The derivative of function z = tan⁻¹(x² + y²), x = sin t, y = t[tex]e^{s}[/tex] using chain rule is ∂z/∂s = t × [tex]e^{s}[/tex] /(1 + (x² + y²)) and ∂z/∂t= 1/(1 +(x² + y²)) [ cos t + [tex]e^{s}[/tex] ].
The function is equal to,
z = tan⁻¹(x² + y²),
x = sin t,
y = t[tex]e^{s}[/tex]
To find ∂z/∂s and ∂z/∂t using the Chain Rule,
Differentiate the expression for z with respect to s and t.
Find ∂z/∂s ,
Differentiate z with respect to x and y.
∂z/∂x = 1 / (1 + (x² + y²))
∂z/∂y = 1 / (1 + (x² + y²))
Let's find ∂z/∂s,
To find ∂z/∂s, differentiate z with respect to s while treating x and y as functions of s.
∂z/∂s = ∂z/∂x × ∂x/∂s + ∂z/∂y × ∂y/∂s
To find ∂z/∂x, differentiate z with respect to x.
∂z/∂x = 1/(1 + (x² + y²))
To find ∂x/∂s, differentiate x with respect to s,
∂x/∂s = d(sin t)/d(s)
Since x = sin t,
differentiating x with respect to s is the same as differentiating sin t with respect to s, which is 0.
The derivative of a constant with respect to any variable is always zero.
To find ∂z/∂y, differentiate z with respect to y.
∂z/∂y = 1/(1 + (x² + y²))
To find ∂y/∂s, differentiate y with respect to s,
∂y/∂s = d(t[tex]e^{s}[/tex])/d(s)
Applying the chain rule to differentiate t[tex]e^{s}[/tex], we get,
∂y/∂s = t × [tex]e^{s}[/tex]
Now ,substitute the values found into the formula for ∂z/∂s,
∂z/∂s = ∂z/∂x × ∂x/∂s + ∂z/∂y × ∂y/∂s
∂z/∂s = 1/(1 + (x² + y²)) × 0 + 1/(1 + (x² + y²)) × t × [tex]e^{s}[/tex]
∂z/∂s = t × [tex]e^{s}[/tex] / (1 + (x² + y²))
Now let us find ∂z/∂t,
To find ∂z/∂t,
Differentiate z with respect to t while treating x and y as functions of t.
∂z/∂t = ∂z/∂x × ∂x/∂t + ∂z/∂y × ∂y/∂t
To find ∂z/∂x, already found it earlier,
∂z/∂x = 1/(1 + (x² + y²))
To find ∂x/∂t, differentiate x = sin t with respect to t,
∂x/∂t = d(sin t)/d(t)
= cos t
To find ∂z/∂y, already found it earlier,
∂z/∂y = 1/(1 + (x² + y²))
To find ∂y/∂t, differentiate y = t[tex]e^{s}[/tex] with respect to t,
∂y/∂t = d(t[tex]e^{s}[/tex])/d(t)
= [tex]e^{s}[/tex]
Now ,substitute the values found into the formula for ∂z/∂t,
∂z/∂t = ∂z/∂x × ∂x/∂t + ∂z/∂y × ∂y/∂t
= 1/(1 + (x² + y²)) × cos t + 1/(1 + (x² + y²)) × [tex]e^{s}[/tex]
= 1/(1 + (x² + y²)) [ cos t + [tex]e^{s}[/tex] ]
Therefore, using chain rule ∂z/∂s = t × [tex]e^{s}[/tex] /(1 + (x² + y²)) and ∂z/∂t= 1/(1 +(x² + y²)) [ cos t + [tex]e^{s}[/tex] ].
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The above question is incomplete, the complete question is:
Use the Chain Rule to find ∂z/∂s and ∂z/∂t.
z = tan⁻¹(x² + y²), x = sin t, y = te^s
2n>20 Solve the inequality. Graph the solution.
Answer:
n>10
Step-by-step explanation:
2n>20
n>20/2
n>10
What is residual value formula?
