Please select a subject first
Advertisements
Advertisements
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
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
Advertisements
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
The sum of three numbers is 6. Thrice the third number when added to the first number, gives 7. On adding three times the first number to the sum of second and third numbers, we get 12. Find the three number 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
