A scale drawing of Julie's living room is shown below:

Mathematics

1 answer:

stealth61 [152]3 years ago

4 0

Answer:

length = 16 feet

width = 12 feet

Step-by-step explanation:

divide the length and width by 2 so you get 3 and 4. then you proceed to Multiply both by 4 and you get 12 and 16

6÷2 = 3

8÷2 = 4

3x4= 12

4x4 = 16

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Jake sold 36 tickets to the school fair, and Jeanne sold 15 tickets. what is the ratio, in simpliest form, to the number of tick

anzhelika [568]

Answer:

I kinda forgot how to do ratios but i think it would be 12 and 5

Step-by-step explanation

Jake Jeanne

36 15

12 5

8 0

3 years ago

A profit of a football club after a takeover is modeled by p(t) = t3 - 14t2 + 20t + 120, which t is the number of years after th

Bogdan [553]

T = 5, so after 5 years
p(t) = t^3 - 14t^2 + 20t + 120

Take derivative to find minimum:
p’(t) = 3t^2 - 28t + 10

Factor to solve for t:
p’(t) = (3t - 2)(t - 5)
0 = (3t - 2)(t - 5)

0 = 3t - 2
2 = 3t
2/3 = t

Plug 2/3 into original equation, this is a maximum. We want the minimum:

0 = t - 5
5 = t

Plug back into original:
5^3 - 14(5)^2 + 20(5) + 120
125 - 14(25) + 100 + 120
125 - 350 + 220
- 225 + 220
p(5) = -5

6 0

3 years ago

Find two unit vectors orthogonal to both given vectors. i j k, 4i k

Maurinko [17]

The cross product of two vectors gives a third vector $\mathbf v$ that is orthogonal to the first two.

$\mathbf v=(\vec i+\vec j+\vec k)\times(4\,\vec i+\vec k)=\begin{vmatrix}\vec i&\vec j&\vec k\\1&1&1\\4&0&1\end{vmatrix}=\vec i+3\,\vec j-4\,\vec k$

Normalize this vector by dividing it by its norm:

$\dfrac{\mathbf v}{\|\mathbf v\|}=\dfrac{\vec i+3\,\vec j-4\,\vec k}{\sqrt{1^2+3^2+(-4)^2}}=\dfrac1{\sqrt{26}}(\vec i+3\,\vec j-4\vec k)$

To get another vector orthogonal to the first two, you can just change the sign and use $-\mathbf v$ .