Given, tanx = - 4/3. Lies in 2nd quadrant. Find sinx/2, cosx/2 and tanx/2.

Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its te

Aleonysh [2.5K]

Answer:

t=5.18 minute

Step-by-step explanation:

Using Newton's law of cooling

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

T is temperature of a cup of coffee at any time t $T_{s}$ , is the temperature of the surrounding and k is a constant of proportionality in this negative because temperature is decreasing.

$T(0)=190\\T(1)=170\\T_{s}=66$

$\frac{dT}{dt}=-k(T-T_{s})\\\frac{dT}{(T-T_{s})}=-k*dt\\\int\limits {\frac{1}{T-T_{s} } } \, dT=-\int\limits {k} \, dt\\ln(T-T_{s})=k*t+C\\e*ln(T-T_{s})=e^{k*t+C} \\T-T_{s}=e^{k*t}*e^{C}\\e^{C}=C\\T-T_{s}=e^{k*t}*C\\T=T_{s}+e^{k*t}*C$

To find constant knowing the time and the temperature the first step of the change of energy in cup of coffee

$T=T_{s} +e^{-k*t}*C\\ C=190-66=124\\170=66+124*e^{-k*2}\\ 170-66=124*e^{-k*2}\\ln(\frac{104}{124})=ln*e^{-k*2}\\-0.175=-k*2\\k=0.08794$

Now using the constant of decreasing can find the time to be a 145 temperature the cup of coffee

$145=66+124*e^{-k*t} \\145-66=124*^{-0.087*t}$

$ln(0.637)=ln*e(-0.087*t)\\-0.45=-0.087*t\\t=5.18minutes$

4 0

3 years ago

End of year assessment

tensa zangetsu [6.8K]

Answer:

Don't fail

Step-by-step explanation:

4 0

3 years ago

If the distribution is really (5.43,0.54)

defon

Answer:

0.7486 = 74.86% observations would be less than 5.79

Step-by-step explanation:

I suppose there was a small typing mistake, so i am going to use the distribution as N (5.43,0.54)

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The general format of the normal distribution is:

N(mean, standard deviation)

Which means that:

$\mu = 5.43, \sigma = 0.54$

What proportion of observations would be less than 5.79?

This is the pvalue of Z when X = 5.79. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{5.79 - 5.43}{0.54}$

$Z = 0.67$

$Z = 0.67$ has a pvalue of 0.7486

0.7486 = 74.86% observations would be less than 5.79

7 0

3 years ago

Use point slope form to write the lines with the given slope and point in slope intercept form.m= -1(-5,-4)

lara31 [8.8K]

The slope point form is

$y-y1=m(x-x1)$

m is the slope

x1, y1 are the coordinates of a point on the line

The slope of the line is -1

m = -1

point (-5, -4) lies on the line

x1 = -5 and y1 = -4

Let us substitute them in the form above

$y-(-4)=-1(x-\lbrack-5\rbrack)$

Remember (-)(-) = (+)

$y+4=-1(x+5)$

The equation of the line in the slope-point form is y + 4 = -1(x + 5)

6 0

1 year ago

If f(x)=x+8 and g(x)=-4-3 find (f+g)(x)

Lilit [14]

Answer:

(f+g)(x) = -3x+5

Step-by-step explanation:

f(x)=x+8 and g(x)=-4x-3

(f+g)(x) = f(x) + g(x)

= x+8+-4x-3

= -3x+5

3 0

3 years ago

Given, tanx = - 4/3. Lies in 2nd quadrant. Find sinx/2, cosx/2 and tanx/2.​

Given, tanx = - 4/3. Lies in 2nd quadrant. Find sinx/2, cosx/2 and tanx/2.