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3 years ago

Write an expression in terms of x that represents the distance between (2,10) and (x,10) for x>2.

Mathematics

1 answer:

ehidna [41]3 years ago

7 0

Answer:

Step-by-step explanation:

$d=\sqrt{(x-2)^2+(10-10)^2} =\sqrt{(x-2)^2}=x-2$

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Please help!! If f (x) = e^x sin x, then f’ (x) =

shusha [124]

Answer:

$f'(x) = {e}^{x}( \sin x + \cos x )$

Step-by-step explanation:

$f(x) = {e}^{x} \sin x \\ \\ f'(x) = \sin x \frac{d}{dx} {e}^{x} + {e}^{x} \frac{d}{dx} \sin x \\ \\ f'(x) = \sin x \: {e}^{x} +{e}^{x} \cos x \\ \\ f'(x) = {e}^{x}( \sin x + \cos x )$

5 0

3 years ago

Find the value of r so the line that passes through the pair of points has the given slope. (3, 5), (−3, r), m=34

frez [133]

The value (y2) of r = 1/2.

This question relates to equation of a straight line but we are looking for the slope in this case.

<h3>Slope</h3>

This is the ratio to which we measure the change along the y-axis to the change along the x-axis. The formula is given as

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Data given;

x1 = 3
x2 = -3
y1 = 5
y2 = r
m = 34 or 3/4

Substitute the values into the equation and solve for the unknown

NB; we are assuming that the slope here is 34 and not 3/4.

$m = \frac{y_2 - y_1}{x_2 - x_1} \\34 = \frac{r - 5}{-3 - 3}\\34 = \frac{r - 5}{-6}\\$

cross multiply both sides and make r the subject of formula

$34 * -6 = r - 5\\-204 = r - 5\\r = -204+5\\r = -199$

the value of r = -199.

This is not mathematically obtainable and we would use 3/4 as the value of slope

$\frac{3}{4}= \frac{r - 5}{-3 - 3}\\\frac{3}{4}=\frac{r - 5}{-6}\\4(r-5) = 3 * -6\\4r- 20 = -18\\4r = -18 +20\\4r = 2\\r = \frac{1}{2}$

The most logical value of r = 1/2

Learn more on slope here;

brainly.com/question/4074386

7 0

3 years ago

According to national data, 5.1% of burglaries are cleared with arrests. A new detective is assigned to six different burglaries

blagie [28]

Answer:

26.95% probability that at least one of them is cleared with an arrest

Step-by-step explanation:

For each burglary, there are only two possible outcomes. Either it is cleared, or it is not. The probability of a burglary being cleared is independent of other burglaries. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$