Answers
Using the chain rule, the value for dz/dt is obtained as [tex]dz/dt = 2(2t + (4 - t^2)e^{(4-t^2)}) ((1 - t)e^{(4-t^2)})[/tex].
What is chain rule?
The chain rule is the formula used to determine the derivative of a composite function, such as cos 2x, log 2x, etc. Another name for it is the composite function rule. Only composite functions are subject to the chain rule.
To find dz/dt using the chain rule, we need to differentiate each term of z with respect to t, then multiply by the derivative of the inner function with respect to t.
First, we have -
x = 2t
Taking the derivative with respect to t, we get -
dx/dt = 2
Next, we have -
y = 4 - t²
Taking the derivative with respect to t, we get -
dy/dt = -2t
Using the chain rule, we have -
[tex]dz/dt = (x + y)e^y \times (\frac{dx}{dt} + \frac{dy}{dt}e^y)[/tex]
Substituting x and y into this equation, we get -
[tex]dz/dt = (2t + (4-t^2))e^{(4-t^2)} \times ((2 - 2t) e^{(4-t^2)})[/tex]
Simplifying this expression, we get -
[tex]dz/dt = 2(2t + (4 - t^2)e^{(4-t^2)}) ((1 - t)e^{(4-t^2)})[/tex]
Therefore, the value is obtained as [tex]dz/dt = 2(2t + (4 - t^2)e^{(4-t^2)}) ((1 - t)e^{(4-t^2)})[/tex].
To learn more about chain rule from the given link
https://brainly.com/question/28350594
#SPJ1
Related Questions
From the candy factory, Stattles candies come in five different colors that are equally distributed (20% orange), and each 14 ounce bag has a random sample of 220 of Stattles.
a. Find the mean and standard deviation of the sampling distribution of p
b. Calculate the probability that Cindy will get at least 48 orange Stattles in her next 14 ounce bag.
Answers
a. The mean of the sampling distribution is 0.2 and the standard deviation is 0.027. b. The probability that Cindy will get at least 48 orange Stattle is approximately 0.0901.
What is the binomial distribution's normal approximation?A method for estimating the probability of a binomial distribution using a normal distribution is known as the normal approximation to the binomial distribution. When the sample size is sizable and the success probability is not too close to 0 or 1, it can be employed. To utilise this approximation, we must first get the binomial distribution's mean and standard deviation, then normalise the distribution using the z-score calculation.
As 20% of the candies are orange, the mean of the sampling distribution of p is equal to the population percentage, which is 0.2.
The standard deviation of the sampling distribution of p can be found using the formula:
σp = sqrt((p * (1 - p)) / n)
Substituting the values:
σp = sqrt((0.2 * 0.8) / 220) = 0.027
So the mean of the sampling distribution is 0.2 and the standard deviation is 0.027.
b. Let X be the number of orange Stattles in the bag.
The z-score is given as:
z = (X - μ) / σ
z = (48 - 44) / 2.974 = 1.34
So the probability that Cindy will get at least 48 orange Stattles in her next 14 ounce bag is approximately 0.0901.
Learn more about mean here:
https://brainly.com/question/29895356
#SPJ1
1/5 + 1/4 greater than or less than 1/2? if anyone knows please help
Answers
Answer:
less than
Step-by-step explanation:
just multiply top and bottom untill the denominator is the same
In the diagram below, triangle PQR is congruent with triangle STR. Complete the statement PQ is congruent with
A. RP
B. QT
C. ST
D. RQ
Answers
Answer:
Step-by-step explanation:
10 + 10 = 20
☁️Answer☁️ I think D.
️Step-by-step explanation️ hope this helps
What is an equation of the line that passes through the points ( 2 , 8 ) (2,8) and ( − 8 , − 7 ) (−8,−7)?
Answers
Therefore , the solution of the given problem of linear equation comes out to be y= (3/2)x + 5 .
Define linear equation.The equation y=mx+b is the basis of a linear regression model. B is the slope, and m is the y-intercept. The aforementioned sentence is repeatedly alluded to as a "math problem with two variables," despite the fact that y and y are distinct parts. In bivariate linear equations, there are only two variables. The application regions for linear equations have no definitive solutions.
