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3 years ago

The map of a walking trail is drawn on a coordinate grid with three points of interest.

Mathematics

1 answer:

rewona [7]3 years ago

6 0

Answer:

12 units

Step-by-step explanation:

Given the points :

R(−3, 2) - - - > S(2, 2) - - - - > T(2, −5).

Distance between R and S

Distance between two points is obtained thus :

D = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Distance between R and S

x1 = - 3 ; y1= 2 ; x2 = 2 ; y2 = 2

D1 = sqrt((2 - (-3))^2 + (2 - 2)^2)

D1 = sqrt((5^2 + 0^2))

D1 = sqrt(25)

D1 = 5

Distance between S and T

x1 = 2 ; y1= 2 ; x2 = 2 ; y2 = - 5

D2 = sqrt((2 - 2)^2 + (-5 - 2)^2)

D2 = sqrt((0^2 + (-7)^2))

D2 = sqrt(49)

D2 = 7

Hence, total length = D1 + D2 = 5 + 7 = 12 units

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3 years ago

In isosceles triangle ABC, BC is the shortest side. If the degree measure of A is a multiple of 10, what is the smallest degree

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3 years ago

Read 2 more answers

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

2x+5=3x=4x-5

elena55 [62]

You would need to isolate the "X" variable because it is common in all 3 equations.

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3 years ago

Sue Brown is a salesperson at a car dealership. She earned a gross pay of $8000 for the month of June. Her state tax rate is 3.5

Neporo4naja [7]

Sue Brown owes $280.00 in state taxes for the month.

Step-by-step explanation:

Given,

Gross pay of Sue in June = $8000

Tax rate = 3.5%

As full amount is taxable; therefore

Amount of tax to be paid = 3.5% of pay of June

Amount of tax to be paid = $\frac{3.5}{100}*8000$

Amount of tax to be paid = 0.035*8000

Amount of tax to be paid = $280.00

Sue Brown owes $280.00 in state taxes for the month.

Keywords: percentage, multiplication

Learn more about percentage at:

#LearnwithBrainly

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3 years ago