The sum of the square roots of 16i is zero, as the positive and negative square roots cancel each other out when summed up.
Explanation:The sum of the square roots of 16i is found by first determining the square roots of the given complex number. The complex number 16i can be expressed in terms of its polar form, which then allows us to apply De Moivre's Theorem in order to find the square roots.
First, 16i is purely imaginary, with a magnitude of 16 and an argument that is π/2 or -3π/2 radians. By taking the square root of its magnitude and halving the argument, we find the two square roots, which are in fact ±4√i. Therefore, if we consider both the positive and negative square roots, the sum of the square roots of 16i would be 4√i + (-4√i), which simplifies to 0.
The sum of the square roots of 16i is 4 + 4i * cos (π/8) + 4i * sin(π/8).
Explanation:To find the sum of the square roots of 16i, we first need to find the square root of 16i. To do this, we can write 16i in polar form.
16i = 16(cos (π/2) + isin(π/2))
Then, we can find the square root of 16i by taking the square root of the magnitude and halving the argument.
√16i = √16(cos (π/4) + isin(π/4))
√16i = √16 * cos (π/8) + √16 * isin(π/8)
√16i = 4(cos (π/8) + isin(π/8))
Therefore, the sum of the square roots of 16i is 4 + 4i * cos (π/8) + 4i * sin(π/8).
y = 3x
x = 25
y = __
how many 6 1/4 -pieces of fabric can be cut from a 75-inch roll
please explain how you got the answer
Answer:
part a.
2/3 = x/6
3x = 12
x = 4
that is the answer
What interval includes all possible values of x, where –3(6 – 2x) ≥ 4x + 12?
(–∞, –3]
[–3, ∞)
(–∞, 15]
[15, ∞)
Answer:
answer d 15 to ifinity
Step-by-step explanation:
Find the solution set for y = 2x + 1, given the replacement set {(-2, -3), (-1, -1), (0, 2), (1, 3), (2, 6)} ...?
the following sequence is an arithmetic sequence.you are now shown very many terms of this sequence,but you are shown enough to fill in the missing number.what number goes in the blank? 14, _,56 ...?
because it is arithmetic not geometric 14,x,56 An = An-1 + d x = 14 +d --> d = x-14 56 = x +d --> d = 56-x By substitution x-14 = 56-x 2x = 70 x = 35 the sequence is 14,35,56
Katrina's bank statement shows a closing balance of $172.62. There are no outstanding checks or deposits. Her checkbook shows a balance of $190.62. What might account for the different balances?
Answer:
trasposing of numbers
Step-by-step explanation:
The leg of a right triangle is 2 units and the hypotenuse is 3 units. What is the length, in units, of the other leg of the triangle?
A.Square root of 5 units
B.Square root of 13 units
C.5 units
D.13 units
B???
a
Square root of 5 units
Step-by-step explanation:
i just had this problem
What are the square roots of 256?
A.
128 and –128
B.
15 and –15
C.
13 and –13
D.
16 and –16
What is the solution set for the open sentence with the given replacement set?
x^2 + 12 = 8x, {2,4,5,8}
A. 2
B. 4
C. 5
D. 8
Write each improper fraction as a mixed number. 15/4
Find the 40th term of the following arithmetic sequence: 16, 6, –4, –14.
A. –545
B. –374
C. –222
D. –105
The 40th term of the given arithmetic sequence is -374. Hence the correct option is B.
The 40th term of the arithmetic sequence is found using the formula for the nth term of an arithmetic sequence: an = a1 + (n-1)d, where a1 is the first term and d is the common difference.
Given the sequence: 16, 6, -4, -14, the common difference d = 6 - 16 = -10. Plugging into the formula: a40 = 16 + (40-1)(-10) = -374.
A map has a scale of 1 cm:12km the distance between the two cities on the map is 6.8cm estimate the actual distance between the cities ...?
Final answer:
The actual distance between two cities on a map with a scale of 1 cm:12 km, where the map distance is 6.8 cm, can be calculated as 6.8 cm × 12 km/cm, resulting in an actual distance of 81.6 kilometers.
Explanation:
Understanding Map Scale Problems
To calculate the actual distance between two cities on a map using the scale given, you would use the following steps:
First, identify the scale of the map provided; in this case, it is 1 cm : 12 km.
Next, measure the distance on the map between the two cities; the distance is 6.8 cm.
Finally, multiply the distance on the map by the scale factor to find the actual distance. That is, 6.8 cm (distance on the map) × 12 km/cm (scale factor) = 81.6 km (actual distance).
Therefore, the estimated actual distance between the two cities is 81.6 kilometers.
One pipe fills a storage pool in 3 hours. A second pipe fills the same pool in 3 hours. When a third pipe is added and all three are used to fill the pool, it takes only 1 hour. Find how long it takes the third pipe to do the job alone.
For the cost function, find the marginal cost at the given production level x. State the units of measurement. (All costs are in dollars.)
C(x) = 15,000 + 70x + 1,000/x ; x = 100
To find the marginal cost at the given production level x, differentiate the cost function C(x) and substitute the value of x. The units of measurement for the marginal cost are dollars per unit (x).
Explanation:To find the marginal cost at the given production level x, we need to find the derivative of the cost function C(x) with respect to x. Let's differentiate the function:
C'(x) = 70 - 1,000/x^2
Now, substitute x = 100 into the derivative:
C'(100) = 70 - 1,000/100^2 = 70 - 1 = 69
The units of measurement for the marginal cost are dollars per unit (x).
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Arthur baked 1 7/12 dozen muffins. Nina baked 1 1/12 dozen muffins. How many dozen muffins did they bake?
