What is the difference between 49 8/9 and 17 1/3

Find area of the isosceles triangle formed by the vertex and the x-intercepts of parabola y=x2+4x−12.

xz_007 [3.2K]

The area of the isosceles triangle is 64 sq units.

Solution:

Part 1: x-intercepts

The x-intercepts occur at the points on the function where y=0

So, we need to solve

$x^2-4x-12=0$

The left side factors fairly easily into:

$(x-6)(x+2)=0$

So solution occur when

$x-6=0\rightarrow x=6$

and

$x+2=0\rightarrow x=(-2)$

So the x-intercepts are at (0,6) and (0,−2)

Part 2: vertex of the parabola

The vertex of a simple quadratic parabola occurs when the derivative of the quadratic is equal to 0.

The derivative of the given quadratic is

$\frac{dy}{dx}=2x-4$

By observation, this is equal to 0 when x=2

When x=2 the original equation becomes

$y=(2)^2-4(2)-12$

$y=-16$

Therefore the vertex of this parabola is at (2,−16)

The endpoints of the base of the isosceles triangle are (-6, 0) and (2, 0)

$\Rightarrow$ so its base is 8

The height of the triangle reaches from the midpoint of the base (-2, 0) and the vertex (2, -16)

$\Rightarrow$ so its height is 16

The area is $\frac{1}{2}\times \text { base }\times \text { height }=\frac{1}{2}\times8\times16=64 \text{ sq units }$

6 0

3 years ago

Find the value of x if 8^3/2^10 = 4^2/16

Dvinal [7]

Wait where’s the x in the equation?

3 0

3 years ago

A cube has a volume of 2197 m^3. Its surface is to be painted. Each can of paint covers about 40 m^2. How many cans of paint are

Gelneren [198K]

Volume= a³
a=edge
2197 = a³
=> a=13 m
Surface area=6a²=6*13²=6*169=1014 m²
 $\frac{1014}{40}$ = 25,35 ≈ 26
=> 26 cans needed

8 0

3 years ago

Need help ASAP!!

Ilia_Sergeevich [38]

An object that is in motion as a projectile follows a path or trajectory of a parabola

The function and values are;

a) The equation of the quadratic function is; $\underline{y = \dfrac{111}{140} \cdot x - \dfrac{3}{140} \cdot x^2}$

b) The maximum height of the ball is approximately 7.334 m

c) Horizontal distance at maximum height 18.8 meters

Reason:

a) Known parameters are;

Let f(x) = a·x² + b·x + c represent the equation of the parabola modelling the path of the ball, we have;

Points on the path of the parabola = (0, 0), (35, 1.5), 37, 0)

Plugging the values gives;

0 = a·0² + b·0 + c

Therefore, c = 0

1.5 = 35²·a + 35·b

0 = 37²·a + 37·b

Solving gives;

a = -3/140, b = 111/140

The equation of the quadratic function is therefore;

$\underline{y = f(x) = \dfrac{111}{140} \cdot x - \dfrac{3}{140} \cdot x^2}$

b) The maximum height is given by the vertex of the parabola

The x-coordinate at the vertex is the point $-\dfrac{b}{2 \cdot a}$

Which gives;

$x-coordinate = \dfrac{\frac{111}{140} }{2 \times \dfrac{3}{140} } = 17.5$

The maximum height is therefore;

$f(x)_{max} = \dfrac{111}{140} \times 17.5 - \dfrac{3}{140} \cdot 17.5^2 \approx 7.334$

The maximum height of the ball is approximately 7.334 m

c) The distance the ball has travelled to horizontally is given by half of the range, R as follows;

The range of the motion, R = 37 meters

$Horizontal \ distance \ to \ maximum \ height = \dfrac{R}{2}$

Therefore;

$Horizontal \ distance \ to \ maximum \ height = \dfrac{37}{2} = 18.5$

The distance the ball has travelled horizontally to reach the maximum height horizontally 18.5 meters

Learn more about the trajectory of a projectile here:

brainly.com/question/13646224

8 0

3 years ago

What is 3 over 8 plus 1 over 2

goblinko [34]

The answer is 0.875 just switch it to a fraction I can’t help you with everything!

7 0

3 years ago

Read 2 more answers