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lakkis [162]
3 years ago
11

The temperature at noon was ­ 8 °. How many degrees colder is 15°?

Mathematics
1 answer:
Nitella [24]3 years ago
6 0

Answer:

7 degrees colder

Step-by-step explanation:

15 degrees - 8 degrees = 7 degrees

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A box with a square base and open top must have a volume of 13,500 cm3. Find the dimensions of the box that minimize the amount
Alex17521 [72]

Answer:

Step-by-step explanation:

Let the side of the square base be x

h be the height of the box

Volume V = x²h

13500 = x²h

h = 13500/x² ..... 1

Surface area =  x² + 2xh + 2xh

Surface area S =  x² + 4xh  ...... 2

Substitute 1 into 2;

From 2; S =  x² + 4xh

S = x² + 4x(13500/x²)

S = x² + 54000/x

To minimize the amount of material used; dS/dx = 0

dS/dx = 2x - 54000/x²

0 = 2x - 54000/x²

0 = 2x³ - 54000

2x³ = 54000

x³ = 27000

x = ∛27000

x = 30cm

Since V = x²h

13500 = 30²h

h = 13500/900

h = 15cm

Hence the dimensions of the box that minimize the amount of material used is 30cm by 30cm by 15cm

5 0
3 years ago
An airplane climbs 100 feet during the first second after takeoff. In each succeeding second it climbs 100 feet more than it cli
tigry1 [53]

Answer:

15 seconds.

Step-by-step explanation:

∵ The distance covered by plane in first second = 100 ft,

Also, in each succeeding second it climbs 100 feet more than it climbed during the previous second,

So, distance covered in second second = 200,

In third second = 300,

In fourth second = 400,

............, so on....

Thus, the total distance covered by plane in n seconds = 100 + 200 + 300 +400......... upto n seconds

=\frac{n}{2}(2\times 100 + (n-1)100)  ( Sum of AP )

=\frac{n}{2}(200+100n-100)

=\frac{n}{2}(100+100n)

=50n+50n^2

Suppose the distance covered in n seconds is 12,000 feet,

\implies 50n+50n^2=12000

n+n^2=240

n^2+n-240=0

n^2+16n-15n-240=0

n(n+16)-15(n+16)=0

(n-15)(n+16)=0

\implies n=15\text{ or }n=-16

∵ n can not be negative,

Hence, after 15 seconds the plane will reach an altitude of 12,000 feet above its takeoff height.

6 0
3 years ago
Read 2 more answers
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