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3 years ago

If you apply the changes below to the cube root parent function, F(x) = 3/x

Mathematics

1 answer:

laiz [17]3 years ago

3 0

9514 1404 393

Answer:

A. G(x) = ∛(x -1) +1

Step-by-step explanation:

The transformation f(x-h) +k represents a translation (right, up) by (h, k) of the parent function f(x).

Your translation of f(x) = ∛x by (1, 1) will give you the function ...

G(x) = ∛(x -1) +1

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Given the sequence in the table below, determine the sigma notation of the sum for term 4 through term 15. N an 1 4 2 −12 3 36 t

Rzqust [24]

By applying basic property of Geometric progression we can say that sum of 15 terms of a sequence whose first three terms are 5, -10 and 2 is $\sum_{n=4}^{15} 5(-2)^{n-1}$$$

<h3>What is sequence ?</h3>

Sequence is collection of numbers with some pattern .

Given sequence

$a_{1}=5\\\\a_{2}=-10\\\\\\a_{3}=20$

We can see that

$\frac{a_1}{a_2}=\frac{-10}{5}=-2\\$

and

$\frac{a_2}{a_3}=\frac{20}{-10}=-2\\$

Hence we can say that given sequence is Geometric progression whose first term is 5 and common ratio is -2

Now $n^{th}$ term of this Geometric progression can be written as

$T_{n}= 5\times(-2)^{n-1}$

So summation of 15 terms can be written as

$\sum_{n=4}^{15} T_{n}\\\\$\\$\sum_{n=4}^{15} 5(-2)^{n-1}$$$

By applying basic property of Geometric progression we can say that sum of 15 terms of a sequence whose first three terms are 5, -10 and 2 is $\sum_{n=4}^{15} 5(-2)^{n-1}$$$

To learn more about Geometric progression visit : brainly.com/question/14320920

8 0

3 years ago

The volume of a sphere can be determined by the formula V = 4/3 πr^3, where r is the radius. What is the volume of a sphere with

allochka39001 [22]

Answer:

$V = \frac{99}{7} x^{9}y^{-6}$

Step-by-step explanation:

Given

$V = \frac{4}{3}\pi r^3$

Required

Find V when

$r = \frac{3}{2}x^3y^{-2$

Substitute $\frac{3}{2}x^3y^{-2$ for r in $V = \frac{4}{3}\pi r^3$

$V = \frac{4}{3}\pi * (\frac{3}{2}x^3y^{-2})^3$

Open bracket

$V = \frac{4}{3}\pi * \frac{3}{2}^3 * x^{3*3}y^{-2*3}$

$V = \frac{4}{3}\pi * \frac{27}{8} * x^{9}y^{-6}$

Simplify the fractions

$V = \pi * \frac{9}{2} * x^{9}y^{-6}$

Let

$\pi = \frac{22}{7}$

So:

$V = \frac{22}{7} * \frac{9}{2} * x^{9}y^{-6}$

$V = \frac{11}{7} * \frac{9}{1} * x^{9}y^{-6}$

$V = \frac{99}{7} * x^{9}y^{-6}$

$V = \frac{99}{7} x^{9}y^{-6}$

6 0

3 years ago

What is the degree of angle YQR

katovenus [111]

Answer: Angle is 3

Step-by-step explanation:

16x - 27 = 5x + 6

-5x -5x

______________

11x - 27 = 6

+ 27 +27

___________

11x = 33

__ __

11 11

x = 3

4 0

3 years ago

The roof of a tower in a castle is shaped like a cone. The height of the roof is 30 ft, and the radius of the base is 15 ft. Wha

xz_007 [3.2K]

Answer:

The area of the roof: ≈2287.44 ft^2, the lateral area of the roof:≈1580.58 ft^2

Step-by-step explanation:

The area of the roof is computed by the equation of the area of a cone:
A = πr(r + $\sqrt{h^{2}+r^(2) }$ )
(r: radius, h: height, πr^2 is the area of the base of the cone, πr $\sqrt{h^{2}+r^(2) }$ is the lateral area of the cone). So:

A = $15\pi (15 + \sqrt{30^{2} +15^{2} } )$ ≈ 2287.44 ft^2.

As I stated earlier, the lateral area of the roof can be computed:

A $L$ = $15\pi \sqrt{30^{2} +15^{2} }$ ≈ 1580.58 ft^2.

5 0

3 years ago

Find the sum of the arithmetic sequence. -1, 2, 5, 8, 11, 14, 17

muminat

56 is you answer you need.

8 0

3 years ago