Step-by-step explanation:
From Trig
1 + tan²x = Sec²x
Also
Sec²x = 1/cos²x
Now
Cot²x = 1/tan²x = cos²x/sin²x
Putting all together
Cot²x(1+tan²x)
= Cot²x(sec²x)
= cos²x/sin²x(1/cos²x)
cos²x on the numerator and that one the denominator cancels out
we have
= 1/sin²x
From Trig
1/sin²x = cosec²x
So Our Answer = cosec²x.
Answer:
i think the answer is b
Step-by-step explanation:
Answer:
The height of the tent = 3 feet
Step-by-step explanation:
Syrus is buying a tent with the dimensions shown below. The volume inside the tent is 36 feet^3. Syrus isn't sure if the tent will be tall enough for him to sit up inside. The tent is the shape of triangular prism whose length is 6 feet and width is 4 feet. What is the height of the tent?
Given:
Length of the tent = 6 feet
Width of the tent = 4 feet
Volume of the tent = 36
Solution:
Since the ten is in shape of triangular prism, so the volume of traingular prism is given as:
where represents length, represents width and represents height of the prism.
Plugging in the know values of the dimension of the tent and the volume to find the height of the tent.
Simplifying.
\frac{36}{12}=\frac{12h}{12}
3=h
∴ h=3
Thus, the height of the tent = 3 feet
Answer:
Equation for the perimeter of prism's square face: 16x + 12
Step-by-step explanation:
Volume of Square prism = Length * Width * Height
= 144 x^3 + 216 x^2 +81 x
taking 9x common = 9x( 16 x^2 + 24 x + 9)
= 9x ( (4x)^2 + 2(4x)(3) + (3)^2 )
= 9x ( 4x+3)^2
so the length is 9x, width is 4x+3 and height is 4x+3
Now, Perimeter of prism's square face = 2* Width + 2 * Height
= 2* (4x+3) + 2* (4x+3)
= 8x +6 + 8x + 6
= 16x +12
Answer:
5
Step-by-step explanation:
