Answers
(3) Differentiating both sides of
[tex]2x^{3/2} + y^{3/2} = 29[/tex]
with respect to x gives
[tex]3x^{1/2} + \dfrac32 y^{1/2} \dfrac{\mathrm dy}{\mathrm dx} = 0[/tex]
Solve for dy/dx :
[tex]\dfrac32 y^{1/2} \dfrac{\mathrm dy}{\mathrm dx} = -3x^{1/2} \\\\ \dfrac{\mathrm dy}{\mathrm dx} = \dfrac{-3x^{1/2}}{\frac32y^{1/2}} = \dfrac{-2x^{1/2}}{y^{1/2}} = -2\sqrt{\dfrac xy}[/tex]
Then the slope of the tangent line to the curve at (1, 9) is
[tex]\dfrac{\mathrm dy}{\mathrm dx} = -2\sqrt{\dfrac19} = -\dfrac23[/tex]
The equation of the tangent line would then be
y - 9 = -2/3 (x - 1) ==> y = -2/3 x + 29/3
(4) The slope of the tangent line to
[tex]y=\dfrac{ax+1}{x-2}[/tex]
at a point (x, y) on the curve is
[tex]\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{a(x-2)-(ax+1)}{(x-2)^2} = -\dfrac{2a+1}{(x-2)^2}[/tex]
When x = -1, we have a slope of 2/3, so
-(2a + 1)/(-1 - 2)² = 2/3
Solve for a :
-(2a + 1)/9 = 2/3
2a + 1 = -18/3 = -6
2a = -7
a = -7/2
Related Questions
Factor and find the zeros. z^2-z+56
Answers
Answer:
Sry its long but if your to lazy to look thru it here is the answer= z = {-7, 8}
Step-by-step explanation:
Simplifying
z2 + -1z + -56 = 0
Reorder the terms:
-56 + -1z + z2 = 0
Solving:
-56 + -1z + z2 = 0
Solving for variable 'z'.
Factor a trinomial.
(-7 + -1z)(8 + -1z) = 0
Subproblem 1
Set the factor '(-7 + -1z)' equal to zero and attempt to solve:
Simplifying:
-7 + -1z = 0
Solving:
-7 + -1z = 0
Move all terms containing z to the left, all other terms to the right.
Add '7' to each side of the equation.
-7 + 7 + -1z = 0 + 7
Combine like terms: -7 + 7 = 0
0 + -1z = 0 + 7
-1z = 0 + 7
Combine like terms: 0 + 7 = 7
-1z = 7
Divide each side by '-1'.
z = -7
Simplifying:
z = -7
Subproblem 2
Set the factor '(8 + -1z)' equal to zero and attempt to solve:
Simplifying:
8 + -1z = 0
Solving:
8 + -1z = 0
Move all terms containing z to the left, all other terms to the right.
Add '-8' to each side of the equation.
8 + -8 + -1z = 0 + -8
Combine like terms: 8 + -8 = 0
0 + -1z = 0 + -8
-1z = 0 + -8
Combine like terms: 0 + -8 = -8
-1z = -8
Divide each side by '-1'.
z = 8
Simplifying:
z = 8
Solution
z = {-7, 8}
Find a solution to dydx=xy+6x+4y+24dydx=xy+6x+4y+24. If necessary, use kk to denote an arbitrary constant
Answers
Answer:
f(x, y) = yx²/2 + 3x² + 4yx + 24x + K
Step-by-step explanation:
Given the expression dy/dx=xy+6x+4y+24
To find the solution, we are to make y the subject of the formula as shown
dy = (xy+6x+4y+24)dx
∫dy =∫(xy+6x+4y+24)dx
y = ∫(xy+6x+4y+24)dx
We are to integrate the function with respect to x keeping y constant. Since all constant are brought out if integral sign we will have;
y = ∫(xy)dx + ∫(6x)dx + ∫(4y)dx + ∫24dx
y = y∫xdx + 6∫xdx + 4y∫dx + 24∫dx
Integrate;
y = yx²/2 + 6x²/2 + 4yx + 24x + K
y = yx²/2 + 3x² + 4yx + 24x + K
Hence the solution to the differential expression is;
f(x, y) = yx²/2 + 3x² + 4yx + 24x + K
Where K is the constant of integration.
A football team lost 2 yards every 5 minutes. Write the integer that represents how many yards the team lost after 15 minutes
Answers
Answer:
6 yards
Step-by-step explanation:
hence, 2x3 = 6
evaluate (distributive property)
9*6= ? sixes + 4 sixes
=30 + ?
=???
