9514 1404 393
Answer:
4. 1.3 cm³
5. 621.2 mm³
6. 116.5 m³
Step-by-step explanation:
The height to the peak of the pyramid is one side of the right triangle that has its hypotenuse equal to the slant height, and one leg equal to half the base side length. The Pythagorean theorem is used to find the height from the slant height (s) and the base length (b):
h = √(s² -(b/2)²)
The volume is found from the formula ...
V = (1/3)b²h
where b is the base length and h is the height found using the previous formula.
The tedious arithmetic is nicely done using a spreadsheet. Results are attached.
Part 1
The graph has even symmetry. You can see that because it is symmetric with respect to the y-axis.
Functions that have even symmetry have the following property:
Part 2
To answer this we can simply check if the property we mentioned earlier holds for this function.
We can see that sine does not have even symmetry.
In fact, sine function has the following property:
This is called odd symetry.
Part 3
Take a look at the function that you attached in the picture. We know that function has even symmetry.
Reflection over x-axis and <span>180° rotation around the origin would give us -f(x). We would not end up with the same function, so these two are out.
</span><span>90° rotation around the origin would mean we swapped x <span>and y</span> so that one is out too. R</span><span>eflection over the line y=x is a property of functions that have an odd symmetry.
We are left with reflection around y-axis and, as mentioned before, this is the property of evenly symmetric functions.</span>
Answer:There will be 10 grams left because you subtract half of the current amount from it every 9 years.
Step-by-step explanation:
Answer:
y=−x−1/3x−8
Step-by-step explanation:
y=8x−1/3x+1
To find the inverse function, swap x and y, and solve the resulting equation for x.
If the initial function is not one-to-one, then there will be more than one inverse.
So, swap the variables: y=8x−1/3x+1 becomes x=8y−1/3y+1.
Now, solve the equation x=8y−1/3y+1 for y.
y=−x−1/3x−8
Sorry I was in a rush and couldn't do the fractions as formulae. Hope it helped anyways.
Answer
t = 2
Step-by-step explanation
Simplify 5-(t+3).
-t+2=-1+2t-3
Subtract 3 from -1
-t+2=2t-4
Move all terms containing to the left side of the equation.
-3t+2=-4
Move all terms not containing t to the right side of the equation.
-3t=-6
Divide each term by -3 and simply.
t = 2
