1. George decided

Mathematics

1 answer:

tester [92]3 years ago

4 0

Answer:

Area painter needs to cover = 64.5 ft²

Step-by-step explanation:

We are given the details of the wall:

Length of the wall = 12 ft

Height of the wall = 8 ft

Area of the wall = 12 · 8 = 96 ft²

The dimension of windows are not given, The dimensions of the windows are found from internet, which are given as.

Length of window = $3\frac{1}{2}= \frac{7}{2}=3.5ft$

Height of window = $4\frac{1}{2}= \frac{9}{2}=4.5ft$

Are of window = 3.5 · 4.5 = 15.75ft²

No. of windows = 2

Total area of windows = 15.75 · 2 = 31.5 ft²

Area painter needs to cover:

96 ft² - 31.5 ft² = 64.5 ft²

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Answer:

Approximately $58.28\; \rm m \cdot s^{-1}$ .

Step-by-step explanation:

The velocity of an object is the rate at which its position changes. In other words, the velocity of an object is equal to the first derivative of its position, with respect to time.

Note that the arrow here is launched upwards. (Assume that the effect of wind on Mars is negligible.) There would be motion in the horizontal direction. The horizontal position of this arrow will stays the same. On the other hand, the vertical position of this arrow is the same as its height: $y = 62\, t - 1.86\, t^2$ .

Apply the power rule to find the first derivative of this $y$ with respect to time $t$ .

By the power rule:

the first derivative of $t$ (same as
the first derivative of $t^2$ (same as $t$ to the second power) with respect to

Therefore:

$\begin{aligned}\frac{dy}{d t} &= \frac{d}{d t}\left[62 \, t - 1.86\, t^2\right] \\ &= 62\,\left(\frac{d}{d t}\left[t\right]\right) - 1.86\, \left(\frac{d}{d t}\left[t^2\right]\right) \\ &= 62 \times 1 - 1.86\times\left(2\, t) = 62 - 3.72\, t\end{aligned}$ .