Here,
We must first determine the slope of the line before using the point-slope form of the equation of a line to determine the equation of the line that goes through two points.
The angle of the line that connects the coordinates (2, 8) and (8, 7) is:
=> slope = (−7 − 8) / (−8 − 2)
=> slope = −15 / −10
=> slope = 3/2
When we express the equation of a line in the point-slope format, where (x1, y1) is one of the line's points and m is its slope, we get the following result:
=> y − y1 = m(x − x1)
By selecting the line's origin (2, 8) and substituting the slope m = 3/2, we obtain:
=> y − 8 = (3/2)(x − 2)
The equation y = mx + b is transformed into the slope-intercept form by condensing and reordering the variables.
=> y = (3/2)x + 5
Consequently, y = (3/2)x + 5 represents the equation of the line going through the points (2, 8) and (8, 7) respectively.
To know more about linear equation visit:
https://brainly.com/question/11897796
#SPJ1
The following are selected transactions of Vaughn Company. Vaughn prepares financial statements quarterly. Jan. 2 Purchased merchandise on account from Nunez Company, $40,000, terms 2/10, n/30. (Vaughn uses the perpetual inventory system.) Feb. 1 Issued a 9%, 2-month, $40,000 note to Nunez in payment of account. Mar. 31 Accrued interest for 2 months on Nunez note. Apr. 1 Paid face value and interest on Nunez note. July 1 Purchased equipment from Marson Equipment paying $10,500 in cash and signing a 10%, 3-month, $68,400 note. Sept. 30 Accrued interest for 3 months on Marson note. Oct. 1 Paid face value and interest on Marson note. Dec. 1 Borrowed $27,600 from the Paola Bank by issuing a 3-month, 8% note with a face value of $27,600. Dec. 31 Recognized interest expense for 1 month on Paola Bank note. 1.Prepare journal entries for the listed transactions and even
Answers
We can state this by responding to the provided question December 31: equation Interest Paid 184 Interest Expensed 184 (To charge interest for one month on the Paola Bank note)
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
The journal entries for the mentioned transactions are as follows:
Jan. 2: 40,000 in product inventory and 40,000 in accounts payable (To record the purchase of merchandise on account)
April 1: Cash 40,600 Accounts Payable 40,000 Interest Payable 600 (To record the payment of the Nunez note and interest)
Oct. 1: Cash 70,110 Notes Payable 68,400 Interest Payable 1,710 (To record the payment of the Marson note and interest)
Cash 27,600 Notes Payable 27,600 as of December 1
(In order to document the note's issuance to Paola Bank)
December 31: Interest Paid 184 Interest Expensed 184
(To charge interest for one month on the Paola Bank note)
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
Given that 224 hours of work need to be done to complete a project. (1) How long will it take 4 men, each working an 8-hour day to complete the project? (II) If each of them is paid 57-50 per hour, how much will it cost to employ them altogether? (iii) How many hours of overtime must they put in per day if the project is to be completed in 4 days? (iv) Given that the overtime rate of payment is l times as much as the regular hourly rate, find the cost of the project now.
Answers
If 4 men, each working an 8-hour day, have to complete 224 hours of work, then the number of days required to complete the work is:
Total number of hours of work / Number of hours of work done by 4 men in a day
= 224 / (4 x 8)
= 7
So, it will take 4 men, each working an 8-hour day, 7 days to complete the project.
II. Each of the 4 men will work for 7 days, and each man works 8 hours a day. So, the total number of hours worked by all the men is:
Total number of men x Total number of days x Number of hours worked by each man per day
= 4 x 7 x 8
= 224 hours
Therefore, the total cost of employing all 4 men is:
Total number of hours x Rate per hour
= 224 x $57.50
= $12,880
III. If the 4 men have to complete the project in 4 days, then the number of hours of work they have to do each day is:
Total number of hours of work / Total number of days to complete the project
= 224 / 4
= 56 hours
Each man works 8 hours a day, so the total number of hours of overtime they have to put in per day is:
Number of hours of work per day - Number of hours worked by each man per day
= 56 - 8
= 48 hours
Therefore, each man must put in 6 hours of overtime per day to complete the project in 4 days.
