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3 years ago

Determine whether each of the functions log(n + 1) and log(n2 + 1) is o(log n)

1 answer:

8 0

Assuming the order required is as n-> inf.

As n->inf, o(log(n+1)) -> o(log(n)) since the 1 is insignificant compared with n.

We can similarly drop the "1" as n-> inf, the expression becomes log(n^2+1) ->
log(n^2)=2log(n) which is still o(log(n)).

So yes, both are o(log(n)).

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Gold has a density of 0.70 pounds per cubic inch and copper has a density of 8.96 grams per cubic centimeter. How much will 1

never [62]

Answer:

1 cubic foot of gold will weigh 1209.6 pounds

1 cubic foot of copper will weigh 559 pounds.

Step-by-step explanation:

Density = Mass/Volume

Mass = Density × Volume

Volume of each metal = 1 ft³

a) Gold

Density of Gold = 0.70 pounds per cubic inch(lb/in³)

We will be converting the Volume of gold from cubic foot to cubic inches

The Volume of gold given in the question = 1 cubic foot = 1 ft³

1 cubic foot = 1728 cubic inches

Hence, the volume of Gold = 1728 in³

Mass of Gold = Density of Gold × Volume of Gold

Mass of Gold = 0.70Ib/in³ × 1728 in³

= 1209.6 lb(pounds)

2) Copper

Density of copper = 8.96 grams per cubic centimeter

Ib = pounds

We convert this density in g/cm³ to ib/in³

453.5g = 1 Ib

8.96g = y Ib

Cross Multiply

= 453.5g × y Ib =8.96g × 1 Ib

= y Ib = 8.96g × 1 Ib/453.5g

y Ib = 0.0197574421 Ib

Density of Copper = 0.0197574421 Ib/cm³

28,316.8 cm³ = 1 ft³

1 cm³ = x ft³

x ft³ = 1 cm³ × 1 ft³/28,316.8cm³

x ft³ = 0.0000353147 ft³

1 cm³ = 0.0000353147 ft³

We have to convert the density of Copper from Ib/cm³ to Ib/ft³

0.0197574421 Ib/cm³ = 0.0197574421 Ib/0.0000353147 ft³

559.46793026 Ib/ft³

Volume of copper = 1ft³

Mass = Density × Volume

Mass of copper = 559.46793026 Ib/ft³ × 1 ft³

= 559.46793026 Ib or pounds

≈ 559 pounds

Therefore , the weight of gold is 1209.6 pounds and the weight of copper will be 559 pounds.

7 0

3 years ago

Help me please 8th grade homework

olga2289 [7]

Ok I will text me at this number 8034124482 I'll help you with the homework on there

7 0

3 years ago

Read 2 more answers

32) In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a m

topjm [15]

Answer:

0.1946 is the probability that the September energy consumption level is between 1100 kWh and 1250 kWh.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 990 kWh

Standard Deviation, σ = 198 kWh

We are given that the distribution of energy consumption levels is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(September energy consumption level is between 1100 kWh and 1250 kWh)

$P(1100 \leq x \leq 1250)\\\\ = P(\displaystyle\frac{1100 - 990}{198} \leq z \leq \displaystyle\frac{1250 -990}{198}) \\\\= P(0.5556 \leq z \leq 1.3131)\\\\= P(z \leq 1.3131) - P(z < 0.5556)\\\\= 0.9054- 0.7108= 0.1946$

0.1946 is the probability that the September energy consumption level is between 1100 kWh and 1250 kWh.

4 0

3 years ago

Find QR. 18+x + 2x+23=17<br>

Tasya [4]

Step-by-step explanation:

1.) x+2x=17-18-23

2)3x=-24

3)x=. -8

3 0

2 years ago

The expression 16x2 +40x+25 represents the area of a square rooftop. Write an expression that represents the perimeter of the ro

Leni [432]

Question

The expression 16x2 +40x+25 represents the area of a square rooftop. Write an expression that represents the perimeter of the rooftop?

Answer:

Step-by-step explanation:

Find the lenght with the inverse formula.

If A = l²

l = √A

then you find the perimeter multipling l * 4

your expression is:

4 * √(16x2 +40x+25)

6 0

3 years ago