Answer: 0.77
Step-by-step explanation:
Answer:14 cubic units
Step-by-step explanation:
Answer:
7, 24, 26
Step-by-step explanation:
6 squared is 36 and 8 squared is 64. Add them together and you get 100, which is 10 squared. Do the same for the other ones and you'll notice that 7 squared and 24 squared added together is 625, which is not 26 squared. In my head 25 squared is 625(check if you don't believe me) so I know that the answer is the third one. The basic formula for a right triangle is a^2 + b^2 = c^2, and that's how you find if three numbers form a right triangle or not. Hope this helps :)
The image of the triangle RST when rotated 90° counterclockwise around the origin is (-15,5), (-15,15) and (-5,10)
<h3>
How to rotate the triangle?</h3>
The coordinates of RST are given as:
R = (5,15)
S = (15,15)
T = (10,5)
The rule of 90° counterclockwise around the origin is:
(x,y) -> (-y,x)
So, we have:
R' = (-15,5)
S' = (-15,15)
T' = (-5,10)
Hence, the image of the triangle when rotated 90° counterclockwise around the origin is (-15,5), (-15,15) and (-5,10)
Read more about rotation at:
brainly.com/question/4289712
#SPJ1
Answer:
![A_{f}=4\pi (\sqrt[3]{36} r)^{2}\\\\V_{f}=\frac{4}{3} \pi (36r^{3})](https://tex.z-dn.net/?f=A_%7Bf%7D%3D4%5Cpi%20%28%5Csqrt%5B3%5D%7B36%7D%20r%29%5E%7B2%7D%5C%5C%5C%5CV_%7Bf%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%2836r%5E%7B3%7D%29)
Step-by-step explanation:
In order to find the final radii of the sphere, we need to calculate the volume, knowing that volumes are additive:
![V_{1}=\frac{4}{3} \pi (r^{3})\\\\V_{2}=\frac{4}{3} \pi (2r)^{3}\\\\V_{3}=\frac{4}{3} \pi (3r)^{3}\\\\V_{f}=\frac{4}{3} \pi (r^{3}+(2r)^{3}+(3r)^{3})\\\\V_{f}=\frac{4}{3} \pi (r^{3}+8r^{3}+27r^{3})\\\\V_{f}=\frac{4}{3} \pi (36r^{3})\\\\V_{f}=\frac{4}{3} \pi R^{3}\\\\R=\sqrt[3]{36} r](https://tex.z-dn.net/?f=V_%7B1%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%28r%5E%7B3%7D%29%5C%5C%5C%5CV_%7B2%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%282r%29%5E%7B3%7D%5C%5C%5C%5CV_%7B3%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%283r%29%5E%7B3%7D%5C%5C%5C%5CV_%7Bf%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%28r%5E%7B3%7D%2B%282r%29%5E%7B3%7D%2B%283r%29%5E%7B3%7D%29%5C%5C%5C%5CV_%7Bf%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%28r%5E%7B3%7D%2B8r%5E%7B3%7D%2B27r%5E%7B3%7D%29%5C%5C%5C%5CV_%7Bf%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%2836r%5E%7B3%7D%29%5C%5C%5C%5CV_%7Bf%7D%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20R%5E%7B3%7D%5C%5C%5C%5CR%3D%5Csqrt%5B3%5D%7B36%7D%20r)
Now that we know the radii of the new sphere, we can calculate the surface area:
![A_{f}=4\pi R^{2}\\\\A_{f}=4\pi (\sqrt[3]{36} r)^{2}](https://tex.z-dn.net/?f=A_%7Bf%7D%3D4%5Cpi%20R%5E%7B2%7D%5C%5C%5C%5CA_%7Bf%7D%3D4%5Cpi%20%28%5Csqrt%5B3%5D%7B36%7D%20r%29%5E%7B2%7D)
