Explanation

y = x\(^2\)(1 + x)\(^{\frac{3}{2}}\)

Let u = x\(^2\)

v = (1 + x)\(^{\frac{3}{2}}\)

\(\frac{du}{dx} 2x\)

\(\frac{dv}{dx} = \frac{3}{2}\)(1 + x)\(^\frac{1}{2}\)

\(\frac{dy}{dx} = v\frac{du}{dx} + u\frac{dv}{dx}\)

= (1 + x)\(^{\frac{3}{2}}\)(2x) + x\(^2\)\(\frac{3}{2}(1 + x)^{\frac{1}{2}}\)

= 2x(1 + x)\(^{\frac{3}{2}}\) + \(\frac{3x^2(1 + x)^{\frac{1}{2}}}{2}\)

(b)

2y - x = 3

when x = 0, y = \(\frac{3}{2}\)

when y = 0, x = -3

h = -3, k = \(\frac{3}{2}\)

Using

(x - h)\(^2\) + (y - k)\(^2\) = r\(^2\)

(x + 3)\(^2\) + (y - \(\frac{3}{2}\))\(^2\) = r\(^2\)

r(2, 3), x = 2, y = 3

(2 + 3)\(^2\) + (3 + \(\frac{3}{2}\))\(^2\) = r\(^2\)

\(\frac{109}{4}\) = r\(^2\)

The equation will give

(x + 3)\(^2\) + (y - \(\frac{3}{2}\))\(^2\)

= \(\frac{109}{4}\)

Correct Answer: D. kind

Correct Answer: C. 5

Explanation

\(\begin{array}{c|c} x & x - x & (x - \bar{x})^2\\ \hline 15 & -6 & 36\\21 & 0 & 0\\17 & -4 & 16\\ 26 & 5 & 25 \\ 18 & -3 &9 \\ 29 & 8 & 64 \end{array}\)

\(E(x - \bar{x})^2\) = 150

N = 6

S.D = \(\sqrt{\frac{(x - x)^2}{N}}\)

S.D = \(\sqrt{\frac{150}{6}}\) = 5

Correct Answer: B. telephone N3,500, credit cash N3,500

Correct Answer: B. 9

Correct Answer: B. fractional distillation

Explanation

A process called fractional distillation is used in oil refineries to separate (as well as join or split) the various lengths of hydrocarbon chains to create different petroleum products from the different distillates.

Explanation

(a) Farm surveying is a series of activities, mainly measurements, performed in the field to locate the farm land, delineate its boundaries, determine its size and produce a map of the farmland.

(b) Six surveying instruments include (i) Prismatic compass (ii) Gunter's chain (iii) Measuring tape (iv) Ranging pole (v) Theodolite (vi) Beacon/Pillars

(c) (i) Ranging poles: These are wood or metal poles used in marking spots or stations during surveying.

(ii) Gunter's chain: This is a surveyor's chain of 100 links. 22 meters long used to measure a piece of land.

(iii) Measuring tapes: These are used in taking short or detailed measurements

(iv) Prismatic compass: This is used to measure horizontal angles between a reference median and a point of interest in order to find the orientation of the point and its bearing.

Correct Answer: A. 3.5

Explanation

When finding the median, you are looking for the middle number. Always arrange the numbers in ascending order. Since, the numbers are inceasing, count the numbers in the set. There are six. Then divide six by two. We do this because we will split the number set in half. Because six does divide evenly into two, this means we can't easily determine the median. Since six divided by two is three, we are going to eliminate three numbers from leftmost in number set toward the right direction and three numbers from rightmost in number set toward the left direction. The last number crossed out in both direction are 3 and 4. To find the middle number, just add both numbers and divide by two. 3+4/2=7/2=3.5 That's the final answer.

Correct Answer: B. 351k

Explanation

T = 78 + 273

= 351k

Correct Answer: A. primary production