Residual=actual y value−predicted y value,ri=yi−^yi. Residual = actual y value − predicted y value , r i = y i − y i ^ . Having a negative residual means that the predicted value is too high, similarly if you have a positive residual it means that the predicted value was too low..
What Exactly Is Residual Value?
The estimated value of an asset that is fixed at the end of its useful life or lease term is its residual value, which is often referred to as salvage value. In lease agreements, the residual value is one of the lessor's main methodologies for calculating the lessee's periodic lease payments.
A good residual value is what?
Check out the Car Lease Ratings section of our Lease Kit for a complete list of high-residual vehicle brands and models.
A car is probably not a good lease deal if the lease-end residual value is less than 50% of the MSRP (for a 36-month lease). 55% to 65% of MSRP would be a nice residual.
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What does an r value of 0.7 mean?
According to the following interpretation, a correlation value of 0.7 between two variables denotes a significant and favorable association between them.
What is Correlation Coefficient?Correlation coefficients demonstrate how strongly two independent variables, x and y, are connected linearly.
A linear correlation coefficient greater than zero indicates a relationship that is favorable.
A value less than zero denotes a bad relationship. To summarize, when x and y have values of 0, there is no link between them.
A statistic that describes how closely two variables' movements are related to one another is the correlation coefficient (r2).
The most widely used correlation coefficient is the Pearson product-moment correlation, which is used to detect if two variables are linearly related.
This correlation value, however, might not always be an accurate predictor of reliance in a non-linear link.
Hence, According to the following interpretation, a correlation value of 0.7 between two variables denotes a significant and favorable association between them.
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What would happen to the graph if she saved $2.50 a week? Use the color green to represent this situation on
the graph provided. Write the equation of the line represented in the graph. Describe how the components of
the equation represent the situation.
The line's equation is y = 25x + 50.A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.
What is meant by line equation?A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system. The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line. A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Wolfram MathWorld's linear.a). I began with a $50 savings because the line's starting point is (0, 50).
b). Money with me after 5 weeks will be $175 since the segment's endpoint is (5, 175).
c). Let y - y' = m(x - x') be the equation for the line shown in the graph.
where a point on the graph is (x', y').
And "m" represents the line's slope.
Slope of the line =
m =
m = 25
Since, the line passes through (0, 50),
y - 50 = 25(x - 0)
y = 25x + 50
y = 25x + 50
For x = 6,
y = 25×6 + 50 = 200
For x = 7,
y = 25×7 + 50 = 225
For x = 8,
y = 25×8 + 50 =250
d). For x = 10 weeks,
y = 25×10 + 50 = $300
e). For x = 15 weeks
y = 25×15 + 50 = $425
f). For x = 50 weeks,
y = 25×50 + 50 = $1300
g). Equation of the line is,
y = 25x + 50
The complete question is:
The graph below shows how much money you have in savings each week. Use
this graph to answer questions (a – g).
a. According to the graph how much money did you start with in your savings?
b. How much money will you have after 5 weeks of saving?
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A fair die has its faces numbered from 1 to 6. Let random variable f represent the number landing face up when the die is tossed. The probability distribution for the random variable has mean 3. 5 and standard deviation 1. 7078. Consider a simulation with 400 trials designed to estimate the sampling distribution of the sample mean for 5 tosses of the die. For each trial, the die is tossed 5 times, and the mean of the 5 values landing face up is recorded.
A fair dice has its faces numbered from 1 to 6. Let random variable f represent the number landing face up when the die is tossed. The probability distribution for the random variable has mean 3. 5 and standard deviation 1. 7078. Consider a simulation with 400 trials designed to estimate the sampling distribution of the sample mean for 5 tosses of the die. For each trial, the die is tossed 5 times, and the mean of the 5 values landing face up is recorded. The mean of the distribution of sample means is 3.5 and the standard deviation of the distribution of sample means is 0.0854.
The mean of the distribution of sample means
μ = 3.5
The standard deviation of the distribution of sample means can be calculate as follows:
σₓ = σ/√n
σₓ = 1.7078/√400
σₓ = 0.0854
Thus, the right answer is provided by the data of Mean 3.5 and Standard Deviation 0.0854.
Your question is incpmplete but most probably your full question was
fair die has its faces numbered from 1 to 6. Let random variable F represent the number landing face up when the die is tossed. The probability distribution for the random variable has mean 3.5
and standard deviation 1.7078. Consider a simulation with 400 trials designed to estimate the sampling distribution of the sample mean for 5 tosses of the die. For each trial, the die is tossed 5 imes, and the mean of the 5 values landing face up is recorded.
The mean and standard deviation of the results of the simulation should be
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Last year, wind turbines along a hilly ridge had an average output of 340 kilowatt hours per year. The turbines were upgraded, and now their average annual output is 90% more. What is the new average yearly output
The required new average is 646-kilowatt hours per year,
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
here,
Last year, wind turbines along a hilly ridge had an average output of 340-kilowatt hours per year. The turbines were upgraded, and now their average annual output is 90% more.
So,
new average = 340 + 90% of 340
new average = 340 + 0.90 × 340
new average = 340 + 306 = 646 kilowatt hours per year,
Thus, the required new average is 646-kilowatt hours per year,
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Determine the type of dilation shown and the scale factor used.
Enlargement with scale factor of 1.5
Enlargement with scale factor of 2.5
Reduction with scale factor of 1.5
Reduction with scale factor of 2.5
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
Ratio of side of bigger rectangle to that to corresponding side of smaller rectangle (as they are similar) is :
[tex]\qquad \sf \dashrightarrow \: \dfrac{15}{6} [/tex]
[tex]\qquad \sf \dashrightarrow \: 2.5[/tex]
So, the bigger rectangle is a scaled up version of the smaller version with a scale factor of 2.5
So, our required answer will be :
Enlargement with scale factor of 2.5
Use the long division method to find the result when 2x³+4x2 + 7x + 5 is divided
by x + 1.
Solving the provided question, we can say that the quadratic equation 2x³+4x2 + 7x + 5 is divided by (x+1) = -2+4-7+5 = 0
What is quadratic equation?A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.
the quadratic equation
2x³+4x2 + 7x + 5 is divided by (x+1)
which means X+1 is factor
so, x = -1
2x³+4x2 + 7x + 5 = -2+4-7+5 = 0
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WILL MARK BRAINLIEST ONLY FOR TWO PARAGRAPHS+50 ppts
“The biblical account of creation is a metaphor.”
Evaluate this statement considering arguments for and against.
In your response you should:
• refer to Christian teachings
• reach a justified conclusion*
*(This is not a maths question, it is a religious studies question)
The statement "biblical account of creation is a metaphor' is a contentious one, as it challenges a traditional and fundamental belief within Christianity.
What are some argument for biblical account of creation?One argument on how biblical account of creation is a metaphor is because it is written in a symbolic and metaphorical language. Many scholars and theologians argue that the creation story in the Bible should not be taken literally, but rather as a symbolic representation of God's power and authority.
Another argument is that the scientific evidence for the origins of the universe and the evolution of life on Earth is incompatible with the literal interpretation of the biblical account of creation. Therefore, the statement that the "biblical account of creation is a metaphor" can be seen as a way of reconciling scientific understanding with religious belief.
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Ix time a number le 20 i the ame a four time the number increaed by 6. Find the number
The number is 14. Dividing both sides by 4 gives -4 = 4 × number, which can be further simplified to number = -4 ÷ 4. This means that the number is 14.
20 = 4 × (number + 6)
20 = 4 × number + 24
20 - 24 = 4 × number
-4 = 4 × number
number = -4 ÷ 4
number = -1
The equation provided is 20 = 4 × (number + 6). Rearranging this equation gives 20 = 4 × number + 24. Subtracting 24 from both sides gives 20 - 24 = 4 × number. Dividing both sides by 4 gives -4 = 4 × number. Dividing both sides by 4 once again gives number = -4 ÷ 4. Therefore, the number is 14.
