = 24x
6x = 18
x = 3
3 multiples of 6: 18 , 24, 30
check: 18+24+30=72
4*18 = 72
11 4/5 + 3 5/6 and you have to add
Answer:
15 19/30
Step-by-step explanation:
IF YOU ANSWER CORRECTLY ILL GIVE BRAINLIEST!!
What number makes the following equation true? -3/4 × -3/8 × □= -3/4
A. -5/4
B. -8/3
C. 8/3
D. 5/4
Let the number be x
[tex]\\ \sf\longmapsto \dfrac{-3}{4}\times\dfrac{-3}{8}x=\dfrac{-3}{4}[/tex]
[tex]\\ \sf\longmapsto \dfrac{-3}{8}x=1[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{-8}{3}[/tex]
Find the slope of the line
Need help, don’t understand
Answer: 3/2
Step-by-step explanation:
1. Slope is rise over run (difference in Y over the difference in X)
2 Look for a point where the line intersect both x and y
(0,0) and (2,3)
3.Starting at (0,0) count up until you reach 3. That is the rise. Now
count over until you reach the 2. That is the run.
4. From 0 to 3 is 3 Rise
From 0 to 2 is 2 Run
5. Slope is Rise over Run: 3/2
Monica uses 3 tablespoons of milk in her custard recipe. The ratio of tablespoons to fluid ounces is 2 : 1. How many fluid ounces of milk does Monica use?
(A) 0.5 fluid oz.
(B) 1 fluid oz.
(C) 1.5 fluid oz.
(D) 3 fluid oz.
(Also no fractions included and please help meh know please)
Answer:
b b b b b b b b b b b b b b b b b b b b b b
2. Arcadia charges players a $15 admission fee to their gaming centre and $5 per game.
b) What is the rate of change for the relation between total cost and number of games and what is its
meaning in this relation?
c) What is the initial value for this relation and what is its meaning?
Answer:
1) The relationship is times 3
2) it is 5x3 so this the teh relation
Step-by-step explanation:
I got 100% in the question and qiz
please help me asap and show your work
Answer:
We need a question
Step-by-step explanation:
find the average rate of change of f(x)=5x^2-3 from 3 to 9
9514 1404 393
Answer:
60
Step-by-step explanation:
The average rate of change on the interval is ...
(f(9) -f(3))/(9 -3) = ((5·9² -3) -(5·3² -3))/(9 -3) = (402 -42)/6 = 60
Please show work if needed if not then just answer!:)
9.
F. Symmetric Property of =.
The Symmetric Property of Equality states that if A = B, then B will = A, and that placement does not matter.
10.
B. Transitive Property of =.
The Transitive Property of Equality states that if A = B and B = C, then A = C.
In this case, AE = FB, FB = EF (meaning that point B is the midpoint), therefore, AE = EF.
please help?!’ answerr
Answer:
The choice Draw 2
Step-by-step explanation:
[tex]3(8 - 4x) < 6(x - 5) \\ 24 - 12x < 6x - 30 \\ 24- 12x + 12x < 6x + 12x - 30 \\ 24 < 18x - 30 \\ 24 + 30 < 18x - 30 + 30 \\ 54 < 18x \\ 54 \div 18 < 18x \div 18 \\ 3 < x \\ x > 3[/tex]
I hope I helped you^_^
Pls help ASAP pls it’s reasoning with fractions
Write a three digit number that gives same answer when rounded to the nearest ten and to the nearest hundred .explain
Answer:
Numbers can be rounded to the nearest ten, the nearest hundred, the nearest thousand, the nearest million, and so on. All the numbers to the right of the place you are rounding to become zeros. Rounded numbers are easier to remember and easier to use.
Solve the equation:
3x + 2 = 6x - 7
Answer:
x=3
Step-by-step explanation:
1) Subtract 3x from both sides
2 = 6x - 7 - 3x
2) Simplify 6x - 7 - 3x to 3x - 7
2 = 3x - 7
3) Add 7 to both sides
2 + 7 = 3x
4) Simplify 2 + 7 to 9
9 = 3x
5) Divide both sides by 3
9/3 = x
6) Simplify 9/3 to 3
3 = x
7) Switch sides
x=3
A box is in the shape of a triangular prism. . The base of the triangular face of the box is 11 centimeters (cm). The height of the triangular face of the box is 7.5 cm. The length of the box is 15 cm. V =1/2hxbxl What is the volume of the box? A 277.5 cm B 577.5 cm C 618.75 cm D1237.5 cm
Answer:
[tex]618.75 cm^{3}[/tex]
Step-by-step explanation:
[tex]\frac{(11 cm)(7.5 cm)(15 cm)}{2} =618.75 cm^{3}[/tex]
HELP PLEASE ITS MATH
Answer:
32 trips.
Step-by-step explanation:
It's a proportion question.
7/84 = x/384
84x = 7*384
84x = 2688
Divide both sides by 84 to isolate x.
x = 2688/84
x = 32
So, Sarah will have to make 32 trips to cycle a total of 384 kilometers.
(I apologize if the answer is wrong!)
What does the slope of the function represent?
Answer:
Hello there!
Your answer is,
The slope of the function represents a steady growth in the amount of money in the cash register after each sale.
Step-by-step explanation:
After they sell a cup of lemonade the graph goes up to represent the money they got and put into the register after the sale.
Question 6(Multiple Choice Worth 1 points)
(05.03 LC)
What is the initial value of the equation shown?
y = - 4x - 3
0-4
0-3
03
04
a square has a perimeter of 6x - 20 units. What is the value of x?
What is the slope y, equals, x, plus, 5?
Answer:
slope = m = 1
Step-by-step explanation:
y = x + 5
slope intercept form is y = mx + b, where m is the slope.
in this case, the m = 1; therefore, the slope is 1
What is the sum of 3/9 and 4/9?
Answer:
7/9
Step-by-step explanation:
Hope this helps you. Have a nice day.
A passenger train leaves the train station 5 hours after a freight train left the same station. The freight train is traveling 30 mph slower than the passenger train. Which equation helps to find the rate of each train, if the passenger train overtakes the freight train in three hours.
3r = 5(r - 30)
3r = 8(r - 30)
3r = 8(r + 30)
5r = 3(r - 30)
Answer:
first one
Step-by-step explanation: doesnt mention the number 8 variable anywhere
Answer:
A. 3r=5(r-30)
Step-by-step explanation:
on edge :)
Use the sequence of operations to answer the question.
1. add 3 to b
2. subtract the result inom 8
3. triple the answer
Answer:
(8-(3+b))3
Step-by-step explanation:
first of all, we have to variables, 3 and b that we are told to add
that is, 3+b
we are now told to subtract the answer from 8
that is 8 minis the answer
= 8- (3+b)
lastly we triple the answer to give
(8-(3+b)3
or
3(8-(3+b)