2 years ago

Write the sum using summation notation, assuming the suggested pattern continues. 2 - 8 + 32 - 128 + ...

1 answer:

4 0

This is a geometric series with first term 2 and common ratio -4. The general term of such a series (an) in terms of the first term (a1) and common rato (r) is written as
an = a1*r^(n-1)

The sum is the sum of such terms.
$sum=\sum\limits_{n=1}^{\infty}{2(-4)^{(n-1)}}$

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The product of sin 30 degrees and sin 60 degrees is the same as the product of

zysi [14]

Answer:

$sin(30\°)*sin(60\°)=cos(60\°)*cos(30\°)$

Step-by-step explanation:

we know that

$sin(\alpha)=cos(\beta)$

when

$\alpha+\beta=90\°$ -------> complementary angles

$sin(30\°)=cos(60\°)$

$sin(60\°)=cos(30\°)$

Because

$30\°+60\°=90\°$ -------> complementary angles

In this problem the product of

$sin(30\°)*sin(60\°)$

is equal to

$cos(60\°)*cos(30\°)$

therefore

$sin(30\°)*sin(60\°)=cos(60\°)*cos(30\°)$

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2 years ago

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The weight y of an object on Jupiter is proportional to the weight x of the object on Earth. An object that weighs 150 pounds on

svetoff [14.1K]

Weight of an object=J
x=J/(379.2/150)
x=J/2.528

y=12.64/2.528
y=5

Hope this helps :)

7 0

2 years ago

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PLEASE HELP!! Which steps can be used to solve 6/7x+1/2=7/8 for x? Check all that apply. A. Divide both sides of the equation by

Anon25 [30]

Answer:

B. first step

6/7x=7/8-1/2

c. second step

6/7x=7/8-4/8=3/8

d. and e are the same

x=3/8x7/6

Step-by-step explanation:

5 0

2 years ago

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Gavin and Jim win some money and share it in the ratio 5:2. Gavin gets £39 more than Jim. How much did they get altogether?

gregori [183]

Answer:

Altogether Gavin and Jim won £95.

Step-by-step explanation:

We are given the following in the question:

Ratio of money won by Gavin and Jim = 5:2

Gavin gets £39 more than Jim.

Let x be the amount of money Won by Jim.

Then, money won by Gavin =

$=(x+39)$

Thus, we can write the equation:

$\dfrac{\text{Gavin}}{\text{Jim}} = \dfrac{5}{2}=\dfrac{x+39}{x}$

Solving, we get,

$\dfrac{5}{2}=\dfrac{x+39}{x}\\\\5x = 2x + 78\\\Rightarrow 3x = 78\\\Rightarrow x = 26\\\Rightarrow (x+39) = 65$

Thus, Gavin won £65 and Jim won £26.

Money won altogether =

$=65 + 26\\=95$

Thus, altogether Gavin and Jim won £95.

5 0

2 years ago

A trinket factory can produce 3,000 trinkets per day. The warehouse has a capacity of 50,000 trinkets. Currently, there are 8,00

Ugo [173]

An equation for the number of trinkets in the warehouse after x days:
8,000 + 3,000x = 50,000

How many days will it take to fill the warehouse?

8,000 + 3,000x = 50,000
3,000x = 42,000
x = 14

7 0

2 years ago