To find the number in the equation given, we can first rearrange the equation so it is in the form of 20 = 4 × number + 24. Then, subtracting 24 from both sides gives us 20 - 24 = 4 × number. Dividing both sides by 4 gives -4 = 4 × number, which can be further simplified to number = -4 ÷ 4. This means that the number is 14.
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Write down a quadratic equation in the form $x^2 + bx + c = 0$ whose solutions are $x = -7$ and $x = 1. $.
Answer:
an average weight of 10student was calculated to be 75. later it was discovered thatone weight wss insread as 35 instead of 50k.g. calculate the correct average weight
Jamal implified the expreion StartRoot 75 x Supercript 5 Baeline y Supercript 8 Baeline EndRoot where x greater-than-or-equal-to 0 and y greater-than-or-equal-to 0. StartRoot 75 x Supercript 5 Baeline y Supercript 8 Baeline EndRoot = StartRoot 25 time 3 time x Supercript 4 Baeline time x time y Supercript 8 Baeline EndRoot = 5 x quared y quared StartRoot 3 x EndRoot
Which decribe the error Jamal made?
He hould have written the quare root of y Supercript 8 in the anwer a y Supercript 4, not y quared. He hould have written the quare root of x Supercript 4 in the anwer a x, not x quared. He hould have written the 5 inide of the radical in the anwer. He hould have written the 3 outide of the radical in the anwer
The error Jamal made is that he should have written the square root of y Supercript 8 in the answer as y Supercript 4, not y squared. He should have written the square root of x Supercript 4 in the answer as x, not x squared. He should have written the 5 inside of the radical in the answer. He should have written the 3 outside of the radical in the answer.
Jamal was trying to simplify the expression StartRoot 75 x Supercript 5 Baeline y Supercript 8 Baeline EndRoot where x greater-than-or-equal-to 0 and y greater-than-or-equal-to 0. He wrote his answer as 5 x quared y quared StartRoot 3 x EndRoot. However, this was incorrect because he should have written the square root of y Supercript 8 in the answer as y Supercript 4, not y squared. He should have written the square root of x Supercript 4 in the answer as x, not x squared. He should have written the 5 inside of the radical in the answer. He should have written the 3 outside of the radical in the answer. The correct answer is StartRoot 25 time 3 time x Supercript 4 Baeline time x time y Supercript 8 Baeline EndRoot = 5 x StartRoot 4 Baeline y Supercript 4 Baeline EndRoot.The error Jamal made is that he should have written the square root of y Supercript 8 in the answer as y Supercript 4, not y squared.
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Solve for x . The polygons in each pair are similar
According to quadrant geometry value of x is 7
What is quadrant in geometry?
The coordinate system's two axes, the x-axis and the y-axis, constitute a region called a quadrant. The quadrants are generated when the two axes, the x-axis and the y-axis, cross at a 90-degree angle. These areas include coordinates, or positive and negative values of the x- and y-axes.
Write a proportion using the side lengths of each similar form to locate the missing side. An equation that makes two ratios equal is called a proportion. By dividing the numerator and denominator of each fraction by two, you can find x.
4(14) = 8(-7+2x)
56 = -56 + 16x
112 = 16x
x=7
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Question:
Solve for x . The polygons in each pair are similar
Work out the perimeter of a semicircle the radius 3cm give you answer I’m terms of pi
The perimeter of a semicircle the radius 3cm give you answer I’m terms of pi is P = 6 + 3pi.
What is perimeter of a semicircle?The complete length of a semicircle's boundary is referred to as the circumference of a semicircle, which is another name for its perimeter. The diameter's length and one-half of the original circle's circumference are added to determine it. Linear units such as "inches," "feet," "metres," or "centimetres," etc. are used to indicate the circle's circumference.
Given that the radius of the semicircle is 3cm.
The formula for the perimeter of a semicircle is:
P = pi(r) + 2r
Substituting the value of r = 3 we have:
P = pi(3) + 2(3)
P = 6 + 3pi
Hence, the perimeter of a semicircle the radius 3cm give you answer I’m terms of pi is P = 6 + 3pi.
