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prohojiy [21]
2 years ago
12

A rectangle is placed around a semicircle as shown below. The length of the rectangle is 3 cm. Find the area if shaded region. U

se the value 3.14 for pie, And do not round your answer.
Mathematics
1 answer:
love history [14]2 years ago
8 0

Answer:

0.9675sq.cm

Step-by-step explanation:

Find a related diagram attached

Area of the shaded region = Area of rectangle - area of semicircle

Area of rectangle = 3cm * 1.5cm

Area of rectangle = 4.5sq.cm

Given

diameter of the semicircle = 3cm

area = πd²/8

Area of the semicircle = 3.14(3)²/8

Area of the semicircle = 3.5325sq.cm

Area of the shaded region = 4.5 - 3.5325

Area of the shaded region = 0.9675sq.cm

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6 0
3 years ago
The function f is continuous on the closed interval [1,15] and has the values shown on the table above. Let g(x) = ∫f(t) dt [1,x
Anna11 [10]
We're looking for the two values being subtracted here. One of these values is easy to find:

<span>g(1) = ∫f(t)dt = 0</span><span>
since taking the integral over an interval of length 0 is 0.
 
The other value we find by taking a Left Riemann Sum, which means that we divide the interval [1,15] into the intervals listed above and find the area of rectangles over those regions:

</span><span>Each integral breaks down like so:

(3-1)*f(1)=4

(6-3)*f(3)=9

(10-6)*f(6)=16

(15-10)*f(10)=10.

So, the sum of all these integrals is 39, which means g(15)=39.
 
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</span>
I hope my answer has come to your help. God bless and have a nice day ahead!
3 0
3 years ago
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Is anyone willing to help me with this? I tried adding this and still no answer. Please help..
GaryK [48]

Answer:   C. (-4, -2)

<u>Step-by-step explanation:</u>

First, eliminate one of the variables and solve for the remaining variable:

2x - 5y = 2      →    3(2x - 5y = 2)      →     6x - 15y = 6

3x + 2y = -16   →  -2(3x + 2y = -16)    →  <u> -6x - 4y = 32</u>

                                                                     -19y = 38

                                                                         y = -2


Next, replace "y" with -2 into either of the original equations to solve for x:

2x - 5y = 2

2x - 5(-2) = 2

2x + 10 = 2

2x         = -8

 x          = -4

                                       x = -4,  y = -2

<u>Check:</u>

Plug in the x- and y-values into the other original equation:

3x + 2y = -16

3(-4) + 2(-2) = -16

-12  +  -4     = -16

      -16         = -16   \checkmark

3 0
3 years ago
Graph the inverse of the function.
Ghella [55]

Answer:

The graph of the inverse function is the same that the graph of the original function

Step-by-step explanation:

step 1

Find the equation of the function in the graph

Let

f(x) ---> the function in the graph

we know that

Is a linear function

take the points (0,6) and (6,0)

<em>Find the slope of the linear function</em>

m=(0-6)/(6-0)\\m=-1

<em>Find the the equation of the linear function in slope intercept form</em>

f(x)=mx+b

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substitute

f(x)=-x+6

step 2

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x=-y+6

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Let

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f^{-1}(x)=f(x)

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