Any point satisfying the relation y = -[1 - (∛x²)]²(1/(∛x)) will be points on the graph where the tangent line has slope 1.
What is the slope of a given line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
Consequently, the formula for the change in y-coordinate with respect to the change in x-coordinate is the slope of a line is represented by the expression m = change in y/change in x =Δy/Δx.
Additionally, the slope of the line can be shown as tan θ = Δy/Δx
So, the slope of a line is tan θ.
The given equation is: (∛x²) + (∛y²) = 1
Therefore, (∛y²) = 1 - (∛x²) ⇒ y² = [1 - (∛x²)]³
Differentiating the equation formed with respect to x, we get
2y(dy/dx) = 3[1 - (∛x²)]²(-2/3)(1/(∛x)) ⇒ dy/dx = (-1/y)[1 - (∛x²)]²(1/(∛x)) -(i)
Given, the slope of the tangent line is = 1 -(ii)
Thus, equating (i) and (ii), we get,
(-1/y)[1 - (∛x²)]²(1/(∛x)) = 1 ⇒ y = -[1 - (∛x²)]²(1/(∛x))
Therefore any point satisfying the relation y = -[1 - (∛x²)]²(1/(∛x)) will be points on the graph where the tangent line has slope 1.
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Selena is 2 years older than Maria, and Sofia is 3 years younger than Maria. If the sum of their ages is 44, then how old is each girl? (Let Maria’s age =
x
.)
Which graph shows the solution to this system of inequalities?
y> 3x-4
y>x +1
Answer:
Step-by-step explanation:
it is D i took the test
Elon sat on the dock with his fishing rod, when suddenly he felt the rod being pulled down! He reeled in his catch, causing it to ascend at a constant rate of 0.10.10, point, 1 meters per second. When it reached the water's surface after 353535 seconds, Elon found it was only an old shoe... Graph the relationship between the shoe's altitude (in meters relative to the water's surface) and time (in seconds).
The relationship between the shoe's altitude (in meters relative to the water's surface) and time (in seconds) has been plotted in the graph shown below.
The equation of a straight line.Mathematically, the standard form of the equation of a straight line is given by;
y = mx + c
Where:
x represents the time measured in secondsy represents the position relative to water surface and measured in meters.m represents the slope.c represents the intercept or initial altitude of the shoe.Next, we would determine the initial altitude as follows:
y = mx + c
0 = (0.1 × 35) + c
0 = 3.5 + c
c = -3.5
Substituting the given points into the formula, we have;
y = 0.1x - 3.5
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Complete Question:
Elon sat on the dock with his fishing rod, when suddenly he felt the rod being pulled down! He reeled in his catch, causing it to ascend at a constant rate of 0.1 meters per second. When it reached the water's surface after 35 seconds, Elon found it was only an old shoe...
Graph the relationship between the shoe's altitude (in meters relative to the water's surface) and time (in seconds).
if 180 is 37.5% of the whole what would be the whole
what do i do to create a graph for c=3p
Answer: Graph the line using the slope and y-intercept, or two points.
Slope: 3
y-intercept: (0,0)
Step-by-step explanation: Example graph for c=3p .
Find the slope of a line that passes through the following two points: (-1, -4) and (2, 2).
Answer:
-2/3
Step-by-step explanation:
y=mx+c
m is the gradient/slope
m= y2-y1 / x2-x1
you can label any point as your x1y1 and x2y2, you will still get the same answer
. A swim coach has at most $800 to buy equipment for the swim team. Each
pull buoy costs $5.50 and each kickboard costs $10. Let X represent the
number of pull buoys and y represent the number of kickboards.
a. Write an inequality for the scenario..
5.50x+10y_< 800 I already wrote the inequality now graph the inequality
A mathematical phrase in which the sides are not equal is referred to as being inequal. The point (80, 35) exists in the solution space. The coach could buy 80 pull buoys and 35 kick boards.
What is meant by inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.
A mathematical phrase in which the sides are not equal exists directed to as being inequal. In essence, a comparison of any two values reveals whether one exists less than, larger than, or equivalent to the value on the opposite side of the equation.
