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Vladimir79 [104]
4 years ago
9

Each student in a pottery class is responsible for cleaning the area around his or her workspace at the end of the lesson. Each

student's area is approximately . There are 13 students in the class. Assuming that each student cleans his or her area, how many square feet in total is cleaned? Solve the problem by each of these methods.
Method 1: Convert the fraction to an improper fraction and multiply.
Method 2: Use addition to rewrite the fraction, and multiply using the distributive property.
Answer:
i need the answer for a and b show your work
Mathematics
1 answer:
Nikolay [14]4 years ago
5 0
Ok this is not as hard as it seems

(4.5 feet)^2 times the number of students (13)

20.25 x 13

263.25 is the correct answer
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devlian [24]
<span>The answer is <span>in the file</span></span>

4 0
3 years ago
(SOMEONE PLEASE HELP!! ) According to these three facts, which statements are true?
Allisa [31]
I would go with the first two because the first one is true but the last two are false for a fact so the second answer would have to be the second check box
5 0
3 years ago
Find the area of the region bounded by the parabola y = 2x^2, the tangent line to this parabola at (4, 32), and the x-axis.
Anna [14]
I have a solution here that has a slight change in given where instead of <span>(4, 32), it is (3, 18). However, since the solution has provided explanations on each process, step-by-step, I believe that by thoroughly analyzing it, you might just answer this problem on your own!
</span>

f(x) = 2x² ← this is the parabola 

f(3) = 2 * 9 = 18 → the parabola passes through A (3 ; 18), so its tangent line too 


f'(x) = 4x ← this is the derivative 

…and the derivative is the slope of the tangent line to the curve at x 

f'(3) = 4 * 3 = 12 ← this is the slope of the tangent line to the curve at x = 3 


Equation of the tangent line 

The typical equation of a line is: y = mx + b → where m: slope and where b: y-intercept 

You know that the slope of the tangent line is 12. 

The equation of the tangent line becomes: y = 12x + b 

The tangent line passes through A (3 ; 18), so these coordinates must verify the equation of the tangent line. 

y = 12x + b 

b = y - 12x → you substitute x and y by the coordinates of the point A (3 ; 18) 

b = 18 - 36 = - 18 

→ The equation of the tangent line is: y = 12x - 18 


Intersection between the tangent line to the curve and the x-axis: → when y = 0 

y = 12x - 18 → when y = 0 

12x - 18 = 0 

12x = 18 

x = 3/2 

→ Point B (3/2 ; 0) 


Intersection between the vertical line passes through the point A and the x-axis: → when x = 3 

→ Point C (3 ; 0) 

The equation of the vertical line is: x = 3 


Area of the region bounded by the parabola y = 2x², the tangent line to this parabola at (3 ; 18), and the x-axis. 

= (area of the region bounded by the parabola y = 2x² and the x-axis) - (area of the triangle ABC) 

= [∫ (from 0 to 3) of the parabola] - [(xC - xB).(yA - yC)/2] 

= [∫ (from 0 to 3) 2x².dx] - [(xC - xB).(yA - yC)/2] 

= { [(2/3).x³] from 0 to 3 } - { [3 - (3/2)].(18 - 0)/2 } 

= [(2/3) * 3³] - { [(6/2) - (3/2)] * 9 } 

= [(2/3) * 27] - { [(3/2) * 9 } 

= 18 - (27/2) 

= (36/2) - (27/2) 

= 9/2 square unit
6 0
3 years ago
robin is making bead necklaces she want to use 717 beads to make 57 necklaces. if she wants each necklaces to have the same numb
EleoNora [17]

717=12\cdot684+33

<u>33 beads</u>

7 0
4 years ago
PLEASE HELP<br> find the vertex of f(x)=x^2+2x+3 (make sure you show your work)
Solnce55 [7]

ANSWER

(-1,2)

EXPLANATION

The given quadratic expression is:

f(x) =  {x}^{2}  + 2x + 3

The coefficient of the quadratic term is already 1.

So we add and subtract the square of half the coefficient of x.

f(x) =  {x}^{2}  + 2x  + 1 - 1+ 3

We factor the first three terms to obtain

f(x) =(x  + 1)^{2}  + 2

This is now in the form:

f(x) =  a({x  -  h)}^{2}  +k

where (h,k) which is equal to (-1,2) is the vertex.

5 0
4 years ago
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