Find the volume of the regular triangular pyramid.

Determine whether the improper integral converges or diverges, and find the value of each that converges.

Ksju [112]

Answer:converge at $I=\frac{1}{3}$

Step-by-step explanation:

Given

Improper Integral I is given as

$I=\int^{\infty}_{3}\frac{1}{x^2}dx$

integration of $\frac{1}{x^2}$ is - $\frac{1}{x}$

$I=\left [ -\frac{1}{x}\right ]^{\infty}_3$

substituting value

$I=-\left [ \frac{1}{\infty }-\frac{1}{3}\right ]$

$I=-\left [ 0-\frac{1}{3}\right ]$

$I=\frac{1}{3}$

so the value of integral converges at $\frac{1}{3}$

8 0

3 years ago

5 1/6 + (7 1/3)l <60

agasfer [191]

Answer:

$l$

Step-by-step explanation:

Given the inequality

$5\dfrac{1}{6}+7\dfrac{1}{3}l$

First, convert mixed numbers to improper fractions:

$5\dfrac{1}{6}=\dfrac{5\cdot 6+1}{6}=\dfrac{31}{6}\\ \\7\dfrac{1}{3}=\dfrac{7\cdot 3+1}{3}=\dfrac{22}{3}$

Now the inequality looks like

$\dfrac{31}{6}+\dfrac{22}{3}l$

Multiply it by 6:

$\dfrac{31}{6}\cdot 6+\dfrac{22}{3}l\cdot 6$

7 0

3 years ago

Colton earns $35 per lawn he mows. In kne day he mows four lawns and he works five days a week for 20 weeks a year. His expenses

yanalaym [24]

Answer:

1) Consider that he makes $1189 every two weeks engaged with work

2) An estimate of the opportunity cost of going on the fishing trip is $1450 in two weeks

3). If he decides to buy the truck, he has to work for about 7 weeks before going on the fishing trip

Step-by-step explanation:

From the given data

Total revenue from lawn mowing per year = 35 × 4× 5×20 = $1400

Similarly total operating costs = $2110

Total profit per annum = $11890

However total revenue per every 2 weeks = $1189

To buy the truck, sell his and go on the fishing trip it will cost = 5200-1500+250 =$3950 hence he has to work for about 6.64 or approximately 7 weeks before going on the fishing trip

2) Opportunity cost will factor in the cost of having someone work for him while away

The cost is = $250 + $120/day

Hence in two weeks it will cost him $1450

3) He has to work for about 7 weeks to be able to afford the truck

7 0

3 years ago

There are 60 people in a class. 10 are women. if we form a committee by randomly choosing 5 people, what is the probability that

IceJOKER [234]

To determine the probability that there will be no women, you need to find the probability of women and subtract it from the total

60 - 10 = 50

so you find the probability with the total number of people being 50, that way the women's probability is eliminated.

5 out of 50 multiplied by the original total of the people, 60

(5÷50)×60 = 6

Therefore the probability of randomly choosing 5 people, excluding women is 6

6 0

3 years ago

Find the value of x pls I’ll give brainleist.

KATRIN_1 [288]

Answer:

x=15°

Step-by-step explanation:

We can see angle 6x-5 has a corresponding angle above it, which is congruent to it. That angle is supplementary with angle 7x-10. We can tell because it forms a straight angle with it. Supplementary angles add to 180°.

(7x-10)+(6x-5)=180

7x-10+6x-5=180

13x-15=180

13x=195

x=15

5 0

3 years ago