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3 years ago

Find an explicit rule for the nth term of the sequence. 7, 21, 63, 189, ...

Mathematics

1 answer:

SpyIntel [72]3 years ago

8 0

Answer:

$7 \times {3}^{n - 1}$

Step-by-step explanation:

using form:

$a \times {r}^{n - 1}$

where a: starting number

where r: common ratio (in this case each next term is 3 times previous term)

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A manufacturer cuts squares from the corners of a rectangular plece of sheet metal that measures 2 inches by 7 inches (see Figur

Vladimir79 [104]

Answer:

The value of x that maximizes the volume enclosed by this box is 0.46 inches

The maximum volume is 3.02 cubic inches

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The volume of the open-topped box is equal to

$V=LWH$

where

$L=(7-2x)\ in\\W=(2-2x)\ in\\H=x\ in$

substitute

$V=(7-2x)(2-2x)x$

Convert to expanded form

$V=(7-2x)(2-2x)x\\V=(14-14x-4x+4x^{2})x\\V=14x-14x^2-4x^2+4x^{3}\\V=4x^{3}-18x^{2} +14x$

using a graphing tool

Graph the cubic equation

Remember that

The domain for x is the interval -----> (0,1)

Because

If x>1

then

the width is negative (W=2-2x)

The maximum is the point (0.46,3.02)

see the attached figure

therefore

The value of x that maximizes the volume enclosed by this box is 0.46 inches

The maximum volume is 3.02 cubic inches

8 0

3 years ago

Round 147.667 & 142.5 to the nearest cent.

Travka [436]

Answer:

147.67 and 142.50

Step-by-step explanation:

Cents are only two digits after the decimal, aka hundredths. So, you have to round each number to the hundredth.

6 0

3 years ago

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Which of these expressions represents the sum of two rational numbers being rational?

GaryK [48]

Answer:

i think its number 2 hope its correct

3 0

3 years ago

A car has 15 gallons of gas in its tank. The car travels 35 miles per gallon of gas. It uses 1/35 of a gallon of gas to go one m

ikadub [295]

Answer:

2.86 gallons

Step-by-step explanation:

If 1/35 gallon of gas = 1 mile

To travel 100 miles,

1/35 × 100

= 0.0286 × 100

= 2.86 gallons

Therefore, the car needs 2.86 gallons of gas to travel 100 miles.

4 0

3 years ago

In a direct variation, y = 18 when x = 3. Write a direct variation equation that shows the

Ronch [10]

Answer:

rounding to the nearest tenth

Step-by-step explanation:

5 0

2 years ago

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