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]
Alyssa purchased 3 pounds of peanuts for $8.25. Write an equation that shows the relationship between the cost and the number of pounds purchased
Answer:$8.25 ÷ 3= x or 3·x =8.25
Step-by-step explanation:
3*x=8.25
3.HELP plz No LINKS AND NO HACKERS i will give brainlyiest NO COPIE D ANSWERSFROM OTHER USERS OR WEBSITE I WILL REPORT!!!! A scuba diver was exploring a reef 32.12 m below sea level. The diver ascended to the surface at a rate of 8.8 m/min.
(a) Write an equation to model the situation. Use the formula d = rt.
(b) Explain why it is reasonable to write the distance, d, as a positive number.
(c) How long did it take the diver to reach the surface?
Answer:
A scuba diver was exploring a reef 32.12 m below sea level. The diver ascended to the surface at a rate of 8.8 m/min.
a. using the formula d = rt, so 32.12 m = 8.8m/min (t)
b. it is reasonable to write the distance as positive because the diver is accending/ going up the surface
c. t = 32.12/ 8.8 = 3.65 min
Step-by-step explanation:
hope this helps
Find the perimeter of the figure below. Notice that one side length is not given.
Step-by-step explanation:
Perimeter of the quadrilateral = sum of the length of all the four sides. Note: Missing side of the quadrilateral = Perimeter of the quadrilateral - Sum of the length of three sides.
Explain step by step please!
Thirty copies of a textbook weigh a total of 75lb. What is the weight of each book?
Answer:
Each book weighs 2.5 pounds.
Step-by-step explanation:
75/2.5 is 30. Or you could also get the answer by 30* 2.5 which it would be 75. So, therefor, the answer is 2.5.
Answer:
2.5lb
Explanation:
In equation form the question is asking for x in
[tex]30(x) = 75[/tex]
Since multiplication is reversible (to be division), we can switch the equation up.
[tex]75[/tex] ÷ [tex]30 = x[/tex]
So the answer is
[tex]75[/tex] ÷ [tex]30 = 2.5[/tex]
Help ME!!! This Homework is Confusing Me
Answer:
I think it is d or a. I might be wrong sorry
Step-by-step explanation:
Y-(-3y) create an equivalent equation
9514 1404 393
Answer:
4y
Step-by-step explanation:
There are an infinite number of equivalent expressions. One of them can be obtained by combining the terms
y -(-3y) = y +3y = y(1 +3) = 4y
__
All of the expressions shown as equal are equivalent.
Subtract 8 1/5 - 4 2/5
. Simplify the answer and write as a mixed number.
Answer:
3 4/5
Step-by-step explanation:
What is the missing value on the number line?
Hello, could you please help me with this? Thanks :)
(brainly says i need more letters so here)
7/8
3 Select the correct answer from each drop-down menu. The boundary of a park is shaped like a circle. The park has a rectangular playground in the center and 2 square flower beds, one on each side of the playground. The length of the playground island its width is w. The length of each side of the flower beds is a Which two equivalent expressions represent the total fencing material required to surround the playground and flower beds. Assume that the playground and beds do not overlap The total fending material required to fence the playground and both flower beds is
Answer:
Get the perimeter of the each shape and add it all up to get the total fencing material required. 2 square flower beds = 2 x 4a = 8a 1 rectangular play ground = 2l + 2w total fencing material = 8a + 2l + 2w
Answer:
2l + 2w + 8a
Step-by-step explanation:
It was recently estimated that homes without children outnumber homes with children by about nine to seven. If there are 4912 homes in a county, how many of them
are homes without children
Answer:
Answer:929
Step-by-step explanation:
Step-by-step explanation:For every 11 children, 7 will have homes
1. What is the radius of the circle?
Worth max points
Answer:
[tex]7[/tex]
Step-by-step explanation:
We see that the circle is centered at [tex](1, 0)[/tex]. We know that because it's centered on the x-axis, one of the diameters will lie on the x-axis.
We know that the circle intersects the x-axis at [tex](8, 0)[/tex]. Therefore the radius of the circle is the distance between these points, in this case [tex]8-1=7[/tex].
So, the answer is [tex]\boxed{7}[/tex] and we're done!
help help help help thankyou
Answer:
3.4×10⁴
Step-by-step explanation:
1.6×10⁴=1.6×10000=16000
5×10⁴=5×10000=50000
5000-16000=34000
=3.4×10⁴
PLEASE HELP ME! Only answer if correct. :)
Answer:
i don't know
im kinda silly lol lol lol lol lol lol lol lol lol
What would be the all step you would take to solve the equation 2x + 1 = 10 - x?
