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2 years ago

5 1/4 divided by 1/3 =

Mathematics

2 answers:

shepuryov [24]2 years ago

5 0

I think it's 1 3/4. I had one similar earlier.

Andrej [43]2 years ago

3 0

I think it's 4 7/12 I use to do stuff like that all the time

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Williiam lost 25% of his marble,gave 1/6 of the remainder to his.Brother and had 120 marbles left.How many marbles did he have a

bija089 [108]

Answer:

Number of marbles with Williams at the starting = 192

Step-by-step explanation:

Let total number of marbles with Williams = m

He lost marbles = 25% of the total number

= $\frac{25}{100}\times m$

= $\frac{m}{4}$

Remaining marbles with Williams = m - $\frac{m}{4}$

= $\frac{3m}{4}$

He gave marbles to his brother = $\frac{1}{6}$ th of the remaining marbles

= $\frac{1}{6}\times \frac{3m}{4}$

= $\frac{m}{8}$

Remaining marbles after giving marbles to his brother = 120

Therefore, $\frac{3m}{4}-\frac{m}{8}=120$

$\frac{6m}{8}-\frac{m}{8}=120$

$\frac{5m}{8}=120$

m = $\frac{120\times 8}{5}$

m = 192

Number of marbles with Williams at the starting = 192

5 0

2 years ago

Let f be defined by the function f(x) = 1/(x^2+9)

riadik2000 [5.3K]

(a)

$\displaystyle\int_3^\infty \frac{\mathrm dx}{x^2+9}=\lim_{b\to\infty}\int_{x=3}^{x=b}\frac{\mathrm dx}{x^2+9}$

Substitute x = 3 tan(t ) and dx = 3 sec²(t ) dt :

$\displaystyle\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\frac{3\sec^2(t)}{(3\tan(t))^2+9}\,\mathrm dt=\frac13\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\mathrm dt$

$=\displaystyle \frac13 \lim_{b\to\infty}\left(\arctan\left(\frac b3\right)-\arctan(1)\right)=\boxed{\dfrac\pi{12}}$

(b) The series

$\displaystyle \sum_{n=3}^\infty \frac1{n^2+9}$

converges by comparison to the convergent p-series,

$\displaystyle\sum_{n=3}^\infty\frac1{n^2}$

$\displaystyle \sum_{n=1}^\infty \frac{(-1)^n (n^2+9)}{e^n}$

converges absolutely, since

$\displaystyle \sum_{n=1}^\infty \left|\frac{(-1)^n (n^2+9)}{e^n}\right|=\sum_{n=1}^\infty \frac{n^2+9}{e^n} < \sum_{n=1}^\infty \frac{n^2}{e^n} < \sum_{n=1}^\infty \frac1{e^n}=\frac1{e-1}$

That is, ∑ (-1)ⁿ (n ² + 9)/eⁿ converges absolutely because ∑ |(-1)ⁿ (n ² + 9)/eⁿ| = ∑ (n ² + 9)/eⁿ in turn converges by comparison to a geometric series.

5 0

2 years ago

Help me! what is the domain or range?

Lapatulllka [165]

Domain is [-10,∞)
2 is included , only at x=2 new function begins
Range is the values of y , so range is [-7]∪[-4,6
I think, it should be like this.

5 0

3 years ago

A boat traveled 240 miles downstream and back. The trip downstream took 12 hours. The trip back took 24 hours. What is the speed

RoseWind [281]

Answer:

rate boat = 15 mph

rate current = 5 mph

explanation:

d = r * t

t = d/r

240 / (r_boat + current) = 12 Multiply both sides by r_boat + r_current.

240 = 12(r_boat + current)

240/ (r_boat - current) = 24 Multiply both sides by r_boat - r_current

240 = 24*(r_boat - current)

Since the distances are the same in both equations, you can equate the right side of each.

12 (r_boat + current) = 24(r_boat - current) Divide by 12

r_boat + current = 2 (r_boat - current) Remove the brackets.

r_boat + current = 2*r_boat - 2* current add 2 currents to both sides

r_boat + 3currents = 2*r_boat Subtract r_boat both sides

3 currents = r_boat.

240 = 12*(r_boat + current. Divide by 12

20 = r_boat + current Put 3 currents in for r_boat

20 = 3currents + 1 current Combine

20 = 4 currents Divide by 4

5 = current

The rate of the current = 5 miles / hour

3 currents = r_boat

3*5 = rate_boat

15 = rate of the boat

8 0

2 years ago

-0.5(x + 0.3) – 0.2x = 4.1

lys-0071 [83]

Answer:

x=-8

Step-by-step explanation:

I always change the decimals into whole numbers by multiplying them by 10. If you do this, it is much easier to solve. All you do is multiply every term by 10.

the equation changes to

-5(x+3)-2x=41

-5x-15-2x=41

combine like terms

-7x-15=41

bring the 15 over to the 41

-7x=56

divide everything by 7

-x=8

change x to a positive

x=-8

3 0

3 years ago