The Typewriters should be guaranteed for 7.72 months, which would give a 5% chance of requiring a major repair before the end of the guarantee period.
Typewriter repair times have a normal distribution, with a mean of 11 months and a standard deviation of 2 months. To find the warranty period at which only her 5% of typewriters fail before the warranty expires, we need to find the corresponding z-score and solve it after the warranty period.
Using the standard normal distribution table, we find that the Z-score corresponding to a cumulative probability of 0.95 is approximately 1.64.
This means that 95% of typewriters will need major repairs after 11 + 1.64 * 2 = 14.28 months.
To ensure that only 5% of typewriters fail before the warranty expires, the warranty period should be set to 11 - 1.64 * 2 = 7.
72 months.
Finally, the typewriter still has about 7.72 months of warranty, and only 5% of cars fail before the warranty runs out.
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A tree in Leila's backyard is 61 centimeters high. The tree grows 8 centimeters each month. Within the first month of planting it, Leila trimmed 6 centimeters off its height. She has not trimmed the tree since then. How long has the tree been growing?
The number of months that the tree has been growing is; 8.375 months
How to solve algebra word problems?The general form for the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Now, we are told that the tree grows 8 centimeters each month. This means the slope is 8 cm.
Now, since she trimmed 6 cm in the first month, it means that the y-intercept will be -6. Thus;
Equation is;
y = 8x - 6
Since the current height is 61 centimeters, then;
61 = 8x - 6
8x = 61 + 6
8x = 67
x = 67/8
x = 8.375 months
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Part E
Using the results from part D and the dimensions of the other surfaces, find the surface area of the
outside of the doghouse. Be sure to include the bottom surface in your calculation.
The figure below is made of 222 rectangular prisms.
What is rectangular prism?A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.The top, bottom, and lateral faces of a rectangular prism are all rectangles, and all the pairings of the opposing faces are congruent. A rectangular prism is a three-dimensional structure with six faces.All six of its faces should be rectangles, with equal distances between the opposite faces and the same cross-section along its length.Rectangular prisms have surfaces equal to the sum of their side areas, and their volumes are equal to their length times breadth times height.Completed question :
Part D
Wendell plans to paint the doghouse after it’s built. He wants to know what the surface area of the outside of the doghouse will be. To find the surface area, first break up any composite shapes into rectangles and triangles. Which shape is considered a composite shape? When the shape is decomposed, what are the dimensions of the resulting shapes necessary for finding surface area?
Given data :
The volume of a rectangular prism is given as follows.
Volume of a rectangular prism = length x breadth x height
Therefore, the volume of 222 rectangular
prism
= 2 x 2 x 2
= 8 cubic units
Volume of 222 rectangular prisms = 222
×Volume of a rectangular prism
=222× 8
= 1776 cubic units
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Answer:
The surface area is 5,052 inches
Find m Please and thank you I would really appreciate it
x=6 m<ABD=20 *I think*
Step-by-step explanation:
Find x
plug in your answer
NEED HELP FAST
Find sn
for the arithmetic series where a1=−20 , n=25 , an=148
The value of Sn for the arithmetic series is, 1,600.
What is Arithmetic sequence?An arithmetic sequence is the sequence of numbers where each consecutive numbers have same difference.
We have to given that;
For the arithmetic series,
⇒ a₁ = - 20
⇒ n = 25
⇒ an = 148
Now, We know that;
The nth partial sum of an arithmetic sequence can be calculated using the first and last terms as follows:
⇒ Sn = n(a₁ + an) / 2
Hence, Substitute all the given values, we get;
⇒ Sn = n(a₁ + an) / 2
⇒ Sn = 25(- 20 + 148) / 2
⇒ Sn = 25 × 128 / 2
⇒ Sn = 1600
Thus, The value of Sn for the arithmetic series = 1,600.
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show that the set of all vectors in r4 satisfying the equations is a subspace of r4. find a basis for this subspace.
