To vertically strech or shrink a function, multily the whole function by the factor taht you want to strech or shrink it by
to horizontally strech or shrink a function, multiply every x by the factor you want to strech or shrink it by
shrinks mean multiplying by a value greater than -1 and less than 1
stetch means multiply by a value greater than 1 or less than -1
first one
horizontal shrink
muliply every x by a fraction
so that is A
2nd one
vertical strech
multiply whole function by a value greater than 1 or less than -1
D is the answer
3rd one
horizontal strech
multiply every x by a value greater than 1 or less than -1
C is the answer
4th one
vertical shrink
multiply whole function by a value greater than -1 and less than 1
B is the answer
X^2 + y^2 = (3x^2 + 2y^2 - x)^2
2x + 2y f'(x) = 2(3x^2 + 2y^2 - x)(6x + 4y f'(x) - 1) = 36x^3 + 24x^2yf'(x) + 24xy^2 + 16y^3f'(x) - 4y^2 - 18x^2 - 8xyf'(x) + x
f'(x)(2y - 24x^2y - 16y^3 + 8xy) = 36x^3 + 24xy^2 - 4y^2 - 18x^2 - x
f'(x) = (36x^3 + 24xy^2 - 4y^2 - 18x^2 - x)/(2y - 24x^2y - 16y^3 + 8xy)
f'(0, 0.5) = -4(0.5)^2/(2(0.5) - 16(0.5)^3) = -1/(1 - 2) = -1/-1 = 1
Let the required equation be y = mx + c; where y = 0.5, m = 1, x = 0
0.5 = 1(0) + c = 0 + c
c = 0.5
Therefore, the tangent line at point (0, 0.5) is
y = x + 0.5
a=16 b=28
this is because you can use the ratio to make the equation 4x+7x=44 which turns to 11x=44 and that simplifies to x=4 so to get a you multiply 4 and 4 or a=4*4 and to get b you multiply 7 and 4 or b=7*4 so a=16 and b=28
Step-by-step explanation:
Part A :-
m(a) , m(b) & m(c) when will get combined ; they will form a straight angle (180°) .
So,
m(a) + m(b) + m(c) = 180°
=> 3x + 5 + 5x - 18 + 7x - 2 = 180°
=> 15x - 15 = 180°
=> 15(x - 1) = 180°
=> x - 1 = 180 / 15
= 12°
=> x = 12 + 1
= 13°
Using the value of x gives the value of m(a) , m(b) & m(c) .
• m(a) = 3 × 13 + 5 = 39 + 5 = 44°
• m(b) = 5 × 13 - 18 = 65 - 18 = 47°
• m(c) = 7 × 13 - 2 = 91 - 2 = 89°
Part B :-
Complementary angles are the pair of angles whose sum is 90° . Here sum of m(a) & m(b) is
44 + 47 = 91°. Hence they are not complementary angles.
The value would be 13112.73 with the simple interest and principal
