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3 years ago

6.106x10^7 in standard form

Mathematics

1 answer:

Aleksandr-060686 [28]3 years ago

3 0

Start with 6.106. move the decimal over 7 spots to the right.
Your answer will be 61,060,000.

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What is the coefficient of the x^5y^5- term in the biomial expansion of (2x-3y)^10

jasenka [17]

Answer:

The coefficient of $x^{5} \times y^{5} \text { is }=\left(252 \times 2^{5} \times(-3)^{5}\right)=252 \times 32 \times 243=1959552$

Solution:

The given expression is $(2 x-3 y)^{10}$

As per binomial theorem, we know,

$(x+y)^{n}=\sum n C_{k} x^{n-k} y^{k}$

Now here a = 2x, b = (- 3y) and n = 10 and k = 0,1,2,….10

Now $x^{5}\times y^5$ will be the 6 term where k =5

Now, $\mathrm{T}_{6}=10 \mathrm{C}_{5} \times(2 \mathrm{x})^{(10-5)} \times(-3 \mathrm{y})^{5}=10 \mathrm{C}_{5} 2^{5} \times \mathrm{x}^{5} \times(-3)^{5} \times \mathrm{y}^{5}$

So, the coefficient of $x^{5} \times y^{5} \text { is }=10\left(5 \times 2^{5} \times(-3)^{5}\right$ .

$10 \mathrm{C}_{5}=\frac{10 !}{5 ! \times(10-5) !}=\frac{10 !}{5 !+5 !}=\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 !}{5 ! \times 5 !}=\frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2 \times 1}=\left(\frac{30240}{120}\right)=252$

The coefficient of $x^{5} \times y^{5} \text { is }=\left(252 \times 2^{5} \times(-3)^{5}\right)=252 \times 32 \times 243=1959552$

6 0

3 years ago

Find the volume of the cylinder if the height is 3 mm and the diameter is 40 mm. Leave the answer in terms of it.

KiRa [710]

The Volume of cylinder is 3770 cubic millimeters

But, the correct option is not available in options given.

Step-by-step explanation:

Height of cylinder = 3mm

Diameter of cylinder = 40mm

Volume of cylinder = ?

The formula used to find Volume of cylinder is:

$Volume = \pi r^2h$

Putting values in the formula:

Since we need radius,

radius = diameter/2

radius = 40/2

radius = 20 mm

So,

$Volume = \pi r^2h\\Volume = 3.14*(20)^2*3\\Volume = 3.14*400*3\\Volume= 3769.91 or \,\,\,Volume\approx 3770\,\,cubic\,\,millimeters$

The Volume of cylinder is 3770 cubic millimeters

But, the correct option is not available in options given.

Keywords: Volume of cylinder

Learn more about Volume of cylinder at:

#learnwithBrainly

6 0

3 years ago

100 pts help me please.

Natalija [7]

Answer:

Carly's expenditure was $240 and the number of boxes of cards was required is 24 boxes.

Step-by-step explanation:

We know that:

48 + 8(b) = Carly's expenditure
10(b) = Carly's expenditure
48 + 8b = 10b
B = Boxes of cards

Work:

48 + 8b = 10b
=> 48 + 8b - 8b = 10b - 8b
=> 48 = 2b
=> b = 24

Now, let's substitute the value of b into any equation.

10(24)
=> 240

Hence, Carly's expenditure was $240 and the number of boxes of cards was required is 24 boxes.

Hoped this helped.

$BrainiacUser1357$

7 0

2 years ago

Find the equation of the line through point (3,−3) and parallel to y=3x−4. Use a forward slash (i.e. "/") for fractions (e.g. 1/

exis [7]

Answer:

y =3x - 12

Step-by-step explanation:

I'm fairly certain this is the answer.

Consider the point (3,-3). In terms of variables this is written (x,y).

Remember that the equation for slope is y = mx + b.

In that equation, "b" is your y-intercept, and "m" is your slope.

If 2 lines are parallel, they have the same slope but different y-intercepts. So you can use the slope from the equation y=3x-4 to find the parallel line. You can also plug in the values 3 and -3 to solve for b, our y-intercept.

If we set up the equation, we have -3 = 3(3) + b.

Now solve for b.

-3 = 9 + b

Combine like terms, so that -12 = b, and you have your y-intercept.

To create the equation, take out the coordinate pair that the line passes through, and only have the SLOPE and the Y-INTERCEPT showing in the equation.

Therefore, y = 3x - 12

5 0

3 years ago

M/9+2/3=7/3 Solve for m.

Aleks04 [339]

M/9+2/3=7/3
M/9 =7/3 - 2/3
M/9 = 5/3
M = 5/3 x 9
M = 15

3 0

3 years ago