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Zolol [24]
3 years ago
14

4.Find the length of the diagonal of a rectangle having dimensions 16 cm and 12 cm.

Mathematics
2 answers:
nignag [31]3 years ago
7 0

Answer:

20 cm

Step-by-step explanation:

So from the problem we get that the two sides of the rctangle are 16 cm 12 cm which are base perpendicular of the right angle triangle. H = 20 cm. So the diagonal of the rectangle = 20 cm.

stiks02 [169]3 years ago
7 0

Answer:

20 cm

Step-by-step explanation:

<em>Here's</em><em> your</em><em> solution</em>

<em> </em><em> </em><em> </em><em> </em><em>=</em>> length of rectangle = 16 cm

=> width of rectangle = 12 cm

=> Diagonal of rectangle = √(l^2 + w^2 )

=> Diagonal = √(16^2 + 12^2)

=> Diagonal = √(256 + 144)

=>. Diagonal = √400

=> Diagonal = 20 cm

hope it helps

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A police helicopter is flying at 150 mph at a constant altitude of 0.5 mile above a straight road. The pilot uses radar to deter
natali 33 [55]

Answer:

a) (see attached picture)

b) d, h, velocity of helicopter, dd/dt

in the direction oposite to the movement of the helicopter.

Step-by-step explanation:

In order to solve this problem we must start by drawing a diagram that will represent the situation (see attached picture). As you may see, there is a right triangle being formed by the helicopter, the car and the graound. We can use this to build the equation we are going to use to model the problem.

d^{2}=h^{2}+x^{2}

we can use this equation to find the value of x at that very time, so we can do that by solving the equation for x, so we get:

x=\sqrt{d^{2}-h^{2}}

and substitute the given values:

x=\sqrt{(1)^{2}-(0.5)^{2}}

which yields:

x=0.866mi

we know that the height of the helicopter is going to be constant, so we rewrite the equation as:

d^{2}=(0.5)^{2}+x^{2}

d^{2}=0.25+x^{2}

Next, we can go ahead and differentiate the equation so we get:

2d\frac{dd}{dt}=2x\frac{dx}{dt}

which can be simplified to:

d\frac{dd}{dt}=x\frac{dx}{dt}

we can next solve the equation for dx/dt so we get:

\frac{dx}{dt}=\frac{d}{x}*\frac{dd}{dt}

so we can now substitue te provided values so we get:

\frac{dx}{dt}=\frac{1}{0.866}*-190

so we get:

\frac{dx}{dt}=-219.40mph

the negative sign means that the x-value is decreasing.

now, this problem deals with relative velocities, so we get that:

Velocity of car about the helicopter = Velocity of the car - Velocity of the helicopter. Or:

V_{ch}=V_{c}-V_{h}

so we can solve this for the actual velocity of the car, so we get:

V_{c}=V_{ch}+V_{h}

so we get:

V_{c}=-219.40mph+150mph

which yields:

V_{c}=-69.4mph

So it has a velocity of 69.4mph in a direction oposite to the helicopter's movement.

4 0
3 years ago
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