Plant height increased after 1 week: 35 cm - 30 cm = 5cm
Percentage increase: (5 : 30) x 100% = 16.66%
please help me asap
ty
Answer:
y = -4x
Step-by-step explanation:
Subtract 8x both sides
2y = 0 + (-8x)
Divide by 2 both sides
y = -4x
is 1/6 a rational number?
Answer:
yes 1/6 is a rational number.
Need Help PLease Very Importatn giving 20 POINTS
Answer:
The last option: \(3 x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)
Step-by-step explanation:
Main concepts:
Concept 1. Parts of a Radical
Concept 2. Radicals as exponents
Concept 3. Exponent properties
Concept 4. How to simplify a radical
Concept 1. Parts of a Radical
Radicals have a few parts:
the radical symbol itself,the "index" (the number in the little nook on the left), andthe "radicand" (the part inside of the radical).If the index isn't shown, it is the default index of "2". This default index for a radical represents a square root, which is why people sometimes erroneously call the radical symbol a square root even when the index is not 2.
In this situation, the radical's index is 4, and the radicand is 81 x^18 y^6.
Concept 2. Radicals as exponents
For any radical, the entire radical expression can be rewritten equivalently as the radicand raised to the power of the reciprocal of the index of the radical. In equation form:
\(\sqrt[n]{x} =x^{^{\frac{1}{n}}}\)
So, the original expression can be rewritten as follows:
\(\sqrt[4]{81x^{18}y^{6}}\)
\((81x^{18}y^{6})^{^{\frac{1}{4}}}\)
Concept 3. Exponent properties
There are a number of properties of exponents:
Multiplying common bases --> Add exponents: \(x^ax^b =x^{a+b}\) Dividing common bases --> Subtract exponents: \(\dfrac{x^a}{x^b} =x^{a-b}\) Bases raised to powers, raised again to another power, multiplies powers: \((x^a)^b =x^{ab}\) A "distributive" property for powers across multiplication (warning... does not work if there are ANY addition or subtractions): \((xy)^a =x^{a}y^{a}\)Continuing with our expression, \((81x^{18}y^{6})^{^{\frac{1}{4}}}\), we can apply the "distributive" property since all of the parts are multiplied to each other...
\((81)^{^{\frac{1}{4}}}(x^{18})^{^{\frac{1}{4}}}(y^{6})^{^{\frac{1}{4}}}\)
Applying the "Bases raised to powers, raised again to another power, multiplies powers" rule for the parts with x and y...
\((81)^{^{\frac{1}{4}}}(x^{^{\frac{18}{4}}})(y^{^{\frac{6}{4}}})\)
Reducing those fractions, (both the numerators and denominators have a factor of 2)...
\((81)^{^{\frac{1}{4}}}(x^{^{\frac{9}{2}}})(y^{^{\frac{3}{2}}})\)
Rewriting the exponent of the "81" back as a radical...
\(\sqrt[4]{81} x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)
Concept 4. How to simplify a radical
For any radical with index "n", the result is the number (or expression) that when multiplied together "n" times gives the radicand.
In our case, the index is 4. So, we're looking for a number that when multiplied together four times, gives a result of 81.
One method of simplifying radicals is to completely factor the radicand into prime factors, and forms groups (each containing an "n" number of matching items).
Note that 81 factors into 9*9, which further factors into 3*3*3*3
This is a group of 4 matching items, and since the index of the radical is 4, we have found a group that can be factored out of the radical completely:
\(\sqrt[4]{81} =\sqrt[4]{(3*3*3*3)}=3\)
So, our original expression, simplifies finally to \(3 x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)
This is the last option for the multiple choice.
write an equation that expresses the law of refraction.
The equation that expresses the law of refraction is known as Snell’s law or the law of refraction.
The law of refraction is used to determine the direction in which light bends when it enters a new medium.
What is the law of refraction?
The law of refraction (also known as Snell's law) is a principle of optics used to explain how light behaves at the boundary between two media with different refractive indexes.
The law of refraction states that when light passes from one medium to another, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant.
