All categories

2 years ago

Find the positive value of k such that the area of the region enclosed between the graph y=kcosx and the graph y=kx^2 is 2

1 answer:

4 0

Both these graphs will pass through the origin so you need to work out the difference in areas by integrating

INtegral k cos x (between the limits 0 and a) - Intgral kx^2 ( between 0 and a) = 2
Find k
(where a is the value of x on positive side of the graph where the 2 curves intersect)

You might be interested in

An employee receives a pay increase from $35,000 per year to $37,500 per year. Calculate the percent increase. Round to the near

arsen [322]

Answer:

The percentage increase in salary of employee is 7.14 %

Step-by-step explanation:

Given as :

The initial pay of employee = $35,000 per year

The increase pay of employee = $37,500 per year

Let The percentage increase in salary = X %

So, X = $\frac{increase salary - initial salary}{initial salary}$ × 100

Or, X = $\frac{$37,500 - $35,000}{$35,000}$ × 100

Or, X = $\frac{$2,500}{$35,000}$ × 100

∴ X = 0.0714 × 100 = 7.14 %

Hence The percentage increase in salary of employee is 7.14 % Answer

8 0

2 years ago

Read 2 more answers

A lottery sells 1000 tickets at $1 apiece. There is one winner who receives $100, and 5 second place winners who receive $50 eac

DaniilM [7]

Chance of winning $100 = 1/1000
<span>chance of winning $50 = 5/1000 = 1/200 </span>
<span>cost of ticket = -1 </span>
<span>E[x] = 100* 1/1000 + 50* 1/200 -1 </span>
<span>= 0.1 + 0.25 - 1 = -0.65

Hope this helps</span>

5 0

2 years ago

Ava wants to figure out the average speed she is driving. She starts checking her car’s clock at mile marker 0. It takes her 4 m

VLD [36.1K]

<h2>Answer:</h2>

The average speed of car is:

0.75 miles per minutes.

The equation of line is:

$n=\dfrac{3}{4}t$

<h2>Step-by-step solution:</h2>

The table that describes the time and number of miles marked is given by:

Time Miles

0 0

4 3

8 6

Clearly we could observe that with the increase in time by every 4 minutes the number of mile increases by 3.

i.e. the average speed is calculated as the ratio of change in miles to the change in time.

Hence,

$Average\ Speed=\dfrac{3-0}{4-0}\\\\\\i.e.\\\\\\Average\ Speed=\dfrac{3}{4}=0.75$

Hence, the average speed=0.75 miles per minutes.

Also we will find the equation of the lines that related the miles and time by using the two-point formula.

i.e. any line passing through (a,b) and (c,d) is calculated by using the formula:

$y-b=\dfrac{d-b}{c-a}\times (x-a)$

Here (a,b)=(0,0) and (c,d)=(4,3)

i.e. the equation is given by:

$n-0=\dfrac{3-0}{4-0}\times (t-0)\\\\i.e.\\\\n=\dfrac{3}{4}t$

6 0

2 years ago

Read 2 more answers

Food Express is running a special promotion in which customers can win a free gallon of milk with their food purchase if there i

frez [133]

In this case probability is the likelihood that from 264 customers one customer wins free gallon of milk with his food purchase, or in other words the probability that one customer receives a star on his receipt.
Probability is the ratio of the number of favorable outcomes to the total number of all possible events. From 264 customers, 219 have not received a star. The opposite is to receive a star and that is the situation: (1-219)/264=0.17,

7 0

2 years ago

Emma's square patio below has been area=31 sq ft. She decides to decrease one dimension by 1 foot and decreases the other dimens

Andreas93 [3]

Answer:

4.57ft by 1.57 ft

Step-by-step explanation:

We are given that

Emma's square patio has been area=31 sq.ft

One dimension decrease by 1 foot and other dimension decrease by 4 feet.

We have to find the new dimensions of Emma's patio.

Let x be the side of Emma's square patio