Which statement compares the two numbers correctly? (2 points) 7 x 10 + 3 x 1 + 3 x 0.1 + 8 x 0.01 + 5 x 0.001 ________ 73.293 G
1 answer:
Answer:
7 × 10 + 3 × 1 + 3 × 0.1 + 8 × 0.01 + 5 × 0.001 > 73.293
Step-by-step explanation:
Given: Numbers are 7 × 10 + 3 × 1 + 3 × 0.1 + 8 × 0.01 + 5 × 0.001 and 73.293
To compare: the two given numbers
Solution:
7 × 10 + 3 × 1 + 3 × 0.1 + 8 × 0.01 + 5 × 0.001 is equal to
Compare the numbers and 73.293
Digits at the ones pace and tens place in both the numbers are same.
Observe the digit at the tenth place in both the numbers.
Digit at the tenth place in 73.385 is 3
Digit at the tenth place in 73.293 is 2
As ,
73.385 > 73.293
So,
7 × 10 + 3 × 1 + 3 × 0.1 + 8 × 0.01 + 5 × 0.001 > 73.293
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Using the slope line formula,
The slope of line y = mx is 1.0315.
We have given that,
parabola equation is y = 5x - 3x²
line passing through origin is in the form of y = mx
==> mx = 5x - 3x²
==> 3x²+ mx - 5x = 0
==> 3x² + x(m -5) = 0
==> x(3x + (m -5)) = 0
==> x = 0 , x = (5 -m)/3
The total area of the bounded region is then the integral of 5x - 3x² from x = 0 to x = (5-m)/3
Area under y = 5x - 3x2 and y = mx is (125/54)/2 = 125/108
==> [0 to (5 -m)/3] ∫(5x - 3x²-mx )dx = 125/108
==> [0 to (5 -m)/3]∫( (5 - m)x - 3x2 )dx = 125/108
==> [0 to (5 -m)/3] ((5 - m)x²/2 - x³ )= 125/108
==> (5 - m)[(5 -m)/3]²/2 - ((5 -m)/3)³ = 125/108
==> (5 -m)³/18 - (5 -m)³/27 = 125/108
==> (5 -m)³/54 = 125/108
==> (5 -m)³ = 125/2
==> (5 -m) = 3.9685
==> m = 5 - 3.9685
==> m = 1.0315
Hence slope of line = 1.0315
To learn more about slope of line , refer:
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