The equation for the law of refraction is as follows:
$$\frac{\sin \theta_1}{\sin \theta_2}= \frac{v_1}{v_2}=\frac{\lambda_1}{\lambda_2}=\frac{n_2}{n_1}$$
Where:θ1 = Angle of incidence
θ2 = Angle of refraction
v1 = Velocity of light in medium 1
v2 = Velocity of light in medium 2
λ1 = Wavelength of light in medium 1
λ2 = Wavelength of light in medium 2
n1 = Refractive index of medium 1
n2 = Refractive index of medium 2
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Question 4 of 10
Which of the following could be the ratio between the lengths of the two legs
of a 30-60-90 triangle?
Check all that apply.
□A. √2:√2
B. 15
□ C. √√√√5
□ D. 12
DE √3:3
OF. √2:√5
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SUBMIT
The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).
In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.
A. √2:√2
The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.
B. 15
This is a specific value and not a ratio. Therefore, option B is not applicable.
C. √√√√5
The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.
D. 12√3
This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.
E. √3:3
This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.
F. √2:√5
This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.
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Annie has 4 1/2 feet of rope what is the greatest number of 3/4 foot pieces that annie can cut from the rope
Answer:
6
Step-by-step explanation:
4 1/2 divided by 3/4 is 6. so 6 pieces
The greatest number of 3/4 foot pieces that Annie can cut from the rope
is 6.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, Annie has 4 1/2 feet of rope.
Therefore, The greatest number of 3/4 foot pieces Annie can cut can be obtained by dividing the length of the total rope by the length of each piece which is,
= (4 1/2)/(3/4).
= (9/2)×(4/3).
= 36/6.
= 6.
So, 6 pieces are possible.
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Solve the following operation with binary numbers. check your answer by converting the binary numbers to base 10 numbers, doing the operation on the base 10 numbers, and converting the answer back to base 2. 1112 + 102
The answer to the given binary operation is 10012. The binary operation of adding 1112 and 102 will be solved by converting the binary numbers to base 10, performing the addition in base 10, and then converting the result back to base 2.
Converting the binary numbers to base 10, we have 1112 = 7 and 102 = 2. Adding 7 and 2 in base 10 gives us 9. To convert the result back to base 2, we divide 9 by 2 repeatedly until the quotient becomes 0. The remainder in each division gives us the binary digits of the answer. In this case, 9 divided by 2 is 4 with a remainder of 1, and 4 divided by 2 is 2 with a remainder of 0. Therefore, the binary representation of 9 is 1001. Hence, the answer to the given binary operation is 10012.
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Determine the range of the function g(x)= 5x^2-2x+1. Enter your answer in interval notation. This is a parabola that turns upward.
The parabola opens upward, the range of the function is [6/5, ∞) in interval notation.
We can find the range of the function by finding the vertex of the parabola, which will give us the minimum value, and then noting that the function increases without bound as x approaches infinity.
First, we need to find the vertex of the parabola. We can do this by finding the x-coordinate of the vertex, which is given by:
x = -b/2a
where a = 5, b = -2. Substituting these values, we get:
x = -(-2)/(2(5)) = 2/5
To find the y-coordinate of the vertex, we can substitute this value of x into the equation for g(x):
g(2/5) = 5(2/5)^2 - 2(2/5) + 1 = 5/5 - 4/5 + 1 = 6/5
So the vertex of the parabola is (2/5, 6/5), which is the minimum value of the function.
Since the parabola opens upward, the range of the function is [6/5, ∞) in interval notation.
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Use the spinner to find the theoretical probability of the event. Write your answer as a fraction or a percent rounded to the nearest tenth.
A spinner is divided into 6 equal sections. Starting from the top and moving in a clockwise direction, the sections are labeled 1 and shaded blue, 2 and shaded purple, 3 and shaded red, 4 and shaded yellow, 5 and shaded green, and 6 and shaded red.
The theoretical probability of spinning a 1 is
As a result, there is a roughly 16.7% chance of turning a 1 in theory.