Answers
Answer:
Step-by-step explanation:
If A, B and C are integers, according to distributive property;
A(B+C) = AB+AB
A is distributed over B and C
Given
9×6 = 5 sixes +4 sixes
5 sixes = 5(6) =30
4 sixes = 4(6) =24
9×6 = 5(6)+4(6)
9×6 = 30+24
9×6 = 54
Hence ? =5,?? =24 ??? = 54
Ballio has a reading goal. he checks three boxes of 9 books out from the library. after finish all the books, he realizes that he beat his goal by four books! how many books did Ballio have as his reading goal
Answers
HELP ME PLEASE geometry only answer if you know please!
Answers
Answer:
2. Reason: Addition Property of Equality
3. Statement: 3x=18
4. Reason: Division property of Equality
5. Statement: x=6 Reason: Simplifying.
Step-by-step explanation:
I'm pretty sure this is correct.
Write the given equation in the form of an equation of a sphere and find its center and radius.
x2 + y2 + z2 = 12x + 2y
equation =
center (x, y, z) =
radius =
Answers
Complete whatever squares you can:
x² - 12x = x² - 12x + 36 - 36 = (x - 6)² - 36
y² - 2y = y² - 2y + 1 - 1 = (y - 1)² - 1
So rewrite the equation as
x² + y² + z² = 12x + 2y
→ x² - 12x + y² - 2y + z² = 0
→ (x - 6)² - 36 + (y - 1)² - 1 + z² = 0
→ (x - 6)² + (y - 1)² + z² = 37
Then the center is (x, y, z) = (6, 1, 0), and its radius is √(37).
Answer:The radius is the square root of the constant term, z
Step-by-step explanation:
edge 2021
On the first circle, what segment is a diameter? How long is it?
Answers
Answer:
The segment that is the diameter is EB
It is 8 cm long
Step-by-step explanation:
At noon, the minute and the hour hands of a clock overlap. In how long will they again overlap?
its one hour but I don't know the minutes
Its not 5 min
Answers
Answer:
Okay. At noon, the hour and minute hand overlap. First, let’s calculate the speed of the hands.
The minute hand rotates once around the clock every hour. It goes 360 degrees in 60 minutes, so it rotates 360/60 or 6 degrees per minute. The hour hand goes once around the clock every 12 hours. Because there are 60 minutes in an hour, it goes 360 degrees 12*60 or 720 minutes. This means it travels at a speed of 360/720 or 0.5 degrees per minute.
Once the clock starts, the minute hand goes ahead and rotates ahead of the hour hand. At 1:00, the minute hand is at 12, and the hour hand is ahead at 1. This is where we will start our calculations.
Now, we have a variable, m, which is the minutes that have passed since the clock started. So, our minute hand speed is 6m, and our hour hand speed is 0.5m. However, because the hour hand is at one, it is at 30 degrees. (360/12 * 1.) This means our equation is 6m = 0.5m+30.
Now, we calculate.
6m = 0.5m+30
5.5m = 30
m = 30/5.5
m = 5.45
So at 5.45 minutes, the minute hand is at the hour hand. However, because one hour has passed since we started, we have to add on one hour.
So, our final total is 1 hour 5 minutes and 27 seconds.
Step-by-step explanation:
Anne’s potato salad recipe requires one pound of potatoes for every four people served. How many pounds of potatoes will Anne need to serve 14 people at her picnic?
Answers
Answer:
4 lbs
Step-by-step explanation:
1:4=4:16
16 is bigger than 14
So 4 lbs
What is the sum of -6 and 12/6
Answers
Answer:
-4
Step-by-step explanation:
Answer:
-4
Step-by-step explanation:
multiply -6 with 6 so we can have common denominator as 12/6
that's gives us -36/6+12/6
-36+12 is -24 so our answer up till now will be -24/6.... this can be simplified by 6 to get -4
pls mark this as brainliest!!!!
Simplify(-3)(-2)(-2) 1 point
Answers
Answer: -12
Step-by-step explanation:
First, multiply the numbers. -3 (-2) = 6 because a negative times a negative is a positive.
Then, multiply 6(-2) = -12 because a negative times a positive is a negative.
Therefore, the answer is -12.
Help please! I’ll give brainliest if correct!
Answers
Answer:
The formula for calculating a z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation. As the formula shows, the z-score is simply the raw score minus the population mean, divided by the population standard deviation.
Step-by-step explanation:
Hope his helps!
If x = 4 and y = 3, then xy – 2x = A 4 B 6 C 19 D 40
Answers
Answer:
A) 4
Step-by-step explanation:
Plug in the value for x and y.
(4 x 3) - 2(4)
12 - 8 = 4
Chris is saving money for his ski trip. He has $62.50,
but his goal is to save at least $200. What is the least
amount Chris needs to save to reach his goal?
a. type the inequality that represents the situation below.
b. solve the inequality to the right.
