Answer:
-
Step-by-step explanation:
Given
f(x) = -
Evaluate f(19) by substituting x = 19 into f(x)
f(19) = -
= -
= - 4
= - = -
Here is one way to solve for x.
Step 1) 2x^2-7=9
Step 2) 2x^2-7+7=9+7
Step 3) 2x^2=16
Step 4) (2x^2)/2=16/2
Step 5) x^2=8
Step 6) sqrt(x^2)=sqrt(8)
Step 7) |x|=sqrt(8)
Step 8) x=sqrt(8) or x=-sqrt(8)
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Below are explanations/reasons to each of the steps above.
Step 1) Original equation
Step 2) Add 7 to both sides
Step 3) Combine like terms
Step 4) Divide both sides by 2
Step 5) Simplify
Step 6) Apply the square root to both sides. The notation "sqrt" is shorthand for "square root"
Step 7) Use the rule that sqrt(x^2) = |x| for all real numbers x
Step 8) Use the rule that if |x| = k then x = k or x = -k for some fixed number k.
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The two solutions are
x = sqrt(8) or x = -sqrt(8)
Answer:
The answer to your question is 10240 mm³
Step-by-step explanation:
Data
length of the base = 32 mm
length of the height = 34 mm
Formula
Volume of a pyramid = 1/3 x Area of the base x length of the height
Process
1.- Calculate the area of the base
Area = side x side
= 32 x 32
= 1024 mm²
2.- Find the height of the pyramid using the Pythagorean theorem
height² = 34² - 16²
height² = 1156 - 256
height² = 900
height = 30
3.- Calculate the volume of the pyramid
Volume = 1/3Area x height
= 1/3(1024 x 30)
= (30720)/3 mm³
= 10240 mm³