IV. If the overtime rate of payment is l times as much as the regular hourly rate, then the overtime rate of payment is:
l x $57.50
= $57.50l
Let the overtime rate of payment be $r per hour. Then:
r = $57.50l
The cost of the project is the sum of the cost of regular hours and the cost of overtime hours. The cost of regular hours is:
Number of regular hours x Regular hourly rate
= 4 x 8 x 7 x $57.50
= $16,240
The cost of overtime hours is:
Number of overtime hours x Overtime hourly rate
= 4 x 6 x 7 x $57.50l
= $12,180l
So, the total cost of the project is:
Total cost = Cost of regular hours + Cost of overtime hours
= $16,240 + $12,180l
Answer:
Step-by-step explanation:
(i) To complete the project, 4 men will need to work a total of 224 hours. Each man works for 8 hours per day. Therefore, the number of days it will take to complete the project is:
Number of days = 224 total hours / (4 men x 8 hours/day) = 7 days
So it will take 4 men, each working 8 hours per day, 7 days to complete the project.
(ii) Each man is paid $57.50 per hour, and they will work for a total of 7 x 8 = 56 hours altogether. Therefore, the total cost of employing them all is:
Total cost = 4 men x $57.50/hour x 56 hours = $12,320
(iii) If the project is to be completed in 4 days, each man will need to work for a total of:
224 total hours / (4 men x 4 days) = 14 hours per day
Since each man already works for 8 hours per day, they will need to put in an additional 6 hours of overtime per day to complete the project in 4 days.
(iv) The regular hourly rate is $57.50 per hour, and the overtime rate is 1.5 times the regular hourly rate (150% of the regular hourly rate). Therefore, the overtime rate is:
Overtime rate = $57.50 x 1.5 = $86.25/hour
To find the total cost of the project, we need to add the cost of the regular hours and the cost of the overtime hours. The cost of the regular hours is:
Regular hours cost = 224 regular hours x $57.50/hour = $12,880
The cost of the overtime hours is:
Overtime cost = (4 men x 6 overtime hours/man/day x 4 days) x $86.25/hour
= 96 x $86.25
Therefore, the total cost of the project is:
Total cost = Regular hours cost + Overtime cost
= $12,880 + $8,280
= $21,160
where the overtime rate is 1.5 times the regular hourly rate.
10. A culture starts with 157 bacteria cells, and the number of cells doubles every 15 minutes.
a. Write an equation for the number of cells C after t 15-minute periods.
b. Use the equation to predict the number of cells after 2 hours.
Answers
The equation for the number of cells after t-15 minute periods is C = 157 x [tex]2^{t/15}[/tex].
The number of cells after 2 hours is 40,192.
What is the number of cells after 2 hours?The equation for the number of cells after t-15 minute periods is an exponential equation.
The form of the equation will be:
Future population = present population x [tex]2^{number of minutes / 15}[/tex]
C = 157 x x [tex]2^{t/15}[/tex].
Number of cells after 2 hours :
First convert 2 hours to minutes = 2 x 60 = 120 minutes
C = 157 x [tex]2^{120/15}[/tex]
157 x [tex]2^{8}[/tex]
C = 40,192
To learn more about exponential functions, please check: https://brainly.com/question/3639390
#SPJ1
Sample A has 780 number of successes from a sample size of 820.
Sample B has 795 number of successes from a sample size of 804.
Find the 90% confidence interval for the difference between the two sample proportions.
Answers
In response to the supplied query, we may state that there is a proportionality statistically significant difference between the two population proportions because the interval comprises 0.
what is proportionality?Relationships are regarded to as proportional when they continuously have the same ratio. For instance, the number of trees in an orchard and the number of apples in a harvest of apples depend on the average number of apples produced by each tree. A linear relationship between two numbers or variables is referred to as being proportional in mathematics.