What does the maths word percentage mean?percent, which is a relative number used to denote hundredths of any amount. Since one percent (symbolised as 1%) is equal to one tenth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
Since the spinner has 6 equal sections, and only one of them is labeled 1, the probability of spinning a 1 is 1/6.
To write this as a percentage rounded to the nearest tenth, we can multiply by 100 and round:
1/6 ≈ 0.1667
0.1667 * 100 ≈ 16.7%
Therefore, the theoretical probability of spinning a 1 is approximately 16.7%.
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in matlab, when you create a graph to track rates of change, you can use a plotyy function which puts different scales on the y axis.T/F
The statement the plotyy function in MATLAB puts different scales on the y-axis when creating a graph to track rates of change is true because it allows for the visualization of multiple data series with distinct scales on the y-axis.
The plotyy function in MATLAB is specifically designed to create graphs with two y-axes, each with its own scale. This feature is particularly useful when plotting multiple data series that have different units or magnitudes of measurement.
By providing two sets of y-axis data and corresponding x-axis data, the plotyy function creates a graph with two y-axes positioned vertically. Each y-axis is assigned to a specific data series, allowing for the comparison of different rates of change or trends.
This functionality enables researchers and analysts to visually examine the relationship between two variables that may have distinct scales, facilitating a more comprehensive understanding of the data and its trends.
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Triangle has side lengths 3, 4, and 5. Triangle has side lengths 6, 7, and 8.
Similar means that all sides need to have the same ratio. So you know that they're not similar because they all have different ratios. So in order to make them similar, you need to come up with the same ratio for all three sides. So all you have to do is create a ratio like 1:2 that applies to all three sides. Multiply all three sides by 2, and then you'll have 2 similar triangles.
If a system reliability of 0. 998 is required, what reliability of two components in series is required?
The reliability of two components in series is 0.996.
To find the reliability of the engine, we need all the two components to work. Each components has a reliability of 0.998, so to find the reliability of the engine we need to find the probability of all two components working.
Reliability is defined as the probability that a product, system, or service will perform its intended function adequately for a specified period of time, or will operate in a defined environment without failure.
We can find this probability multiplying all the ten reliabilities:
P = 0.998^2 = 0.996004
Rounding to three decimal places, we have P = 0.996
The reliability of the engine is 0.996.
Hence,
The reliability of two components in series is 0.996.
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12.5 points If a side started out with a side length of 14 and ended with a side length of 27 what is the dilation's scale factor? Write your answer to the nearest hundredths place Type your answer...
The dilation's scale factor for the side length is found as 1.93.
What is defined as the dilation's scale factor?Dilation is the process of increasing the dimensions of an object without altering the shape. The scale factor determines whether the object's size is increased or decreased. A square with a side of 5 units can be dilated to a square with a side of 15 units, however the shape of the square continues to remain the same.There are two types of dilation:Expansion is the process by which the size of an item is increased.Contraction is the process of reducing the size of an item.For the given question;
Initial side length = 14 units.
End side length = 27 units.
Thus, for finding dilation factor simply divide 27 by 14.
Dilation = 27/14
Dilation = 1.93
Thus, the dilation's scale factor for the side length is found as 1.93.
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2) The cost of gasoline is directly proportional to the number of gallons of gasoline purchased. Ms. Butcher paid $25.20 for 12 gallons of gas. If c represents the cost in dollars and grepresents the gallons of gas purchased, which equation best represents this relationship?
(a) c = 0.489
(b) c = 2.1g
(c) c = 25.20g
(d) c = 302.4g
Answer:
62/87,21
Write the rate of blue paint to yellow paint for each quart in simplest form.
The rates are not equal. So, the amount of yellow paint is not proportional to the amount of blue paint.
$16:(5
No; the rates are not equal.
62/87,21
Write the rate of ice tea mix to sugar for each quart in simplest form.
Each rate is equal to . So, the amount of sugar is proportional to the amount of ice tea mix.
$16:(5
Yes; each rate is equal to .
GASOLINE The cost of 13 gallons of gasoline is $41.47. Write an equation relating cost to the number of gallons of
gasoline. How much does 18.5 gallons of gasoline cost?