Answer:
3
Step-by-step explanation:
Move the terms : 2x + 1 =10 -x
Collect like terms
Calculate : 2x + x=10-1
Divide both sides
3x = 9
x = 3
what is the domain of f in the equation f(x)=2(x-1)^2-4
Answer:
[tex](-\infty, \infty)[/tex]
Step-by-step explanation:
There are no restrictions on the possible values of [tex]x[/tex], because you can square any number.
Because [tex]x[/tex] can be anything, the domain is all reals or [tex]\boxed{(-\infty, \infty)}[/tex] which means [tex]x[/tex] can be any real number.
There are 5 roses and 6 daisies in a vase.
Answer:
11 flowers
Step-by-step explanation:
There are 6 triangles and 8 squares. What is the simplest ratio of triangles to total shapes?
Answer:
3:7
Step-by-step explanation:
The number of triangles is 6.
The number of squares is 8.
The total number of shapes is 14.
The unsimplified ratio of triangles to total shapes is 6:14.
The bigger number that both 6 and 14 can be divided by is 3.
That makes the ratio 3:7, and it cannot be simplified further.
Write an equation of the line that passes through the point (3,3) and is Parallel to the line y=-1/2x+3
Answer:
[tex]y = - \frac{1}{2} x + \frac{9}{2} [/tex]
Step-by-step explanation:
find the y-intercept
[tex]3 = - \frac{1}{2} (3) + b \\ 3 = - \frac{3}{2} + b \\ \frac{6}{2} + \frac{3}{2} = b \\ b = \frac{9}{2} [/tex]
3r+(7+8)/(t-3)when r=4, s=3 and t=5
Answer:
19.5
Step-by-step explanation:
3r+(7+8)/(t-3)
3(4)+(15)/(5-3)
12+(15/2)
12+7.5
19.5
The elevation of a submarine with respect to sea level is displayed as - 125 feet. Which statement is correct?
A. The submarine is 125 feet above sea level.
B. The submarine is 125 feet below sea level.
C. The submarine is -125 feet above sea level.
D. The submarine is -125 feet below sea level.
B. The submarine is 125 feet below sea level.
Step-by-step explanation:
-124 feet because - (negative) means the submarine is 124 meters below sea level (masl).
Answer:
The elevation of a submarine with respect to sea level is displayed as - 125 feet. Which statement is correct?
A. The submarine is 125 feet above sea level.
B. The submarine is 125 feet below sea level.
C. The submarine is -125 feet above sea level.
D. The submarine is -125 feet below sea level.
Step-by-step explanation:
The keyword is below so it means it is a negative integer. Therefore the answer is letter D.If a baby weighs 7 lbs at birth and 12 Ibs after 20 weeks, how much did the baby weigh after 4 weeks, assuming linear growth? [?] lbs
Answer: 8lbs
Step-by-step explanation:
The baby gained one pound
Assuming linear growth, the baby would weigh approximately 8 lbs after 4 weeks.
How to determine the weight of the babyAssuming linear growth, we can use the concept of a slope to estimate the baby's weight after 4 weeks.
Given information:
Weight at birth (0 weeks): 7 lbs
Weight after 20 weeks: 12 lbs
We can calculate the rate of change (slope) of the baby's weight per week:
Slope = (Change in weight) / (Change in weeks)
Slope = (12 lbs - 7 lbs) / (20 weeks - 0 weeks)
Slope = 5 lbs / 20 weeks
Slope = 0.25 lbs/week
Now, using the slope, we can estimate the baby's weight after 4 weeks:
Estimated weight change = Slope * Number of weeks
Estimated weight change = 0.25 lbs/week * 4 weeks
Estimated weight change = 1 lb
So, the baby's weight after 4 weeks would be the initial weight (7 lbs) plus the estimated weight change (1 lb):
Estimated weight after 4 weeks = Initial weight + Estimated weight change
Estimated weight after 4 weeks = 7 lbs + 1 lb
Estimated weight after 4 weeks = 8 lbs
Learn more about linear equation
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If the figure below is a regular polygon, find the value of x.
(9x - 18)
Given that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. Find the z score associated with the probability that a randomly selected adult has an IQ greater than 115.
Answer:
0.8413
Step-by-step explanation:
bad explainer srry
Answer:
Step-by-step explanation:
[tex](\frac{115-100}{15})=1[/tex]
because we're looking for the zscore associated with it being greater than we flip the sign
so the answer is just -1
16 - 2 to the 3rd power over 16
Step-by-step explanation:
the explantion is in the photo
Answer:
1/2
Step-by-step explanation:
Your equation is 16-2^3/16
First, you find out what 2^3 is equal to
2 x 2 x 2=8
Your equation will then be 16-8/16
Next, you subtract 8 from 16
16-8=8
Your equation will then be 8/16
divide both 8 and 16 by 4
8/4=2, 16/4=4
=2/4
You then simplify 2/4 to it's lowest terms
2/2=1 , 4/2=2
=1/2
1 A boat travels at an average speed of 15 km/h for 1 hour.
a Calculate the distance it travels in one hour.
b At what average speed will the boat have to travel to cover the
same distance in 2 hours?
