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3 years ago

11

Evaluate ∫ e3x dx. ExplAin answers please

1 answer:

Rufina [12.5K]3 years ago

7 0

Hello,
PLease, see the attached file.
Thanks.

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If 6 workers can paint a house in 2 days; how

FinnZ [79.3K]

Answer:

0, because the house is already painted. If this isn't a riddle then, it should take 4 days because that is half the people, two times the workload per person.

6 0

3 years ago

Read 2 more answers

The sum of two terms of gp is 6 and that of first four terms is 15/2.Find the sum of first six terms.

Gnoma [55]

Given:

The sum of two terms of GP is 6 and that of first four terms is $\dfrac{15}{2}.$

To find:

The sum of first six terms.

Solution:

We have,

$S_2=6$

$S_4=\dfrac{15}{2}$

Sum of first n terms of a GP is

$S_n=\dfrac{a(1-r^n)}{1-r}$ ...(i)

Putting n=2, we get

$S_2=\dfrac{a(1-r^2)}{1-r}$

$6=\dfrac{a(1-r)(1+r)}{1-r}$

$6=a(1+r)$ ...(ii)

Putting n=4, we get

$S_4=\dfrac{a(1-r^4)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1-r^2)(1+r^2)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1+r)(1-r)(1+r^2)}{1-r}$

$\dfrac{15}{2}=6(1+r^2)$ (Using (ii))

Divide both sides by 6.

$\dfrac{15}{12}=(1+r^2)$

$\dfrac{5}{4}-1=r^2$

$\dfrac{5-4}{4}=r^2$

$\dfrac{1}{4}=r^2$

Taking square root on both sides, we get

$\pm \sqrt{\dfrac{1}{4}}=r$

$\pm \dfrac{1}{2}=r$

$\pm 0.5=r$

Case 1: If r is positive, then using (ii) we get

$6=a(1+0.5)$

$6=a(1.5)$

$\dfrac{6}{1.5}=a$

$4=a$

The sum of first 6 terms is

$S_6=\dfrac{4(1-(0.5)^6)}{(1-0.5)}$

$S_6=\dfrac{4(1-0.015625)}{0.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Case 2: If r is negative, then using (ii) we get

$6=a(1-0.5)$

$6=a(0.5)$

$\dfrac{6}{0.5}=a$

$12=a$

The sum of first 6 terms is

$S_6=\dfrac{12(1-(-0.5)^6)}{(1+0.5)}$

$S_6=\dfrac{12(1-0.015625)}{1.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Therefore, the sum of the first six terms is 7.875.

5 0

3 years ago

Jackson's hair was 7 centimeters long after his last haircut, and it grows 5 centimeters every year. Jackson last got his hair c

ahrayia [7]

37 cm sijsuensneneuxkeme

7 0

3 years ago

According to this diagram, what is the sin of 28?

vivado [14]

I think the answer may be C

8 0

3 years ago

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A cardboard box without a top is to have volume 62500 cubic cm. find the dimensions which minimize the amount of material used.

bezimeni [28]

Answer: A cardboard box without a lid is to have a volume of 32,000 cubic cm. Find the dimensions that minimize the amount of cardboard used

. ans: base 40 x 40, height = 20

Solution:

The typical box might look like the one below

where . In addition we have xyz = 32000 ,so we need to minimize .

We have,

From the geometry of the problem so y = x. So or x = 40.

Finally, y = x = 40 and z = 32000/(xy)=20.

8 0

3 years ago