The function for the outside temperature is represented by $T(t) = 85\º + 15\º \cdot \sin \left[\frac{t-6\,h}{24\,h} \right]$ , where t is measured in hours.

Step-by-step explanation:

Since outside temperature can be modelled as a sinusoidal function, the period is of 24 hours and amplitude of temperature and average temperature are, respectively:

Amplitude

$A = \frac{100\º-70\º}{2}$

$A = 15\º$

Mean temperature

$\bar T = \frac{70\º+100\º}{2}$

$\bar T = 85\º$

Given that average temperature occurs six hours after the lowest temperature is registered. The temperature function is expressed as:

$T(t) = \bar T + A \cdot \sin \left[2\pi\cdot\frac{t-6\,h}{\tau} \right]$

Where:

$\bar T$ - Mean temperature, measured in degrees.

$A$ - Amplitude, measured in degrees.

$\tau$ - Daily period, measured in hours.

$t$ - Time, measured in hours. (where t = 0 corresponds with 5 AM).

If $\bar T = 85\º$ , $A = 15\º$ and $\tau = 24\,h$ , the resulting function for the outside temperature is:

$T(t) = 85\º + 15\º \cdot \sin \left[\frac{t-6\,h}{24\,h} \right]$

3 0

2 years ago

What name best describes this shape?

EastWind [94]

Answer: Quadrilateral

Explanation:

Any four sided polygon is considered a quadrilateral since "quad" means "four". You can think of a quad bike, which has four wheels, to help remember this math term.

Usually in problems like this, we'll be given information about if certain sides are parallel or the same length. However, we don't this info, so we cannot narrow down this classification anymore.

7 0

2 years ago

PLEASE HELP WITH 1-3 ILL MARK U THE BRAINLIEST

sammy [17]

Answer:

1:A(-6,-1) B(-14,0) C(-11,4)

2:D(6,-3) E(2,-3) F(3, -4.5) G(5, -4.5)

3:H(-4,1) I(-4, 6) J(0,6) K(0,1)

Step-by-step explanation:

Before we begin, lets define the transformations:

(x, y)

T(a, b) = (x+a, y +b)

Rxaxis = (x, -y)

Ryaxis = (-x, y)

r(180, 0) = (-x, -y)

D.5(1/2x, 1/2y)

R(-90, O) = (-y, x)

1. T. A(6,-1) B(14,0) C(11,4)

Rx. A(6, 1) B(14,0) C(11,-4)

r180 A(-6,-1) B(-14,0) C(-11,4)

2. Rx D(-12,-6) E(-4,-6) F(-6, -9) G(-10, -9)

Ry D(12,-6) E(4,-6) F(6, -9) G(10, -9)

D.5 D(6,-3) E(2,-3) F(3, -4.5) G(5, -4.5)

3. Rx=1 H(-1,2) I(4, 2) J(4,-2) K(-1,-2)

T H(1,4) I(6, 4) J(6,0) K(1,0)

r-90 H(-4,1) I(-4, 6) J(0,6) K(0,1)

4 0

2 years ago