Figure ABCD has vertices A(-2,3), B(4,3), C(4,-2), and D(-2,0). What is the area of figure ABCD
1 answer:
Answer:
24 units
Step-by-step explanation:
As we can see in the attached picture. The area will be given by the sum of the area of the rectangle and the area of the triangle in the bottom.
The rectangle has a base of 6 units and a height of 3 units. Therefore:
A1 = bh = 6*3 = 18 units.
The triangle has a base of 6 units and a height of 2 units. Therefore:
A2 = (1/2)bh = (6*2)/ 2 = 6 units
Then, the total area is:
A = A1 + A2 = 6 + 18 = 24 units
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Answer:
1 - Option C - 10,000
2 - 3x+5 will be 12 more than 3x-7.
Step-by-step explanation:
1) To find : With what number must 3.475817 be multiplied in order to obtain the number 34,758.17?
Solution :
The number 3.475817 is multiplied by number to obtain 34,758.17.
As we see that, the decimal is moved four places to the right.
Which means the number is multiplied by 10000.
i.e.
Therefore, option C is correct.
2) To find : How much greater is the value of 3x+5 than the value of 3x−7?
Solution ;
Assuming that x is the same value in each equation,
In order to determine the difference between the two values,
We ignore the 3x part as it is the same on both of the equations.
So, from 5 to -7 i.e. 7+5=12.
Therefore, 3x+5 will be 12 more than 3x-7.
Answer:
The correct answer B) The volumes are equal.
Step-by-step explanation:
The area of a disk of revolution at any x about the x- axis is πy² where y=2x. If we integrate this area on the given range of values of x from x=0 to x=1 , we will get the volume of revolution about the x-axis, which here equals,
which when evaluated gives 4pi/3.
Now we have to calculate the volume of revolution about the y-axis. For that we have to first see by drawing the diagram that the area of the CD like disk centered about the y-axis for any y, as we rotate the triangular area given in the question would be pi - pi*x². if we integrate this area over the range of value of y that is from y=0 to y=2 , we will obtain the volume of revolution about the y-axis, which is given by,
If we just evaluate the integral as usual we will get 4pi/3 again(In the second step i have just replaced x with y/2 as given by the equation of the line), which is the same answer we got for the volume of revolution about the x-axis. Which means that the answer B) is correct.