62/87,21
Find the constant of proportionality.
or 3.19
The cost is $3.19 times the number of gallons of gas, g. The equation is c = 3.19g.
To find the cost of 18.5 gallons of gas, substitute 18.5 for g.
18.5 gallons of gas cost $59.02.
$16:(5
c = 3.19g; $59.02
Determine whether the set of numbers in each table is proportional. Explain.
62/87,21
Write the rates of cans of concentrate to cans of water in simplest form
Each rate is equal to . So, the amount of cans of water is proportional to the amount of cans of concentrate.
$16:(5
Yes; each rate is equal to .
62/87,21
Write the rates of shaded squares to total squares in simplest form.
The rates are not equal. So, the number of total squares is not proportional to the number of shaded squares.
$16:(5
No; the rates are not equal.
62/87,21
Write the rates of junk e-mails to total e-mails in simplest form.
Each rate is equal to . So, the number of total e-mails is proportional to the number of junk e-mails.
$16:(5
Yes; each rate is equal to
62/87,21
Write the rates of weeks to days in simplest form.
Each rate is equal to . So, the number of days is proportional to the number of weeks.
$16:(5
Yes; each rate is equal to .
62/87,21
Write the rates of the heat index to air temperature.
The rates are not equal. So, the air temperature is not proportional to the heat index.
$16:(5
No; the rates are not equal.
62/87,21
Write the rates of jars to jelly beans in simplest form.
The rates are not equal. So, the number of jelly beans is not proportional to the number of jars.
$16:(5
No; the rates are not equal.
For Exercises 10 and 11, write and solve an equation.
FINANCIAL LITERACY A store is having a sale where all jeans are off the regular price. Write an equation
relating the sale price to the regular price. How much would a pair of $29 jeans cost on sale?
g
Cost
7g
6 7(6) = $42
7 7(7) = $49
8 7(8) = $56
9 7(9) = $63
10 7(10) = $70
$16:(5
yes
Complete each conversion. Round to the nearest hundredth, if necessary.
LQ§B cm
62/87,21
8VHLQ§FHQWLPHWHUV
$16:(5
10.16
/§ B gal
62/87,21
8VH/§JDO
$16:(5
1.32
OE§B kg
62/87,21
8VHOE§NJ
$16:(5
681
\G§ _ m
62/87,21
8VH\G§P
$16:(5
12.8
Express each rate as a unit rate. Round to the nearest tenth, if necessary.
140 miles on 6 gallons
62/87,21
The unit rate is 23.3 miles per gallon.
$16:(5
23.3 miles per gallon
19 yards in 2.5 minutes
62/87,21
The unit rate is 7.6 yards in 1 minute.
$16:(5
7.6 yards per minute
236.7 miles in 4.5 days
62/87,21
The unit rate is 52.6 miles per day.
$16:(5
52.6 miles per day
331.5 pages in 8.5 weeks
62/87,21
The unit rate is 39 pages per week.
$16:(5
39 pages per week
eSolutions Manual - Powered by Cognero Page 1
6-4 Proportional and Nonproportional Relationships
Determine whether the set of numbers in each table is proportional. Explain.
62/87,21
Write the rate of blue paint to yellow paint for each quart in simplest form.
The rates are not equal. So, the amount of yellow paint is not proportional to the amount of blue paint.
$16:(5
No; the rates are not equal.
62/87,21
Write the rate of ice tea mix to sugar for each quart in simplest form.
Each rate is equal to . So, the amount of sugar is proportional to the amount of ice tea mix.
$16:(5
Yes; each rate is equal to .
GASOLINE The cost of 13 gallons of gasoline is $41.47. Write an equation relating cost to the number of gallons of
gasoline. How much does 18.5 gallons of gasoline cost?
62/87,21
Find the constant of proportionality.
or 3.19
The cost is $3.19 times the number of gallons of gas, g. The equation is c = 3.19g.
To find the cost of 18.5 gallons of gas, substitute 18.5 for g.
18.5 gallons of gas cost $59.02.
Step-by-step explanation: sorry the answer is C
Which of the following is true about coral reefs?
Coral reefs are found in cool waters.
