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Whitepunk [10]
3 years ago
9

Evaluate the expression without using a calculator. 74 · 6

Mathematics
1 answer:
Reil [10]3 years ago
4 0
The dot means to times, so in reality it's 74 times 6.
=
444
aka
d
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Find the length of line segment KH if K(-1,2) and H(3,5). Round to the nearest tenth if needed
Molodets [167]

   i think that that the answer is 13   Step-by-step explanation:

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3 years ago
2(x + 3) = x - 4 <br>And <br>4(5x-2)=2(9x+3)<br>​
weqwewe [10]

2x+6 - х -4

2x - x = - 4 - 6

x=-10

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3 years ago
The height h(n) of a bouncing ball is an exponential function of the number n of bounces.
Digiron [165]

Answer:

The height of a bouncing ball is defined by h(n) = 6\cdot \left(\frac{4}{6} \right)^{n-1}.

Step-by-step explanation:

According to this statement, we need to derive the expression of the height of a bouncing ball, that is, a function of the number of bounces. The exponential expression of the bouncing ball is of the form:

h = h_{o}\cdot r^{n-1}, n \in \mathbb{N}, 0 < r < 1 (1)

Where:

h_{o} - Height reached by the ball on the first bounce, measured in feet.

r - Decrease rate, no unit.

n - Number of bounces, no unit.

h - Height reached by the ball on the n-th bounce, measured in feet.

The decrease rate is the ratio between heights of two consecutive bounces, that is:

r = \frac{h_{1}}{h_{o}} (2)

Where h_{1} is the height reached by the ball on the second bounce, measured in feet.

If we know that h_{o} = 6\,ft and h_{1} = 4\,ft, then the expression for the height of the bouncing ball is:

h(n) = 6\cdot \left(\frac{4}{6} \right)^{n-1}

The height of a bouncing ball is defined by h(n) = 6\cdot \left(\frac{4}{6} \right)^{n-1}.

5 0
3 years ago
Read 2 more answers
POS<br> 15<br> D<br> 7<br> G<br> Find each length<br> 10<br> CF=<br> FE<br> J.cz<br> E<br> *FD = 22
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3 years ago
A rectangular box is to have a square base and a volume of 40 ft3. If the material for the base costs $0.36/ft2, the material fo
blagie [28]

Answer:

  • length: 2 ft
  • width: 2 ft
  • height: 10 ft

Step-by-step explanation:

The total cost of the top and bottom is $0.36 + 0.14 = $0.50 per square foot.

The total cost of a pair of opposite sides is $0.05 +0.05 = $0.10 per square foot.

A minimum-cost box will have the cost of any pair of opposite sides be the same. Here, that means the box will have a side area that is 5 times the area of the top or bottom.

Since the base is square, that means the box is the shape of 5 cubes stacked one on the other. Each of those would be 8 ft³, so would have edge dimensions of ∛8 = 2 feet. The height is 5 times that, or 10 ft.

The box is 2 feet square by 10 feet high:

  • length: 2 ft
  • width: 2 ft
  • height: 10 ft

_____

If you feel the need to write an equation, you can let x represent the edge length of the base. Then the cost of the top and bottom will be ...

  top&bottom cost = 0.50·x²

The height of the box is 40/x², so the cost of the four sides will be ...

  side cost = (0.05)(4x)(40/x²) = 8/x

This is minimized when the derivative of the sum of these costs is zero:

  cost = top&bottom cost + side cost

  cost = 0.50x² + 8/x

  d(cost)/dx = 1.00x -8/x² = 0

Multiplying by x², we get ...

  x³ -8 = 0

  x = ∛8 = 2 . . . . . . as above

  height = 40/x² = 40/4 = 10 . . . . . as above

6 0
3 years ago
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