30.1 divided by 1.75= 17.2, since this means we can make 17.2 ribbons that length we round down so 17 ribbons that full length can be made.
Volume of the cone is 17 cm³
Step-by-step explanation:
- Step 1: Volume of a cone = 1/3 πr²h. Find volume of the cone where r = 2 inches and h = 4 cm.
Volume = 1/3 × 3.14 × 2² × 4
= 16.75 cm³ ≈ 17 cm³ (rounding off to nearest whole number)
Answer:
x=9
Step-by-step explanation:
Answer:
y=-1/4x-6
Step-by-step explanation:
The problem wants the form y=mx+b where m is the slope and b is the y-intercept.
The y-intercept in this case is -6 (where the line intercepts the y-axis).
We can use points (0,-6) and (4,-7) to calculate the slope. We just divide the difference in y-values by the difference in x-values.
-6-(-7)/0-4=-6+7/-4=1/-4=-1/4
So the equation of the line is y=-1/4x-6
Answer:
The real roots are
and ![x=\frac{(-3-\sqrt{37})}{4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%28-3-%5Csqrt%7B37%7D%29%7D%7B4%7D)
The sum of the squares of these roots is ![\frac{-3}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B-3%7D%7B2%7D)
Step-by-step explanation:
The given quadratic equation is
has two real roots.
To find the roots .
![8x^2+12x-14=0](https://tex.z-dn.net/?f=8x%5E2%2B12x-14%3D0)
Dividing the above equation by 2
![\frac{1}{2}(8x^2+12x-14)=\frac{0}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%288x%5E2%2B12x-14%29%3D%5Cfrac%7B0%7D%7B2%7D)
![4x^2+6x-7=0](https://tex.z-dn.net/?f=4x%5E2%2B6x-7%3D0)
For quadratic equation
the solution is ![x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
Where a and b are coefficents of
and x respectively, c is a constant.
For given quadratic equation
a=4, b=6, c=-7
![x=\frac{-6\pm\sqrt{6^2-4(4)(-7)}}{2(4)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-6%5Cpm%5Csqrt%7B6%5E2-4%284%29%28-7%29%7D%7D%7B2%284%29%7D)
![=\frac{-6\pm\sqrt{36+112}}{8}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B-6%5Cpm%5Csqrt%7B36%2B112%7D%7D%7B8%7D)
![=\frac{-6\pm\sqrt{148}}{8}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B-6%5Cpm%5Csqrt%7B148%7D%7D%7B8%7D)
![=\frac{-6\pm\sqrt{37\times 4}}{8}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B-6%5Cpm%5Csqrt%7B37%5Ctimes%204%7D%7D%7B8%7D)
![=\frac{-6\pm\sqrt{37}\times\sqrt{4}}{8}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B-6%5Cpm%5Csqrt%7B37%7D%5Ctimes%5Csqrt%7B4%7D%7D%7B8%7D)
![=\frac{-6\pm\sqrt{37}\times 2}{8}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B-6%5Cpm%5Csqrt%7B37%7D%5Ctimes%202%7D%7B8%7D)
![=2\frac{(-3\pm\sqrt{37})}{8}](https://tex.z-dn.net/?f=%3D2%5Cfrac%7B%28-3%5Cpm%5Csqrt%7B37%7D%29%7D%7B8%7D)
![=\frac{-3\pm\sqrt{37}}{4}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B-3%5Cpm%5Csqrt%7B37%7D%7D%7B4%7D)
![x=\frac{(-3\pm\sqrt{37})}{4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%28-3%5Cpm%5Csqrt%7B37%7D%29%7D%7B4%7D)
The real roots are
and ![x=\frac{(-3-\sqrt{37})}{4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%28-3-%5Csqrt%7B37%7D%29%7D%7B4%7D)
Now to find the sum of the squares of these roots
![\left[\frac{-3+\sqrt{37}}{4}+\frac{(-3-\sqrt{37})}{4}\right]^2=\frac{-3+\sqrt{37}-3-\sqrt{37}}{4}](https://tex.z-dn.net/?f=%5Cleft%5B%5Cfrac%7B-3%2B%5Csqrt%7B37%7D%7D%7B4%7D%2B%5Cfrac%7B%28-3-%5Csqrt%7B37%7D%29%7D%7B4%7D%5Cright%5D%5E2%3D%5Cfrac%7B-3%2B%5Csqrt%7B37%7D-3-%5Csqrt%7B37%7D%7D%7B4%7D)
![=\frac{-6}{4}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B-6%7D%7B4%7D)
![=\frac{-3}{2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B-3%7D%7B2%7D)
![\left[\frac{-3+\sqrt{37}}{4}+\frac{(-3-\sqrt{37})}{4}\right]^2=\frac{-3}{2}](https://tex.z-dn.net/?f=%5Cleft%5B%5Cfrac%7B-3%2B%5Csqrt%7B37%7D%7D%7B4%7D%2B%5Cfrac%7B%28-3-%5Csqrt%7B37%7D%29%7D%7B4%7D%5Cright%5D%5E2%3D%5Cfrac%7B-3%7D%7B2%7D)
Therefore the sum of the squares of these roots is ![\frac{-3}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B-3%7D%7B2%7D)