The following is the point estimate for the variance between the two sample proportions:
ME is equal to z/2 * [p1(1 - p1) / n1 + p2(1 - p2) / n2]
where:
The z-score that corresponds to the required degree of confidence, in this case 90%, is z/2, or 1.645.
The proportions of the sample are p1 and p2.
These are the sample sizes, n1 and n2.
When we enter the values, we obtain:
ME = 1.645 * √[(0.9512)(1 - 0.9512) / 820 + (0.9891)(1 - 0.9891) / 804]
ME = 0.0528
-0.0379 ± 0.0528
or
-0.0907 to 0.0149
As a result, we have 90% confidence that the actual change in population proportions is between -0.0907 and 0.0149. We cannot infer that there is a statistically significant difference between the two population proportions because the interval comprises 0.
To know more about proportionality visit:
https://brainly.com/question/29126727
#SPJ1
LOOK AT THE IMAGE BLEOW TO SEE THE PROBLE:
Answers
π - This is an irrational number. 22/7 - The number is rational but not an integer. 3.3 - The number is an integer but not a whole number.
What is rational and irrational numbers?The term "rational number" refers to any number that can be stated as a fraction, as well as a positive, negative, or zero. If q is not equal to zero, it may be expressed as p/q.
Irrational numbers are those that are not logical in nature. Let's explain; irrational numbers may be expressed as decimals but not as fractions, hence they cannot be expressed as the ratio of two integers.
π - This is an irrational number.
22/7 - The number is rational but not an integer.
3.3 - The number is an integer but not a whole number.
The number is a whole number but not a natural number.
9 -This number can be written as a natural number.
Learn more about rational numbers here:
https://brainly.com/question/24540810
#SPJ1
The sequence of the differences, 2, 4, 8, 16, 32, … is a geometric sequence with:
a1=
and r=
Just putting out the answers :)
Answers
The formula used to find any term of the geometric sequence is found as: an = 2(2)ⁿ⁻¹.
Explain about the geometric sequence?A series must have a constant ratio between each term and the term before it in order to be considered geometric.If they all have the same characteristics, then the value of r represents the common difference.The geometric sequence equations has the general form an=a1rⁿ⁻¹, where r denotes the common ratio, a1 denotes the first term, and n denotes the term's position in the sequence.
sequence: 2, 4, 8, 16, 32, …
a1 = 2
r = 4/2 = 2
So,
an = 2(2)ⁿ⁻¹
Thus, the formula used to find any term of the geometric sequence is found as: an = 2(2)ⁿ⁻¹.
Know more about the geometric sequence,
https://brainly.com/question/24643676
#SPJ1
Necesito estas respuestas
Answers
The scale factor for the given transformation is -
{k} = 2/3.
What is scale factor in mathematics?A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object.
Given is a figure {Q} that is a transformation of figure {P}.
The base length of the figure {P} is 15 cm. The base length for figure {Q} is 10 cm. So, we can write the scale factor as -
{K} = 10/15
{K} = 2/3
Therefore, the scale factor for the given transformation is -
{k} = 2/3.
To solve more questions on scale factor, visit the link-
https://brainly.com/question/30952307
#SPJ1
meter. Mary negotiates and is allowed 15% cash discount. How much will Mary pay if she decides to pay cash for 3m of irrigation pipe. (4) 4.4 3 3 10 5 calculate During a Mathematics lesson, Sipho was given the sum 4- +1/ step by step for the rest of the class. Analyse each step that Sipho did and explain the misconception on every step. You may write fractions in words e.g. 1 over 4 or in the form 14. (8) 4 3 10 34 10 34 10 - 3 5 3 1 5 4 ÷ 2280ײ/201 1 4 step 1 step 2 step 3
Answers
Answer:
ambiguous question dear!!
Step-by-step explanation:
Use the Associative Property to write an expression equivalent to (5.1u+8) +6.
Which expression is equivalent to (5.1u+8) + 6 using the Associative Property?
