Answer:
a=9
Step-by-step explanation:
a^2+b^2=c^2
a^2+5.6^2=10.6^2
a^2+ 31.36=112.36
-31.36 -31.36
a^2=81
a=![\sqrt{81}](https://tex.z-dn.net/?f=%5Csqrt%7B81%7D)
a=9
The total surface area of the given pyramid is:
A = 39ft²
<h3>
How to get the surface area of the given figure?</h3>
The total surface area will be equal to the sum of the areas of the square and the 4 triangles.
Remember that for a square of side length S, the area is:
A = S².
In this case, S = 3ft, then:
A = (3ft)² = 9ft².
Now, the area of a triangle of base B and height H is:
A = B*H/2.
Here we can see that the triangles have a base of 3ft (the sides of the square) and a height of 5ft, then the area of each triangle is:
A = (3ft)*(5ft)/2 = 7.5 ft²
Then the total area of the figure is:
A = 4*(7.5 ft²) + 9ft² = 39ft²
If you want to learn more about pyramids:
brainly.com/question/10042135
#SPJ1
Answer:
3. - 9/8
4. 9/26
Step-by-step explanation:
Let x ft be the length of the base square and y ft be the height of the box.
The volume of the box is
![V=x\cdot x\cdot y\ ft^3.](https://tex.z-dn.net/?f=V%3Dx%5Ccdot%20x%5Ccdot%20y%5C%20ft%5E3.)
Since the box has a volume of 15 cubic feet, then
![x^2y=15,\\ \\y=\dfrac{15}{x^2}.](https://tex.z-dn.net/?f=x%5E2y%3D15%2C%5C%5C%20%5C%5Cy%3D%5Cdfrac%7B15%7D%7Bx%5E2%7D.)
You need to construct two squares from the metal that cost $3 per square foot.
The area of each square is
and the total cost for these two squares is ![2\cdot x^2\cdot 3=6x^2.](https://tex.z-dn.net/?f=2%5Ccdot%20x%5E2%5Ccdot%203%3D6x%5E2.)
The area of each side face is
Then the total cost for sides is ![4\cdot \dfrac{15}{x}\cdot 10=\dfrac{600}{x}.](https://tex.z-dn.net/?f=4%5Ccdot%20%5Cdfrac%7B15%7D%7Bx%7D%5Ccdot%2010%3D%5Cdfrac%7B600%7D%7Bx%7D.)
Let S(x) be the function that represents total cost of the box, then
![S(x)=6x^2+\dfrac{600}{x}.](https://tex.z-dn.net/?f=S%28x%29%3D6x%5E2%2B%5Cdfrac%7B600%7D%7Bx%7D.)
Find the derivative:
![S'(x)=12x-\dfrac{600}{x^2}.](https://tex.z-dn.net/?f=S%27%28x%29%3D12x-%5Cdfrac%7B600%7D%7Bx%5E2%7D.)
When
then ![12x-\dfrac{600}{x^2}=0,\\ \\12x^3=600,\\ \\x^3=50,\\ \\x=\sqrt[3]{50}\ ft.](https://tex.z-dn.net/?f=12x-%5Cdfrac%7B600%7D%7Bx%5E2%7D%3D0%2C%5C%5C%20%5C%5C12x%5E3%3D600%2C%5C%5C%20%5C%5Cx%5E3%3D50%2C%5C%5C%20%5C%5Cx%3D%5Csqrt%5B3%5D%7B50%7D%5C%20ft.)
The dimensions of the box are:
length and width - ![\sqrt[3]{50}\ ft](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B50%7D%5C%20ft)
height - ![\dfrac{15}{\sqrt[3]{2500}}\ ft.](https://tex.z-dn.net/?f=%5Cdfrac%7B15%7D%7B%5Csqrt%5B3%5D%7B2500%7D%7D%5C%20ft.)