All categories

4 years ago

30 POINTS! Please help with this goemtery question.

Mathematics

1 answer:

n200080 [17]4 years ago

3 0

Answer:

(28*12)-(18*5) or 246 meters squared

Step-by-step explanation:

It is actually easy really, all you have to do is find the area of the larger polygon (28*12) or 336 and subtract the smaller polygon (18*5) or 90 and subtract it from the larger polygon getting you 246 meters squared

You might be interested in

Evaluate the expression. -3 + (-2)

mart [117]

That's answer exactly is -5

6 0

3 years ago

Why does it help to rearrange

hichkok12 [17]

Answer:

You don't really need to do it, but it helps you keep things more organized and easier to follow. Imagine if you're doing some multi-variable equation,

2a + 5b + 4d + 3c + b + a + 2d

that looks like a mess, it'll be easier to look at if you put all the similar variables next to each others like this:

a + 2a + b + 5b + 3c + 2d + 4d

(a + 2a) + (b + 5b) + 3c + (2d + 4d)

now you can add them up much easier.

8 0

3 years ago

Consider the differential equation x2y′′ − 9xy′ + 24y = 0; x4, x6, (0, [infinity]). Verify that the given functions form a funda

pantera1 [17]

Answer:

The functions satisfy the differential equation and linearly independent since W(x)≠0

Therefore the general solution is

$y= c_1x^4+c_2x^6$

Step-by-step explanation:

Given equation is

$x^2y'' - 9xy+24y=0$

This Euler Cauchy type differential equation.

So, we can let

$y=x^m$

Differentiate with respect to x

$y'= mx^{m-1}$

Again differentiate with respect to x

$y''= m(m-1)x^{m-2}$

Putting the value of y, y' and y'' in the differential equation

$x^2m(m-1) x^{m-2} - 9 x m x^{m-1}+24x^m=0$

$\Rightarrow m(m-1)x^m-9mx^m+24x^m=0$

$\Rightarrow m^2-m-9m+24=0$

⇒m²-10m +24=0

⇒m²-6m -4m+24=0

⇒m(m-6)-4(m-6)=0

⇒(m-6)(m-4)=0

⇒m = 6,4

Therefore the auxiliary equation has two distinct and unequal root.

The general solution of this equation is

$y_1(x)=x^4$

and

$y_2(x)=x^6$

First we compute the Wronskian

$W(x)= \left|\begin{array}{cc}y_1(x)&y_2(x)\\y'_1(x)&y'_2(x)\end{array}\right|$

$= \left|\begin{array}{cc}x^4&x^6\\4x^3&6x^5\end{array}\right|$

=x⁴×6x⁵- x⁶×4x³

=6x⁹-4x⁹

=2x⁹

≠0

The functions satisfy the differential equation and linearly independent since W(x)≠0

Therefore the general solution is

$y= c_1x^4+c_2x^6$

5 0

3 years ago

6. A sector of a circle is a region bound by an arc and the two radii that share the arc's endpoints. Suppose you have a dartboa

Aliun [14]

Given the dartboard of diameter $20in$ , divided into 20 congruent sectors,

The central angle is $18^\circ$

The fraction of a circle taken up by one sector is $\frac{1}{20}$

The area of one sector is $15.7in^2$ to the nearest tenth

The area of a circle is given by the formula

$A=\pi r^2$

A sector of a circle is a fraction of a circle. The fraction is given by $\frac{\theta}{360^\circ}$ . Where $\theta$ is the angle subtended by the sector at the center of the circle.

The formula for computing the area of a sector, given the angle at the center is

$A_s=\dfrac{\theta}{360^\circ}\times \pi r^2$

<h3>Given information</h3>

We given a circle (the dartboard) with diameter of $20in$ , divided into 20 equal(or, congruent) sectors

<h3>Part I: Finding the central angle</h3>

To find the central angle, divide $360^\circ$ by the number of sectors. Let $\alpha$ denote the central angle, then

$\alpha=\dfrac{360^\circ}{20}\\\\\alpha=18^\circ$

<h3>Part II: Find the fraction of the circle that one sector takes</h3>

The fraction of the circle that one sector takes up is found by dividing the angle a sector takes up by $360^\circ$ . The angle has already been computed in Part I (the central angle, $\alpha$ ). The fraction is

$f=\dfrac{\alpha}{360^\circ}\\\\f=\dfrac{18^\circ}{360^\circ}=\dfrac{1}{20}$

<h3>Part III: Find the area of one sector to the nearest tenth</h3>

The area of one sector can be gotten by multiplying the fraction gotten from Part II, with the area formula. That is

$A_s=f\times \pi r^2\\=\dfrac{1}{20}\times3.14\times\left(\dfrac{20}{2}\right)^2\\\\=\dfrac{1}{20}\times3.14\times10^2=15.7in^2$

Learn more about sectors of a circle brainly.com/question/3432053

8 0

3 years ago

A hotel manager believes that 14% of the hotel rooms are booked. If the manager is right, what is the probability that the propo

lara [203]

Answer:

0.4996

Step-by-step explanation:

We are given;

Population proportion; p = 14% = 0.14

Sample size; n = 804

Sample proportion; p^ = 13% = 0.13

Standard deviation; σ = √np(1 - p)

σ = √(804 × 0.14 × (1 - 0.14))

σ = 9.8388

Formula for z-score is;

z = (p^ - p)/σ

z = (0.13 - 0.14)/9.8388

z = -0.01/9.8388

z = -0.001

From online z-score and probability converter attached, we have;

P(Z < -0.001) = 0.4996

5 0

3 years ago