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Serhud [2]
3 years ago
8

How you solve this??

Mathematics
1 answer:
FrozenT [24]3 years ago
4 0
I have no idea sorry
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Ralph is painting the barn below, including the sides and roof.  He wants to know how much paint to purchase. 
grandymaker [24]
PART A

The barn is constructed by the following 2D shapes

Two triangles of height = 4' and base = 20'
Area = 2 × (0.5×4×20) = 80

Two rectangles of length = 20' and width = 15'
Area = 2 × 20 × 15 = 600

Two rectangles of length = 45' and width = 15'
Area = 2 × 45' × 15' = 1350

One base of length = 45' and width = 15'
Area = 45 × 15 = 675

Two rectangles on each on one side of the roof. We have the length = 45'  but not the width. We can work out the width by using Pythagoras theorem

w² = 4² + 10²
w² = 16 + 100
w² = 116
w = √116 = 10.77

Area of the two rectangles on the roof part is = 2 ×10.77 × 45 = 969.33

Total area to paint = 969.33+675+1350+600+80 = 3674.33 ≈ 3700 (to the nearest hundreth)


PART B

Numbers of paint cans needed = 3700 ÷ 57 = 64.9 ≈ 65 cans

PART C

Total cost of paint = 65 × 23.50 = $1527.50

PART D

The barn is constructed by a cuboid and a rectangular prism

V of cuboid = length × width × height
V of cuboid = 20 × 45 × 15
V of cuboid = 13500

V of triangular prism = Area of cross section × depth
V = [0.5×4×20] × 45
V = 1800

Total volume = 1800 + 13500 = 15300


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| 9. The distance between Town A and Town B was 108 km. A car and a van left Town A at 12 00 for Town B. On reaching Town B, the
Westkost [7]

Answer:

a)  Time until both vehicles meet is 1.5 hours after starting at noon.  That makes it 1:30PM.

b)  Average speed of car is 84 km/h

Step-by-step explanation:

A -----------------------z------------B

          <u>Left</u>      <u>Speed(km/h)</u>      <u>Time</u>

Car:   12PM            X  

Van:   12PM           60

Car/Van

DistanceCar        AB + z

DistanceVan       Az

Ratio:                  (AB+z)/Az  = 7/5

Time until both meet = T (in hours)

Distance Car:            xT

Distance Van:           60T

====

  xT = AB + z

  60T = Az

---

(xT/60T)= (7/5)

x = 60(7/5)

x = 84 km/h

=====

Time for car to reach B is:    time (hr) = 108 km/(84 km/h)

                                                 time = 1.286 hours

Distance for at 1.289 hours is:    distance (km) = (60 km/h)*(1.286 h)

                                                   distance = 77.14 km

At 1.286 hours, the car reverses direction.  The van is (108 km - 77.14 km) or 30.86 km away.

Add the distances travelled by both vehicles after the car reverses direction at 1.286 hours.  The sum will be 30.86 km when they meet, at time of T.

Car Distance + Van Distance = 30.86 km

T(84 km/h) + t(60 km)

They meet when they are 0 km apart, which can be modeled with the following equation:

Van travel Distance - Car Travel Distance = 0 starting at 1.286 hr.

Let <u>t</u> be the time <u>after</u> 1.286 hours that both vehicles meet/collide.

t*(60 km/h)  +  t(84 km/h) = 30.86 km

t(60+84) = 30.86 km

t(144 km/h) = 30.86 km

t = 0.2143 hr

Total time until the car and van meet is 1.286 hr + 0.2143 hr for a total of 1.50 hours.

=================

a)  Time until both vehicles meet is 1.5 hours after starting at noon.  That makes it 1:30PM.

b)  Average speed of car is 84 km/h

==============

<u>CHECK</u>

Is the ratio of the distance travelled by the car and the van until they meet in the ratio of 7/5?

Car distance is (1.5 hr)(84 km/h) = 126 km

Van distance is (1.5 hr)(60 km/h) = 90.0 km

Ratio is 126/90 or 1.4

Ratio of 7/5 is 1.4

<u><em>YES</em></u>

     

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If the dimension increased by doubled, tripled or quadrupled, then it will be 2x, 3x, or 4x for each dimension.

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