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Arte-miy333 [17]
3 years ago
7

In the accompanying figure, triangle ABC has coordinates A(0,3), B(7,3), C(7,7). What is the area of triangle ABC in square unit

s?

Mathematics
1 answer:
ElenaW [278]3 years ago
4 0

We know area of triangle = \frac{1}{2}  * base * height

In triangle ABC , AB is the base and BC is the height

Now we find the distance between A and B

Distance formula is \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}

A(0,3), B(7,3)

Distance AB = \sqrt{(7-0)^2 + (3-3)^2}

= \sqrt{(7)^2 } = 7

B(7,3), C(7,7)

Distance BC = \sqrt{(7-7)^2 + (7-3)^2}

= \sqrt{(4)^2 } = 4

area of triangle = \frac{1}{2}  * base * height

area of triangle = \frac{1}{2}  * AB * BC

= \frac{1}{2}  * 7 * 4 = 14 units ^2

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A bucket that weighs 5 lb and a rope of negligible weight are used to draw water from a well that is 60 ft deep. The bucket is f
mestny [16]

Answer:

The value is W= 2640 \  ft \cdot lb

Step-by-step explanation:

From the question we are told that

The weight of the bucket is F =  5 lb

The depth of the well is x_1 =  60 \ ft

The weight of the water is W_w  =  42 lb

The rate at which the bucket with water is pulled is v  = 1.5 \  ft/s

The rate of the leak is r = 0.15 lb/s

Generally the workdone is mathematically represented as

W =  \int\limits^{x_1}_{x_o} {G(x)} \, dx]

Here G(x) is a function defining the weight of the system (water and bucket ) and it is mathematically represented as

G(x) =  F  +  (W_w- Ix)

Here I is the rate of water loss in lb/ft mathematically represented as

I  = \frac{r}{v}

=> I  = \frac{0.15 }{1.5 }

=> I  = 0.1

So

G(x) =  5  +  (42- 0.1x)

=> G(x) =  47- 0.1x)

So

W =  \int\limits^{60}_{0} {47- 0.1x} \, dx]

=> W =  [47x - \frac{0.1x^2}{2} ]|\left 60} \atop {0}} \right.

=> W= [47(60) - 0.05(60)^2]

=> W= 2640 \  ft \cdot lb

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3 years ago
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