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3 years ago

What is the sum of the geometric sequence 1,-6,36... if there are 6 terms

1 answer:

7 0

$a_1=1;\ a_2=-6;\ a_3=36;\ ...\\\\r=a_2:a_1\to r=-6:1=-6\\\\S_n=\dfrac{a_1(1-r^n)}{1-r}\\\\a_1=1;\ r=-6;\ n=6\\\\subtitute\\\\S_6=\dfrac{1(1-(-6)^6)}{1-(-6)}=\dfrac{1-46656}{1+6}=\dfrac{46655}{7}=6665$

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Solve for x: <br> 3x+2y=7

iVinArrow [24]

$3x+2y=7\ \ \ |subract\ 2y\ from\ both\ sides\\\\3x=7-2y\ \ \ |divide\ both\ sides\ by\ 3\\\\\boxed{x=\dfrac{7-2y}{3}}$

8 0

3 years ago

If 63,000 = 6.3 x 10n, then what is n

tatyana61 [14]

Answer:

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4 0

3 years ago

Read 2 more answers

Use the figure below to answer the questions.

Archy [21]

Answer:

a. What is the name of the 3D shape?

The name of the 3D shape is Prism

b. What is the formula for total surface area for this shape?

Total surface area:

$S=2A_{b}+P_{b}h$

c. What is the surface area of the figure?

The surface area of the figure is 144 cm²

Step-by-step explanation:

a. What is the name of the 3D shape?

The 3D shape has two congruent and parallel faces (triangles) and the other faces are parallelograms, then the 3D shape is a prism

b. What is the formula for total surface area for this shape?

Total Surface area:

$S=2A_{b}+P_{b}h$

where:

Area of the base of the prism: Ab

Perimeter of the base: Pb

Height of the prism: h

c. What is the surface area of the figure?

The base of the prism is a triangle. Then to calculate the area of the base, we must use the formula to calculate the area of a triangle:

$A_{b}=\frac{bh}{2}\\ A_{b}=\frac{(4 cm)(3 cm)}{2}\\ A_{b}=\frac{12cm^{2} }{2}\\ A_{b}=6cm^{2}$

The perimeter of the base is the perimeter of the triangle, equal to the sum of the sides of the triangle:

$P_{b}=4cm+3cm+5cm\\ P_{b}=12cm$

h: Height of the prism is the distance between the bases of the prism (the triangle), then h=11 cm

Then, replacing in the formula the known values:

$S=2(6 cm^{2})+(12 cm)(11 cm)\\ S=12 cm^{2}+132 cm^{2}\\ S=144 cm^{2}$

8 0

3 years ago

PLS HELP!!

lord [1]

Answer:

The height of the cone-shaped cup is 6 inches and the diameter at the top is 3 inches. ... To find the volume of the cone, you use a formula similar to that of a pyramid, ... \begin{align*}V & = \frac{1}{3} \pi r^2 h \\ V & = \frac{1}{3} (3.14)(5^2 )(7) ... The answer is the volume of the cone is 183.16 cubic inches.

Step-by-step explanation:

i think thats it it was right on gogle

5 0

3 years ago

Nick is a great baby sitter.He makes $9 an hour.Julia is an even better babysitter She makes $12 an hour.Julia works 6 hours eac

serg [7]

Answer:

Nick has to work 8 hours

Step-by-step explanation:

Nick makes 9 works x

Julia makes 12 works 6

first find out how much Julia makes you can do that by multiplying 12 by 6 witch = 72

and we know we are trying to find how many hours Nick needs to work to equal Julia so we knew they are equal

so we have 9X=72

we just have to solve...

divide 72 by 9

leaving use with X=8

4 0

3 years ago