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3 years ago

In a parallel circuit, ET = 277 V, R = 33 kΩ, and XL = 42 kΩ. What is Z?

Mathematics

1 answer:

Nesterboy [21]3 years ago

8 0

Given:

Resistance $(X_{R}) = 33 k ohm$

Inductive reactance $(X_{R}) = 42 k ohm$

We can calculate total impedance (Z) in parallel circuit, by using a reciprocal formula (identical to that used in calculating parallel resistances in DC circuits) as follows.

$1/Z = 1/X_{R} + 1/X_{L}$

$1/Z = 1/33 + 1/42$

solving this we get, Z = 18.4798 kΩ

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Find the sum of all positive rational numbers that are less than 5, and that has a denominator of 30 when written in lowest term

Gennadij [26K]

Answer with explanation:

We have to evaluate the sum of all positive rational numbers that are less than 5, and that has a denominator of 30 when written in lowest terms.

Factors of 30 are=1,2,3,5,6,10,15,30.

So, all these fractions will begin from and has sum

$\rightarrow\frac{1}{30}+\frac{7}{30}+\frac{11}{30}+\frac{13}{30}+\frac{17}{30}+\frac{19}{30}+\frac{23}{30}+\frac{29}{30}+\frac{31}{30}+\frac{37}{30}+\frac{41}{30}+\frac{43}{30}+\frac{47}{30}+\frac{49}{30}+\frac{53}{30}+\frac{59}{30}+\frac{61}{30}+\frac{67}{30}+\frac{71}{30}+\frac{73}{30}+\frac{77}{30}+\frac{79}{30}+\frac{83}{30}+\frac{89}{30}+\frac{91}{30}+\frac{97}{30}+\frac{101}{30}+\frac{103}{30}+\frac{107}{30}+\frac{109}{30}+\frac{113}{30}+\frac{119}{30}+\frac{121}{30}+\frac{127}{30}+\frac{131}{30}$

$\frac{133}{30}+\frac{137}{30}+\frac{139}{30}+\frac{143}{30}+\frac{147}{30}+\frac{149}{30}\\\\=\frac{3147}{30}\\\\=104.9$

4 0

3 years ago

The distants around the edge of the pool is 38 feet. What is the area the pool with cover

kvv77 [185]

Answer:

$114.93 ft$

Step-by-step explanation:

$\pi = 3.14$

Given formula to find the area:

$\pi * r^2$

Find radius first:

$Circumference = \pi * 2 * r$

The circumference in this situation would be 38 feet.

$38ft = \pi * 2 * r$

$38 ft = 3.14 * 2 * r$

$3.14 * 2 = 6.28$

$38ft = 6.28 * r$

Since we need to find radius, do division to 38 by 6.28.

$38ft / 6.28 = 6.05$

Our radius is 6.05

Now back to the original formula which is:

$\pi * r^2$

Substitute:

$A = 3.14 * 6.05^2$

$6.05^2 = 36.6$

$A = 3.14 * 36.6$

$==> 114.93ft$

8 0

3 years ago

Two Step Equations with Fractional Coefficients 23+2/3c=45

Firlakuza [10]

Answer:

c = 33

Step-by-step explanation:

23 + 2/3c = 45

Subtract 23 from oth sides

2/3c = 22

multiply both sides by 3/2

c = 33

4 0

3 years ago

A recipe calls for 2 cups of sugar for each 5 cups of flour. How many cups of sugar needed for 15 cups of flour?

jonny [76]

Answer:

6 cups of sugar

Step-by-step explanation:

2/5=x/15

x=6

8 0

3 years ago

Five million bacteria live in an organism. The doubling period is 1.5 hours. How many will there be after:

finlep [7]

We write the generic exponential equation:
y = A (b) ^ t
Where,
A: initial population
B: growth rate
t: time in hours.
Substituting values we have:
y = 5 (2) ^ ((1 / 1.5) * t)
For t = 9 hours we have:
y = 5 (2) ^ ((1 / 1.5) * 9)
y = 320 million
For t = 24 hours (one day) we have:
y = 5 (2) ^ ((1 / 1.5) * 24)
y = 327680 million
For t = 2 hours we have:
y = 5 (2) ^ ((1 / 1.5) * 2)
y = 12.5992105 million
Answer:
a) t hours?
y = 5 (2) ^ ((1 / 1.5) * t)
b) 9 hours?
y = 320 million
c) 1 day?
y = 327680 million
d) 2 hours?
y = 12.5992105 million

8 0

3 years ago