The set of all vectors in r4 satisfying the equation is,
( x, R , y ) = ( 1 , R , 1/2 ) ( 2 , R , 1 ) ( 3 , R , 3/2 ) ( 4 , R , 2 ) ( 5 , R , 5/2 ) ( 6 , R , 3 ) ( 7 , R , 7/2 ) ( 8 , R , 4 )
A basis for R4 always consists of 4 vectors. (TRUE: Vectors in a basis must be linearly independent AND span.) 4. The union of two subspaces is a subspace.
If S is a subspace of R4, then the zero vector 0=[0000] in R4 must lie in S. 2x+4y+3z+7w+1=0. So 0∉S, and we conclude that S is not subspace of R4.
The space R4 is four-dimensional, and so is the space M of 2 by 2 matrices. Vectors in those spaces are determined by four numbers. The solution space Y is two-dimensional, because second order differential equations have two independent solutions.
The interval of x is known and the relation of x , y is known.
So,
x = 2y ; x = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 }
Then,
1 = 2y , 2 = 2y , 3 = 2y , 4 = 2y , 5 = 2y , 6 = 2y , 7 = 2y , 8 = 2y ,
We can write,
y = { 1/2 , 1 , 3/2 , 2 , 5/2 , 3 , 7/2 , 4 }
Therefore,
The set of all vectors in r4 satisfying the equation is,
( x, R , y ) = ( 1 , R , 1/2 ) ( 2 , R , 1 ) ( 3 , R , 3/2 ) ( 4 , R , 2 ) ( 5 , R , 5/2 ) ( 6 , R , 3 ) ( 7 , R , 7/2 ) ( 8 , R , 4 )
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Simplify: (-7x - 5) - (-9x2 + 8x + 7). Choose the standard form of the answer.
A. -16x2 – 15x – 12
B. 9x2 - 15x - 12
O
C. -9x2 + x-2
D. 9x2 + 56x – 35
The standard form from (-7x - 5) - (-9[tex]x^{2}[/tex] + 8x + 7) is B) 9[tex]x^{2}[/tex] - 15x - 12.
This is a quadratic equation. To simplify the equation, we need to arrange the equation to be standard form or quadratic equation which is
a[tex]x^{2}[/tex] + bx + c
(-7x - 5) - (-9[tex]x^{2}[/tex] + 8x + 7) = -7x -5 + 9[tex]x^{2}[/tex] - 8x -7
Group of a[tex]x^{2}[/tex] --> It will be 9[tex]x^{2}[/tex]
Group of bx ---> It will be -7x-8x = -15x
Group of c ---> It will be -5-7 = -12
We just combine the group into standard equation
(-7x - 5) - (-9[tex]x^{2}[/tex] + 8x + 7) = -7x -5 + 9[tex]x^{2}[/tex] - 8x -7
= 9[tex]x^{2}[/tex] -15x - 12
So the simplification of equation (-7x - 5) - (-9[tex]x^{2}[/tex] + 8x + 7) is 9[tex]x^{2}[/tex] - 15x - 12, or from the answer, it's B)
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A helicopter pilot is paid $506.75 per week. Calculate his equivalent monthly pay
Answer: $2171.79
Step-by-step explanation:
How many gallon of a 14%-alt olution mut be mixed with 6 gallon of a 25%-alt olution to obtain a 20%-alt olution?
The no of gallon of a 14%-salt solution must be mixed with 6 gallon of a 25%-salt solution to obtain a 20%-salt solution is 5 gallon
What is Gallon?
The gallon is a volume unit used in imperial and customary units in the United States. There are now three versions in use: the imperial gallon, which is equal to 4.54609 litres
Given
14%-alt solution must be mixed with 6 gallon of a 25%-salt solution to obtain a 20%-salt solution
.14x +.25*6 = .20(x+6)
.14x + 1.5 = .20x + 1.2
.14x - .20x = 1.2 - 1.5
-0.06x = -0.3
x = 5 gallon
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The no of gallon of a 14%-salt solution must be mixed with 6 gallon of a 25%-salt solution to obtain a 20%-salt solution is 5 gallon
What is Gallon?