Answers
Solve 4X squared minus X -5 equals zero
Answers
your answer should be 1/3 if I did my math right
Abdul has bought 30 pounds of dog food. He feeds his dog
2/3 pounds for each meal. For how many meals will the food last?
Answers
Answer: I think its 45 days
Step-by-step explanation: hope this helps
PLS Help! SHOW WORK ON IT
Answers
Answer:
Perimeter of Triangle ABC is 21
Step-by-step explanation:
According to the Midpoint Theorem, if the line segment adjoins midpoints of any of the sides of a triangle, then the line segment is said to be parallel to all the remaining sides, and it measures about half of the remaining sides.
In this case, since XY=7, then AZ+ZC will need to equal 14 as that's opposite of half. Since AZ=ZC given that they are congruent, then AZ=7. Therefore the perimeter is XA+XZ+AZ=5+9+7=21
Which percent is represented by the diagram below? 2 area models with 100 squares. In the first model, 100 squares are shaded. In the second model, 25 squares are shaded and 75 are unshaded. 1.25% 12.5% 125% 1250%
Answers
Answer:
125%
Step-by-step explanation:
Answer:
C- 125
on edge
Step-by-step explanation:
PLZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELP ME!!!!!!!I BEGGING YOUUUUUUUU
Solve each equation for the variable. Show every step in your work
1. 2(x+12)=20
2. -4x-2=10
Answers
Answer:
Answers are below :)
Step-by-step explanation:
Q1- Divide both sides by 2
x +12 = 20/2
Simplify 20/2 to 10
x + 12 =10
Subtract 12 from both sides
x = 10 - 12
Simplify 10 - 12 to -2
x = -2
Q2. Add 2 to both sides
-4x = 10 + 2
Simplify 10 + 2 to 12
-4x=12
Divide both sides by -4
x = -12/4
Simplify 12/4 to 3
x = -3
Answer:
1. x=-2
2. X=-3
Step-by-step explanation:
1. 2(X+12)
2x+24=20
2x= -4
x= -2
2. -4x-2=10
-4x=12
x=-3
The amounts a soft drink machine is designed to dispense for each drink are normally distributed, with a mean of 12.1 fluid ounces and a standard deviation of 0.3 fluid ounce. A drink is randomly selected.
Required:
a. Find the probability that the drink is less than fluid ounces.
b. Find the probability that the drink is between and fluid ounces.
c. Find the probability that the drink is more than fluid ounces. Can this be considered an unusual event? Explain your reasoning.
Answers
Complete Question
The amounts a soft drink machine is designed to dispense for each drink are normally distributed, with a mean of 12.1 fluid ounces and a standard deviation of 0.3 fluid ounce. A drink is randomly selected.
Required:
a) Find the probability that the drink is less than 11.9 fluid ounces
b) Find the probability that the drink is between 11.6 and 11.9 fluid ounces
c) Find the probability that the drink is more than 12.6 fluid ounces. Can this be considered an unusual event? Explain your reasoning.
Answer:
a
[tex] P(X < 11.9 ) = 0.25239 [/tex ]
b
[tex]P( 11.6 < X < 11.9 ) = 0.20463 [/tex]
c
[tex] P(X > 12.6 ) = 0.047757 [/tex ]
Yes It is an unusual event
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 12.1[/tex]
The standard deviation is [tex]\sigma =0.3[/tex]
Generally the probability that the drink is less than 11.9 fluid ounces is mathematically represented as
P(X < 11.9 ) = P(\frac{X -\mu}{\sigma } < \frac{11.9 - 12.1}{0.3} )
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
[tex] P(X < 11.9 ) = P(Z< -0.667 ) [/tex ]
From the z table the area under the normal curve to the left corresponding to -0.667 is
P(Z< -0.667 ) = 0.25239
So
[tex] P(X < 11.9 ) = 0.25239 [/tex ]
Generally the probability that the drink is between 11.6 and 11.9 fluid ounces is mathematically represented as
[tex] P( 11.6 < X < 11.9 ) = P( \frac{11.6 -12.1}{0.3} < \frac{X -\mu}{\sigma } < \frac{11.9 - 12.1}{0.3} ) [/tex]
[tex]P( 11.6 < X < 11.9 ) = P( -1.667 < Z < -0.667 ) [/tex]
=> [tex]P( 11.6 < X < 11.9 ) = P( Z < -0.667) - P ( Z < -1.667 ) [/tex]
From the z table the area under the normal curve to the left corresponding to -1.667 is
P(Z< -1.667 ) = 0.047757
So
[tex]P( 11.6 < X < 11.9 ) = 0.25239 - 0.047757 [/tex]
=> [tex]P( 11.6 < X < 11.9 ) = 0.20463 [/tex]
Generally the probability that the drink is more than 12.6 fluid ounces is mathematically represented as
P(X > 12.6 ) = P(\frac{X -\mu}{\sigma } > \frac{12.6 - 12.1}{0.3} )
[tex] P(X >12.6 ) = P(Z> 1.667 ) [/tex ]
From the z table the area under the normal curve to the right corresponding to 1.667 is
P(Z> 1.667 ) = 0.047757
So
[tex] P(X > 12.6 ) = 0.047757 [/tex ]
Given that this probability is less than 0.05 , it mean it is an unusual event
Write the improper fraction 62/9 as a mixed number.
