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3 years ago

4. If the sides of a square measure 9V3 units, then find the length of the diagonal.

Mathematics

1 answer:

Nitella [24]3 years ago

7 0

Answer:

Step-by-step explanation:

To find the diagonal, use Pythagorean theorem,

diagonal² = side² + side²

= (9√3)² + (9√3)²

= 9²(√3)² + 9²(√3)²

= 81*3 + 81*3

= 243 + 243

= 486

diagonal = √486 = 22.05 units

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Shaan walks 2.5 meters per second. His brother Dhvan walks 1 meter

MissTica

Answer:

The race must be up to 29 meters for Dhvan to win.

Step-by-step explanation:

Since Shaan walks 2.5 meters per second, while his brother Dhvan walks 1 meter per second, and Dhvan wants to have a race, and Shaan knows that he walks faster, but he wants to give his brother a head start of 45 meters, so it doesn't seem that he is allowing him to win, to determine how many meters long should the race be in order for Dhvan to win the following calculation must be performed:

45 / (2.5 - 1) = X

45 / 1.5 = X

30 = X

Therefore, the race must be up to 29 meters for Dhvan to win.

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Find a formula for the described function. A rectangle has perimeter 16 m. Express the area A of the rectangle as a function of

Alex17521 [72]

Part A:

Let the length of one of the sides of the rectangle be L, then the length of the other side is obtained as follow.

Let the length of the other side be x, then

$2(L+x)=16 \\ \\ \Rightarrow L+x=8 \\ \\ \Rightarrow x=8-L$

Thus, if the length of one of the side is x, the length of the other side is 8 - L.

Hence, the area of the rectangle in terms of L is given by

$L(8 - L) = 8L-L^2$

Part B:

To find the domain of A

Recall that the domain of a function is the set of values which can be assumed by the independent variable. In this case, the domain is the set of values that L can take.

Notice that the length of a side of a rectangle cannot be negative or 0, thus L cannot be 8 as 8 - 8 = 0 or any number greater than 8.

Hence the domain of the area are the set of values between 0 and 8 not inclusive.

Therefore,

$dom(Area)=0\ \textless \ L\ \textless \ 8 \ or \ (0, 8)$

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