Correct Answer: C. 4

Explanation

Given the equation of the circle \(x^{2} + y^{2} - 8x - 2y + 1 = 0\).

The equation of a circle is given as \((x - a)^{2} + (y - b)^{2} = r^{2}\)

Expanding, we have \(x^{2} - 2ax + a^{2} + y^{2} - 2by + b^{2} = r^{2} \equiv x^{2} - 2ax + y^{2} - 2by = r^{2} - a^{2} - b^{2}\)

Comparing the RHS of the equation above with the equation rewritten as \(x^{2} + y^{2} - 8x - 2y = -1\), we have

\(-2a = -8; -2b = -2 \implies a = 4, b = 1\)

\(\therefore r^{2} - 4^{2} - 1^{2} = -1 \implies r^{2} = -1 + 16 + 1 = 16\)

\(r = \sqrt{16} = 4\)

Correct Answer: D. the faithfulness of Judah had become unpardonable

Correct Answer: D. reduce the heat produced by reducing the eddy current

Explanation

The core of an efficient transformer should consist of laminated pieces of metal in order to D. reduce the heat produced by reducing the eddy current.

Here's why:

1. Eddy Currents: When a changing magnetic flux passes through a conductive material (like the iron core of a transformer), it induces circulating currents within the material itself. These are called eddy currents.

2. Heat Production: These eddy currents flow through the resistance of the core material, generating heat (I²R losses). This heat represents wasted energy and reduces the transformer's efficiency.

3. Lamination: By making the core out of thin sheets (laminations) of metal that are insulated from each other, the path for these circulating eddy currents is greatly restricted. Each lamination acts as a small, isolated conductor, preventing large eddy current loops from forming across the entire core.

4. Result: Reducing the magnitude and path of the eddy currents significantly reduces the heat generated by them, thus increasing the efficiency of the transformer.

Correct Answer: C. crust

Explanation

a. Location of industry may be defined as the sitting or establishment of a firm or industry in a particular place. An industry may be established either by individuals or government, either for economic or political reasons.

bi. Cement producing industries should be located close to sources of raw materials to reduce cost of transportation. Perishable goods like fruits, palm oil industries, etc should be located near their raw materials.

bii. There should be ready market for the products of any industry to be sited in a place. Fragile goods like glass, bulky goods like cement and other perishable goods should be located near the market. Such industries located or directed towards the market are called market-oriented industries.

biii. Government can encourage the location of industries through certain policies like: direct participation in setting up of industries. Creation of industrial zones in the country, provision of infrastructures like electricity, pipe-borne water, roads and tele-communications.

c.

- It encourages development: the growth of industries leads to an increase in production of goods and services.

- Emergence of subsidiary firms: as major firms concentrate in one area, other subsidiary service firms that assist those major firms in the production of goods usually emerge.

- Generation of employment: the concentration of many industries in an area leads to the creation of many job opportunities.

Correct Answer: d. 5550km

Correct Answer: C. mass 1kg, the temperature rises by 1K

Explanation

The specific heat capacity of a body is the heat energy required to raise a body of mass 1kg through a temperature of 1K.

Correct Answer: B. think

Correct Answer: A. epigram

Correct Answer: D. extinct