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Mashutka [201]
3 years ago
8

Find (if possible) the complement and the supplement of each angle. (if not possible, enter impossible.) (a) π 10 complement rad

ians supplement radians (b) 9π 10 complement radians supplement radians
Mathematics
1 answer:
blagie [28]3 years ago
4 0

In this question, we have to find the complement and supplement of the given angles .

Complementary angles are those angles whose sum is 90 degree and supplementary angles are those angles whose sum is 180 degree.

So to find the complement and supplement angles, we need to subtract the given angles from pi/2 and pi respectively .

a.

\frac{ \pi}{10}
\\
complement  \ angle = \frac{ \pi}{2} - \frac{ \pi}{10}     \\                             = \frac{4 \pi}{10} = \frac{ 2 \pi}{5}
\\
Supplement  \ angle = \pi - \frac{ \pi}{10} = \frac{9 \pi}{10}

b.

\frac{9 \pi}{10}
\\
Complement \ angle = \frac{ \pi}{2} - \frac{9 \pi}{10} = \frac{-4 \pi}{10} = -\frac{2 \pi}{5}
\\
Supplement \ angle = \pi - \frac{9 \pi}{10} = \frac{ \pi}{10}

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(40x9)÷(4x8)=x solve for variable of x
nikklg [1K]
The answer is:  " x = 11 ¼ "  ; or write as:  " x = 11.25 " .
_________________________________________________
Explanation:
_________________________________________________
  (40*9) ÷ (4*8) = x  ;  Solve for "x" ;

(40 * 9 = 360) .

(4 * 8 = 32) .

(360) ÷ (32) = 45/4 = 11 ¼  ; or write as:  11.25 .
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3 years ago
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cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup. The material for the sides of the can costs 0
Dafna11 [192]

Answer:

Radius=2.09 cm

Height,h=14.57 cm

Step-by-step explanation:

We are given that

Volume of cylinderical shaped can=200 cubic cm.

Cost of sides of can=0.02 cents per square cm

Cost of top and bottom of the can =0.07 cents per square cm

Curved surface area of cylinder=2\pi rh

Area of circular base=Area of circular top=\pi r^2

Total cost,C(r)=0.02\times 2\pi rh+2\pi r^2\times 0.07

Volume of cylinder,V=\pi r^2 h

200=\pi r^2 h

h=\frac{200}{\pi r^2}

Substitute the value of h

C(r)=0.02\times 2\pi r\times \frac{200}{\pi r^2}+2\pi r^2\times 0.07

C(r)=\frac{8}{r}+0.14\pi r^2

Differentiate w.r.t r

C'(r)=-\frac{8}{r^2}+0.28\pi r

C'(r)=0

-\frac{8}{r^2}+0.28\pi r=0

0.28\pi r=\frac{8}{r^2}

r^3=\frac{8}{0.28\pi}=9.095

r=(9.095)^{\frac{1}{3}}=2.09

Again, differentiate w.r.t r

C''(r)=\frac{16}{r^3}+0.28\pi

Substitute the value of r

C''(2.09)=\frac{16}{(2.09)^3}+0.28\pi=2.63>0

Therefore,the product cost is minimum at r=2.09

h=\frac{200}{\pi (2.09)^2}=14.57

Radius of can,r=2.09 cm

Height of cone,h=14.57 cm

4 0
3 years ago
The base of an isosceles triangle is one and a half times the length of the other two sides.A smaller triangle has a perimeter t
Anna11 [10]

Answer:

Perimeter of the smaller triangle = 1.75x

Step-by-step explanation:

Let the two equal sides of an isosceles triangle = x

Therefore, length of the base = (1\frac{1}{2})x

Perimeter of this isosceles triangle = x + x + (1\frac{1}{2})x

                                                          = 2x + (1+\frac{1}{2})x

                                                          = 2x + x + \frac{x}{2}

                                                          = \frac{5x}{2}

Since, smaller triangle has a perimeter that is half the perimeter of the larger triangle,

Length of each corresponding side of smaller triangle will be half of the larger triangle.

Length of sides of the smaller triangle = \frac{x}{2},\frac{x}{2},(1\frac{1}{2})\frac{x}{2}

Perimeter of the smaller triangle = \frac{x}{2}+\frac{x}{2}+(1\frac{1}{2})\frac{x}{2}

                                                      = x + \frac{x}{2}+\frac{x}{4}

                                                      = \frac{3}{2}x+\frac{x}{4}

                                                      = \frac{6}{4}x+\frac{x}{4}

                                                      = \frac{7}{4}x

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Therefore, expression that represents the perimeter of the smaller triangle is (1.75x)        

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