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Zinaida [17]
3 years ago
9

The second on a watch is 14mm long. What area does it sweep through in 30 seconds

Mathematics
1 answer:
skad [1K]3 years ago
3 0

Exact Area = 98pi  

Approximate Area = 307.8760800518 (use calculator stored version of pi)

Approximate Area = 307.72 (using pi = 3.14)

Units are in square millimeters

======================================================

Explanation:

In 60 seconds, the hand sweeps out a full circle of radius 14. The area of this circle is

A = pi*r^2 = pi*14^2 = 196pi

Half of this is what the hand sweeps out in 30 seconds, so A/2 = (196pi)/2 = 98pi is the exact area it sweeps out. Your calculator would then show 98pi = 307.8760800518 approximately

If instead you use pi = 3.14, then the approximate area is 98*3.14 = 307.72

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g The tangent plane to z=f(x,y) at the point (1,2) is z=5x+2y−10. (a) Find fx(1,2) and fy(1,2). fx(1,2)= Number fy(1,2)= Number
murzikaleks [220]

Answer:

The values for Fx(1,2) and Fy(1,2) are 5 and 2 respectively.

Approximation at points (1.1,1.9) is 0.7

Step-by-step explanation:

Given:

Tangent plane to  a surface z=5x+2y-10 as the function at point (1,2)

To find :

f(x,y) at (1,2)

partial derivatives of function w.r.t. (x and y) and value of that function at given points.

Solution:(refer the attachment also)

Now we know that

the equation of tangent plane at given points to the surface is given by,

f(x1,y1,z1) and z=f(x,y)

z-z1=Fx(x1,y1)*(x-x1)+Fy(x1,y1)*(y-y1)

here Fx(x1,y1) and Fy(x1,y1) are the partial derivatives of x and y.

now

taking partial derivative w.r.t. x we get

Fx(x1`,y1)=\frac{d}{dx} (5x+2y-10)

=5.

Then w.r.t y we get

Fy(x1,y1)=

\frac{d}{dy}(5x+2y-10)

=2.

The values for Fx(1,2) and Fy(1,2) are 5 and 2 respectively.

Using the Linearization or linear approximation we get

L(x,y)=f(x1,y1)+Fx(x,y)*(x-x1)+Fy(x,y)(y-y1)

=-1+5(x-1)+2(y-2)

=5x+2y-10

Approximation at F(1.1,1.9)

=5(1.1)+2(1.9)-10

=5.5+3.8-10

=0.7

Approximation at points (1.1,1.9) is 0.7

6 0
2 years ago
65 POINTS!!! The price of an Ipad is $499. It is on sale for 18% off at the Apple Store on Mac Monday's. Find the Sales price yo
sineoko [7]

Answer:

The student added the discount instead of subtracting the discount.

They also did not calculate the tax correctly.

Step-by-step explanation:

Original price is 499

Discount = original price * percent off

Discount = 499 * .18

               =89.82

The sale price = original price minus the discount

sale price = 499-89.82

sale price = 409.18

Sales tax = sale price * tax rate

                = 409.18 * 8.875%

                =409.18*.08875

                 =36.314725

Rounding to the nearest cent

                     36.31

Final cost = sale price + sales tax

                  =409.18+36.31

                   445.49

The student added the discount instead of subtracting the discount.

They also did not calculate the tax correctly.

6 0
3 years ago
How do you know when a question is a division problem
Aleksandr [31]
If the problem says by or divided by
5 0
3 years ago
Read 2 more answers
If BE bisects _ABD and mŁABE = 28°, find m_ABD.
slamgirl [31]

Answer:

m<ABD = 56 degrees

Step-by-step explanation:

If a segment/ray/line bisects an angle, it divides it into 2 equal parts

Since BE bisects ABD, it will divide it into 2 equal parts, one of which is 28 degrees (given)

Now we can find the measure of ABD by doing 28*2=56

8 0
2 years ago
0.09×0.7 <br>help me please
dem82 [27]

0.09x0.7= 0.063

That its the answer

7 0
3 years ago
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