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nexus9112 [7]
3 years ago
13

Can you please help me solve for the area

Mathematics
1 answer:
ycow [4]3 years ago
8 0

Answer:

area is equal to 198 cm^2

Step-by-step explanation:

the height h of the left triangle can be obtained by

Pytagoras theorem:

5^2+h^2=13^2\\25+h^2=169\\h^2=169-25\\h^2=144\\h=\sqrt{144} \\h=12

the, the area of the left triangle is

A_1=\frac{5*12}{2} \\A_1=5*6\\A_1=30

the area of the right triangle is

A_2=\frac{2*12}{2} \\A_2=12

and the area of the rectangle in the middle is

A_3=(13)(12)\\A_3=156

Por tanto, el area total sera

A=A_1+A_2+A_3\\A=30+12+156\\A=198

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Answer:

Austin will have to buy 180 squares of carpeting.

Step-by-step explanation:

First find the dimension of the room. We do that by multiplying the width times the length and then subtracting the cut out region in the top right. And, in order to know how big that region we cut out is, we have to do a little subtraction.

We know the room is 18' long on the left side and 12' long on the right side. We subtract 12 from 18 to get 6, and we know that the cut out region is 6' long. We do the same thing with the width, 25' wide at the bottom minus 10' wide at the top and we see that the cut out is 15' wide.

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3 years ago
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Answer:

The value of x at this instant is 3.

Step-by-step explanation:

Let x\cdot y = 18, we get an additional equation by implicit differentiation:

x\cdot \frac{dy}{dt}+y\cdot \frac{dx}{dt} = 0 (1)

From the first equation we find that:

x = \frac{18}{y} (2)

By applying (2) in (1), we get the resulting expression:

\frac{18}{y}\cdot \frac{dy}{dt}+y\cdot \frac{dx}{dt} = 0 (3)

y\cdot \frac{dx}{dt}=-\frac{18}{y}\cdot \frac{dy}{dt}

\frac{dx}{dt} = -\frac{18}{y^{2}} \cdot \frac{dy}{dt}

If we know that y = 6 and \frac{dy}{dt} = 8, then the first derivative of x in time is:

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From (1) we determine the value of x at this instant:

x\cdot \frac{dy}{dt} = -y\cdot \frac{dx}{dt}

x = -y\cdot \left(\frac{\frac{dx}{dt} }{\frac{dy}{dt} } \right)

x = -6\cdot \left(\frac{-4}{8} \right)

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The value of x at this instant is 3.

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3 years ago
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