Answer: 15km, 7.5kmh
Step-by-step explanation:
a. Distance travelled = speed * time = 15* 1 =15km
b. Distance = 15
time = 2hrs
Speed = distance/time = 15/2 = 7.5kmh
4. k(x) × g(x) × f(x)
[tex]k(x) \times f(x)[/tex]
[tex](2x + 5) \times (x - 1)[/tex]
[tex]2 x(x - 1) + 5(x - 1)[/tex]
[tex] ({2 x }^{2} - 2x) + (5x - 5)[/tex]
[tex] {2x}^{2} - 3x - 5[/tex]
________________________________
[tex]k(x) \times g(x) \times f(x)[/tex]
[tex]g(x) \times (k(x) \times f(x))[/tex]
[tex] ({6x }^{2} - 4x + {3x}^{4} ) \times ( {2x}^{2} - 3x - 5)[/tex]
[tex] {6x}^{2} ( {2x}^{2} - 3x - 5) - 4x ( {2x}^{2} - 3x - 5) + {3x}^{4} ( {2x}^{2} - 3x - 5)[/tex]
[tex]12 {x}^{4} - 18 {x}^{3} - 30 {x}^{2} - {8x}^{3} - 12 {x}^{2} - 20x + {6x}^{6} - 9x {}^{5} - {15x}^{4} [/tex]
CAN SOMEONE PLEASE DO THESE 4 QUESTIONS
3.2x-1.7x+5.5=10
3/4x-1/4x+14=3
3(2x+1)+x=-39
m+4(2m-3)+-3
I WILL GIVE BRAINLIEST AND YOU ARE A LIFESAVER
ALSO PLEASE SHOW STEPS!!
THANKS!!!!!
Problem
3.2x-1.7x+5.5=10
Steps:
1.5x + 5.5 = 10
1.5x X 10 + 5.5 X 10 = 10 X 10
15x + 55 - 55 = 100 - 55
15x = 45
15x/15 = 45/15
x = 3
Therefore questions ones answer is x = 3
Problem
3/4x-1/4x+14=3
Steps:
3/4x - 1/4x + 14 = 3
3/4x - 1/4x + 14 - 14 = 3 - 14
3/4x - 1/4x = -11
3/4x X 4 - 1/4x X 4 = -11 X 4
2x = -44
2x/2 = -44/2
x = -22
Therefore question two's answer is x = -22
Problem
3(2x+1)+x=-39
Steps:
7x + 3 = -39
7x + 3 - 3 = -39 - 3
7x = -42
7x/7 = -42/7
x = -6
Therefore question three's answer is x = -6
Problem
m+4(2m-3)+-3
Steps:
= m + 4 (2m - 3) - 3
= m + 8m - 12 - 3
= 9m - 15
Therefore question four's answer is 9m - 15
How can distributive property be used to solve 7 x 391
Answer:
7x ³⁹¹
Step-by-step explanation:
1: "x3" was replaced by "x^3".
Write the equation of a line that goes through the point (2, 4) that is parallel to the
line y = 3x - 6.
Answer:
y = 3x - 2
Step-by-step explanation:
Parallel lines have the same gradient in this case 3 is the gradient.
We will use the point (2,4) to form our own equation.
4 will be y, 3 will be m, 2 will be x
All we need is to find the C in the equation y=mx + c
4 = 3(2) + c
4 = 6 + c
C = -2
Therefore;
y = 3x - 2
what new realization do you have about finding the nth term of the arithmetic sequence and finding the arithmetic means how would you use this in making decision
Step-by-step explanation:
Arithmetic Sequnce in our daily life
The knowledge of calculating the nth term of a sequence can be very helpful. Calculating loans, discounts, salary, savings are some of the use of arithmetic method. If I save P5 per day for 5 years, I can simply use arithmetic sequence to find how much I saved from day 1 to last. Salary increase can also be solved using arithmetic sequence. Below is an example.
Sample real life problem:
1. I earn P300 on the first day. After each succeeding day, I earn P2 more than the previous day. How much should I be able to earn after 30 days?
In this situation, I would use the arithmetic sequence formula which is:
an = a1 + (n - 1)d
an is the nth term
a1 is the first term
n is the term position
d is the common difference
Lets subsitute:
an = P300 + (30 - 1)P2
an = P358
I should earn P348 at the end of 30 days