A gallon is a volume unit used in imperial and customary units in the United States. There are now three versions in use: the imperial gallon, which is equal to 4.54609 litres
Given
14%-alt solution must be mixed with 6 gallon of a 25%-salt solution to obtain a 20%-salt solution
.14x +.25*6 = .20(x+6)
.14x + 1.5 = .20x + 1.2
.14x - .20x = 1.2 - 1.5
-0.06x = -0.3
x = 5 gallon
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the numerical value of the standard deviation can never be positive, true or false?
Answer:
False - The standard deviation is always positive.
Simplify your answer and write is as a proper fraction mixed number or integer
if RS=x+4, ST=8 and RT=3x then value of RS is 10 units.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that RS=x+4, ST=8 and RT=3x
We have to find RS
RS=RT-ST
x+4=3x-8
Take the variable terms on one side and constants on other side
12=2x
Divide both sides by 2
x=6
So RS is 6+4=10 units
Hence, if RS=x+4, ST=8 and RT=3x then value of RS is 10 units.
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a rectangular storage container with an open top is to have a volume of 24 cubic meters. the length of its base is twice the width. material for the base costs 12 dollars per square meter. material for the sides costs 6 dollars per square meter. find the cost of materials for the cheapest such container.\
The cost of the materials for the cheapest rectangular storage container with an open top to have a volume of 24 cubic meters is $288.
Let the width of the base be x, then the length of the base is 2x. The height of the container is
[tex]24/(x2x) = 24/2x^2[/tex].
The total area of the base is[tex]x2x = 2x^2[/tex] and the total area of the sides is
[tex]2(x*24/2x^2) = 24x/x^2[/tex]= 24/x.
The cost of the base is
[tex]2x^2[/tex] * $12 = $24[tex]x^2[/tex] and the cost of the sides is
24/x * $6 = $144/x.
The total cost is $24[tex]x^2[/tex] + $144/x.
To find the cheapest container, we want to minimize the cost, which is equivalent to finding the minimum value of $24[tex]x^2[/tex] + $144/x.
We can use calculus to find the minimum, or we can use trial and error to find a reasonable value for x that minimizes the cost.
For x = 2, the cost is
$24 * [tex]2^2[/tex] + $144/2 = $96 + $72 = $168
which is less than $288.
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complete the conversion from 24.1 kg of body weight to milligrams (mg) of cephalexin administered per day.
The formula is also used to ensure that the patient is not overdosed or underdosed ,24.1 kg of body weight, 723 mg of cephalexin should be administered per day.
The conversion from 24.1 kg of body weight to milligrams (mg) of cephalexin administered per day can be calculated using the following formula:
Dose (mg) = Desired dose (mg/kg) x Body Weight (kg).
In this case, the Desired dose is 30 mg/kg. So, to calculate the total dose of cephalexin per day:
Dose (mg) = 30 mg/kg x 24.1 kg
Dose (mg) = 723 mg/day
Thus, for 24.1 kg of body weight, 723 mg of cephalexin should be administered per day.
The formula used in this calculation is a standard formula used to calculate the dose of medication to be administered to a patient based on their body weight. The formula is used to ensure that the patient receives the appropriate dosage of medication and that the medication is safe and effective. The formula is also used to ensure that the patient is not overdosed or underdosed, which can cause side effects or other medical problems.
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let us call a positive integer $n$ 'fortunate' if the sum of its digits is a multiple of 7, and 'superfortunate' if it is fortunate and if none of the numbers $n 1, n 2,\dots, n 12$ is fortunate. find the smallest superfortunate number.
The smallest superfortunate number is 993
What is super fortunate number?
A Fortunate number, named after Reo Fortune, is the lowest integer m > 1 for which pn# + m is a prime number for a given positive integer n, where the primorial pn# is the product of the first n prime numbers.
