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worty [1.4K]
3 years ago
7

the width of an architects desk is represented by four times x squared and the length is represented by the expression 2x cubed.

what represents the area of the tabletop
Mathematics
1 answer:
Alika [10]3 years ago
4 0
You will use the formula A=lw to find the area. Substitute 2x^3 in for the length and 4x^2 for the width. You would multiply both of these. 2×4 = 8, and x cubed times x squared equals X to the fifth power. You will add the exponents together because the exponent tells you how many times to multiply that value. If there are three x multiplied together (in x cubes) and two x multiplied together(in x squared) that makes five x multiplied together. The answer is represented as A=8x^5. ^ means to the power of.
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Newton's Law of Cooling states that the rate of change of the temperature of an object, T, is proportional to the difference of
maria [59]

Answer:

  305 °F

Step-by-step explanation:

The core temperature of the object after 4 hours can be found using an exponential decay formula to model the decay of the difference between core temperature and ambient.

<h3>Cooling Model</h3>

The solution to the differential equation described by Newton's law of cooling is the exponential equation ...

  y = ab^t +c

where 'a' is the initial core temperature difference from ambient, 'b' is the decay factor of that difference in 1 unit of time period t. 'c' is the ambient temperature.

For this problem, the ambient temperature is c=80, and the differences of interest are ...

  a = 1200 -80 = 1120

  b = (830 -80)/1120 = 75/112

Using these values in the model gives ...

  y = 1120(75/112)^t +80 . . . . . . where y(t) is the core temperature at time t

Note that units of time are hours.

<h3>Application</h3>

We want y when t=4.

  y = 1120(75/112)^4 +80 ≈ 1120(0.20108) +80 ≈ 305.212

The core temperature after 4 hours is about 305 °F.

__

<em>Additional comment</em>

The differential equation will have a solution of the form ...

  T-T_R=(T_0-T_R)e^{kt}

where k = ln(75/112) ≈ -0.40101

In the above, we defined b = e^k = 75/112. Accuracy with this fraction can be better than using a truncated value of k.

5 0
2 years ago
Rewrite in slope-intercept form and show your work.<br> -2x + 5y = 10
bearhunter [10]
Slope intercept form
y = mx + b
-2x + 5y = 10
5y = 2x + 10
Divide by 5
y = 2/5x + 2
8 0
2 years ago
Read 2 more answers
Your sock drawer has 3 pairs of black socks, 4 pairs of brown socks, 1 pair of yellow socks and 5 pairs of blue socks. you reach
erik [133]
All socks together: 13
Black socks: 3

Probability to pick out black socks: 3/13

After one pick out (You picked out a pair of black socks):

Probability to pick out black socks: 2/12

Multiply them:

2/12 * 3/13 = 1/26 ≈ 0,038

8 0
3 years ago
Which function increases at a faster rate on 0 to infinity, f(x) = x2 or g(x) = 2x? Explain your reasoning.
pochemuha

Using a table of values, the outputs of f(x) for whole numbers are 0, 1, 4, 9, 16, 25, 36, and so on. For the same input values, g(x) has outputs of 1, 2, 4, 8, 16, 32, and 64. Continuing to double the output each time results in larger outputs than those of f(x). The exponential function, g(x), has a constant multiplicative rate of change and will increase at a faster rate than the quadratic function.

(ed. just click all of them)


9 0
3 years ago
Read 2 more answers
Use the given equation to find the number<br><br> 1/2x-19.7=-4.1
Leokris [45]

Answer:

the number is 31.2

Step-by-step explanation:

Given that:

1/2x-19.7=-4.1

Adding 19.7 on both sides:

1/2x-19.7 + 19.7=-4.1 + 19.7

1/2x = 15.6

Multiplying both sides by 2:

x = 15.6 * 2

x = 31.2

So the number is 31.2

i hope it will help you!

7 0
3 years ago
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