Answer:
The rate of change is of of the area when the radius is 4 centimeters 
square centimeters.
Step-by-step explanation:
Area of a circle:
The area of a circle of radius r is given by:
Implicit derivative:
To solve this question, we have to derivate implictly the equation as a function of t. Thus:
The radius of a circle is increasing at a rate of 6 centimeters per minute.
This means that 
Find the rate of change of the area when the radius is 4 centimeters.
This is 
when 
. Thus
The rate of change is of of the area when the radius is 4 centimeters square centimeters.
<h3>
Answer: b) 18 cm </h3>
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Work Shown:
Since the parallelogram has perpendicular diagonals, this means that we're dealing with a rhombus. A rhombus has all four sides equal to one another.
One diagonal is bisected, or cut in half, to form the smaller pieces of length (150/x) + 10 and x-10. Set these two expressions equal to each other and solve for x
(150/x) + 10 = x-10
1500/x = x-10-10
1500/x = x-20
1500 = x(x-20)
1500 = x^2-20x
0 = x^2-20x-1500
x^2-20x-1500 = 0
(x-50)(x+30) = 0
x-50 = 0 or x+30 = 0
x = 50 or x = -30
We'll ignore the negative x value as it leads to a negative length which doesn't make sense.
If x = 50, then
- x-10 = 50-10 = 40
- (150/x)+10 = (150/50)+10 = 30+10 = 40
Each piece of this diagonal is 40 cm long.
The two smaller pieces combine to 40+40 = 80, which is the length of one of the diagonals. If this was the shorter diagonal, then 80 would be listed as part of the answer choices. However, 80 is not one of the answers.
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Note how the two diagonals of the rhombus cut the figure into four right triangles.
Each right triangle has one known leg to be 40 and an unknown leg of y. The hypotenuse is 164/4 = 41 since we divide the perimeter by the four equal sides of the rhombus.
We'll use the pythagorean theorem to find the value of y
a^2 + b^2 = c^2
40^2 + y^2 = 41^2
1600 + y^2 = 1681
y^2 = 1681-1600
y^2 = 81
y = sqrt(81)
y = 9
This represents half of the other diagonal, so the full length of this other diagonal is 2*9 = 18 cm.
Answer:
Step-by-step explanation:
Let h be the number of hats Elliott makes and s be the number of scarves she makes.
Each hat uses 0.2 kilograms of yarn and each scarf uses 0.1 kilograms of yarn. Elliott wants to use twice as much yarn for scarves as for hats. This is expressed as
h = 2s
The total number of hats and scarves that she wants to make is 20. This is expressed as
h + s = 20
Therefore, the system of equations that represents this situation are
h = 2s
h + s = 20
Answer:
uh... 6%? sorry, i suck at math
Step-by-step explanation:
The table is usually the shape of a rectangle. The area is equal to the length times the width. To make sure, let's recalculate the solution.
Area = length × width
Area = 103.50 cm × 73.75 cm
Area = <span>7,633.125 cm</span>²
So, we established that the answer is correct. Now, I'll introduce the concept of significant figures. There are rules regarding significant figures to be applied conventionally in measurements and calculations. This is to increase precision of the data. Significant figures are digits that carry meaning. When you are given data with a specific number of significant figures, the final answer should also contain the same number of significant figures. In convention, the rule says that the zero's after non-zero digits after the decimal point are significant. Also, all non-zero digits are significant. The value 103.50 has 5 significant figures, and 73.75 has 4. When it comes to multiplication, the answer should contain the least significant figures. So, we should have 4 significant figures. Therefore, the final answer to be reported should be 7,633 cm².
