The answer is: 15 .
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{Note: If this is a physics problem ; and the formula: "F = m*a" is for:
"Force = mass * acceleration" ; be sure that the correct units are used!}.
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Explanation:
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F = m * a ;
Given m = 5 ;
a = 3 ;
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F = 5 * 3 = 15 .
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32.
V = L*w*h
Where:
V= Volume
L= Length = x+5
w= width = x-2
h= height = 6
Replacing with the values given:
V= (x+5) * (x-2) * 6
V =[ (x*x) + (x*-2) + (5*X) +5*-2) ] * 6
V= [ x^2 - 2x + 5x - 10 ] * 6
V= [ x^2 + 3x - 10] *6
V= (x^2*6) + (3x*6)+ ( - 10 * 6)
V= 6x^2 + 18x - 60
Convert each mixed number to an improper fraction
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Convert 6&1/2 to an improper fraction
6&1/2 = (6*2+1)/2
6&1/2 = (12+1)/2
6&1/2 = 13/2
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Do the same for 9&1/4
9&1/4 = (9*4+1)/4
9&1/4 = (36+1)/4
9&1/4 = 37/4
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Now multiply the improper fractions 13/2 and 37/4. Multiply straight across
(13/2)*(37/4) = (13*37)/(2*4)
(13/2)*(37/4) = 481/8
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The last step is to use long division to find the mixed number equivalent of 481/8
Or we an say
60*8 = 480
So 60*8+1 = 480+1
which means
481/8 = (480+1)/8 = 480/8+1/8 = 60&1/8
Making the final answer to be choice C
Another way to get the answer is to convert 481/8 into a decimal to get 60.125 and then convert that back to a mixed number. You should get 60&1/8
Answer: area = 379.7 mm²
Perimeter = 95.84 mm
Step-by-step explanation:
The composite shape contains a semi circle and a trapezoid.
The area of a semi circle is
1/2 × πr²
Radius = diameter/2
Radius = 20/2 = 10 mm
Area = 1/2 × 3.14 × 10 = 15.7 mm²
Area of trapezoid is expressed as
1/2(a + b)h
Area = 1/2 × (20 + 32)14
Area = 1/2 × 52 × 14) = 364mm²
Area of the composite shape is
15.7 + 364 = 379.7 mm²
Formula for determining the perimeter of the semicircle is
1/2 × πd
Perimeter = 1/2 × 3.14 × 20 = 31.4mm
Looking at the attached photo, we would determine the slant height,h, by applying Pythagorean theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
h² = 12² + 14² = 340
h = √340/= 18.44
Perimeter of the composite shape is
31.4 + 14 + 32 + 18.44 =95.84 mm
The answer is x>0 on apex for x value
