How many unique triangles can be drawn with given side lengths of 8 inches,10.3 inches,and 13 inches?

Mathematics

1 answer:

goldfiish [28.3K]3 years ago

3 0

Answer:

3 unique triangles

Step-by-step explanation:

If you use the Triangle Inequality Theorem, it states that the sum of 2 sides of the triangle would equal more than the third side. So three triangles can be made with those side lengths.

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The side of the base of a square prism is decreasing at a rate of 7 kilometers per minute and the height of the prism is increas

Ber [7]

Answer:

dV = - 5.73*10⁹ m³/s

Step-by-step explanation:

Question: What is the rate of change of the volume of the prism at that instant (in cubic meters per second) ?

A function can be dependent on one or more variables. The change in the function due to a change in one o its variables is given by the functions derivative with respect to that variable. For functions that are composed of products of its variables, we may use the product rule to determine its derivative.

The volume of a square prism with base a and height h is given by

V = a²h

When the base and height are changing, we have

dV = 2ah(da/dt) + a²(dh/dt)

Given

a = 4 Km

h = 9 Km

da/dt = - 7 Km/min

dh/dt = 10 Km/min

we have

dV = 2(4 Km)(9 Km)(- 7 Km/min) + (4 Km)²(10 Km/min)

⇒ dV = - 504 Km³/min + 160 Km³/min = - 344 Km³/min