All categories

2 years ago

The area of this trapezium

Mathematics

1 answer:

Vikentia [17]2 years ago

4 0

H=5cm as we use 1/2(a+b)h which is trapezium formula

1/2(10+6)h=40
h=5

You might be interested in

Find the volume of the solid.

dmitriy555 [2]

In Cartesian coordinates, the region (call it $R$ ) is the set

$R = \left\{(x,y,z) ~:~ x\ge0 \text{ and } y\ge0 \text{ and } 2 \le z \le 4-x^2-y^2\right\}$

In the plane $z=2$ , we have

$2 = 4 - x^2 - y^2 \implies x^2 + y^2 = 2 = \left(\sqrt2\right)^2$

which is a circle with radius $\sqrt2$ . Then we can better describe the solid by

$R = \left\{(x,y,z) ~:~ 0 \le x \le \sqrt2 \text{ and } 0 \le y \le \sqrt{2 - x^2} \text{ and } 2 \le z \le 4 - x^2 - y^2 \right\}$

so that the volume is

$\displaystyle \iiint_R dV = \int_0^{\sqrt2} \int_0^{\sqrt{2-x^2}} \int_2^{4-x^2-y^2} dz \, dy \, dx$

While doable, it's easier to compute the volume in cylindrical coordinates.

$\begin{cases} x = r \cos(\theta) \\ y = r\sin(\theta) \\ z = \zeta \end{cases} \implies \begin{cases}x^2 + y^2 = r^2 \\ dV = r\,dr\,d\theta\,d\zeta\end{cases}$

Then we can describe $R$ in cylindrical coordinates by

$R = \left\{(r,\theta,\zeta) ~:~ 0 \le r \le \sqrt2 \text{ and } 0 \le \theta \le\dfrac\pi2 \text{ and } 2 \le \zeta \le 4 - r^2\right\}$

so that the volume is

$\displaystyle \iiint_R dV = \int_0^{\pi/2} \int_0^{\sqrt2} \int_2^{4-r^2} r \, d\zeta \, dr \, d\theta \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} \int_2^{4-r^2} r \, d\zeta\,dr \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} r((4 - r^2) - 2) \, dr \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} (2r-r^3) \, dr \\\\ ~~~~~~~~ = \frac\pi2 \left(\left(\sqrt2\right)^2 - \frac{\left(\sqrt2\right)^4}4\right) = \boxed{\frac\pi2}$

3 0

1 year ago

Can someone please help me I can’t afford to get anymore wrong

yuradex [85]

You answer would be B. Vehicle B needs fewer repairs then Vehicle A on average and its repair rate is more consistant

3 0

3 years ago

What is the solution to the system of equations represented by these two lines?

Andrei [34K]

Answer:

(3,2)

Step-by-step explanation:

this is an intersecting lines which means it has one solution

8 0

2 years ago

A=8 square root of 3<br> B=16<br> C=12<br> D=8

gulaghasi [49]

Step-by-step explanation:

8√383 by √3√333.

8√3⋅√3√383⋅33

Combine and simplify the denominator.

Tap for more steps...

8√33833

The result can be shown in multiple forms.

Exact Form:

8√33833

Decimal Form:

4.61880215

4 0

3 years ago

Read 2 more answers

A cell phone company charges $100 to activate a phone line and then $50 a month after that. Which of the following functions rel

Flura [38]

Y= 100+50x should be a correct function

4 0

2 years ago