A. 6+(5.1u+8)
B. 5.1u+(8+6)
C. (5.1u+6) +8
D. 5.1u+8+6
Answers
An equivalent expression of (5.1u + 8) + 6 is 5.1u + (8 + 6)
How to write an equivalent expressionFrom the question, we have the following parameters that can be used in our computation:
(5.1u + 8) + 6
The associative property states that
(a + b) + c = a + (b + c)
Using the above as a guide, we have the following equation
(5.1u + 8) + 6 = 5.1u + (8 + 6)
Hence, the expression is 5.1u + (8 + 6)
Read more about equivalent expression at
https://brainly.com/question/15775046
#SPJ1
Simplify expression 6+(-4)(2-3)^2=
Answers
Answer:
We can simplify the expression as follows:
First, we need to evaluate the exponent in parentheses:
2-3 = -1
Next, we need to square -1:
(-1)^2 = 1
Now, we can substitute 1 back into the expression:
+(-4)(1)
Finally, we can simplify:
+(-4) = -4
Therefore,
+(-4)(2-3)^2 = -4.
Step-by-step explanation:
Which expressions are polynomials?
Select each correct answer.
-7x²+ 5/3x
6x² + 5x
x^2+ 5x1/5
-x^2+5x
Answers
Answer:
The polynomials are:
-7x²+ 5/3x
6x² + 5x
-x^2+5x
The expression x^2+ 5x1/5 is not a polynomial because it contains a fraction with x in the denominator.
b) Work out the size of angle x. Give your
answer in degrees (º).
56°
X
59°
77°
Answers
Answer:
Step-by-step explanation how do I use this appp :
how many feel long is the remaining piece ?
Answers
The remaining feet long is A. 3 7/12 feet long
How to determine this
Kelsey has a board of 6 1/3 feet long
When he uses 2.75 feet
To calculate the remaining feet
= 6 1/3 - 2.75 feet long
By converting 2.75 to fraction
2.75 = 2 3/4
= 11/4
6 1/3 = 19/3
So, 19/3 - 11/4
= 43/12
= 3 7/12
Therefore, the remaining piece is 3 7/12 feet long
Read more about Word Problem
https://brainly.com/question/28669193
#SPJ1
How to solve this question
Answers
Answer:
201.5km
Step-by-step explanation:
50000cm = 500m
1000m + 500m = 1500m
1km = 1000m
So 1.5km = 1500m then..
200km + 1.5km = 201.5km
If an atom has a diameter of 4 x 10^-8 cm and it’s nucleus has a diameter of 8 x 10^-13cm, find the ratio of the diameter of the nucleus to the diameter of the atom.
Answers
The ratio of the diameter of the nucleus to the diameter of the atom is [tex]2 \times 10^{-5}[/tex] .
What is a ratio?A ratio is a mathematical relationship between two or more numbers that shows how much one number is in relation to the other.
As per the given data:
Diameter of an atom = [tex]4 \times 10^{-8}[/tex] cm
Diameter of the nucleus = [tex]8 \times 10^{-13}[/tex] cm
To find the ratio of the diameter of the nucleus to the diameter of the atom:
Ratio = (diameter of the nucleus) / (diameter of the atom)
Ratio = [tex]\frac{8 \times 10^{-13}}{4 \times 10^{-8}}[/tex]
[tex]= 2 \times 10^{-13 + 8}\\ = 2 \times 10^{-5}\\[/tex]
Hence, the ratio of the diameter of the nucleus to the diameter of the atom is [tex]2 \times 10^{-5}[/tex] .
To know more about ratios, click:
brainly.com/question/20653958
#SPJ9
How is the total price including sales tax calculated? a. (purchase price) times (percent sales tax); then added to original amount c. (purchase price) times (percent sales tax); then divided by the original amount b. (purchase price) times (percent sales tax); then subtracted from original amount d. (purchase price) times (percent sales tax); then multiplied by the original amount
Answers
Answer: PP(Percentage) + PP or PP(1.%)
Step-by-step explanation:
this is due tomorrow
Answers
Answer: C
Step-by-step explanation:
(d.) (I + 2A)
−1 =
−1 2
4 5 !
where I is the identity matrix
Answers
We can write the addition matrix as -
(I + 2A) →
[- 1 4]
[8 11]
What is identity matrix?The identity matrix is the only idempotent matrix with non-zero determinant.
