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Express the following equations in matrix form and solve them by the method of reduction:
`x + y = 1, y + z = 5/3, z + x 4/33`.
Concept: undefined >> undefined
Express the following equations in matrix form and solve them by the method of reduction:
2x - y + z = 1, x + 2y + 3z = 8, 3x + y - 4z = 1.
Concept: undefined >> undefined
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Express the following equations in matrix form and solve them by the method of reduction:
x + 2y + z = 8, 2x + 3y – z = 11, 3x – y – 2z = 5.
Concept: undefined >> undefined
The cost of 4 pencils, 3 pens, and 2 books is ₹ 150. The cost of 1 pencil, 2 pens, and 3 books is ₹ 125. The cost of 6 pencils, 2 pens, and 3 books is ₹ 175. Find the cost of each item by using matrices.
Concept: undefined >> undefined
An amount of ₹ 5000 is invested in three types of investments, at interest rates 6%, 7%, 8% per annum respectively. The total annual income from these investments is ₹ 350. If the total annual income from the first two investments is ₹ 70 more than the income from the third, find the amount of each investment using matrix method.
Concept: undefined >> undefined
Solve the following equations by the method of inversion:
2x + 3y = - 5, 3x + y = 3
Concept: undefined >> undefined
Express the following equations in matrix form and solve them by the method of reduction:
x + 3y + 2z = 6,
3x − 2y + 5z = 5,
2x − 3y + 6z = 7
Concept: undefined >> undefined
A table of values of f, g, f' and g' is given :
| x | f(x) | g(x) | f'(x) | g'(x) |
| 2 | 1 | 6 | –3 | 4 |
| 4 | 3 | 4 | 5 | -6 |
| 6 | 5 | 2 | –4 | 7 |
If r(x) =f [g(x)] find r' (2).
Concept: undefined >> undefined
A table of values of f, g, f' and g' is given :
| x | f(x) | g(x) | f'(x) | g'(x) |
| 2 | 1 | 6 | –3 | 4 |
| 4 | 3 | 4 | 5 | -6 |
| 6 | 5 | 2 | –4 | 7 |
If R(x) =g[3 + f(x)] find R'(4).
Concept: undefined >> undefined
A table of values of f, g, f' and g' is given:
| x | f(x) | g(x) | f'(x) | g'(x) |
| 2 | 1 | 6 | –3 | 4 |
| 4 | 3 | 4 | 5 | –6 |
| 6 | 5 | 2 | –4 | 7 |
If s(x) = f[9 − f (x)] find s'(4).
Concept: undefined >> undefined
A table of values of f, g, f' and g' is given :
| x | f(x) | g(x) | f'(x) | g'(x) |
| 2 | 1 | 6 | –3 | 4 |
| 4 | 3 | 4 | 5 | -6 |
| 6 | 5 | 2 | –4 | 7 |
If S(x) =g [g(x)] find S'(6).
Concept: undefined >> undefined
Assume that `f'(3) = -1,"g"'(2) = 5, "g"(2) = 3 and y = f["g"(x)], "then" ["dy"/"dx"]_(x = 2) = ?`
Concept: undefined >> undefined
If h(x) = `sqrt(4f(x) + 3"g"(x)), f(1) = 4, "g"(1) = 3, f'(1) = 3, "g"'(1) = 4, "find h"'(1)`.
Concept: undefined >> undefined
Find the x co-ordinates of all the points on the curve y = sin 2x − 2 sin x, 0 ≤ x < 2π, where `"dy"/"dx"` = 0.
Concept: undefined >> undefined
Select the appropriate hint from the hint basket and fill up the blank spaces in the following paragraph. [Activity]:
"Let f(x) = x2 + 5 and g (x) = ex + 3 then
f[g(x)] = .......... and g[f(x)] =...........
Now f'(x) = .......... and g'(x) = ..........
The derivative of f[g(x)] w. r. t. x in terms of f and g is ..........
Therefore `"d"/"dx"[f["g"(x)]]` = .......... and
`["d"/"dx"[f["g"(x)]]]_(x = 0)` = ..........
The derivative of g[f(x)] w. r. t. x in terms of f and g is
Therefore `"d"/"dx"["g"[f(x)]]` = .......... and
`["d"/"dx"["g"[f(x)]]]_(x = -1)` = .........."
Hint basket : `{f'["g"(x)]·"g"'(x), 2e^(2x) + 6e^x, 8, "g"' [ f (x)]· f'(x),2xe^(x^2+5), − 2e^6,e^(2x) + 6e^x + 14, e^(x^2+5) + 3, 2x, e^x}`
Concept: undefined >> undefined
Find the approximate values of : `sqrt(8.95)`
Concept: undefined >> undefined
Find the approximate values of: `root(3)(28)`
Concept: undefined >> undefined
Find the approximate values of : `root(5)(31.98)`
Concept: undefined >> undefined
Find the approximate values of : (3.97)4
Concept: undefined >> undefined
Find the approximate values of (4.01)3
Concept: undefined >> undefined