Answers
Answer:
62/9
Step-by-step explanation:
Determine the value of y, if x = -3.
y = |x + |1|
Answers
Answer:
Step-by-step explanation:
, if x = -3.
y = |x + |1|
So value of Y is
Y=|-3|+|1|
Y=3+1
Y=4
Answer is 4
[tex]y = 4[/tex]
Step-by-step explanation:[tex]y = |x + |1|\\[/tex]
| | = absolute value (how far it is from 0)
[tex]y = |-3 + |1|\\\\\\|-3| =3\\\\|3 +1| =3 + 1 \\3 + 1= 4\\[/tex][tex]\LARGE\boxed {y = 4}[/tex]
Let me know if you have any other questions or concerns!~[tex]InLoveWithPugs[/tex]
[tex]Moderator\\Math\ Enthusiast[/tex]
A quadrilateral has no pairs of parallel sides, what two shapes could it be?
Answers
Answer:
Kite
Step-by-step explanation:
Def of kite has no parallel sides
Answer:
Kite and TrapeziumStep-by-step explanation:
Each of them do not have any parallel lines or sides
if the graph of an exponential function is increasing is the domain always all real numbers
Answers
Answer:
D) The domain of the function is all real numbers
Step-by-step explanation:
5 people are sharing 12 kilograms of apples. How many kilograms of apples should each person get?
Answers
Answer:
2.4 kilograms
Step-by-step explanation:
5 people=12 kilograms
1 person= 12 divided by 5
Therefore, 1 person=2.4 kilograms
PLS HELP MEEEEEE
Two babysitters have the following price schedules: Susan charges $5 per hour plus a $2 base fee. Sarah charges $7 per hour. Use graphing to find the point where the two
will charge the same amount.
Answers
Answer:
hhhhhhhhhhhhhhhhhhjhhhhhhhhh
evaluate the expression for x = 3 y= 1/3 and z= 5. 12 x - 3y over 4 x - Z
Answers
Answer:
35.786
12(3) - 3(1/2)/4(3) - 5
This is then further simplified to:
36 - 1.5/7
And when you divide 1.5 by 7, the number (rounded) is .214.
Thus, subtract, and gain the final answer of 35.786.
Hope this helps!
Step-by-step explanation:
Can you please mark me brainliest
Hey there!
12x - 3y / 4x - z
= 12(3) - 3(1/3) / 4(3) - 5
= 36 - 1 / 12 - 5
= 35 / 7
= 5
Therefore, your answer is: 5
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Which inequality is equivalent to -y> 18
Answers
Answer:
you forgot to add the options.
Step-by-step explanation:
Answer:
y≤−18
Step-by-step explanation:
A truck with 30-inch diameter wheels is traveling at 70 mi/h. Find the angular speed of the wheels in radians per minute. ___ radians per minute How many revolutions per minute do the wheels make? (Round your answer to three decimal places.) ____ revolutions per minute
Answers
Answer:
a) 9676.1053731 rad/min
b) 1540 rpm
Step-by-step explanation:
A truck with 30-inch diameter wheels is traveling at 70 mi/h. Find the angular speed of the wheels in radians per minute. ___ radians per minute How many revolutions per minute do the wheels make? (Round your answer to three decimal places.) ____ revolutions per minute
truck with 30-in.-diameter wheels is traveling at 70 mi/h.
---------
1 mile per hour = 88 feet per minute
70 mi/hr = 6160ft/minute
----------
Each revolution = pi*d feet = 4pi feet
(b) How many revolutions per minute do the wheels make?
rev/min
-------------
Each revolution = pi*d feet = 4pi feet
rpm = 6160 ft/min / 4pi feet = 990/pi rpm
=~ 1540 rpm
---------------
(a) Find the angular speed of the wheels in rad/min.
rad/min
-------------
rad/min = rpm*2*pi
= 1540 rpm × 2× π
= 9676.1053731 rad/min