What is Prime Number?
A prime number is a natural number larger than one that cannot be calculated as the product of two lesser natural numbers. A composite number is a natural number greater than one that is not prime. 5 is prime, for example, because the only methods to write it as a product, 1 5 or 5 1, involve 5 itself.
993 is the smallest superfortunate number.
You can obtain this by letting the digits of n
be ...a99...9b
where a<9 and there are, say, k 9s. Then look at the results of adding 1,2,3 ... ,12.
The smallest number is 993.
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The smallest superfortunate number is 993
What is super fortunate number?
A Fortunate number, named after Reo Fortune, is the lowest integer m > 1 for which pn# + m is a prime number for a given positive integer n, where the primorial pn# is the product of the first n prime numbers.
What is Prime Number?
A prime number is a natural number larger than one that cannot be calculated as the product of two lesser natural numbers. A composite number is a natural number greater than one that is not prime. 5 is prime, for example, because the only methods to write it as a product, 1 5 or 5 1, involve 5 itself.
993 is the smallest superfortunate number.
You can obtain this by letting the digits of n
be ...a99...9b
where a<9 and there are, say, k 9s. Then look at the results of adding 1,2,3 ... ,12.
The smallest number is 993.
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Tamera found the solution of x squared =64 to be x=8
Answer:
x = ± 8
Step-by-step explanation:
x² = 64 ( take square root of both sides )
x = ± [tex]\sqrt{64}[/tex] = ± 8
solutions are x = 8 and x = - 8 , since
8 × 8 = 64 and - 8 × - 8 = 64
if a ray of light strikes mirror 1 with an angle of incidence of 41 ∘ , find the angle of reflection of the ray when it leaves mirror 2.
The angle of reflection for the ray leaving mirror 2 will be 41 degrees, as this is equal to the angle of incidence for the ray striking mirror 2.
The angle of incidence is the angle between the incoming ray and the surface of the mirror, and the angle of reflection is the angle between the reflected ray and the surface of the mirror.
In the given scenario, a ray of light strikes mirror 1 with an angle of incidence of 41 degrees.
The angle of reflection can be calculated using the law of reflection, which states that the angle of incidence is equal to the angle of reflection.
Therefore, the angle of reflection of the ray when it leaves mirror 1 will be 41 degrees.
However, the ray of light continues its journey and strikes mirror 2.
When this happens, the angle of incidence is the angle between the reflected ray from mirror 1 and the surface of mirror 2.
The angle of reflection for the ray leaving mirror 2 can be calculated using the same law of reflection.
The angle of reflection will be equal to the angle of incidence, which is 41 degrees.
The angle of reflection is a crucial concept in understanding the reflection of light and is used in various applications such as mirrors, prisms, and lenses.
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In thi activity, you'll analyze everal gym memberhip plan to help Mateo elect the one that i bet for him. What information do you think will be important in helping Mateo decide?
Mateo will be able to choose a gym membership plan that best meets his needs and budget.
To help Mateo decide on the best gym membership plan, the following information would be important:
Cost: the price of each plan, including any sign-up fees or monthly fees.Location: the proximity of the gym to Mateo's home or workplace.Amenities: what each gym offers, such as equipment, classes, and hours of operation.Contract terms: the length of the commitment and any cancellation policies.Reputation: the quality of the gym, including customer reviews and ratings.Personal fitness goals: what Mateo wants to achieve through his gym membership, such as weight loss or strength training.Special features: any additional features that may be important to Mateo, such as access to a pool or sauna.By considering these factors, Mateo will be able to choose a gym membership plan that best meets his needs and budget.
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Her older sister is making similar wall hangings with a diameter that is 134 inches longer than Poppy's. How much more wire did her sister use per wall hanging than Poppy? Use 3.14 for π. Write your answer as a decimal rounded to the nearest hundredth.
