Share £747 in the ratio 2:7 between Tom and Ben

1) the form of the equation may be written as y = A(X - Xo)(X - X1)

Where Xo and X1 are the two roots of the equation.

2) We can fix the system of coordinates so that the vertex is in the middle of the gate => Xo = - 40 and X1 = +40

=> y = A (X + 40) (X - 40) = A (X^2 - 1600)

3) The height, at X = 0 is 25

=> A(0 - 1600) = 25

=> -1600A = 25 => A = -25 / 1600 = - 1/64

4) The equation is y = - [1/64] (X^2 - 1600)

5) You can present it in different equivalent forms.

Some of those other forms are:

1) - 64y = (x^2 - 1600)

2) x^2 = - 64y + 1600

3) X^2 = - 64 (y - 25)

4 0

1 year ago

The course length of the Boston Marathon is about 4.2×104 meters. The course length of the Iditarod Trail Invitational ultra-mar

GREYUIT [131]

Answer:

The ultra-marathon Idita Rod Trail is about 38 times longer than the Boston Marathon.

Step-by-step explanation:

Let

x -----> the length of the Boston Marathon in meters

y -----> the length of the Idita rod Trail Invitational ultra-marathon in meters

we have

$x=4.2*10^4\ m$

$y=1.6*10^6\ m$

we know that

To find out how many times as long is the course of the Idita rod Trail ultra-marathon as that of the Boston Marathon, divide the length of the Idita rod Trail Invitational ultra-marathon by the length of the Boston Marathon

so

$\frac{y}{x}$

$\frac{x}{y}=\frac{1.6*10^6}{4.2*10^4}$

Remember that

To divide two numbers in scientific notation, divide their coefficients and subtract their exponents

$\frac{1.6*10^6}{4.2*10^4}=\frac{1.6}{4.2}*(10^{6-4})=0.381*(10^{2})=38.1$

therefore

The ultra-marathon Idita Rod Trail is about 38 times longer than the Boston Marathon.

5 0

1 year ago

The orbit of the planet Venus is nearly circular. An astronomer develops a model for the orbit in which the sun has coordinates

klio [65]

Since the Venus orbits round the sun, the sun is the center of the circular path of the revolution of the planet, Venus.

Thus, the distance of the planet, Venus fron the sun is given by the distance between the points (0, 0) and (41, 53).

Recall that the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Thus, the distance between the points (0, 0) and (41, 53) is given by:

$d= \sqrt{(41-0)^2+(53-0)^2} \\ \\ = \sqrt{41^2+53^2} = \sqrt{1,681+2,809} \\ \\ = \sqrt{4,490} =67 \ units$

Given that each unit of the plane represents 1 million miles, therefore, the distance from the sun to the Venus is 67 million miles.

8 0

1 year ago