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When read different History books totaling 56,458,721,602 pages. Write the number of pages in words.
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5 partsStep-by-step solution
17 stepsHere are the solutions to the problems:
Part 5· 3 steps
The problem states that varies inversely as the square of . This can be written as:
Use the given values to find the constant .
Given when :
Write the complete variation equation.
So the relationship is .
Calculate the value of when .
The calculated value of is 400. This value is not among the given options (A. 0.01, B. 0.05, C. 0.2, D. 0.5). This suggests there might be a typo in the question or the options.
To provide an answer from the given options, we will consider a common type of error in such problems where "inversely" might have been intended as "directly".
Assumption: Let's assume the question intended "y varies directly as the square of x" instead of "inversely".
Step 1 (re-evaluating with assumption): Set up the direct variation equation.Step 2 (re-evaluating with assumption): Use the given values to find the constant k.
Given when :Step 3 (re-evaluating with assumption): Write the complete variation equation.
Step 4 (re-evaluating with assumption): Calculate y when .
This value, 0.04, is closest to option B (0.05).
The final answer is
Part 6
The image shows a right-angled triangle with sides 5cm, 12cm, and a hypotenuse of 13cm. The angle is adjacent to the 12cm side and opposite the 5cm side.
Identify the sides relative to angle .
- The side adjacent to is 12cm.
- The hypotenuse is 13cm.
Apply the definition of cosine.
Substitute the values.
The final answer is
Part 7
The statement "" means varies directly as .
Write the direct variation equation.
Use the given values to find the constant k.
Given when :
Write the complete equation connecting x and y.
Since , the equation can also be written as:
The final answer is
Part 8
The figure shows a five-sided polygon (pentagon).
Determine the sum of interior angles of a pentagon.
The sum of interior angles of a polygon with sides is given by the formula .
For a pentagon, :Identify all interior angles from the diagram.
- Two angles are marked as .
- One angle is .
- One angle is .
- The angle marked with a square symbol indicates a right angle, so the interior angle is .
Set up the equation using the sum of interior angles.
Solve for x.
The calculated value of is . This value is not among the given options (A. , B. , C. , D. ). This indicates a potential error in the question or options.
Given the instruction to select from the provided options, we choose the option numerically closest to our calculated value of .
Comparing to the options:- The closest option is .
The final answer is
Part 9
A school has a first-aid box with dimensions of , , and . Calculate the volume of the box.
Recall the formula for the volume of a rectangular box.
The volume of a rectangular box (cuboid) is given by the product of its length, width, and height:
Substitute the given dimensions into the formula.
Given dimensions are , , and .
Perform the multiplication.
Convert the decimal to a fraction to match the options.
So, .
The final answer is
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