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ser-zykov [4K]
2 years ago
12

What’s the length of AZ. If A is between Y and Z, Y A = 22, AZ = 16x, and Y Z = 166

Mathematics
1 answer:
VLD [36.1K]2 years ago
7 0

Answer:

c) 144

Step-by-step explanation:

Since A is between Y and Z,

YZ = YA + AZ

116 = 22 + 16x\\16x = 116 - 22\\16x = 144\\x = 9

however, the question asks for the length of AZ, not the value of x.

Thus,

AZ = 16x

AZ = 16\\ × 9

AZ = 144

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In a certain region of space, the potential is given by v=2x−5x2y 3yz2. How much is the magnitude of the electric field at point
Masja [62]

The magnitude of the electric field at the point (-2, 2, 0) is 46.52 V/m

<h3>How to calculate the electric field?</h3>

Since in a certain region of space, the potential is given by v = 2x − 5x²y 3yz²,

The electric field, E = -grad(V) where grad(V) = (dV/dx)i + (dV/dy)j + (dV/dz)k

Since V = 2x − 5x²y + 3yz²

dV/dx = d(2x − 5x²y + 3yz²)/dx

= d2x/dx - d5x²y/dx + d3yz²/dx

= 2 - 10xy + 0

= 2 - 10xy

dV/dy = d(2x − 5x²y + 3yz²)/dy

= d2x/dy - d5x²y/dy + d3yz²/dy

= 0 - 5x² + 3z²

=  - 5x² + 3z²

dV/dz = d(2x − 5x²y + 3yz²)/dz

= d2x/dz - d5x²y/dz + d3yz²/dz

= 0 - 0 + 6z

=  6z

<h3>The electric field</h3>

So, E = -grad(V)

= -[(dV/dx)i + (dV/dy)j + (dV/dz)k]

= -[(2 - 10xy)i + (- 5x² + 3z²)j + (6z)k]

So, the electric field at (-2, 2, 0) is

E = -[(2 - 10xy)i + (- 5x² + 3z²)j + (6z)k]

E = -[(2 - 10(-2)(2))i + (- 5(2)² + 3(0)²)j + (6(0))k]

E = -[(2 + 40)i + (- 5(4) + 0)j + (0)k]

E = -[42i + (-20 + 0)j + (0)k]

E = -[42i - 20j + 0k]

E = -42i + 20j - 0k

<h3>The magnitude of the electric field</h3>

So, the magnitude of E at (-2, 2, 0) is

|E| = √[(-42)² + 20² + 0²]

=  √[1764 + 400 + 0]

= √2164

= 46.52 V/m

So, the magnitude of the electric field at the point (-2, 2, 0) is 46.52 V/m

Learn more about electric field here:

brainly.com/question/25751825

#SPJ12

3 0
2 years ago
According to a survey, the average American person watches TV for 3 hours per week. To test if the amount of TV in New York City
Neporo4naja [7]

Answer:

Test statistic (t-value) of this one-mean hypothesis test is -2.422.

Step-by-step explanation:

We are given that according to a survey, the average American person watches TV for 3 hours per week. She surveys 19 New Yorkers randomly and asks them about their amount of TV each week, on average. From the data, the sample mean time is 2.5 hours per week, and the sample standard deviation (s) is 0.9 hours.

We have to test if the amount of TV in New York City is less than the national average.

Let Null Hypothesis, H_0 : \mu \leq 3  {means that the amount of TV in New York City is less than the national average}

Alternate Hypothesis, H_1 : \mu > 3   {means that the amount of TV in New York City is more than the national average}

The test statistics that will be used here is One-sample t-test statistics;

        T.S. = \frac{\bar X - \mu}{\frac{s}{\sqrt{n} } } ~ t_n_-_1

where, \bar X = sample mean time = 2.5 hours per week

             s = sample standard deviation = 0.09 hours

             n = sample size = 19

So, <u>test statistics</u> = \frac{2.5 - 3}{\frac{0.9}{\sqrt{19} } } ~ t_1_8

                              = -2.422

Therefore, the test statistic (t-value) of this one-mean hypothesis test (with σ unknown) is -2.422.

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How much more does $1,000 earn in eight years, compounded daily at 3%, than $1,000 over eight years at 3%, compounded semiannual
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Answer:

Step-by-step explanation:

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A construction company can remove 1/4 metric tons of dirt from a construction site in 1/8 hours. What is the unit rate in metric
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3 years ago
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