Sister uses 420.76 inches more wire per wall than Poppy.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
We have,
Poppy's diameter = d
Older sister diameter.
D = d + 134
Now,
The circumference of the wall hangings.
= 2πr
= πd
Now,
The circumference of the wall hangings by the older sister.
= πD
= π (d + 134)
The circumference of the wall hangings by the Poppy.
= πd
Now,
The difference between the length of the wire.
= π (d + 134) - πd
= πd + π x 134 - πd
= 3.14 x 134
= 420.76 inches.
Thus,
Sister uses 420.76 inches more wire.
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A bag of marbles has 1 red, 1 green, and 3 yellow marbles, what is the probability of selecting a yellow and then a yellow without replacement?
The probability of selecting a yellow and then a yellow without replacement is 3/10.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Number of red marbles = 1
Number of green marbles = 1
Number of yellow marbles = 3
Total number of marbles = 5
The probability of selecting a yellow and then a yellow without replacement.
= 3/5 x 2/4
= 6/20
= 3/10
We are using 2/4 since yellow marbles become 2 and the total marbles become 4 when the condition of without replacement is given.
Thus,
The required probability is 3/10.
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The volume of a gas was measured as its temperature was increased from 10 K to 15 K at intervals of 1 K. The volumes were 1. 5, 2. 2, 3. 38, 5. 1, and 7. 6 cm3. Would a linear or exponential function better approximate the data described? Explain why
A linear function would better approximate the data.
A linear function would better approximate the data described. This is because a linear function has a constant rate of change, while an exponential function has a changing rate of change. For example, if we take the data from 10 K to 15 K, we can calculate the rate of change for each 1 K increase in temperature. The rate of change of volume for a 1 K increase in temperature is calculated by taking the difference between the volumes at the two temperatures and dividing by the difference in the temperatures. With the given data, this would yield a rate of change of 0.7 cm3/K, 0.38 cm3/K, 0.92 cm3/K, 1.4 cm3/K, and 1.6 cm3/K. As we can see, the rate of change does not remain constant, but increases over the temperature range, indicating a nonlinear relationship. Therefore, a linear function would better approximate the data.
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Can anyone help me solve this problem step by step?
Find the probability that in 200 tosses of a fair die, we will obtain at most 30 fives. Use the normal distribution to approximate the desired probability.
Answer:
0.2643
Step-by-step explanation:
Find the probability that in 200 tosses of a fair die, we will obtain at most 30 fives Summary: When a fair die is tossed 200 times, the probability of obtaining at most 30 fives is 0.2643.
S2 22/23 Math 6 B (CL),7.20 / 1. Ratios, Proportions, and Perce
X
Find the value that makes the pair of ratios equivalent.
12:42, 2:x
The value that makes the pair of ratios equivalent is x = 7.
What is cross multiplication?To discover the unknown values in a mathematical equation, we cross multiply the numbers in the equation. The method of cross multiplication is frequently employed to identify the missing variable in an equation. We multiply both the numerator and denominator of the provided expression or fractions.
The given pair of ratios is:
12:42 = 2:x
12 /42 = 2/ x
Using cross multiplication we have:
12x = 2(42)
x = 7
Hence the value that makes the pair of ratios equivalent is x = 7.
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Suppose a shoe factory produce both low grade and high grade shoes. The factory produces at least twice as many low grade as highgrade shoes. The maximum possible production is 500 pairs of shoes. A dealer calls for delivery of at least 100 high garde pairs of shoes per day. Suppose the operation makes a profit of birr 2. 00 per a pair of shoes on high grade shoes and birr 1. 00 per pairs of shoes on low grade shoes. How many pairs of shoes of each type should be produced for maximum profit?
Factory should produce 100 high-grade shoes and 200 low-grade shoes for maximum profit.
