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Katena32 [7]
1 year ago
8

Please help!! maths functions

Mathematics
2 answers:
Deffense [45]1 year ago
4 0

Answer:

Point C:  (3, 3)

Point D:  (3, -22)

Step-by-step explanation:

If the <u>distance</u> between points C and D is <u>25 units</u>, the <u>y-value of point D</u> will be <u>25 less</u> than the <u>y-value of point C</u>.  The x-values of the two points are the <u>same</u>.

Therefore:

\textsf{Equation 1}: \quad y=2x-3

\textsf{Equation 2}: \quad y-25=-3x^2+5

As the x-values are the same, substitute the first equation into the second equation and solve for x to find the x-value of points C and D:

\implies 2x-3-25=-3x^2+5

\implies 3x^2+2x-33=0

\implies 3x^2-9x+11x-33=0

\implies 3x(x-3)+11(x-3)=0

\implies (x-3)(3x+11)=0

\implies x=3, -\dfrac{11}{3}

From inspection of the given graph, the x-value of points C and D is positive, therefore x = 3.

To find the y-value of points C and D, <u>substitute</u> the found value of x into the two <u>original equations of the lines</u>:

\begin{aligned} \textsf{Point C}: \quad 2x-3 & =y\\2(3)-3 & =3\\ \implies & (3, 3)\end{aligned}

\begin{aligned} \textsf{Point D}: \quad -3x^2+5 & = y \\ -3(3)^2+5 & =-22\\  \implies & (3, -22)\end{aligned}

Therefore, point C is (3, 3) and point D is (3, -22).

PSYCHO15rus [73]1 year ago
3 0

Answer:

The Co-ordinate of C is (4/3, -1/2)

Step-by-step explanation:

We have two equation one is of straight line equation which is:

                                              y=2x-3           (i)

Other equation is of quadratic function which is:

                                         y=-3x^2+5         (ii)

Put the value of y from equation (i) in equation (ii)

So, we have:

                                     2x-3=-3x^2+5

                                      3x^2+2x-8=0

By factorization:

                                    3x^2+6x-4x-8=0

                                   3x(x+2)-4x(x+2)=0

                                        (x+2)(3x-4)=0

              x+2=0                             ;                      3x-4=0

              x=-2                                ;                       x=4/3

Put first x=-2 in equation (i)

                                                y=2(-2)-3

                                                  y=-4-3

                                                    y=-7

Now Put x=4/3 in equation (i)

                                             y=2(4/3)-3

                                                 y=8/3-3

                                                   y=-1/2

So, we have two Order pair One is (-2 , -7) and Second one is (4/3 , -1/2)

Hence the Co-ordinate of C is:

                                               C=(4/3 , -1/2)

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