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3 years ago

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What is the sum of two numbers that do not have a common factor?

1 answer:

damaskus [11]3 years ago

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the first and last term arithmetic sequence are 9 and 165 respectively.if the sum of all the terms of the arithmetic sequence is

diamong [38]

Answer:

40 terms

Step-by-step explanation:

<u>Sum of n terms formula:</u>

Sn = 1/2n(a1 + an)

<u>Solving for n</u>

3480 = 1/2n(9 + 165)
3480 = 87n
n = 3480/87
n = 40

3 0

3 years ago

Read 2 more answers

I don't understand linear relationships. Can someone explain how it works

Vesna [10]

Linear relationships can be expressed in a graphical format where the variable and the constant are connected via a straight line or in a mathematical format where the independent variable is multiplied by the slope coefficient, added by a constant, which determines the dependent variable.

5 0

2 years ago

Determine whether the improper integral converges or diverges, and find the value of each that converges.

Brrunno [24]

Answer:

Converges at -1

Step-by-step explanation:

The integral converges if the limit exists, if the limit does not exist or if the limit is infinity it diverges.

We will make use of integral by parts to determine:

let:

$u=x$ $dv=e^(2x)\cdot{dx}$

$du=dx$ $v=2\cdot{e^(2x)}$

$\int\limits^a_b {u} \, dv = uv -\int\limits^a_b {v} \, du$

$\int\limits^a_b {x\cdot{e^2^x} \, dx =2xe^2^x- \int\limits^a_b {2e^2^x} \, dx$

$\int\limits^a_b {xe^2^x} \, dx = 2xe^2^x-2e^2^x-C$

We can therefore determine that if x tends to 0 the limit is -1

$\lim_{x \to \0} 2xe^2^x-2e^2^x=0-1=-1$

5 0

3 years ago

Find f(-3) if f(x) = x 2.

vlabodo [156]

Answer:

f(-3) = 9

Step-by-step explanation:

Lets define f(a) first where a is any integer,

f(a) is found out by putting the integer in the function in place of the variable

So for the given question

$f(x) = x^{2}$

In order to find f(-3) we will put -3 in place of x

So putting -3,

$f(-3) = (-3)^{2}$

$f(-3) = 9$

So, the value of function at -3 is 9 ..

5 0

3 years ago

Read 2 more answers

a carpenter has been asked to build an open box with a sqaure base. the sides of the box will cost $3 per m^2 and the base will

slamgirl [31]

<h2>Dimension of box is 2 m x 2 m x 1.33 m</h2>

Step-by-step explanation:

Let a be base side and h be the height.

Volume of box, V = a²h

The sides of the box will cost $3 per m² and the base will cost $4 per m². Cost for making is $48.

That is

4a² + 3 x 4 x a x h = 48

4a² + 12 a x h = 48

a² + 3 ah = 12

$h=\frac{12-a^2}{3a}$

So volume is

$V=a^2\times \frac{12-a^2}{3a}=4a-\frac{a^3}{3}$

At maximum volume we have derivative is zero,

$dV=4da-3\times \frac{a^2}{3}da\\\\0=4-a^2\\\\a=\pm 2$

Negative side is not possible, hence side of square base is 2m.

Substituting in a² + 3 ah = 12

2² + 3 x 2 x h = 12

h = 1.33 m

Dimension of box is 2 m x 2 m x 1.33 m

5 0

3 years ago