Let x be the number of high-grade shoes produced, then the number of low-grade shoes produced is at least 2x. The maximum number of shoes the factory can produce is 500, so we have the following constraints:
x + 2x ≥ 500 (production constraint)
x ≥ 100 (delivery constraint)
x ≥ 0 (non-negative constraint)
The profit for each type of shoe is given as birr 2.00 for high-grade shoes and birr 1.00 for low-grade shoes, so the total profit is:
Profit = 2x * 2.00 + 1.00 * 2x = 4.00x + 2x = 6.00x
The objective is to maximize the profit, subject to the constraints above. So, the feasible solution is x = 100, which means the factory should produce 100 high-grade shoes and 200 low-grade shoes. This is the maximum possible profit of 600 birr.
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A real etate office manage an apartment complex with 40 unit. When the rent i $780 per month, all 40 unit are occupied. However, when the rent i $852, the average number of occupied unit drop to 36. Aume that the relationhip between the monthly rent p and the demand x i linear. (Note: the term demand refer to the number of occupied unit. )
(a) Write a linear equation giving the demand x in term of the rent p
The linear demand equation: x = m(p) + b, where x is the number of occupied units, p is the monthly rent, and m and b are constants and the linear demand equation in this case is:
x = -1.04p + 44.16
To find the linear equation, we need to determine the slope (m) and the y-intercept (b). Using the two points provided, we can write a system of equations:
When p = $780, x = 40 units
40 = m($780) + b
When p = $852, x = 36 units
36 = m($852) + b
Solving for m and b, we get:
m = -1.04 and b = 44.16
So, the linear demand equation is:
x = -1.04p + 44.16
This equation represents the inverse relationship between the monthly rent and the demand, where a higher rent results in a lower demand and vice versa.
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let ω0, ω1, . . . , ωn−1 denote the n distinct nth roots of unity, so that ωnk = 1 for each k = 0, . . . , n −1. what is the value of the sum ω0 ··· ωn−1? prove your answer.
The sum of the n distinct nth roots of unity is equal to 0, i.e. ω0 + ω1 + ... + ωn-1 = 0.
To prove this:
Consider a complex number z = cos(2π/n) + i sin(2π/n). It is a primitive nth root of unity, i.e.[tex]z^n[/tex] = 1.
Let w = [tex]z^k[/tex] for k = 1, 2, ..., n-1, then w is also a primitive nth root of unity.
So the sum of all the nth roots of unity can be expressed as:
[tex]1 + w + w^2 + ... + w^{(n-1)} = \frac{(1 + w + w^2 + ... + w^{(n-1)}}{z^{(n-1)}} = \frac{(z^n - 1)}{(z - 1) }= 0[/tex]
Hence, the sum of the n distinct nth roots of unity is equal to 0.
A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. It is the combination of a real number and an imaginary number. Complex numbers are used in many areas of mathematics, including algebra, calculus, and number theory.
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the logarithm is important when working with exponential dynamics. what is the relation between both?
The logarithm and exponential functions are inverse of each other. The exponential function raises a number to a power and the logarithm gives the power that the number has to be raised to in order to equal a given value. In other words, the exponential function expresses exponential growth, while the logarithm expresses exponential decay.
For example, if y = 2^x, then x = log2(y). This logarithmic relationship is useful in solving exponential problems and understanding exponential dynamics.
In exponential dynamics, logarithms are used to study and model changes that occur at exponential rates, such as population growth or decay, interest rate calculations, and many other real-world applications. The logarithmic relationship helps to simplify the exponential equations and make them easier to work with.
In summary, the logarithm and exponential functions are important in understanding exponential dynamics because the logarithmic relationship helps to simplify exponential problems and make them easier to solve.
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Help me on this hurry!!! :))))
Answer: In statistics, the term linear model is used in different ways according to the context.
