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IrinaVladis [17]
3 years ago
7

A rectangular room is 1.6 times as long as it is wide, and its perimeter is 34 meters. Find the dimensions of the room.​

Mathematics
1 answer:
Papessa [141]3 years ago
7 0

Answer:

Step-by-step explanation:

x=1.6w and 2w+2x=34.

Simply substitute for x in the perimeter equation, and solve for w. Now compute x.

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Find the distance traveled by a particle with position (x, y) as t varies in the given time interval. x = 5 sin2 t, y = 5 cos2 t
rodikova [14]
\begin{cases}x(t)=5\sin2t\\y(t)=5\cos2t\end{cases}\implies\begin{cases}\frac{\mathrm dx}{\mathrm dt}=10\cos2t\\\frac{\mathrm dy}{\mathrm dt}=-10\sin2t\end{cases}

The distance traveled by the particle is given by the definite integral

\displaystyle\int_C\mathrm dS=\int_0^{3\pi}\sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt

where C is the path of the particle. The distance is then

\displaystyle\int_0^{3\pi}\sqrt{100\cos^22t+100\sin^22t}\,\mathrm dt=10\int_0^{3\pi}\mathrm dt=30\pi
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3 years ago
A system of equations that has at least one solution is called inconsistent.
solmaris [256]

False. Because if it has one then it is consistent.

Source: If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent. (https://www.varsitytutors.com/hotmath/hotmath.../consistent-and-dependent-systems)

8 0
3 years ago
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Will mark brainliest !!
ikadub [295]

Given Fig.is a triangle

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1/3x + 7/x^2 + (x+2)/x

=[ x+ 21 + 3x(x+2)]/3x^2

= (x+ 21 + 3x^2 + 6x)/3x^2

= (3x^2 + 7x +21)/3x^2

7 0
3 years ago
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vladimir1956 [14]
Neptune's distance from the sun is d₁ = 4.503 x 10⁹ km.
Mercury's distance from the sun is d₂ = 5.791 x 10⁷ km.

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\frac{d_{1}}{d_{2}} = \frac{4.503 \times 10^{9}}{5.791 \times 10^{7}} = 77.75859

Answer: 7.7759 x 10⁻¹ times
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3 years ago
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LenKa [72]

Answer:

x = ±2

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