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3 years ago

A semicircle is attached to the side of a rectangle as shown.

Mathematics

2 answers:

laiz [17]3 years ago

4 0

Answer:

$58.8\ mm^2$

Step-by-step explanation:

we know that

The area of the figure is equal to the area of rectangle plus the area of semicircle

step 1

Find the area of rectangle

The area of rectangle is equal to

$A=bh$

where

$b=9\ mm\\h=3\ mm$

substitute

$A=(9)(3)=27\ mm^2$

step 2

Find the area of semicircle

The area of semicircle is equal to

$A=\frac{1}{2}\pi r^{2}$

we have

$r=9/2=4.5\ mm$ ---> the radius is half the diameter

$\pi =3.14$

substitute

$A=\frac{1}{2}(3.14) (4.5)^{2}$

$A=31.8\ mm^2$

step 3

Find the area of the figure

$A=27+31.8=58.8\ mm^2$

Diano4ka-milaya [45]3 years ago

4 0

Answer:

Step-by-step explanation:

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3 years ago

Please help me with these, oh sweet jesus

Lelechka [254]

Answer:

77. $\cot^{6} x = \cot^{4} x \csc^{2}x - \cot^{4} x$ Proved

78. $\sec^{4}x \tan^{2} x = \sec^{2}x [\tan^{2}x + \tan^{4}x ]$ Proved

79. $\cos^{3} x\sin^{2} x = [\sin^{2}x - \sin^{4}x] \cos x$ Proved.

80. $\sin^{4}x - \cos^{4}x = 1 - 2\cos^{2}x + 2 \cos^{4} x$ Proved.

Step-by-step explanation:

77. Left hand side

= $\cot^{6} x$

= $\cot^{4} x \times \cot^{2} x$

= $\cot^{4}x [\csc^{2}x - 1]$

{Since we know, $\csc^{2} x - \cot^{2}x = 1$ }

= $\cot^{4} x \csc^{2}x - \cot^{4} x$

= Right hand side (Proved)

78. Left hand side

= $\sec^{4}x \tan^{2} x$

= $\sec^{2} x [1 + \tan^{2}x] \tan^{2} x$

{Since $\sec^{2}x - \tan^{2}x = 1$ }

= $\sec^{2}x [\tan^{2}x + \tan^{4}x ]$

= Right hand side (Proved)

79. Left hand side

= $\cos^{3} x\sin^{2} x$

= $\cos x[1 - \sin^{2} x] \sin^{2} x$

{Since $\sin^{2}x + \cos^{2} x = 1$ }

= $[\sin^{2}x - \sin^{4}x] \cos x$

= Right hand side

80. Left hand side

= $\sin^{4}x - \cos^{4}x$

= $[\sin^{2}x + \cos^{2}x]^{2} - 2\sin^{2} x \cos^{2}x$

{Since $\sin^{2}x + \cos^{2} x = 1$ }

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7 0

3 years ago

I need this answer too please help

VMariaS [17]

Answer:

x = 6

Step-by-step explanation:

When 2 chords of a circle intersect then the product of the parts of one is equal to the product of the parts of the other, that is

2x = 3 × 4, that is

2x = 12 ( divide both sides by 2 )

x = 6

7 0

3 years ago

Find x. Then find the measure of angles A, B and C.

mafiozo [28]

Answer:

x= 11

A=59

B= 37

C = 84

Step-by-step explanation:

A triangle adds up to 180 °.

So the equation will be a °+ b° + c° = 180°

Next, you combine like terms.

$6x + 3x + 9x+4-15-7 = 180\\18x-18=180$

Then inverse operation,

$18x-18=180\\18x=198\\x=11$

After to get a, b, and c you just need to plug in x.

$6(11)-7=a\\3(11)+4 = b\\9(11)-15=c$

4 0

3 years ago

State the linear programming problem in mathematical terms, identifying the objective function and the constraints. A firm makes

Sedbober [7]

Answer:

Maximum profit at (3,0) is $27.

Step-by-step explanation:

Let quantity of products A=x

Quantity of products B=y

Product A takes time on machine L=2 hours

Product A takes time on machine M=2 hours

Product B takes time on machineL= 4 hours

Product B takes time on machine M=3 hours

Machine L can used total time= 8hours

Machine M can used total time= 6hours

Profit on product A= $9

Profit on product B=$7

According to question

Objective function Z= $9x+7y$

Constraints:

$2x+3y\leq 6$

$2x+4y\leq 8$

Where $x\geq 0, y\geq 0$

I equation $2x+3y\leq 6$

I equation in inequality change into equality we get

$2x+3y=6$

Put x=0 then we get

y=2

If we put y=0 then we get

x= 3

Therefore , we get two points A (0,2) and B (3,0) and plot the graph for equation I

Now put x=0 and y=0 in I equation in inequality

Then we get $0\leq 6$

Hence, this equation is true then shaded regoin is below the line .

Similarly , for II equation

First change inequality equation into equality equation

we get $2x+4y=8$

Put x= 0 then we get

y=2

Put y=0 Then we get

x=4

Therefore, we get two points C(0,2)a nd D(4,0) and plot the graph for equation II

Point A and C are same

Put x=0 and y=0 in the in inequality equation II then we get

$0\leq 8$

Hence, this equation is true .Therefore, the shaded region is below the line.

By graph we can see both line intersect at the points A(0,2)

The feasible region is AOBA and bounded.

To find the value of objective function on points

A (0,2), O(0,0) and B(3,0)

Put A(0,2)

Z= $9\times 0+7\times 2=14$

At point O(0,0)

Z=0

At point B(3,0)

Z= $9\times3+7\times0=27$

Hence maximum value of z= 27 at point B(3,0)

Therefore, the maximum profit is $27.

6 0

3 years ago