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In a certain board game, a 12-sided number cube showing numbers 1–12 is rolled. if three such number cubes are rolled, what is the probability that all three show a number 10 or larger? a. (startfraction 1 over 12 endfraction) cubed b. (startfraction 2 over 12 endfraction) cubed c. (startfraction 3 over 12 endfraction) cubed d. (startfraction 10 over 12 endfraction) cubed
The correct answer is d. (start fraction 10 over 12 end fraction) cubed
Explanation:
Probability is a measure of the likelihood of an event happening. It is a number between 0 and 1, with 0 indicating that an event will not happen and 1 indicating that an event will happen. A probability of 0.5, for example, indicates that an event has a 50% chance of happening.
Probability is usually expressed as a fraction, decimal or percentage.
It can be calculated by taking the number of favourable outcomes divided by the number of total possible outcomes. For example, if you wanted to calculate the probability of rolling a 4 on a fair 6-sided die, you would divide the number of favourable outcomes (1) by the number of possible outcomes (6), giving you a probability of 1/6 or 0.1667.
The probability of rolling a number 10 or greater on a single 12-sided die is 10/12 or 5/6. Since the question asks for the probability that all three dice will roll a number 10 or greater, we must cube the probability of rolling a number 10 or greater on a single die, which is (10/12)^3 = (5/6)^3 = (125/216) = (10/18) = (10/12)^3.
Therefore the the probability that all three show a number 10 or larger is [tex](\frac{10}{12}) ^{3}[/tex].
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Joshua makes $12 per hour. Next monster, he will be making $14 per hour. What rate of increase does this represent? ROUND TO THE NEAREST PERCENT.
The percentage rate of increase in Joshua wages is 17%
What is rate in increase?Rate of increase or decrease is often referred to as rate of change. Rate of change refers to how quickly something changes over time.
To calculate the rate of decrease we subtract the original value from the new value, then divide the result by the original value. Multiply the result by 100. The answer is the percent increase.
This means percentage rate in increase = (new wage - original wage )/original wage × 100
= (14-12)/12 ×100
= 2/12 ×100
= 100/6 = 17% ( nearest percent)
Therefore the percentage increase in Joshua wage is 17%
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what is 1+1+6+5+8+(+(+8+*8766735
Answer:
your answer is 561,072,052
Can anyone help me with this question?
Solve -2x^2 + 5x + 12 > or = 0
Answer: its 3.7 but you have to round.
Step-by-step explanation:
The sides of the triangle shown increase in such a way that
dz/dt=1, and dx/dt=3 dy/dt At the instant when x = 12 and y= 5, what is the value of dx/dt?
Therefore , the solution of pythgoras theorem is the value of is dx/dt = 0.95, when x = 12 and y =5.
What is Pythagoras theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.
Here,
It is given that -
dz/dt = 1,
dx/dt = 3(dy/dt)
⇒dy/dt = 1/3 (dx/dt)
As shown in the diagram x = base, y = perpendicular and z = hypotenuse.
According to the Pythagoras theorem -
z² = x² + y²
Differentiating both sides -
d/dt (z²) = d/dt (x² + y²)
2z dz/dt = 2x dx/dt + 2y dy/dt
z dz/dt = x dx/dt + y dy/dt
Substituting the value of dy/dt -
z dz/dt = x dx/dt + y/3 (dx/dt)
z dz/dt = dx/dt (x + y/3)
dx/dt = (z dz/dt)/(x + y/3)....equation 1
So, when x = 12 and y = 5, the value of z -
z = √[(12)² + (5)²]
z = √(144+25)
z = √169
z = 13
Substituting the value of x, y, z and dz/dt in equation 1 -
dx/dt = (13 × 1)/(12 + 5/3)
dx/dt = 13 / 41/3
dx/dt = (13 × 3)/41
dx/dt = 39/41
dx/dt = 0.95
Therefore, the value of dx/dt = 0.95.
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Therefore , the solution of pythgoras theorem is the value of is dx/dt = 0.95, when x = 12 and y =5.
What is Pythagoras theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.
Here,
It is given that -
dz/dt = 1,
dx/dt = 3(dy/dt)
⇒dy/dt = 1/3 (dx/dt)
As shown in the diagram x = base, y = perpendicular and z = hypotenuse.