Step-by-step explanation: The most common occurrence is in connection with regression models and the term is often taken as synonymous with linear regression model. However, the term is also used in time series analysis with a different meaning.
the helix r(t) = cos(πt/2), sin (πt/2),t) intersects the sphere x^2 + y^2 + z^2 = 2 in two points. Find the angle of intersection at each point.
the helix r(t) = cos(πt/2), sin (πt/2),t) intersects the sphere x^2 + y^2 + z^2 = 2 in two points.
the angle of intersection at each point: θ = cos⁻¹ (√2/√π²+4)
the angle of intersection at each point: α = cos⁻¹(-√2 /(√π² +4))
What is helix?Scientists in the fields of physics, engineering, and biology all do research on helices, which are a significant topic in the theory of curves in differential geometry. Helix (or generic helix) is defined as tangent vector field in 3-dimensional Euclidean space establishing a fixed angle with the curve's direction. A curve for which the tangent forms a constant angle with a fixed line is referred to as a helix or coil.
helix: r(t) = < cos(πt/2), sin(πt/2), t > sphere: x² + y² + z² = 2
put it in the sphere's equation we get:
next, {cos(πt/2)}² + {sin(πt/2)}² + t² = 2
or, 1 + t² = 2
or, t² = 1
or, t = ± 1
thus, points of intersection r(1) = < cos(π/2), sin(π/2), 1 > = < 0, 1, 1 >
r(-1) = < cos(-π/2), sin(-π/2), -1 > = < 0, -1, -1 >
angle intersection is angle between their tangent:
helix:
r(t) = < -π/2 sin(πt/2), π/2 cos(πt/2), 1 >
r'(1) = < -π/2, 0, 1 > .........(i)
r'(-1) = < π/2, 0, 1 > ......... (ii)
sphere:
f = (x² + y² + z² - 2) = 0
Δf = <2x, 2y, 2z>
Δf (0,1,1) = <0,2,2> ................ (iii)
Δf (0,-1,-1) = <0,-2,-2> .............(iv)
angle between (i) and (iii) (at, t = 1)
cosθ = {r'(1) Δf (0,1,1)} / {|r'(1)| |Δf (0,1,1)|]
θ = cos⁻¹ (√2/√π²+4)
angle between (ii) and (iv) (at, t = 1)
cosα = r'(-1)Δf (0,-1,-1) / ||r'(-1)|| ||Δf (0,-1,-1) ||
cos α = -√2 /(√π² +4)
α = cos⁻¹(-√2 /(√π² +4))
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) b. estimate the circumference, in centimeters, of a circle with a diameter of 4.50 cm. circumference (cm) 14.2 saved (1pts) c. estimate the diameter, in centimeters, of a circle with a circumference of 3.94 inches. diameter (cm)
The circumference of the circle with the diagram of 2.25 cm is 14.13 cm.
What is circumference?The circumference, also known as the length of a circle, is its circumference. By using the radius or diameter, we can calculate the circumference of a circle.
An irregular plane figure is a circle. Every point on the circle is equally distant from the circle's fixed centre. It has a radius of 1, making it a 2D shape. The Latin word "circulus," which means "small ring," is the source of the English word "circle."
Given that the diameter of the circle is 4.50 cm. The circumference of the circle is calculated as:-
C = 2πr
C = 2 x π x 2.25
C = 14.13 cm
Therefore, the circumference of the circle with the diagram of 2.25 cm is 14.13 cm.
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How to convert micrometers to meters
1 micrometer equals 1e-6 meters. Dividing by 1000000 will convert your number from micrometers to meters.
Does equate to m?Microns are denoted by the letter "m," while micrometers are denoted by the letter "." 1 m = 1.00. The size of a micron is one millionth of a meter or 1/25,400 of an inch. Microns, a metric unit of length, are frequently used to quantify particles.The micrometre, sometimes referred to as the micron, is a unit of length in the metric system equal to 0.001 mm, or around 0.000039 inch. Its symbol is m.Micrometer A millimeter and a micrometer are separated by a distance of one thousand. There are 1000 micrometers in a millimeter (mm).1 micrometer equals 1e-6 meters. Dividing by 1000000 will convert your number from micrometers to meters.To learn more about micrometers refer to:
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