A) The sum of costs must not exceed the budget:
5.50x +10.00y ≤ 800
B) Let the inequality be 5.50(0) +10.00(50) = 500 ≤ 800
Yes, the coach could buy these
C) Let the inequality be 5.50(125) +10.00(25) = 937.50 > 800
No, they cost too much
D) The point (80, 35) exists in the solution space. The coach could buy 80 pull buoys and 35 kick boards.
The complete question is:
A swim coach has at most $800 to buy equipment for the swim team. Each pull buoy costs $5.50 and each kickboard costs $10. Let x represent the number of pull buoys and y represent the number of kickboards.
A) Write an inequality for the scenario
B) could the coach purchase zeros pull buoys and 50 kickboards?
C) could the coach purchase 125 pull buoys and 25 kickboards?
D) What other combination of pull buoys and kickboards works for your inequality?
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V = 2/9πr³
Solve for r
Answer:
Step-by-step explanation:
step 1: multiply both sides by 9π to get V9πr³=2
step 2: divide both sides by V9π to get r³=2/(V9π)
step 3: take the cubed root of both sides to get r=∛[2/(V9π)]
The length, d, of a violin string varies inversely as the frequency, f, of its vibrations (cycles per second). Suppose it is known that a 16-in.-long violin string vibrates 320 cycles per second.
A. Write an inverse variation equation modeling this information
B. Use your inverse variation equation from Part A to determine the frequency of an 8-inch-long violin string.
An 8-inch violin string has a frequency of 640 cycles per second using the inverse variation equation.
Who defines frequency?The pace of direction changes in current per second is known as frequency. It is expressed in hertz (Hz), a unit of measurement that is used internationally. One hertz is equivalent to one cycle per second. One hertz (Hz) is equivalent to one cycle per second.Given: A 16-inch violin string is known to vibrate at 320 cycles per second.
We know that,
Using the frequency equation where l for the length of the string and f for the frequency.
f = k/l
320 = k/16
k = 5120
So, the equation becomes f = k/l
For l = 8
f = 5120/8
f = 640
Therefore, the frequency of an 8-inch-long violin string is 640 cycles per second.
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Please help and provide a real step by step explanation
What is the equation of the line that passes through Point (3, -4) and has a Slope of 0.
Step-by-step explanation:
the slope of a line is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.
a slope = 0 means that the y coordinate change is always 0, so y does not change anywhere on the line.
that makes y a constant c, and x can be any value completely independent of y.
the line is the summary of all points that have c as their y coordinate.
so, the general equation for such a line is simply
y = c
what is c ?
as we have one point on the line, remember the statement above : the line is the summary of all points that have c as their y coordinate.
that means (3, -4) must have the same y coordinate.
so, c = -4.
the equation of the line is therefore
y = -4
Size Weight (lbs)
Extra large 6/1/2
Medium 3/1/4
Small 1/5/8
How many times as heavy is the extra large pizza than the small pizza?
uite in simplest form.
After doing some mathematical operations, we conclude that extra large pizza is 4x times heavier than small size pizza.
What exactly are mathematical operations?The rules that specify the order in which we should perform multiple operations to solve an expression are known as the order of operations. Parentheses, Exponents, Multiplication, Division (from left to right), Addition, and Subtraction are in the following order: PEMDAS (from left to right). A function in mathematics known as an operation is one that transforms zero or more input values into a clearly defined output value. The operation's complexity is determined by its operand count.So, times extra large pizza is heavy than small pizza:
Extra large pizza: 6½ ⇒ 13/2Small pizza: 1⅝ ⇒ 13/8Now, perform operations as follows:
(13/2)/(13/8)13/2 × 8/138/24Therefore, after doing some mathematical operations, we conclude that extra large pizza is 4x times heavier than small size pizza.
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The correct question is given below:
Use the Table that shows the weights of three sizes of pizza.
Extra Large Pizza - 6 1/2
Medium Pizza - 3 1/4
Small Pizza - 1 5/8
(A) How many times as heavy is the extra large pizza than the small pizza?