Given is the matrix relation as -
(I + 2A)
We can write the addition of matrix as -
(I + 2A) →
[1 0]
[0 1]
+
2[-1 2]
2[4 5]
(I + 2A) →
[1 0]
[0 1]
+
[-2 4]
[8 10]
(I + 2A) →
[- 1 4]
[8 11]
Therefore, we can write the addition matrix as -
(I + 2A) →
[- 1 4]
[8 11]
To solve more questions on matrices, visit the link below-
https://brainly.com/question/30672622
#SPJ1
12 - ___ =7.32
What is the missing blank
Answers
Answer:
Your blank answer is 4.68
Step-by-step explanation:
Well lets make the missing blank into a variable.
12 - x = 7.32
This way we can solve for x. Simplify.
Add x to both side.
12 = 7.32 + x
Subtract 7.32 to both side leaving you x.
12 - 7.32 = x
x = 4.68
Answer:
12 - 4.68 = 7.32
Step-by-step explanation:
Now we have to,
→ Find the missing number in the equation.
Let us assume that,
→ Missing number = m
Forming the equation,
→ 12 - m = 7.32
Then the value of m will be,
→ 12 - m = 7.32
→ -m = 7.32 - 12
→ -m = -4.68
→ [ m = 4.68 ]
Hence, the answer is 4.68.
Please find the scale scale factor
Answers
The scale factor of the dilation is 1/2.
What is Dilation?Dilation is a type of transformation where the figure is enlarged or made smaller such that it preserves the shape but not size.
Every dilated image are similar figures to the original figure.
Here given that blue figure is the dilated image of the black figure.
Dilation is the reduction.
The bottom left point is (2, 2) and top let point is (2, 4) of blue figure.
Length of the left segment of blue figure = [tex]\sqrt{(2-2)^2+(4-2)^2}[/tex]
= 2
The bottom left point is (4, 4) and top let point is (4, 8) of black figure.
Length of the left segment of black figure = [tex]\sqrt{(4-4)^2+(8-4)^2}[/tex]
= 4
Scale factor = Ratio of corresponding sides
= 2/4
= 1/2
This will be the same if we take another corresponding sides.
Hence the scale factor is 1/2.
Learn more about Dilation here :
https://brainly.com/question/29229399
#SPJ1
Solve the system of inequalities by graphing.
y < 6
y > x + 3
Answers
The solution to the inequalities, y < 6 and y > x + 3 is the common intersecting region.
What are inequalities and it's types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, y < 6.
Now, To determine wether it inclues the origin or not we'll set, y = 0.
So, 0 < 6 is true so y < 6 includes the origin.
Now, y > x + 3.
0 > 0 + 4 is not true therefore, y > x + 3 doest not inclue the origin.
The solution to these now can be determine by the common intersecting region.
learn more about inequalities here :
https://brainly.com/question/30228778
#SPJ9
Which solid figure is made of only triangular faces?
triangular pyramid
triangular prism
cone
square pyramid
Answers
A triangular pyramid is a solid figure made of only triangular faces.
Describe Triangular Pyramid?A triangular pyramid is a type of pyramid that has a triangular base and three triangular faces that meet at a common point or apex. The triangular base is usually referred to as the base face of the pyramid, while the remaining three triangular faces are called lateral faces.
The properties of a triangular pyramid include:
It has one base face and three lateral faces.
All four faces are triangles.
It has four vertices or points.
It has six edges or line segments.
To find the volume of a triangular pyramid, the area of the base face and the height of the pyramid must be known.
Triangular pyramids can be found in many real-world applications, such as in the design of buildings and structures, in geometry and mathematics, and in the study of crystals and minerals. They are also used in computer graphics to create 3D models of objects and environments.
A triangular pyramid is a solid figure made of only triangular faces.
To know more about geometry visit:
https://brainly.com/question/28972506
#SPJ1
What is the area of this polygon?
16 cm2
24 cm2
40 cm2
18 cm2
Answers
Answer:
Where's the question...
8. DEF is an equilateral triangle.
The midsegments of ADEF form AAB.
