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3 years ago

2hr 57min+3hrs42min

Mathematics

2 answers:

Mademuasel [1]3 years ago

6 0

Answer:

6hr 39 min

Step-by-step explanation:

Add both

2hr 57 min

+ 3hr 42 min

5hr 99 min

we know that 1 hr = 60 min

then , 99 min = 1hr 39 min

so, 5hr + 1hr 39min

= 6hr 39 min

Ber [7]3 years ago

4 0

Answer:

6 hrs 33 minutes

Step-by-step explanation:

2hr 57min

+3hrs42min

----------------------

5 hrs 99 minutes

But 1 hr = 60 minutes so subtract 60 minutes and add 1 hour

6 hrs 33 minutes

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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

2 years ago

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cupoosta [38]

3 because I did the quiz and got it right txt me if you need help

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3 years ago

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A Theater Has 35 seats in the first row, 38 seats in the second row, 41 seats in the third row, and so on. How many seats are th

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2 years ago

Find the distance (-4,5) and (7,18)

seropon [69]

Answer:

$\sqrt{290}\ units$

Step-by-step explanation:

The distance between points $(x_1,y_1)$ and $(x_2,y_2)$ is

$\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

Hence, the distance between points $(-4,5)$ and $(7,18)$ is

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3 0

3 years ago

A cottage has a gable roof. To the nearest foot, how wide is the cottage?A. 12 ftB. 24 ftC. 35 ftD. 70 ft

Sergio [31]

Answer: the answer is B: 24ft

Step-by-step explanation: To find how wide the triangle is identify your angles. You have a right angle which is equal to 90° and an angle that measures 46°. Add up both of these angles and you'll get 136°. A triangle can only have three angles that add up to 180. So subtract 180 and 136 you get 44. Multiply the hypotenuse by sin(46) to get the length of the side facing the opposite way of the angle that measures 44°. You will get 11.8 which is about 12. The other triangle is a congruent triangle meaning that it's angles and sides are the same. Add both 12's up and you have 24ft as your width for the cottage.

7 0

2 years ago

2hr 57min+3hrs42min​

2hr 57min+3hrs42min