Question 3(Multiple Choice Worth 1 points)
(03.01 LC)
Rewrite the radical expression as an expression with a rational exponent.
the cube root of five to the seventh power
x21
x4
five to the seven thirds power
five to the three sevenths power
The representation of the radical expression; the cube root of five to the seventh power as an expression with a rational exponent is; five to the seven thirds power.
Which rational exponent expression is equivalent to the radical expression; ³√5⁷?It follows from the task content that the radical expression given; ³√5⁷ is to be expressed as a rational exponent expression.
Recall that the converse of the rational exponent law of indices is such that; ³√x = (x)^⅓.
Hence, it follows that the expression given;
³√5⁷ = (5⁷)^⅓.
Also, it follows from the power of power law of indices that the expression above can be written as;
5^(7/3).
Ultimately, the equivalent rational exponent expression is; five to the seven thirds power; 5^(7/3).
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How could you use parallel lines to compare figures Q and R? Explain your
reasoning.
Answer:
Answer down below!
Step-by-step explanation:
Using your knowledge of parallel lines, you know that parallel lines are most often time never touching, but on the same plane. The top of R and the bottom line of Q are parallel because they don't intersect each other.
We also notice that the shapes are the same length, so we have this conclusion!
Q and R are identical because they share opposite, parallel lines.
Which number is not in scientific notation? (3 points)
Group of answer choices
0.5 ⋅ 103
2.01 ⋅ 10−2
1.3 ⋅ 10−4
6 ⋅ 1025
Answer:
0.5 ⋅ 103
Step-by-step explanation:
A flight to Sydney to Auckland takes 3 hours and 12 minutes, Auckland times is 2 hours ahead of Sydney's if the flight departed Sydney at 10:10 am at what time did it arrive at Auckland
Flight will reach Auckland at 11:22 am with respect to Auckland time.
We have the following given information which states as follows
A flight to Sydney to Auckland takes 3 hours and 12 minutes.
∴ Total journey time = 3hr 12min.
Auckland times is 2 hours ahead of Sydney's time.
∴ Change in time will be 2hr
The flight departed Sydney at 10:10 am
∴ Flight will reach Auckland after the journey time
∴ Flight will reach Auckland after 3hr 12min
∴ Flight will reach Auckland at 01:22 pm
But Auckland times is 2 hours ahead of Sydney's time.
∴ Change in time will be 2hr
∴ Flight will reach Auckland 2hr less than the considered reach time with respect to Sydney.
∴ Flight will reach Auckland at 11:22 am.
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Determine which integer(s) from the set S:{−18, 2, 15, 20} will make the inequality five sixths m minus four is less than one third m plus 5 false.
Number 20 from the set S:{−18, 2, 15, 20} will make the inequality five sixth "m" minus four less than one third "m" plus 5 false.
As per the question statement, we are supposed to find the integer(s) from the set S:{−18, 2, 15, 20} will make the inequality five sixth "m" minus four less than one third "m" plus 5 false.
Let's write the given statement in numeric form first, we get
[tex]\frac{5m}{6} -4 < \frac{m}{3} +5[/tex]
Let's solve the inequality for "m"
We get 3m/6 <9
or 3m <54
or m < 18
Therefore all values of m < 18 will make the inequality true and m>18 will make the inequality false.
The value of m > 18 in the above given set S:{−18, 2, 15, 20} is 20, hence number 20 from the set S:{−18, 2, 15, 20} will make the inequality five sixth "m" minus four less than one third "m" plus 5 false.
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Answer: its 20 or 15 i belieive its 20 tho
Step-by-step explanation:
Given equal probabilities of the birth of a xy or xx, what is the probability that a group of four siblings includes all xy? all xx? all xy or all xx?.
The probability that a group of four siblings includes all XY is 1/16 (6.5%), while the probability all XX offspring is 1/16 (6.5%). It is a simple genetic probability calculation.
Genetic probabilities and chromosomes
Females inherit two chromosomes X, whereas males inherit one chromosome X and one chromosome Y.
