5 is a _______ number. prime composite

100 POINTS Evaluate the derivative of the function number 38

patriot [66]

Answer:

1/ sqrt(1+ln^2(x)) * 1/(ln^2x +1) * 1/x

Step-by-step explanation:

f(x) = sin (tan^-1 (ln(x)))

u substitution

d/du (sin u) * du /dx

cos (u) * du/dx

Let u =(tan^-1 (ln(x))) du/dx =d/dx (tan^-1 (ln(x)))

v substitution

Let v = ln x dv/dx = 1/x

d/dv (tan ^-1 v) dv/dx

1/( v^2+1) * dv/dx

=1/(ln^2x +1) * 1/x

Substituting this back in for du/dx

cos (tan^-1 (ln(x)) * 1/(ln^2x +1) * 1/x

We know that cos (tan^-1 (a)) = 1/ sqrt(1+a^2)

cos (tan^-1 (ln(x)) * 1/(ln^2x +1) * 1/x

1/ sqrt(1+ln^2(x)) * 1/(ln^2x +1) * 1/x

8 0

3 years ago

Read 2 more answers

PLEASE HEP ME QUICK!!!!: Tom travels between the two mile markers shown and then finds his average speed in miles per hour. Sele

slega [8]

Answer:

$speed=\frac{195\ miles}{3\ hours}$

$3\ hours=\frac{195\ miles}{speed}$

$3\ hours*(speed)=195\ miles$

Step-by-step explanation:

we know that

The speed is equal to divide the distance by the time

Let

x -----> the distance in miles

y ----> the time in hours

$speed=\frac{x}{y}$

we have

The distance is equal to subtract 35 miles from 230 miles

$x=230-35=195\ miles$

The time is equal to subtract 1:30 pm from 4:30 pm

$y=4:30\ pm-1:30\ pm=3\ hours$

substitute in the formula of speed

$speed=\frac{195\ miles}{3\ hours}$

Isolate 3 hours

$3\ hours=\frac{195\ miles}{speed}$

Isolate 195 miles

$195\ miles=3\ hours*(speed)$

7 0

3 years ago

Jemer lost his ball and decided to buy a new one. the new ball cost $300. which is three times the price of his old ball. how mu

shusha [124]

Answer:

The cost of the old ball was $100.

Step-by-step explanation:

The cost of the new ball = $300

The new ball has three times the price of his old ball.

So, let the price of the old ball be = x

As per situation, we get the equation:

$3x=300$

Dividing both sides by 3:

$\frac{3x}{3}= \frac{300}{3}$

=> x = 100

Hence, the cost of the old ball was $100.

8 0

3 years ago

Zane buys a standard class train ticket.

GaryK [48]

Step-by-step explanation:

15 / 100 × 34

5.1 price he save

6 0

2 years ago

Read 2 more answers

Regina brought 8 7/8 pound of fruit for her family . She brought 3 1/2 pound of oranges and 2 3/4 pound of peaches and some appl

butalik [34]

Answer:

Regina has bought $2\frac{5}{8}\ pounds$ of apples.

Step-by-step explanation:

Given:

Amount of fruit brought = $8\frac{7}{8}\ pounds$

Now given number is in mixed fraction we will convert into improper fraction.

To convert a mixed fraction to an improper fraction, we will Multiply the whole number part by the fraction's denominator. Add that to the numerator,Then write the result on top of the denominator.

So we can say that;

$8\frac{7}{8}\ pounds$ can be Rewritten as $\frac{71}{8}\ pounds$

Amount of fruit brought = $\frac{71}{8}\ pounds$

Also given:

Amount of oranges bought = $3\frac12\ pounds$

$3\frac12\ pounds$ can be Rewritten as $\frac{7}{2}\ pounds$

Amount of oranges bought = $\frac{7}{2}\ pounds$

Amount of peaches bought = $2 \frac34\ pounds$

$2 \frac34\ pounds$ can be Rewritten as $\frac{11}{4}\ pounds$

Amount of peaches bought = $\frac{11}{4}\ pounds$

We need to find amount of apples bought by Regina.

Solution:

Let the amount of apples bought be 'x'

Now we know that;

Amount of fruit brought is equal to sum of Amount of oranges bought and Amount of peaches bought amount of apples.

framing in equation form we get;

$\frac{71}{8}=\frac{7}{2}+\frac{11}{4}+x\\\\x=\frac{71}{8}-\frac{7}{2}-\frac{11}{4}$

Now we will make the denominator common using LCM we get.

$x=\frac{71\times 1}{8\times 1}-\frac{7\times4}{2\times4}-\frac{11\times2}{4\times2}\\\\x=\frac{71}{8}-\frac{28}{8}-\frac{22}{8}$

Now denominators are same so we will solve the numerator.

$x=\frac{71-28-22}{8}\\\\x=\frac{21}{8}\ pounds$

Now $\frac{21}{8}\ pounds$ can be Rewritten as $2\frac{5}{8}\ pounds$

Hence Regina has bought $2\frac{5}{8}\ pounds$ of apples.

5 0

3 years ago