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2 years ago

1/6(j-1)+4=1/5(3j+1)

Mathematics

1 answer:

svp [43]2 years ago

5 0

Answer:8.385

Step-by-step explanation:

Step 1: multiply both sides by 30 (this sounds crazy, but that's 5 and 6's least common multiple) 1/6(j-1)+4=1/5(3j+1) -> 5(j-1)+120=6(3j+1)

Step 2: Distribute 5(j-1)+120=6(3j+1) -> 5j-5+120=18j+6

Step 3: Combine like terms 5j-5+120=18j+6 -> 5j+115=18j+6

Step 4: Isolate the variable 5j+115=18j+6 -> 109=13j

Step 5: Divide to further isolate 109/13=j= 8.385

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If an object is moving at a speed of 6 meters per second for a time of 5 seconds, how far did the object travel? A. 35 meters B.

Cerrena [4.2K]

Answer: D 30 meters

Step-by-step explanation:

5 multiplied by 6 is 30

3 0

3 years ago

15+ Points for Best Answers!!

Bogdan [553]

1) mesure of an arc= R.Ф, where R is the radius & Ф the angle <span>IN RADIAN

32</span>°===>8π/45 OR 0.5585, So mes of Arc CD = 6x0.5585 = 3.35 cm

2) DAC = 31° & CAD =27° , these 2 angles being adjacent I can write that

Angle(DAC +CAB=DCB) ==>Angle DCB =(31°+27°=58°)

To remember that any vertex of an angle on the circles, its sides intercept an arc which mesure is twice the angle,

Hence since mes Angle DCB=58°, that means the ARC intercepted, namely DB has a length of 2x 58 = 116°

6 0

4 years ago

The total surface area of a closed cylinder is

Degger [83]

The maximum volume of the cylinder is 27147.355 at the maximum point $r = \frac{50}{\sqrt{3} }$ .

<h3>How do you find the maximum volume of the cylinder?</h3>

The formula for the volume of the cylinder v = $\pi$ $r^{2}$ h, To find the maximum volume of the cylinder we apply the condition of maxima $\frac{\mathrm{d} v}{\mathrm{d} r}$ = 0.

Let r cm be the radius and h cm be the height of the closed cylinder.

Then, Total surface area of the cylinder = $2\pi r(r+h)$

$5000$ = $2\pi r^{2} +2\pi rh$

$h$ = $\frac{5000-2\pi r^{2} }{2\pi rh}$ .............(1)

Volume of the cylinder v = $\pi r^{2} h$

Substitute the value of $h$ in the above equation

$\Rightarrow$ = $\pi r^{2}$ × $\left [ \frac{5000-2\pi r^{2}}{2\pi r} \right ]$

$\Rightarrow$ = $\frac{r}{2}$ × $(5000-2\pi r^{2} )$

$\Rightarrow$ v = $2500r-\pi r^{3}$ ..............(2)

Now, for the maximum volume of the cylinder $\frac{\mathrm{d} v}{\mathrm{d} r}$ = 0

$\Rightarrow$ $\frac{\mathrm{d} (2500r-\pi r^{3})}{\mathrm{d} r} = 0$

$\Rightarrow$ $3\pi r^{2} = 2500$

$\Rightarrow$ $r^{2} = \frac{2500}{3\pi }$

$\Rightarrow$ $r = \frac{50}{\sqrt{3\pi } }$

Volume is maximum for $r = \frac{50}{\sqrt{3\pi } }$

Then, v = $2500r-\pi r^{3}$

$\Rightarrow$ = $2500 \frac{50}{\sqrt{3\pi } } -\pi (\frac{50}{\sqrt{3\pi } } )^{3}$

$\Rightarrow$ = $\frac{125000}{\sqrt{3\pi } } - \frac{125000}{3\sqrt{3\pi } }$

$\Rightarrow$ = $\frac{125000}{\sqrt{3\pi } }$ × $\frac{2}{3}$

$\Rightarrow$ = $\frac{250000}{3\sqrt{3\pi } }$

$\Rightarrow$ v = 27147.355

Hence, The maximum volume of the cylinder is 27147.355 at the maximum point $r = \frac{50}{\sqrt{3} }$ .

To learn more about total surface area and volume of the cylinder from the given link

brainly.com/question/16095729

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3 0

2 years ago

The circumference of a circle is 56.52 meters. What is the radius of the circle?

NISA [10]

2*pi*r = 56.52 ........................................ r = 56.52/2pi ........................................... r = 56.52/6.28 ........................................ r = 9..............

8 0

3 years ago

Pleaseeee help on question 3 and 5 pleaseeeee wuick thank youuuuuuuuu

elena55 [62]

Answer:

3a, 13cm 5, 1:200

Step-by-step explanation:

In the question 3 you just have to divide all of those numbers with that 5000, maybe also make them cm so it makes more sense. So 650m = 65000cm:5000= 13cm

then for the question 5, make the km to cm, so 4.2km would be 420000cm. Then you have to divide that 420000cm with the 21 cm, so 420000:21= 200. Then the scale should be 1:200

I had difficulties with these as well. If you need extra help with the task 3 please pm me :)

7 0

4 years ago