The probabilities of inherent two chromosomes X (females) are 1/2 (50%), while the probabilities of inherent one chromosome X and one chromosome Y (males) are also 1/2.
In consequence, the probability that a group of four siblings includes all XY is 1/16 (because it is equal to 1/2 x 1/2 x 1/2 x 1/2 = 1/16), the same for the probability all XX offspring (1/16).
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Find the area of the rectangle.
1 1/2 yd
58/ 8 yd
Answer:
[tex]\sf Area = 10\dfrac{7}{8} \yd^2[/tex]
Step-by-step explanation:
Area of rectangle:Area = length *breadth
Convert the mixed fraction to improper fraction.
[tex]\sf 1\dfrac{1}{2}=\dfrac{3}{2} \ yd[/tex]
[tex]\sf area = \dfrac{3}{2}*\dfrac{58}{8}\\\\[/tex]
[tex]\sf = \dfrac{3*29}{8}\\\\=\dfrac{87}{8}\\\\= 10\dfrac{7}{8} \ yd^2[/tex]
Can someone please help me
Answer:
Y=-3x+7
Step-by-step explanation:
it hit the y axis at 7
And it is going down by 3
If benzene has a density of 0.8787 g/mL, what is the volume of 131.8 g of benzene?
The benzene has a volume value of 149.99 mL
How to determine the volume of the benzene?From the question, the given parameters are
Density of benzene = 0.8787 g/mL
Mass of benzene = 131.8 g
The volume of the benzene is then calculated using
Density = Mass/Volume
Make Volume the subject of the formula
So, we have
Volume = Mass/Density
Substitute the known values in the above equation
So, we have the following equation
Volume = 131.8/0.8787
Evaluate the quotients in the equation
Volume = 149.99
Hence, the volume of the benzene is 149.99 mL
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What is the vertex form of the equation?
y = x² + 8x-6
Oy=(x-4)²-22
Oy=(x-4)² + 22
O y = (x+4)² - 22
Oy = (x+4)² + 22
Answer:
C
Step-by-step explanation:
One of the quick ways of getting the answer is to graph the equation. I have done that for you at the bottom of this answer. However, I think you want the written solution.
Equation
y = x^2 + 8x - 6 Put brackets around the first 2 terms
y = (x^2 + 8x) - 6 Take 1/2 the second term and square
8/2 = 4; 4^2 = 16 Put 16 after the second term
y = (x^2 + 8x + 16) - 6 Subtract 16 and put it after the 6
y = (x^2 + 8x + 16) -6-16 Combine
y = (x^2 + 8x + 16) - 22
The first 3 terms make a perfect square (x^2 + 8x + 16) = (x + 4)^2
So the answer is between C and A
y = (x + 4)^2 - 22
uestion 14 (2 points)
3
What is the equation of a line that passes through point (3,-5) and is perpendicular to y = -x+5?
Enter your answer with no spaces.
A/
A line that passes through point (3,-5) and is perpendicular to y = -x+5 has the equation y = x - 8.
What is a straight line equation?A straight line has an equation of y=mx + c, where m is the gradient and c is the constant, also known as the y-intercept, at which the line crosses the y-axis.
How do you determine the line's equation?In order to put the equation in y-intercept (y = mx + b) form and determine the equation of a graphed line, first determine the slope and y-intercept.
It is given that a line's equation passes through point (3,-5) and is perpendicular to y = -x+5.
Slope of given line = -1
Slope of line perpendicular to the given line = Negative of the reciprocal of the slope of a given line = 1
We have the slope and point (3,-5) of the required line. So, we can find the constant of this equation.
y = mx + c
-5 = 1(3) + c
c = -5 - 3
c = -8
Substituting c = -8 and m = 1 to get the equation of required line.
y = mx + c
y = x - 8
As a result, the equation of a line passing through point (3,-5) and perpendicular to y = -x+5 is y = x - 8.
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Which of these ordered pairs is NOT a solution to this system
Answer:
C
Step-by-step explanation:
to determine which ordered pair is not a solution , substitute the coordinates of the point into the inequalities and check the validity. Note that both inequalities must be true for the point to be a solution.