According to the Pythagoras theorem -
z² = x² + y²
Differentiating both sides -
d/dt (z²) = d/dt (x² + y²)
2z dz/dt = 2x dx/dt + 2y dy/dt
z dz/dt = x dx/dt + y dy/dt
Substituting the value of dy/dt -
z dz/dt = x dx/dt + y/3 (dx/dt)
z dz/dt = dx/dt (x + y/3)
dx/dt = (z dz/dt)/(x + y/3)....equation 1
So, when x = 12 and y = 5, the value of z -
z = √[(12)² + (5)²]
z = √(144+25)
z = √169
z = 13
Substituting the value of x, y, z and dz/dt in equation 1 -
dx/dt = (13 × 1)/(12 + 5/3)
dx/dt = 13 / 41/3
dx/dt = (13 × 3)/41
dx/dt = 39/41
dx/dt = 0.95
Therefore, the value of dx/dt = 0.95.
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what measrment is equal to 6 kilograms
Answer:
6000000 mg
13.2277 lb
6000 g
13.2276 pounds
Step-by-step explanation:
Hopefully I am right but those are all I can find that are equal to 6 kilograms.
Brooo this is sooo hard please helpppo
Answer:
Step-by-step explanation:
divided by nine ;)
part b pls
This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Javier bought 3 bags of balloons for a party. He used 8 balloons from each bag.
Which equation can be used to determine how many balloons, b, were originally in each bag if there were 21 balloons left over?
Multiple choice question.
cross out
A)
3b−8=21
cross out
B)
8b−3=21
cross out
C)
3(b−8)=21
cross out
D)
8(b−3)=21
Part B
Determine how many balloons were originally in each bag.
__ balloon(s)
The equation which is used to determine number of balloons were originally in bag is 3(b-8)=21 and the number of balloons in each bag on?
What is equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Based on the given conditions, formulate: 3×(b-8)=21
Reduce the greatest common factor on both sides of the equation:
b-8 =7
Rearrange unknown terms to the left side of the equation: b = 7+8
Calculate the sum or difference: b=15
The equation which is used to determine number of balloons were originally in bag is 3(b-8)=21 and the number of balloons in each bag is 15.
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Different dealers may sell the same car for different prices. The sale prices for a particular car are normally distributed with a mean and standard deviation of 262626 thousand dollars and 222 thousand dollars, respectively. Suppose we select one of these cars at random. Let x=x=x, equals the sale price (in thousands of dollars) for the selected car. Find p(26
The probability of P(26 < X < 30) is 0.48.
In this case, the given parameters are:
Mean μ = 26
Standard deviation σ = 2
So, the probability P(26 < X < 30) will be represented as:
P(26 < X < 30)
= P(z1 < z < z2)
where:
z = (X – μ) / σ
Thus, now we have:
P(26 < X < 30)
= P((26 – 26) / 2 < z < (30 – 26) / 2)
= P(0 / 2 < z < 4 / 2)
= P(0 < z < 2)
= P(z < 2) – P(z < 0)
For z-score of probabilities, we have:
P(26 < X < 30)
= P(z < 2) – P(z < 0)
= 0.97725 – 0.5
= 0.47725
= 0.48
Hence, the probability of P(26 < X < 30) is 0.48.
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Although part of your question is missing, you might be referring to this full question: Different dealers may sell the same car for different prices. The sale prices for a particular car are normally distributed with a mean and standard deviation of 26 thousand dollars and 2 thousand dollars, respectively. Suppose we select one of these cars at random. Let X represent the sale price (in thousands of dollars) for the selected car. Find P(26< X<30).
What is the simplest radical form of the expression?
(x4y7) ¾/
x³ ys √x
x²y² √√x²y²
xy² √√xy
x6 y ¹0 √y
The simplest radical form of the expression (x^4y^7)^3/4 is x^2|x|y^5[tex]\sqrt[4]{y}[/tex].
What is a radical?