Answer:
Total number of dozen muffins they both bake is [tex]2\frac{8}{12}[/tex]
Step-by-step explanation:
Given : Arthur baked [tex]1\frac{7}{12}[/tex] dozen muffins. Nina baked [tex]1\frac{1}{12}[/tex] dozen muffins.
We have to find the total number of dozen muffins did they both bake.
To find the total number of dozen muffins did they both bake is equal to number of dozen of muffins Arthur bake and number of dozen of muffins Nina bake
That is
Mathematically written as ,
Total number of dozen muffins = number of dozen of muffins Arthur bake + number of dozen of muffins Nina bake
Given : Arthur baked [tex]1\frac{7}{12}[/tex] dozen muffins
and Nina baked [tex]1\frac{1}{12}[/tex] dozen muffins.
Total number of dozen muffins = [tex]1\frac{7}{12}+1\frac{1}{12}[/tex]
Simplify, we get,
Total number of dozen muffins = [tex]1\frac{19}{12}+\frac{13}{12}[/tex]
Adding, we get,
Total number of dozen muffins = [tex]1\frac{19+13}{12}=\frac{32}{12}[/tex]
Thus, Total number of dozen muffins they both bake is [tex]2\frac{8}{12}[/tex]
4 x 3/5 as a mixed number
Aaron borrows $150 from his friend austin. he promises to pay back the money in 4 monthly installments. each month he wants to pay half the amount he paid the previous month. assuming austin does not charge any interest, how much should aaron pay the first month to repay the money as scheduled?
Aaron should pay $80 in the first month to satisfy the conditions of repaying $150 in 4 monthly installments, with each subsequent payment being half of the previous one.
Explanation:Aaron needs to pay back a total of $150 in 4 monthly installments, with each payment being half the amount of the previous month. Let's denote the first payment amount as X. Then, the second payment would be X/2, the third would be X/4, and the fourth would be X/8. These four payments need to sum up to $150, which is the total amount Aaron borrowed.
To find the value of X, we can set up the following equation based on the aforementioned information:
X + X/2 + X/4 + X/8 = 150
To solve this equation, we should find a common denominator, which is 8 in this case, and rewrite the equation as:
8X/8 + 4X/8 + 2X/8 + X/8 = 150
Adding the numerators together gives us:
(8X + 4X + 2X + X) / 8 = 150
15X / 8 = 150
Multiplying both sides by 8 and then dividing by 15 gives us:
X = (150 × 8) / 15
X = 1200 / 15
X = 80
Thus, Aaron should pay $80 in the first month to repay the money on schedule as he promised.
What is 10 plus 10. what is 456 plus 543.?
Answer:
10 + 10 = 20 ; 456 + 543 = 999
Step-by-step explanation:
adam scored x points. imran scored 3 points fewer than adam . shakeel scored twice as many points as imran. together they scored 39 points..... Write down in terms of x an expression for the number of points scored by shakeel.
The value of x is 12 and Shakeel got 18 points.
What is an equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Adam scored x points. Imran scored 3 points fewer than Adam. Shakeel scored twice as many points as Imran. together they scored 39 points
Establishing the equation, we get
Adam scored x points.
Imran scored x-3 points.
Shakeel scored 2(x-3) points.
Together they scored 39 points:
x + (x-3) + 2(x-3) = 39
x + x -3 + 2x - 6 = 39
4x = 48
x = 12
∵ Shakeel scored = 2(x-3) points.
Putting x = 12, to get the marks scored by him,
Shakeel's score = 2(12-3) = 18
Hence, The value of x is 12 and Shakeel got 18 points.
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Using the following arithmetic sequence, find the 29th term: –36, –32, –28, –24.
A. 100
B. 64
C. 76
D. 73
If a rectangle has a perimeter of 70, a length of x and a width of x - 9, find the value of the length of the rectangle.
Hannah brought 3 / 4 yards of felt for a project. she use 1/8 yard.what fraction of a yard of fill did she have left over?
Which property states that adding zero to a quantity does not change the quantity?
A. Associative
B. Additive identity
C. Commutative
D. Reflexive ...?
The strength of a cable is proportional to the square of its diameter. If a 2-cm cable will support 800kg, how much will a 3-cm cable support?
The strength of a cable is directly proportional to the square of its diameter. This relationship allows us to compute the strength of a cable of given diameter. Using given data, a cable with 3cm diameter can support 1800kg.
Explanation:The strength of a cable is said to be proportional to the square of its diameter. This is a mathematical concept of direct proportionality. In this specific case, the proportionality can be written as S=k(D^2), where S is the strength (or weight it can support), D is the diameter and k is a constant.
For a 2-cm cable, we can plug the values into the equation to find the constant: 800= k(2^2), therefore k=800/4=200.
Now, knowing that k=200, we can calculate the strength of a 3-cm cable by plugging in the values: S=200*(3^2) =1800. Therefore, a cable with a 3-cm diameter can support 1800kg.
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Write in scientific notation:
527,000
Find the factored form of 4x3 – 8x2 – 12x
TRUE or FALSE. If chord AB Is 3 inches from the center and chord CD is 5 inches from the center of the same circle, then chord CD is the longer chord.
The answer to this is: TRUE
which number is greater [-6.809]___[-6.812]
Simplify completely x^2 + 12x +35
________________
3x + 15 ...?
Answer: x + 7/ 3
Assuming the said quantity is divided by 3x+15 as a denominator in fraction form.
After dividing, the simplest form, x + 7/ 3, can be found after dividing both the numerators and the denominators by the smallest common factor.
Proof of validity is shown below.