Coral reefs are all the same color.
Predatory animals rely on reefs for food.
Predatory animals avoid coral reefs.
Answer:
Predatory animals rely on reefs for food.
Step-by-step explanation:
More animals live there instead of open ocean so this answer makes the most sence.
Have a good day!
Answer:
Predatory animals rely on reefs for food.
Step-by-step explanation:
global warming make waters temp go up not down
dead reefs are gray which is a different color just an obvious example
the last two contradict each other and fish use them as home so fish that eat those fish will go towards the food not away
how many times greater is the value of 3 in 2,341 than the value of 3 in 1,234?
In order to find how many times greater is the value of 3 in 2,341 than the value of 3 in 1,234 first we would need to find the value of 3 in 2,341 and the value of 3 in 1,234.
The value of 3 in 2,341 is 300
The value of 3 in 1234 is 30.
Therefore, to calculate how many times greater is the value of 3 in 2,341 than the value of 3 in 1,234 we would use the following formula:
ratio many times greater=The value of 3 in 2,341/The value of 3 in 1234
ratio many times greater=300/30
ratio many times greater=10
The value of 3 in 2,341 is 10 times greater than the value of 3 in 1,234
The perimeter of a rectangle is 20 centimetres. The length is 6centimeters.
what is the area of the rectangle
Answer:
Perimeter =20cm
Length =6
Breath = X
P= 2(l+b)
20 =2(6+x)
20=12+2x
20-12=2x
8=2x
x=8/2
x=4
Step-by-step explanation:
Answer:
The Width is 4cm
The Area is 24cm²
Step-by-step explanation:
2(6cm+xcm)=20
12+2x=20
(collect like terms)
2x=20-12
2x=8
(divide both sides by the coefficient of x)
2x=8
2 2
x=4cm is our width
so for the area our formular is L*B=6*4=24cm²
you are planning on applying to the nezog institute for a well-regarded program in eastern healing methods. the average salary for a new graduate trained in these eastern healing methods is normally distributed with an average of $50,000 per year with a standard deviation of $3,900. somewhat skeptical (but hopeful), you decide to take a random sample of salaries from 15 new graduates of nezog and you get an average of $53,100. use 95% significance. Test the claim that first-year Nezog employees make more than $50,000 a year. Use all six steps please, and use a p-value to make your decision about the null.
Find a 95% confidence interval to capture the average first-year salary with NEZOG.
Explain how your hypothesis test and confidence interval are consistent (or not).
In conclusion, our hypothesis test and confidence interval are consistent. We failed to reject the null hypothesis due to the large p-value, but the confidence interval did not contain the population mean of $50,000 and therefore suggests that the true population mean is likely greater than $50,000.
In order to test the claim that first-year Nezog employees make more than $50,000 per year, we must first state our hypotheses. The null hypothesis, H0, is that the mean salary of first-year Nezog employees is equal to $50,000. The alternative hypothesis, HA, is that the mean salary of first-year Nezog employees is greater than $50,000.
Next, we must calculate a test statistic and its associated p-value. The test statistic we will use is the z-score, which can be calculated using the formula z = (x - μ)/σ, where x is the sample mean, μ is the population mean, and σ is the population standard deviation. The z-score for our test is z = \((53,100 - 50,000)/3,900 = 1.41\). This corresponds to a p-value of 0.09.
Now, we must set a level of significance for our test. For this test, we will set the level of significance at 95%, meaning that we are willing to accept a 5% chance of making a Type I error. Since the p-value of 0.09 is greater than our level of significance, we fail to reject the null hypothesis.
Lastly, we can calculate a confidence interval to further examine the consistency of our results. The 95% confidence interval for the mean salary of first-year Nezog employees is (51,937.39, 54,262.61). This is consistent with our results because it does not contain the population mean of $50,000, and therefore supports the alternative hypothesis that first-year Nezog employees make more than $50,000 per year.
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If Susan is at the store and can buy any two fruits (the store sells apples, oranges, pears, bananas, plums and kiwis), how many combinations of fruit can she choose
Answer:
Susan has 15 different combinations of fruit she can choose from.
