All categories

3 years ago

Please help me out with this

Mathematics

1 answer:

Anettt [7]3 years ago

7 0

Answer:

81.75 ft²

Step-by-step explanation:

The area (A) of a trapezoid is calculated using the formula

A = $\frac{1}{2}$ h (a + b)

where a, b are the parallel bases and h is the perpendicular height

Calculate h using the right triangle and the sine ratio

sin30° = $\frac{opposite }{hypotenuse}$ = $\frac{h}{10}$

Multiply both sides by 10

10 × sin30° = h, thus

h = 5

a = 12 and b = 8.7 + 12 = 20.7, hence

A = $\frac{1}{2}$ × 5 × (12 + 20.7)

= 0.5 × 5 ×32.7

= 81.75 ft²

You might be interested in

Oscar has 6 tubular neon lights in order to spell out the word VISION to promote his lighting business.It costs £2 to add a corn

anyanavicka [17]

It is £15 for the words, but I don’t understand the second part

8 0

3 years ago

In five consecutive tosses of a coin, what is the probability of not getting a tail until the 5th coin toss?

jasenka [17]

The proabability would be 50% always

3 0

3 years ago

erica earned 30,000 bonus points on her computer assignment this is ten times as many points as she earned last week how many bo

alisha [4.7K]

If last week she made x points, and this week she made 30, 000
then 30 000 = 10x (solve for x)
30 000/10 = x
so she made 3000 points last week

3 0

3 years ago

3. The roof of a castle tower is shaped like a cone. The base of the cone is 24 m across and the height is 16 m. The slant heigh

Katyanochek1 [597]

C=hypotenuse=slant height
a=base=radius= 12 m
b=height=16 m
thus the slant height will be:
c^2=16^2+12^2
c^2=256+144
c^2=400
⇒c=sqrt (400)
c=20

<span>Therefore, thaaa answer is 20
</span>
<span>Hope This Help................ Have A Nice Daaaay! </span>

8 0

3 years ago

Calculate s f(x, y, z) ds for the given surface and function. g(r, θ) = (r cos θ, r sin θ, θ), 0 ≤ r ≤ 4, 0 ≤ θ ≤ 2π; f(x, y, z)

Triss [41]

$g(r,\theta)=(r\cos\theta,r\sin\theta,\theta)\implies\begin{cases}g_r=(\cos\theta,\sin\theta,0)\\g_\theta=(-r\sin\theta,r\cos\theta,1)\end{cases}$

The surface element is

$\mathrm dS=\|g_r\times g_\theta\|\,\mathrm dr\,\mathrm d\theta=\sqrt{1+r^2}\,\mathrm dr\,\mathrm d\theta$

and the integral is

$\displaystyle\iint_Sx^2+y^2\,\mathrm dS=\int_0^{2\pi}\int_0^4((r\cos\theta)^2+(r\sin\theta)^2)\sqrt{1+r^2}\,\mathrm dr\,\mathrm d\theta$

$=\displaystyle2\pi\int_0^4r^2\sqrt{1+r^2}\,\mathrm dr=\frac\pi4(132\sqrt{17}-\sinh^{-1}4)$

###

To compute the last integral, you can integrate by parts:

$u=r\implies\mathrm du=\mathrm dr$

$\mathrm dv=r\sqrt{1+r^2}\,\mathrm dr\implies v=\dfrac13(1+r^2)^{3/2}$

$\displaystyle\int_0^4r^2\sqrt{1+r^2}\,\mathrm dr=\frac r3(1+r^2)^{3/2}\bigg|_0^4-\frac13\int_0^4(1+r^2)^{3/2}\,\mathrm dr$

For this integral, consider a substitution of

$r=\sinh s\implies\mathrm dr=\cosh s\,\mathrm ds$

$\displaystyle\int_0^4(1+r^2)^{3/2}\,\mathrm dr=\int_0^{\sinh^{-1}4}(1+\sinh^2s)^{3/2}\cosh s\,\mathrm ds$

$\displaystyle=\int_0^{\sinh^{-1}4}\cosh^4s\,\mathrm ds$

$=\displaystyle\frac18\int_0^{\sinh^{-1}4}(3+4\cosh2s+\cosh4s)\,\mathrm ds$

and the result above follows.

4 0

4 years ago