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Brums [2.3K]
1 year ago
10

Tyler has a rectangular garden measuring 12m by 20m that he wants to split diagonally from corner to corner using a fence. How l

ong does his fence need to be? Round your answer to the nearest tenth.
Mathematics
2 answers:
VARVARA [1.3K]1 year ago
8 0

Answer:

Length of diagonal of the rectangle=

√( length) ²+( breadth) ²

=√(20) ²+(12) ²

=√400+144

√544 m

. '. Length of fence= √544 m

Perimeter of the triangle formed by the diagonal of the rectangle =(12+20+√544)

=(32+√544) m

Sergeeva-Olga [200]1 year ago
5 0

Answer:

23.32 m to the nearest hundredth.

Step-by-step explanation:

Use the Pythagoras theorem:

The diagonal is the hypotenuse of the right angled triangles formed.

x^2 = 12^2 + 20^2

x^2 = 544

x = 23.32 m.

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Answer:

11 km/hr.

Step-by-step explanation:

Given information:

Simulated speed = 20/km/h

Time = 15 mins = 1/4 hr = 0.25 hr

Distance Covered as per simulated speed = 20\times \frac{1}{4}=5km

Position of Julian according to the app = -2\frac{1}{4}=-2.25.

Actual distance covered by the bike is

Distance= 5 - 2.25 = 2.75km

Formula for speed:

\text{Average Speed}=\frac{Distance}{Time}

\text{Average Speed}=\frac{2.75}{0.25}

\text{Average Speed}=11

Therefore, the average speed of Julian is 11 km/hr.

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2 years ago
A 120 watt light bulb uses about 0.1 kilowatt of electricity per hour.if electricity costs $0.20 per kilowatt hour how much does
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A 120 watt light bulb uses about 0.1 kilowatt of electricity per hour.if electricity costs $0.20 per kilowatt hour. Let's solve how much does it cost to have a bulb on for an hour. => 120 watt = 0.1 kilowatt per hour which costs 0.20 per kilowatt per => 0.1 kilowatt per hour * 0.20 = 0.02 dollars in an hour.
8 0
1 year ago
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use the drop-down menus to describe the key aspects of the function f(x) = –x2 – 2x – 1. the vertex is the . the function is inc
timurjin [86]

Answer:

The vertex of the parabola is the maximum value, i.e.,(-1,0). The function is increasing x<-1. the function is decreasing x>-1. the domain of the function is all real numbers. the range of the function is all real numbers less than or equal to 0.

Step-by-step explanation:

The given function is

f(x)=-x^2-2x-1

f(x)=-[x^2+2x+1]

f(x)=-(x+1)^2                 ....(1)

The general vertex form of the parabola is

f(x)=a(x-h)^2+k           .....(2)

Where, (h,k) is vertex and a is stretch factor.

On comparing (1) and (2), we get

a=-1

h=-1

k=0

The vertex of the parabola is (-1,0). Since a=-1<1 so it is a downward parabola.

The axis of symmetry is x=-1. So, before -1 the function is increasing and after -1 the function is decreasing.

The vertex of a downward parabola is the point of maxima. So, the rang of the function can not exceed 0.

Therefore the vertex of the parabola is the maximum value, i.e.,(-1,0). The function is increasing x<-1. the function is decreasing x>-1. the domain of the function is all real numbers. the range of the function is all real numbers less than or equal to 0.

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2 years ago
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A sailboat is sitting at rest near its dock. A rope attached to the bow of the boat is drawn in over a pulley that stands on a p
irina [24]

Answer:

The boat is approaching the dock at rate of 2.14 ft/s

Step-by-step explanation:

The situation given in the question can be modeled as a triangle, please refer to the attached diagram.

A rope attached to the bow of the boat is drawn in over a pulley that stands on a post on the end of the dock that is 5 feet higher than the bow that means x = 5 ft.

The length of rope from bow to pulley is 13 feet that means y = 13 ft.

We know that Pythagorean theorem is given by

x^{2} + y^{2} = z^{2}

Differentiating the above equation with respect to time yields,

2x\frac{dx}{dt}  + 2y\frac{dy}{dt} = 2z\frac{dz}{dt}

x\frac{dx}{dt}  + y\frac{dy}{dt} = z\frac{dz}{dt}

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y\frac{dy}{dt} = z\frac{dz}{dt}

\frac{dy}{dt} = \frac{z}{y} \frac{dz}{dt}

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First we need to find z

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\frac{dy}{dt} = \frac{z}{y} \frac{dz}{dt}

\frac{dy}{dt} = \frac{13.93}{13}(2)

\frac{dy}{dt} = 2.14 ft/s

Therefore, the boat is approaching the dock at rate of 2.14 ft/s

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