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3 years ago

32x+16=32 solve for x

Mathematics

2 answers:

Pepsi [2]3 years ago

4 0

Answer:

x=0.5

Step-by-step explanation:

32x+16=32

-16 -16

32x=16

÷32 ÷32

x=0.5 or x=1/2

NemiM [27]3 years ago

4 0

Answer:

x=0.5

Step-by-step explanation:

First things first we need to get x on a side by it self. So we subtract 16 from 32 and your new equation looks like this

32x=16

Next we can divide 16/32 and we get 0.5

So x=0.5

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Find all solutions to the equation in the interval [0, 2π).<br><br> cos 4x - cos 2x = 0

Andrew [12]

Solve cos(4x)-cos(2x)=0 ∀ 0<=x<=2pi ..............(0)

Normal solution:
1. use the double angle formula to decompose, and recall cos^2(x)+sin^2(x)=1
cos(4x)=cos^2(2x)-sin^2(2x)=2cos^2(2x)-1 .................(1)
2. substitute (1) in (0)
2cos^2(2x)-1-cos(2x)=0
3. substitute u=cos(2x)
2u^2-u-1=0
4. Solve for x
factor
(u-1)(u+1/2)=0
=> u=1 or u=-1/2
However, since cos(x) is an even function, so solutions to
{cos(2x)=1, cos(-2x)=1, cos(2x)=-1/2 and cos(-2x)} ...........(2)
are all solutions.
5. The cosine function is symmetrical about pi, therefore
cos(-2x)=cos(2*pi-2x),
solution (2) above becomes
{cos(2x)=1, cos(2pi-2x)=1, cos(2x)=-1/2, cos(2pi-2x)=-1/2}
6. Solve each case
cos(2x)=1 => x=0
cos(2pi-2x)=1 => cos(2pi-0)=1 => x=pi
cos(2x)=-1/2 => 2x=2pi/3 or 2x=4pi/3 => x=pi/3 or 2pi/3
cos(2pi-2x)=-1/2 => 2pi-2x=2pi/3 or 2pi-2x=4pi/3 => x=2pi/3 or x=4pi/3
Summing up,
x={0,pi/3, 2pi/3, pi, 4pi/3}

3 0

3 years ago

A particular dam contains approximately 1,900,000,000,000 cubic feet of water. for a week long spike flood, the dam released at

Fantom [35]

Answer:

a) How much water was released during the flood?

14878080000 cubic feet or 14,878,080,000ft³

b) What percentage of the dam was released during the flood?

0.78%

Step-by-step explanation:

a) How much water was released during the flood?

The first step would be to find out how many seconds are in a week

60 seconds = 1 minute

60 minutes = 1 hour

24 hours = 1 day

7 days = 1 week

Hence, the number of seconds in a week =

1 week × (7 days/1 week)× (24 hours/1 day )×( 60 minutes/1 hour) ×( 60 seconds/1 minute)

= 604800 seconds

Therefore, the quantity of water released per week =

604800 seconds × 24,600 cubic feet per second

= 14,878,080,000 cubic feet or 14,878,080,000ft³

b) What percentage of the dam was released during the flood?

This is calculated as quantity released during the week ÷ Quantity of water in the dam × 100%

Quantity of water released during the flood in a week = 14,878,080,000 cubic feet

Quantity of water in the dam= 1,900,000,000,000 cubic feet of water

Percentage of the dam released during the flood =

14,878,080,000 cubic feet ÷ 1,900,000,000,000 × 100

= 0.7830568421%

Approximately = 0.78%

7 0

3 years ago

The environmental club at Paul sells gum and candy bars as a fundraiser. One afternoon, they sold $200 worth of candy. They need

Marysya12 [62]

Answer:

210 candy bars

85 gum

Step-by-step explanation:

$200=0.75cb+0.50gum

cb+gum=295

gum=295-cb

substitute

$200=0.75cb+0.50(295-cb)

$200=0.75cb+147.5-0.50cb

$200=0.25cb+147.5

0.25cb=52.5

cb=210

gum=295-210=85

8 0

3 years ago

Suppose you have a 100-ml cup a 300-ml cup and a 500-ml cup. List two different ways you can measure exactly 1 L.

Vera_Pavlovna [14]

500ml + 500ml=1L
300ml+100ml+100ml=1L

5 0

4 years ago

Rodrigo's math certificate is 20 centimeters tall and 27 centimeters wide. Rodrigo wants to put the certificate in a fancy frame

Lapatulllka [165]

Answer:

the cost that used to frame the math certificate is $847.80

Step-by-step explanation:

The computation of the cost that used to frame the math certificate is shown below:

= 27 wide × 20 tall × $1.57 per centimeter

= $847.80

Hence, the cost that used to frame the math certificate is $847.80

5 0

3 years ago