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3 years ago

14. Find the real-number solutions to the equation p3 - 4p2 = 0

Mathematics

1 answer:

forsale [732]3 years ago

7 0

Answer:

p=0 or p=4

Step-by-step explanation:

first simplify the equation

p^3-4p^2=0

p(p^2-4p)=0

p(p-4)(p-0)=0( factorise p^2-4p)

p=0 p=0. p-4=0,p=4

therefore,p=0 or p=4

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Help, ive been stuck on this for 2 hours

kramer

This looks super complicated, but it can actually be solved with the application of a couple of area equations.

Let's establish one fact before we start this question that may have been the reason why this was so confusing for you. No matter what kind of triangle, the area will always be $\frac{1}{2}$ times the length of the base times height.

Alright, with that established, let's start trying to solve for the area.

In this question, we seem to have a triangle with a circle shape taken out of it. We are told to find the area of the shaded area.

The overall equation would be:

$Area_{triangle}$ - $Area_{circle}$

This makes sense, right? If we find the area of the triangle and subtract the area of the circle within it, it should give us the total shaded area.

Now, let's begin solving for said shaded area:

$Area_{triangle}$ - $Area_{circle}$

( $\frac{1}{2}$ * base * height) - (π* $r^{2}$ )

The given base of the triangle is 40 km, the height 27 km, and the circle's diameter is 12. Therefore:

( $\frac{1}{2}$ * 40 * 27) - (π * $(\frac{12}{2})^{2}$ )

(540) - (π * $6^{2}$ )

540 - 36π

Use 3.14 as the value for pi:

540 - 36(3.14)

426.96

Round to the nearest tenth:

427.0

Shaded area = 427 ( $km^{2}$ )

If you have any questions on how I got to the answer, don't be afraid to ask!

- breezyツ

3 0

2 years ago

What is the percent of 85?

Hitman42 [59]

100 i think, sorry if I’m wrong lol

5 0

2 years ago

PLEASE HELP!!! WILL GIVE BRAINLIEST!!!

777dan777 [17]

Answer: (2,2) and (-5,16)

Step-by-step explanation:

Here we have both Line (Linear Function) and Parabola (Quadratic Function)

So I am gonna write these equations here,

$y=x^2+x-4\\y=-2x+6$

The first equation has Parabola graph (Since it's second degree.)

and the second equation has line graph.

To find the intersection, you have to substitute either -2x+6 in first equation (Quadratic) or x^2+x-4 in second equation (Linear)

For me, I am going to substitute x^2+x-4 in y=-2x+6.

$x^2+x-4=-2x+6$

Now solve the equation and find the value of x.

Since it's Quadratic Equation (Because there's x^2) I'd move -2x+6 to the left side.

$x^2+x-4+2x-6=0$ Finish things here (Subtract and Addition)

$x^2+3x-10=0$ What two numbers multiply to 10? Find the factors of 10, that are [1 and 10] and [2 and 5]

Now think about it, do you think that if 1 and 10 subtract or even addition, do you think that it'd be 3? No, of course not.

So 2 and 5 is right.

$(x-2)(x+5)=0$ (5-2 = 3) and (5*(-2) = -10)

Then we get both x, $x=2,-5$

However, this is not it. You have to substitute both x in Linear Equation.

Substitute x = 2 in y=-2x+6

$y=-2(2)+6\\y=-4+6\\y=2$

Order = $(2,2)$

Then substitute x = -5 in y=-2x+6

$y=-2(-5)+6\\y=10+6\\y=16$

Order = $(-5,16)$

So the intersections are both (2,2) and (-5,16) as shown in graph below.

4 0

3 years ago

What is the greatest common factor of 18,42,24?

Dmitry_Shevchenko [17]

6 is the gcf of all those numbers

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3 years ago

Alan hikes 4.5 miles in 3 hours. Determine whether quantities (distance and time) vary directly or inversely and find the consta

Mrac [35]

V = x/t = 4.5 mil / 3 h = 1.5 mph
Since, v = 1.5 mph (or we can say that v is constant), distance and time vary directly and the constant of variation is 1.5 mph.

3 0

2 years ago