A radical in mathematics is the opposite of an exponent, which is symbolised by the sign "√" also known as root. The number before the symbol or radical is regarded as an index number or degree, and it can either be a square root or a cube root.
The given expression is -
(x^4y^7)^3/4
To solve apply the exponent rule → (a·b)^n =a^nb^n
(x^4y^7)^3/4 = [(x^4)^3/4 · (y^7)^3/4]
= x^3 · y^21/4
= x^3y^21/4
=x^2|x|y^5[tex]\sqrt[4]{y}[/tex]
Therefore, the simplest radical form is x^2|x|y^5[tex]\sqrt[4]{y}[/tex].
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A rope of length 205 m is cut into 10 pieces of one length and 5 pieces of another
length. The total length of three of the first 10 lengths exceeds that of two the second
length by 2 m. Find the lengths of the pieces.
12 m length rope of 10 pieces and 17 m rope of 5 pieces.
What is equation with two variables?
The equation that has two variable terms and another equation is needed to solve both equations simultaneously is called equation with two variables.
What is the length of the rope pieces?
Given, total length of rope = 205 m.
The rope is cut into 10+5 = 15 pieces, in where 10 pieces rope are the same size, and the remaining 5 pieces are different size.
assume, length of first 10 piece = X m
length of last 5 piece = Y m
As per the first condition, total length of three of the first 10 length exceeds that of two the second length by 2 m.
hence, 3X - 2Y = 2
again, we know the total length = 205 m
10X + 5Y = 205
from the first equation, 3X = 2 +2Y
X = (2+2Y) / 3
putting the X value to the 2nd equation and we get
10(2+2Y)/3 + 5Y = 205
20+ 20Y+15Y = 615
35Y = 595
Y = 17 m
X = (2+2×17) /3 = 12 m
10 pieces of X length = 10 pieces of 12 m length
5 pieces of Y length = 5 pieces of 17 m length
10×12 = 120m
5×17 = 85m
120m + 85m = 205m
hence, verified.
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What is the roots of the equation x² 7x 10?
Answer:
-5 and -2
Step-by-step explanation:
What is the domain of f/x )= x?
The domain of f(x) = x is all real numbers. This is because the input (x) is the same as the output (f(x)).
This means that any value that is inputted into the function will result in the same value as the output, regardless of the value. The domain of the function can be expressed mathematically as:
Domain of f(x) = x = {x ∈ R}
This means that the domain of f(x) is all real numbers, as any real number put into the function will result in that same real number being outputted. For example, if x = 5, then f(x) = 5. This illustrates that the domain of f(x) = x is all real numbers.
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Calculate The length of a staircase that is 3.2m and has a standard height of 4.7 m
answer: hello
Step-by-step explanation:
If you get the answer then tell me
If XP = 5x - 1 and PZ = 4x + 1, what is XZ?
By adding the two given segments, we will get:
XZ = XP + PZ
XZ = 9x
How to find the length of XZ?Here we have a segment called XZ, such that it has a midpoint P.
We know that:
XP = 5x - 1
PZ = 4x + 1
Notice that above we divided our segment into two smaller ones, but the first one ends at P and the second one starts at P, then we can write:
XZ = XP + PZ
Then XZ is just the sum of the two expressions above:
XZ = 5x - 1 + 4x + 1
XZ = 9x + 1 - 1
XZ = 9x
Where x is a variable.
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Is a coordinate plane 2 dimensional?
Yes, a coordinate plane 2 dimensional
A coordinated plane is an area formed by the intersection of two lines and so is called 2-Dimensional. The horizontal line is called X-axis and the vertical line is called Y-axis. The intersection point of these two lines is called origin.
Coordinates are set of two numbers used to locate a specific point on the plane. They are represented in form of (x,y). The points can be positive zero or negative. They are used to plot graphs pin points draw lines etc.
A coordinated plane has 4 quadrants. A quadrant can be defined as a region on a plane where both X,Y axis is perpendicular. They are:
First quadrant: x > 0, y > Second quadrant: x < 0, y > 0Third quadrant: x < 0, y < 0Fourth quadrant: x > 0, y < 0.To know more about the coordinated plane visit:
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