Answer:
Fourth option
Step-by-step explanation:
Given the expression in the picture:
Apply Power of Power Rule
The left side of the equation option had this in the fourth option so the fourth option is right
The base of a solid right pyramid is a regular hexagon with a radius of 2x units and an apothem of units. A solid right pyramid
has a regular hexagonal base with a radius of 2 x units and an apothem of x StartRoot 3 EndRoot units. Which expression represents the area of the base of the pyramid? x squared StartRoot 3 EndRoot units2 3 x squared StartRoot 3 EndRoot units2 4 x squared StartRoot 3 EndRoot units2 6 x squared StartRoot 3 EndRoot units2
2 answers:
Answer:
Step-by-step explanation:
The base of the pyramid we need to study is a hexagon.
Let's look at the attached image of an hexagon to understand how we are going to find the area of this figure.
Notice that an hexagon is the combination of 6 exactly equal equilateral triangles in our case of size "2x" (notice that the "radius" of the hexagon is given as "2x")
Therefore the area of the hexagon is going to be 6 times the area of one of those equilateral triangles.
We know the area of a triangle is the product of its base times its height, divided by 2:
We notice that the triangle's height is exactly what is called the "apothem" of the hexagon (depicted in green in our figure) which measures , so replacing this value in the formula above for the area of one of the triangles:
Then we multiply this area times 6 to get the total area of the hexagon (6 of these triangles):
Area of hexagon =
which is the last option given in the list.
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To model this situation, we are going to use the compound interest formula: 
where
is the final amount after 
years
is the initial deposit
is the interest rate in decimal form
is the number of times the interest is compounded per year
is the time in years
For account A:
We know for our problem that
and 
. Since the interest is compounded monthly, it is compounded 12 times per year; therefore, 
. Lets replace those values in our formula:
For account B:
, 
, . Lest replace those values in our formula:
Since we want to find the time,, <span>when the sum of the balance in both accounts is at least 5000, we need to add both accounts and set that sum equal to 5000:
</span>
Now that we have our equation, we just need to solve for:
![2000[(1+ \frac{0.0225}{12} )^{12t}+(1+ \frac{0.03}{12} )^{12t}]=5000](https://tex.z-dn.net/?f=2000%5B%281%2B%20%5Cfrac%7B0.0225%7D%7B12%7D%20%29%5E%7B12t%7D%2B%281%2B%20%5Cfrac%7B0.03%7D%7B12%7D%20%29%5E%7B12t%7D%5D%3D5000%20)
![t[12ln(1.001875)+12ln(1.0025 )]=ln( \frac{5} {2})](https://tex.z-dn.net/?f=t%5B12ln%281.001875%29%2B12ln%281.0025%20%29%5D%3Dln%28%20%5Cfrac%7B5%7D%20%7B2%7D%29)
We can conclude that after 17.47 years <span>the sum of the balance in both accounts will be at least 5000.</span>
where
For account A:
We know for our problem that
For account B:
Since we want to find the time,
</span>
Now that we have our equation, we just need to solve for
We can conclude that after 17.47 years <span>the sum of the balance in both accounts will be at least 5000.</span>