It's the first one because surface area is l*w of each side and add that all together which is 288 sq in.
Answer:
11. 60
12. 73
Step-by-step explanation:
11. Three solid lines mean all of the angles are the same. this honestly could only be applied to triangles with 60 degrees because each triangle adds up to 180.
12. The angles are the same on each end meaning their both 73. The other end of the triangle is 34.
Let's try to tease out a function for the area of our hypothetical rectangle:
We know that the area of a rectangle is Base x Height, and the base will be the length of the x-axis portion of the rectangle. Looking at a graph of y=27 - x^2 will help with intuition on this.
The length of the base will be 2x, since it will be the distance from the (0,0) axis in the positive direction and in the negative direction.
So our rectangle will have an area of 2x, multiplied by the height.
What is the height? The height will be our y value.
Therefore,
A = 2x * y, where x is x-value of the positive vertex.
We already know what y is as a function of x:
y= 27 - x^2
That means our equation for the area of the rectangle is:
A = 2x (27 - x^2) Distribute the terms....
A = 54x - 2x^3
This is essentially a calculus optimization problem. We want to find the Maximum for A, so let's find where the derivative of A is equal to zero.
First, we find the derivative:
A = 54x - 2x^3
A' = 54 - 6x^2
Set A' equal to zero to find the maximum value for A
0 = 54 - 6x^2
6x^2 = 54
x^2 = 9
x = 3
We got our x-value! Now let's find the y value at that point:
y= 27 - x^2
y = 27 - 9
y = 18
The height our rectangle will be 18, and our base will be 2*x = 2*3 = 6
Area = base x height = 18 * 6 = 108
The answer is B) 108.
Times means multiplication
sum means addition
is means the equal sign
lets call our number 'n'
That as an expression would be
The th number in the sequence can be expressed as
Extracting the th term from the sum gives
and . 3 divides both 12 and 21, so and 21 contribute no remainder.
This leaves us with
Recall that a decimal integer is divisible by 3 if its digits add to a multiple of 3. The digits in are copies of 2 and one 0, so the digital sum is .
- If for , then the digital sum is , which is not divisible by 3.
- If , then the sum is , which is not divisible by 3.
- If , then the sum is , which is always divisble by 3.
This means that roughly 1/3 of the first numbers in this sequence are divisible by 3; among the first 100 terms, they occur for , of which there are 33.