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Setler [38]
3 years ago
5

A building that is 100 ft tall casts a shadow that makes a 30 degree angle with the ground. Approximately how long, in feet, is

the shadow across the ground?
Mathematics
1 answer:
zhannawk [14.2K]3 years ago
7 0
Rounds to about 58 use the 30 60 90 formula
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A container in the shape of a square-based prism has a volume of 2744 cm'. What dimensions give the
Vinvika [58]

Answer:

The dimensions that give the minimum surface area are:

Length = 14cm

width = 14cm

height = 14cm

And the minimum surface is:

S = 1,176 cm^2

Step-by-step explanation:

A regular rectangular prism has the measures: length L, width W and height H.

The volume of this prism is:

V = L*W*H

The surface of this prism is:

S = 2*(L*W + H*L + H*W)

If the base of the prism is a square, then we have L = W

Then the equations become:

V = L*L*H = L^2*H

S = 2*(L^2 + 2*H*L)

We know that the volume of the figure is 2744 cm^3

Then:

V = 2744 cm^3 = H*(L^2)

In this equation, we can isolate H.

H = (2744 cm^3)/(L^2)

Now we can replace this on the surface equation:

S = 2*(L^2 + 2*L* (2744 cm^3)/(L^2))

S = 2*L^2 + 4(2744 cm^3)/L

Now we want to minimize the surface area, then we need to find the zeros of the first derivative of S.

S' = 2*(2*L) - 4*(2744 cm^3)/L^2

This is equal to zero when:

0 = 2*(2*L) - 4*(2744 cm^3)/L^2

0 = 4*L*L^2 - 4*(2744 cm^3)

4*(2744 cm^3) = 4*L^3

2744 cm^3 = L^3

∛(2744 cm^3) = L = 14cm

Then the length of the base that minimizes the surface is L = 14.

Then we have:

H = (2744 cm^3)/(L^2) = (2744 cm^3)/(14cm)^2 = 14cm

Then the surface is:

S = 2*(L^2 + 2*L*H) = 2*( (14cm)^2 + 2*(14cm)*(14cm)) = 1,176 cm^2

8 0
3 years ago
Angles 1 and 2 are complementary, and angle 1=3x+3 and angle 2=10x-4, find the degree measure of each angle
tensa zangetsu [6.8K]

Answer:

The measure of the angles:

24°  and   66°

Step-by-step explanation:

Complementary angles sum 90°

then:

(3x + 3) + (10x-4) = 90

3x + 10x + 3 - 4 = 90

13x - 1 = 90

13x = 90+1

13x = 91

x = 91/13

x = 7°

then:

  • angle 1:

3x+3 = 3*7 + 3 = 21+3 = 24°

  • angle 2

10x - 4 = 10*7  - 4 = 70 - 4 = 66°

Check:

66° + 24° = 90°

7 0
3 years ago
5x + 2 (x+7) =14x - 7
qaws [65]
The answer is x=-23/21
5 0
3 years ago
The diameter of a sphere is 21.6 cm. What is the sphere's volume? Round to the nearest tenth, if necessary.
NeX [460]
By definition, the volume of a sphere is:
 V =  \frac{4}{3}  (\pi) (r ^ 3)

 Where,
 r: sphere radio
 Substituting values we have:
 V =  \frac{4}{3}(3.14)(( \frac{21.6}{2} ) ^ 3)

 V = 5273.99424
 Rounding the result to the nearest tenth:
 V = 5274.0 cm ^ 3
 Answer:
 the sphere's volume is:
 V = 5274.0 cm ^ 3
5 0
3 years ago
Allison can complete a sales route by herself in 6 hours. working with an associate, she completes the route in 4 hours. How lon
allsm [11]
We know that
if <span>Allison can complete a sales route by herself in 6 hours
then
100% of the sales route---------------> 6 hours
x%--------------------------> 1 hour
x=100/6-----> x=16.67%/hour


Allison </span><span>working with an associate, she completes the route in 4 hours
</span>then 
100%------------------> 4 hours
x%----------------> 1 hour
x=100/4-----> x=25%

An associate in 1 hour complete-------> 25%-16.67%----> 8.33%
then
 an associate complete in 1 hour--------> 8.33%
 x hour--------------------------> 100%
x=100/8.33-----> x=12 hours

the answer is
12 hours

4 0
3 years ago
Read 2 more answers
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