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docker41 [41]
3 years ago
14

A square pyramid with a height of 7 inches has a volume of 47.25 cubic inches. Find the side length of the square base.

Mathematics
1 answer:
Romashka [77]3 years ago
5 0

Answer:

4.5 inches

Step-by-step explanation:

volume= 1/3 (base area) × height

47.25= 1/3 ( base area) × 7

20.25 = base area

now since the base is a square we can evaluate base area = length²

20.25= length²

length = 4.5 inches

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Aleksandr [31]
There is 8 fluid oz in a cup. To figure out how many fluid oz are in 5 cups we multiply 5 by 8. 5*8=40 . Therefore, there are 40 fluid oz in 5 cups. 

Therefore, 5 cups is the same as 40 fluid oz, not greather than it.
8 0
2 years ago
When would a set of data be described as variable?
valina [46]
I guess when the data isn't consitant

8 0
3 years ago
(a)5%)Let fx, y) = x^4 + y^4 - 4xy + 1. and classify each critical point Find all critical points of fx,y) as a local minimum, l
lara31 [8.8K]

f(x,y)=x^4+y^4-4xy+1

has critical points wherever the partial derivatives vanish:

f_x=4x^3-4y=0\implies x^3=y

f_y=4y^3-4x=0\implies y^3=x

Then

x^3=y\implies x^9=x\implies x(x^8-1)=0\implies x=0\text{ or }x=\pm1

  • If x=0, then y=0; critical point at (0, 0)
  • If x=1, then y=1; critical point at (1, 1)
  • If x=-1, then y=-1; critical point at (-1, -1)

f(x,y) has Hessian matrix

H(x,y)=\begin{bmatrix}12x^2&-4\\-4&12y^2\end{bmatrix}

with determinant

\det H(x,y)=144x^2y^2-16

  • At (0, 0), the Hessian determinant is -16, which indicates a saddle point.
  • At (1, 1), the determinant is 128, and f_{xx}(1,1)=12, which indicates a local minimum.
  • At (-1, -1), the determinant is again 128, and f_{xx}(-1,-1)=12, which indicates another local minimum.
4 0
3 years ago
Which answers are examples of deductive reasoning?<br><br> Select each correct answer.
sergejj [24]
Why didn’t you put the answer choices down below ?
7 0
3 years ago
Sissy wants to enlarge a picture of a princess so that she can put it on the wall in her daughter’s room. What will be the area
alisha [4.7K]

Answer:

= 486 in²

Step-by-step explanation:

Linear scale factor = Image distance/object distance

Therefore; Linear scale factor = OL'/OL

                                                 = 54/ 12

                                                 = 9/2

Area scale factor is equivalent to the square of linear scale factor

Thus;

Area scale factor = (9/2)²

                             = 81/4

Hence; 81/4 = Area of larger rectangle/Area of smaller rectangle

Area of the smaller rectangle = 4 ×6 = 24 in²

Therefore;

Area of enlarged or larger pic = 81/4× 24

                                                  <u>= 486 in²</u>

3 0
3 years ago
Read 2 more answers
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