Step-by-step explanation:
I need help with this question
The length of the legs of the right triangle are 2.83 units.
How to find the side of a right triangle?A right tangle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, the legs of the triangle can be found using trigonometric ratios.
Hence,
sin 45 = opposite / hypotenuse
sin 45 = a / 4
cross multiply
a = 4 × 0.70710678118
a = 2.83 units
Therefore,
cos 45 = b / 4
cross multiply
b = 0.70710678118 × 4
b = 2.82842712475
b = 2.83 units
Therefore, the legs are 2,83 units
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add 1 and 1/3 + (-5/6)
Answer:
1/2
Explanation:
Let's remember how to sum 2 fractions:
\(\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d+b\cdot c}{b\cdot d}\)So, 1/3 + (-5/6) is equal to:
\(\frac{1}{3}+\frac{-5}{6}=\frac{(1\cdot6)+3\cdot(-5)}{3\cdot6}=\frac{6-15}{18}=\frac{-9}{18}\)Then, the addition of 1 and -9/18 is equal to:
\(1+\frac{-9}{18}=\frac{1}{1}+\frac{-9}{18}=\frac{(1\cdot18)+1\cdot(-9)}{1\cdot18}=\frac{18-9}{18}=\frac{9}{18}\)Now, we can divide the numerator and the denominator by 9 to get an equivalent fraction, so:
\(\frac{9}{18}=\frac{9\div9}{18\div9}=\frac{1}{2}\)Therefore, the answer is 1/2
Theo is putting lights around a right triangular sign that has a base of 10 feet and a height of 9 feet. If a box of lights will cover 15 square feet, how many boxes will he need to buy?
Answer:
2 Boxs
Step-by-step explanation:
PLEASE ANSWER IF YOU KNOW THIS ALGEBRA
Alternate interior angles are congruent if the two parallel lines are intersected by the transversal.
How to find the angles in parallel lines?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles etc.
The parallel lines in the diagram has two red arrows on it.
The transversal line is the one that cut the other two parallel lines.
The angles formed are 9x + 5 and 10x - 5.
Therefore, if the two parallel lines are intersected by the transversal then alternate interior angles are congruent.
Hence,
9x + 5 = 10x - 5
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1) Bob weighed 200 lbs, but after dieting for 6 months, he weighed 170 lbs.
find the percent increase or decrease
Answer: 15%
Step-by-step explanation:
The Percentage decrease will be:
= Decrease in weight / Old weight × 100
= (200 - 170) / 200 × 100
= 30/200 × 100
= 15%
The Percentage decrease is 15%
use green's theorem to find the counterclockwise circulation and outward flux for the field f=(7x−4y)i (9y−4x)j and curve c: the square bounded by x=0, x=4, y=0, y=4.
The counterclockwise circulation around c is 12 and the outward flux through c is zero.
Green's theorem is a useful tool for calculating the circulation and flux of a vector field around a closed curve in two-dimensional space.
In this case,
we have a field f=(7x−4y)i+(9y−4x)j and
a square curve c bounded by x=0, x=4, y=0, y=4.
To find the counterclockwise circulation, we can use the line integral of f along c, which is equal to the double integral of the curl of f over the region enclosed by c.
The curl of f is given by (0,0,3), so the line integral evaluates to 12.
To find the outward flux, we can use the double integral of the divergence of f over the same region, which is equal to zero since the divergence of f is also zero.
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If you made $300 one week and had a total of $75 worth of deductions, how much did you actually take home?
Answer:
$225
Step-by-step explanation:
A water pail in your backyard has a small hole in it. You notice that it has drained a total of 2.5 liters in 4 days. What is the average change in water volume each day?
The average change in water volume is (answer here)iter(s) per day.
The average change in the volume of water per day is obtained as 0.625 litres.
What is the rate change of volume?The rate change of volume is the change of volume with respect to time.
For instantaneous change the derivative of the expression of volume can be taken.
The average change in the volume of water can be obtained as follows,
Average change = Volume of water ÷ Number of days
= 2.5 ÷ 4 = 0.625
Hence, the average change in water volume is given as 0.625 liters per day.
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Consider the circle C of radius 8, centered at the origin. a. Find a parametrization for C inducing a counterclockwise orientation and starting at (8, 0). c(t) = ?, 0 ≤ t ≤ 2π b. Find a parametrization for C inducing a clockwise orientation and starting at (0, 8).
c(t) = ?, 0 ≤ t ≤ 2π c. Find a parametrization for C if it is now centered at the point (2, 4). c(t) = ?, 0 ≤ t ≤ 2π
The parametrization for C inducing a counterclockwise orientation and starting at (8, 0) is c(t) (8cos, 8sin) 0 ≤ t ≤ 2π, the parametrization for C inducing a clockwise orientation and starting at (0, 8) is c(t) (8cos, 8sin) 0 ≤ t ≤ 2π and parametrization for C if it is now centered at the point (2, 4) is C(t) = (4+ 8 cos, 2+ 8 Sin), 0 ≤ t ≤ 2π
The circle C of radius 8, centered at the origin, parametrization for C inducing a counterclockwise orientation and starting at (8, 0). c(t) :0 ≤ t ≤ 2π,
a) equation of the circle is x² + y² = 64.
starting point it (80) and orientation Counterclockwise.
c(t) (8cos, 8sin) 0 ≤ t ≤ 2π
b) Starting point is (0,8) and orientation is clockwise
c(t) (8cos, 8sin) 0 ≤ t ≤ 2π
c) equation of circle is (x-4)²+ (4-2)² - 64
For counterclockwise orientation
C(t) = (4+ 8 cos, 2+ 8 Sin), 0 ≤ t ≤ 2π
Therefore, the parametrization for C inducing a counterclockwise orientation and starting at (8, 0) is c(t) (8cos, 8sin) 0 ≤ t ≤ 2π, the parametrization for C inducing a clockwise orientation and starting at (0, 8) is c(t) (8cos, 8sin) 0 ≤ t ≤ 2π and parametrization for C if it is now centered at the point (2, 4) is C(t) = (4+ 8 cos, 2+ 8 Sin), 0 ≤ t ≤ 2π
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please help me quickly ! giving brainliest !
Answer: -57
Step-by-step explanation:
-50+21/-3
-50+-7
-57
Use this equation to find dy/dx for the following.
y^3+ x^4y^6 = 5+ ye^x
To find dy/dx for the given equation y^3 + x^4y^6 = 5 + ye^x, we'll differentiate both sides of the equation with respect to x using the chain rule and product rule as needed.
Differentiating y^3 + x^4y^6 = 5 + ye^x with respect to x:
Differentiating y^3 with respect to x:
(d/dx)(y^3) = 3y^2 * dy/dx
Differentiating x^4y^6 with respect to x using the product rule:
(d/dx)(x^4y^6) = 4x^3 * y^6 + x^4 * 6y^5 * dy/dx
Differentiating 5 with respect to x:
(d/dx)(5) = 0
Differentiating ye^x with respect to x using the product rule:
(d/dx)(ye^x) = e^x * dy/dx + y * e^x
Putting it all together, we have:
3y^2 * dy/dx + 4x^3 * y^6 + 6x^4 * y^5 * dy/dx = e^x * dy/dx + y * e^x
Now, let's solve for dy/dx by isolating the terms with dy/dx:
3y^2 * dy/dx + 6x^4 * y^5 * dy/dx - e^x * dy/dx = -4x^3 * y^6 - y * e^x
Factoring out dy/dx:
(3y^2 + 6x^4 * y^5 - e^x) * dy/dx = -4x^3 * y^6 - y * e^x
Dividing both sides by (3y^2 + 6x^4 * y^5 - e^x):
dy/dx = (-4x^3 * y^6 - y * e^x) / (3y^2 + 6x^4 * y^5 - e^x)
Therefore, dy/dx for the given equation y^3 + x^4y^6 = 5 + ye^x is given by the expression:
dy/dx = (-4x^3 * y^6 - y * e^x) / (3y^2 + 6x^4 * y^5 - e^x)
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