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3 years ago

Find the 11th term of the arithmetic sequence -2x,-8,-9x,-11,-16x,-14

Mathematics

1 answer:

Valentin [98]3 years ago

5 0

Answer:

in an arithmetic series, an = a0+ (n-1) *d

that means the nth term is equal to the first term plus n-1 times the common difference.

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Which factorization is equivalent to this expression<br> -32xy + 20y - 14

densk [106]

Answer:

-2(16xy-10y+7)

Step-by-step explanation:

-2(16xy-10y-7)= -2×16xy-2(-10y)-2×7

-2(16xy-10y+7)= -32xy+20y-14

3 0

3 years ago

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A 748-N man stands in the middle of a frozen pond of radius 4.0 m. He is unable to get to the other side because of a lack of fr

Ber [7]

Answer:

The man will take 64 seconds to reach to the south shore of the frozen pond.

Step-by-step explanation:

Given:

Weight of the man = 748 N Mass of the man, $(m)= \frac{W}{g}$ = $\frac{748}{9.8}$ = $76.32$ kg

Radius of the pond $(r)$ = 4 m

Mass of the textbook = 1.2 kg

Velocity at which the textbook is thrown = 4 ms^1

We have to find the velocity of the man after the throw.

Let the velocity is $V_m$ .

Now using law of conservation of momentum we can find the $V_m$ value.

$m_(_b_)V_b_(_i_) +m_(_m_)V_m_(_i_) =m_(_b_)V_b_(_f_)+m_(_m_) V_m_(_f_)$

Considering $V_m_(_f_)=V_m$

And initial velocity of both the man and book i.e $V_b_(_i_)=0,\ V_m_(i_)=0$

So,

⇒ $0 =m_(_b_)V_b_(_f_)+m_(_m_) V_m$

⇒ Plugging the values.

⇒ $V_m=-\frac{m_(_b_)V_b_(_f_)}{m_(_m_)}$

⇒ $V_m=-\frac{1.2\times 4}{76.32}$

⇒ $V_m=-0.062$ ms^-1

Here the negative velocity is meant for opposite direction of the throw.

Numerically we will write, $V_m = 0.062$

With this velocity the man will move towards south.

We have to calculate the time taken by the man to move to its south shore.

And we know $velocity(v)\times time(t) = distance(d)$

Let the time taken be $t$ and $v\times t = d$ and $d=r$ then, $V_m\times t=r$

Then

⇒ $t=\frac{radius\ (r)}{V_m}$

⇒ Plugging the values.

⇒ $t=\frac{4}{0.062}$

⇒ $t =64$ sec

The man will take 64 seconds to reach to the south shore of the frozen pond (circular).

5 0

3 years ago

The value of the surface area of the cylinder is equal to the value of the volume of the cylinder. Find the value of x.

zlopas [31]

Answer:

$x = 2.5$

Step-by-step explanation:

Surface area of cylinder = 2πr(h + r)

Volume of cylinder = πr²h

Given that S.A = Volume of the cylinder, therefore, we have:

2πr(h + r) = πr²h

Radius (r) is given as 2.5 cm

height (h) = x cm

Input the values and solve for x

2πr(h + r) = πr²h

2πr(h + r) = πr(rh)

2(h + r) = rh (πr cancels πr)

$2(x + 2.5) = 2.5*x$

$2x + 5 = 2.5x$

Subtract 2x from both sides

$2x + 5 - 2x = 2.5x - 2x$

$5 = 0.5x$

Divide both sides by 0.5

$\frac{5}{0.5} = \frac{0.5x}{0.5}$

$2.5 = x$

$x = 2.5$

8 0

3 years ago

a 4.50 g coin of copper absorbed 54 calories of heat. what was the final temperature of the copper if the initial temperature wa

I am Lyosha [343]

The final temperature of copper is 155.43°C.

Step-by-step explanation:

The formula to apply is Q=m*Δt*c where ;

Q=heat energy, m=mass, c=specific heat capacity and Δt= change in temperature

Given that Q=54 calories , m=4.50 g and c=0.092 cal/g°C

In this question find Δt then ,the final temperature.

Δt=Q/m*c

Δt=54/4.50*0.092 =130.43°C

To find final temperature, apply the formula;

Δt=Final temperature - Initial temperature

130.43°C=Final temperature-25°C

130.43°C+25°C=Final temperature

155.43°C

Learn More

Specific Heat Capacity : brainly.com/question/12431744

Keyword : specific heat capacity

#LearnwithBrainly

3 0

3 years ago

How many time larger is 9x10^-8 than 3x10^-12

kkurt [141]

Step-by-step explanation:

$\frac{9 \times 10 {}^{ - 8} }{3 \times 10 {}^{ - 12} }$

Apply Quoteint of Powers. Divide the intergers. serpately.

Note that Quotient of Powers is

$\frac{a {}^{x} }{a {}^{y} } = a {}^{x - y}$

So the answer is

$3 \times 10 {}^{ - 8 + 12} = 3 \times 10 {}^{4}$

The answer is

$3 \times 10 {}^{4}$

$30000$

3 0

3 years ago

Read 2 more answers