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tamaranim1 [39]
3 years ago
9

Find the perimeter of a rectangle whose length is 15 cm and length of one diagonal is 17cm

Mathematics
1 answer:
Ulleksa [173]3 years ago
6 0

Answer:

<h2>46 cm</h2>

Step-by-step explanation:

first ,we use the Pythagorean theorem to determine the width:

width = √(17^2-15^2) = 8

then

perimeter = 2(width+lengt) = 2(8 + 15) = 2×23 = 46

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PLEASE HELP A flight across the US takes longer east to west then it does west to east. This is due to the plane having a headwi
il63 [147K]
To solve our questions, we are going to use the kinematic equation for distance: d=vt
where
d is distance 
v is speed  
t is time 

1. Let v_{w} be the speed of the wind, t_{w} be time of the westward trip, and t_{e} the time of the eastward trip. We know from our problem that the distance between the cities is 2,400 miles, so d=2400. We also know that the speed of the plane is 450 mi/hr, so v=450. Now we can use our equation the relate the unknown quantities with the quantities that we know:

<span>Going westward:
The plane is flying against the wind, so we need to subtract the speed of the wind form the speed of the plane:
</span>d=vt
2400=(450-v_{w})t_{w}

Going eastward:
The plane is flying with the wind, so we need to add the speed of the wind to the speed of the plane:
d=vt
2400=(450+v_{w})t_{e}

We can conclude that you should complete the chart as follows:
Going westward -Distance: 2400 Rate:450-v_w Time:t_w
Going eastward -Distance: 2400 Rate:450+v_w Time:t_e

2. Notice that we already have to equations:
Going westward: 2400=(450-v_{w})t_{w} equation(1)
Going eastward: 2400=(450+v_{w})t_{e} equation (2)

Let t_{t} be the time of the round trip. We know from our problem that the round trip takes 11 hours, so t_{t}=11, but we also know that the time round trip is the time of the westward trip plus the time of the eastward trip, so t_{t}=t_w+t_e. Using this equation we can express t_w in terms of t_e:
t_{t}=t_w+t_e
11=t_w+t_e equation
t_w=11-t_e equation (3)
Now, we can replace equation (3) in equation (1) to create a system of equations with two unknowns: 
2400=(450-v_{w})t_{w}
2400=(450-v_{w})(11-t_e) 

We can conclude that the system of equations that represent the situation if the round trip takes 11 hours is:
2400=(450-v_{w})(11-t_e) equation (1)
2400=(450+v_{w})t_{e} equation (2)

3. Lets solve our system of equations to find the speed of the wind: 
2400=(450-v_{w})(11-t_e) equation (1)
2400=(450+v_{w})t_{e} equation (2)

Step 1. Solve for t_{e} in equation (2)
2400=(450+v_{w})t_{e}
t_{e}= \frac{2400}{450+v_{w}} equation (3)

Step 2. Replace equation (3) in equation (1) and solve for v_w:
2400=(450-v_{w})(11-t_e)
2400=(450-v_{w})(11-\frac{2400}{450+v_{w}} )
2400=(450-v_{w})( \frac{4950+11v_w-2400}{450+v_{w}} )
2400=(450-v_{w})( \frac{255011v_w}{450+v_{w}} )
2400= \frac{1147500+4950v_w-2550v_w-11(v_w)^2}{450+v_{w}}
2400(450+v_{w})=1147500+2400v_w-11(v_w)^2
1080000+2400v_w=1147500+2400v_w-11(v_w)^2
(11v_w)^2-67500=0
11(v_w)^2=67500
(v_w)^2= \frac{67500}{11}
v_w= \sqrt{\frac{67500}{11}}
v_w=78

We can conclude that the speed of the wind is 78 mi/hr.
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A circular pond is to be surrounded by a gravel path. Use the diagram to find the square feet of gravel needed if we know the po
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2 years ago
Which could be the dimensions of a rectangular prism to service area is less than 160 ft.² check all that apply
raketka [301]

Area of rectangular prism is given by:

A=2(wl+hl+lw)

where w=width h=height, l=length

checking for given options

1. 8 ft, by 4ft by 3ft

Area = 136 square feet

5. 3 feet by 5 feet by 7 feet

Area =142 square feet

so our first and last option matches the requirement of area less than 160 square feet.

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3 years ago
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Greatest common factor <br>3a^3+9a^2​
BaLLatris [955]

Answer:

27A+81A =108

Step-by-step explanation:

7 0
2 years ago
A tv costs £800. Work out the price after a 3% discount.
Blababa [14]

3% = 800/ 100 = 8, 8x3= 24

800-24 = 776

£776

5 0
2 years ago
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