A (- 3, 3 )
3 ≥ - 3 - 5
3 ≥ - 8 ← true
3(3) < - 6(- 3) + 3
9 < 18 + 3
9 < 21 ← true
------------------------------------------
B ( - 1, 2 )
2 ≥ - 1 - 5
2 ≥ - 6 ← true
3(2) < - 6(- 1) + 3
6 < 6 + 3
6 < 9 ← true
------------------------------------------
C (4, 5 )
5 ≥ 4 - 5
5 ≥ - 1 ← true
3(5) < - 6(4) + 3
15 < - 24 + 3
15 < - 21 ← false
-------------------------------------------
D (- 6, 0 )
0 ≥ - 6 - 5
0 ≥ - 11 ← true
3(0) < - 6(- 6) + 3
0 < 36 + 3
0 < 39 ← true
--------------------------------------------
Both inequalities are true in A, B , D
Both inequalities in C are not true so (4, 5 ) is not a solution to the system
name a pair of vertical angles.
Answer:
The vertical angles are
1 and 3
2 and 4
no joking around and no links
NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by 4.9t² + 142t+ 346. h(t) Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
A.The rocket splashes down after seconds. Round your answer to the nearest second.
B.How high above sea-level does the rocket get at its peak? The rocket peaks at meters above sea-level. Round your answer to the nearest meter.
a. The rocket splashes down after 31.23 seconds.
b. The rocket is 1374.7 meters above sea level.
NASA launches a rocket at t=0 seconds.
Its height, in meters above sea-level, as a function of time is given by
h(t)=-4.9t²+142t+346.
Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
When splash down occurs, h(t) = 0, therefore
-4.9t²+142t+346 = 0
find t using the quadratic formula; a=4.9, b=142, c=346
t = -142 ± √(142)² - 4(-4.9)(346) / 2(-4.9)
t = -142 ± 164.15 / -9.8
t = -142+164.15/-9.8 , -142-164.15/-9.8
t = 22.15/-9.8 , -306.15/-9.8
t = -2.26 , 31.23
time cannot be negative so t = 31.23
The rocket splashes down after 35.8229 seconds.
The max occurs on the axis of symmetry, use x=-b/(2a) to find it
t = -142/2(-4.9)
t = 142/9.8
t = 14.48 sec
replace t with 17.2449 in the equation
h(t) = -4.9(14.48)² + 142(14.48) + 346
= 1374.7 m
The rocket peaks at 1374.7 meters above sea-level.
Hence we get the answers.
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2. Write in standard form: one hundred dollars and fourteen cents
Answer:
$100.14
Step-by-step explanation:
convert to a number
thirteen thousand, forty-one and six ten-thousandths in numbers
also
thirteen thousand, forty-one and six ten-thousandths in numbers
Answer: for number 1 13,416
Step-by-step explanation: i think that is the correct answer i could be wrong
Simplify 0.4i−i.
For those of you who have this question the answer is actually -0.6i
Have A Great Day Ya'll
Answer:-0.9.45
Step-by-step explanation:
-0945
Answer: -0.6i
Step-by-step explanation:
[tex]0.4i-i=\\\\i(0.4-1)=\\\\i(-0.6)=\\\\-0.6i[/tex]
x-y=5 find the x and y intercepts
PLEASe HELP I NEED NUMBER 1 there is an ex sample I need the answer and work to it that looks like the ex sample
a) 20% 60 of is 12
b) 25% of 24 is 6
c) 4% of 600 is 24
Here the problem we are dealing with is related to percentage, which could be a division or a proportion in which the value of the entire is continuously 100. is represented by the symbol "%".
a) let us consider the missing number to be x
so, the problem will be 20% of x= 12
=> 20/1000* x= 12
=>20x= 12*100
=> x= 12*100/20 = 60
b) let the percentage be x
so, the problem will be x% of 24 =6
=>x/100* 24= 6
=>24x=600
=>x=600/24 =25
c) here, we are given 4% of 600=?
=4/100* 600
=24
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