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2 years ago

length of a rectangle is 4x^2 + 12x and the area of the rectangle is 24x^4 + 72x^3 what is the width of the rectangle

Mathematics

1 answer:

Valentin [98]2 years ago

3 0

Square Perimeter = 4(4x-1)

Rectangle Perimeter = 2(2x+1) + 2(x+2)

Square Perimeter = Rectangle Perimeter

4(4x-1) = 2(2x+1) + 2(x+2)

16x - 4 = 4x + 2 + 2x + 4

16x - 4 = 6x + 6

-6x +4 -6x +4

10x = 10

x = 1

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Find r if 0=pi/6 rad sector 64m^2

kap26 [50]

Given:

Area of a sector = 64 m²

The central angle is $\theta=\dfrac{\pi}{6}$ .

To find:

The radius or the value of r.

Solution:

Area of a sector is:

$A=\dfrac{1}{2}r^2\theta$

Where, r is the radius of the circle and $\theta$ is the central angle of the sector in radian.

Putting $A=64,\theta=\dfrac{\pi}{6}$ , we get

$64=\dfrac{1}{2}r^2\times \dfrac{\pi}{6}$

$64=\dfrac{\pi}{12}r^2$

$64\times \dfrac{12}{\pi}=r^2$

$\dfrac{768}{\pi}=r^2$

Taking square root on both sides, we get

$\sqrt{\dfrac{768}{\pi}}=r$

$16\sqrt{\dfrac{3}{\pi}}=r$

Therefore, the value of r is $16\sqrt{\dfrac{3}{\pi}}$ m.

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2 years ago

Evaluate the expression (- n) ^ (n + n) + n ^ (n - n) , when n = 2

sladkih [1.3K]

Answer:

Step-by-step explanation:

Substitute the value of the variable and simplify.

$(-(2))^{(2+2)} +2^{(2-2)}$

$-2x^{2+2} =2^{4} = 16$

$2^{2-2} =2^{0}$

Anything raised to the power of 0 is one.

16 + 1 = 17

5 0

3 years ago

Find the sum of the first six terms of the sequence. S6 = ⇒ 84

k0ka [10]

Answer:

Explained below.

Step-by-step explanation:

Consider the series is a set of first 6 natural numbers.

Sum of first n terms is:

$\text{Sum of n terms}=\frac{n(n+1)}{2}$

$\text{Sum of first 6 terms}=\frac{6(6+1)}{2}$

$=3\times7\\=21$

Consider the series is an arithmetic sequence.

Sum of first n terms is:

$S_{n}=\frac{n}{2} [2a+(n-1)d]$

Here,

a = first term

d = common difference

Consider the series is an geometric sequence.

Sum of first n terms is:

$S_{n}=\frac{a_{1}\cdot(1-r^{n})}{(1-r)}$

Here,

a₁ = first term

r = common ratio

7 0

2 years ago

A city has a populationof 370,000 people. Suppose that each year the population grows 7%. What will the population be after 8 ye

maksim [4K]

Answer:

577,220 will be the population I think

Step-by-step explanation:

370,000/100=3700=1%

3,700*7=25,900

25,900*8=207,200

370,000+207,200=577,220

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3 years ago

Write the expression that is represented by the phrase below.

Inga [223]

Answer:

y^2-(x+4)

Step-by-step explanation:

y^2-(x+4)

3 0

2 years ago

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