Which angle measures create a triangle with three different side lengths?

Mathematics

1 answer:

kenny6666 [7]2 years ago

8 0

13°, 66°, and 101° ......

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Each problem is worth 10 points each. (For each problem show your work and give a brief explanation of how you solved your probl

maxonik [38]

It’s a big problem it’s deserve 20 points you can’t play people make it fair

5 0

2 years ago

How many solutions exist for the given equation?<br> 12x + 1 = 3(4x + 1) - 2

VladimirAG [237]

Answer:

Infinite

Step-by-step explanation:

3(4x + 1) - 2

= 12x + 3 - 2 (Multiply the sum in the bracket by 3)

= 12x + 1 (Simplify)

This means that:

12x + 1 = 3(4x + 1) - 2

is the same as

12x + 1 = 12x + 1

Hence, anything that is used to substitute x is correct.

4 0

3 years ago

. A right cylindrical drum is to hold 7.35 cubic feet of liquid. Find the dimensions (radius of the base and height) of the drum

Drupady [299]

Answer:

$r=1.05\ \text{ft}$

$h=2.12\ \text{ft}$

$20.91\ \text{ft}^3$

Step-by-step explanation:

r = Radius

h = Height

Volume of cylinder = $7.35\ \text{ft}^3$

$V=\pi r^2h\\\Rightarrow h=\dfrac{V}{\pi r^2}\\\Rightarrow h=\dfrac{7.35}{\pi r^2}$

Surface area is given by

$A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi r^2+2\pi r\dfrac{7.35}{\pi r^2}\\\Rightarrow A=2\pi r^2+\dfrac{14.7}{r}$

Differentiating with respect to radius we get

$\dfrac{dA}{dr}=4\pi r-\dfrac{14.7}{r^2}$

Equating with zero we get

$0=4\pi r-\dfrac{14.7}{r^2}\\\Rightarrow 4\pi r=\dfrac{14.7}{r^2}\\\Rightarrow r^3=\dfrac{14.7}{4\pi}\\\Rightarrow r=(\dfrac{14.7}{4\pi})^{\dfrac{1}{3}}\\\Rightarrow r=1.05$

$\dfrac{d^2A}{dr^2}=4\pi-2\times \dfrac{14.7}{r^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=4\pi+2\times \dfrac{14.7}{1.05^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=37.96>0$