Write the equation of a line with a slope of O through the point (3, -1).

Newton’s law of cooling states that the temperature of an object changes at a rate proportionalto the difference between the tem

Verizon [17]

Answer:

$\frac{dT}{dt} = -0.05\;min^{-1} (T-70\ºF)$

Step-by-step explanation:

Hi!

Lets call:

T = temprature of the object

T₀ = temperature of surroundings

t = time

The rate of change of T is its derivative with respecto to time. If T > T₀, the object looses heat, so T decreases. Then, being k > 0:

$\frac{dT}{dt} = -k(T-T_0) \\$

In this case T₀ = 70ºF and k = 0.05/min. Then the differential equation is:

$\frac{dT}{dt} = -0.05\;min^{-1} (T-70\ºF)$

3 0

3 years ago

4) Choose the correct inequality for this situation.

Ksenya-84 [330]

Answer:

B. 21x + 40 ≤ 124

Step-by-step Explanation:

Maximum amount budgeted = $124 (this means they can't spend more than this)

x = number of people

Cost per head = $21

Given that Mr Walter already spent $40, which is part of the money budgeted, the number of people that can go canoeing cam be expressed with the following inequality:

21x + 40 ≤ 124

(note: the amount total to be spent will either be equal to or greater than $124, because it's the maximum amount budgeted for spending).

6 0

3 years ago

Write the first four terms in the following sequences. A(n+1)=12 A(n) for n≥1 and A(1)=4 .

ycow [4]

Answer:Such sequences can be expressed in terms of the nth term of the sequence. In this case, the nth term = 2n. To find the 1st term, put n = 1 into the formula, to find the 4th term, replace the n's by 4's: 4th term = 2 × 4 = 8

3 0

3 years ago

Each morning, Hungry Harry eats some eggs. On any given morning, the number of eggs he eats is equally likely to be 1, 2, 3, 4,

mamaluj [8]

Answer:

Mean = 35

Variance = 291.7

Step-by-step explanation:

Data provided in the question:

X : 1, 2, 3, 4, 5, 6

All the data are independent

Thus,

The mean for this case will be given as:

Mean, E[X] = $\frac{\textup{Sum of all the observations}}{\textup{Total number of observations}}$

or

E[X] = $\frac{\textup{1+2+3+4+5+6}}{\textup{6}}$

or

E[X] = 3.5

For 10 days, Mean = 3.5 × 10 = 35

And,

variance = E[X²] - ( E[X] )²

Now, for this case of independent value,

E[X²] = $\frac{1^2+2^2+3^2+4^2+5^2+6^2}{\textup{6}}$

or

E[X²] = $\frac{1+4+9+16+25+36}{\textup{6}}$

or

E[X²] = $\frac{91}{\textup{6}}$

or

E[X²] = 15.167

Therefore,

variance = E[X²] - ( E[X] )²

or

variance = 15.167 - 3.5²

or

Variance = 2.917

For 10 days = Variance × Days²

= 2.917 × 10²

= 291.7

3 0

3 years ago

Can someone help me with this

melisa1 [442]

First part
option 2 p=KB

second part
p=$155,000k

or we can also find the value of k first
then the answer will be different :/

7 0

2 years ago