What type of triangle is AABC? Explain your reasoning.
Answers
The type of triangle AABC is an equilateral triangle, as it is formed by the midsegments of the equilateral triangle ADEF.
What are the coordinates of midpoint of the line segment AB?Since the midsegments of a triangle are parallel to its opposite sides and half the length of the opposite sides, the midsegments of an equilateral triangle are congruent to each other, and their length is half the length of the sides of the equilateral triangle.
Suppose we've two endpoints of a line segment as:
A(p,q), and B(m,n)
Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:
[tex]x = \dfrac{p+m}{2} and y = \dfrac{q+n}{2}[/tex]
We are given that;
An equilateral triangle DEF
AAB is formed by the midsegments of triangle ADEF, which means that AAB is also an equilateral triangle. To see why this is true, we can use the following argument:
The midsegment of DE is parallel to AB and has half the length of AB.
The midsegment of EF is parallel to AA' and has half the length of AA'.
The midsegment of FD is parallel to BB' and has half the length of BB'.
Therefore, AB = AA' = BB', and the angles at A and B are both 60 degrees (since DEF is equilateral).
Thus, AAB is an equilateral triangle, because all its sides are equal in length and all its angles are equal to 60 degrees.
Therefore, by midpoint the answer will be equilateral triangle.
Learn more about midpoint here;
https://brainly.com/question/5127660
#SPJ1
9. A segment has endpoints at A(-4,2) and B(2,10) . The perpendicular bisector of AB passes through point M, which lies on AB Find the coordinates of 'point M.
(pls n ty)
Answers
In response to the aforementioned query, we may say that Point M's slope coordinates are therefore (39/25, 69/25).
what is slope?A line's slope determines how steep it is. The gradient is mathematically expressed as gradient overflow. By dividing the vertical change (run) between two spots by the height change (rise) between the same two locations, the slope is determined. The equation for a straight line, y = mx + b, is written as a curve form of an expression. When the slope is m, b is b, and the line's y-intercept is located (0, b). For instance, the y-intercept and slope of the equation y = 3x - 7 (0, 7). The location of the y-intercept is where the slope of the path is m, b is b, and (0, b).
A and B's respective y-coordinates are at the midpoint of the triangle AB.
[tex]((x A + x B)/2, (y A + y B)/2)[/tex]is the midpoint.
[tex]((-4 + 2)/2, (2 + 10)/2)[/tex] is the midpoint.
Midway = [tex]( -1, 6 )\\[/tex]
Slope of AB: The slope of AB is equal to the product of the y-value and the x-value, or:
slope is equal to [tex](y B-y A) / (x B-x A).\\[/tex]
slope = [tex](10 - 2) / (2 - (-4))\\[/tex]
slope = 8/6 = 4/3
[tex]y - y 1 = m * (x - x 1)\\y - 6 = (-3/4) * (x + 1)\\y - 6 = (-3/4)\\x - (3/4)\sy = (-3/4)x + (21/4)[/tex]
Point M's coordinates are:
[tex]y = (-3/4)x + (21/4)\\4x/3 + 2 = (-3/4)x + (21/4)\\16x + 24 = -9x + 63\s25x = 39\ = 39/25\\y = (-3/4)(39/25) + (21/4) = 69/25\\[/tex]
Point M's coordinates are therefore (39/25, 69/25).
To know more about slope visit:
https://brainly.com/question/3605446
#SPJ1
If they were originally 12 apples at home, the number of apples after a 50% increase would be:
Answers
The number of apples after the increase will be 18.
How many apples would there be?Percentage is the fraction of an amount that is usually expressed as a number out of hundred. The sign that is used to represent percentage is %. In order to change a number to a percentage, multiply by 100.
After the apples are increased, the new number of apples would be half more than the initial number of apples.
The formula that can be used to determine the new number of apples is: New number of apples = original number of apples x (1 + increase/100)
= 12 x (1 + 50/100)
= 12 x (1 + 0.5)
= 12 x 1.5 = 18
To learn more about percentages, please check: https://brainly.com/question/25764815
#SPJ1