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3 years ago

Find all solutions to the equation equation (x - 1)^2 = -4.

Mathematics

1 answer:

tatuchka [14]3 years ago

6 0

Answer:

x = 1±2i

Step-by-step explanation:

(x - 1)^2 = -4.

Take the square root of each side

sqrt( (x - 1)^2) = sqrt(-4)

Sqrt(ab) = sqrt(a)sqrt(b)

We know the sqrt(4) = 2 and the sqrt(-1) = ±i

x-1 = ±2i

Add 1 to each side

x-1+1 = 1±2i

x = 1±2i

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What is container B that is full after the pumping is complete ?

scoray [572]

Answer

68.4%

Step-by-step explanation

The volume of a cylinder is calculated as follows:

$V=\pi r^2h$

where r is the radius and h is the height of the cylinder.

In the case of cylinder A, its radius is r = 5 ft (= 10/2) and its height is h = 14 ft. Then, its volume is:

$\begin{gathered} V_A=\pi\cdot5^2\cdot14 \\ V_A=350\pi\text{ ft}^3 \end{gathered}$

In the case of cylinder B, its radius is r = 8 ft (= 16/2) and its height is h = 8 ft. Then, its volume is:

$\begin{gathered} V_B=\pi\cdot8^2\cdot8 \\ V_B=512\pi\text{ ft}^3 \end{gathered}$

After the pumping is completed all the liquid in cylinder A, which was full, is placed in cylinder B. If the volume of cylinder B represents 100%, then we need to find what percent, x, represents the volume of cylinder A. We can do this with the help of the next proportion:

$\frac{512\pi\text{ ft}^3}{350\pi\text{ ft}^3}=\frac{100\text{ \%}}{x\text{ \%}}$

Solving for x:

$\begin{gathered} 512\pi\cdot x=100\cdot350\pi \\ x=\frac{100\cdot350\pi}{512\pi} \\ x\approx68.4\text{ \%} \end{gathered}$

6 0

2 years ago

PLEASE HELP IM CONFUSED!!

Ronch [10]

Answer:

31/6 or 5 1/6

Step-by-step explanation:

First, turn 1.5 into a fraction as “fraction answer” means it wants a answer in the form of a fraction.

1.5 as a fraction is 1 1/2

So the equation is:

2 1/3 - 1 1/2

Now, turn the mixed fractions into improper fractions.

2 1/3 becomes 7/3 and 1 1/2 becomes 3/2

Now the equation is

7/3 - 3/2

To subtract fractions you must make the denominator (bottom number) the same number by finding the lowest common multiple.

3 and 2’s Lowest common multiple is 6.

When making the denominator 6 you also multiply the numerator.

3 x 2 = 6 and 7 x 2 = 14

So the first fraction is now: 14/6

Now:

2 x 3 = 6 and 3 x 3 = 9.

The other fraction is now 9/6

Now:

14/6 - 9/ = 5/6

Now:

6 - 5/6

Now turn 6 into a fraction.

6/1 - 5/6

Now turn the 6/1’s denominator into 6

6 x 6 = 36; 1 x 6 = 6

36/6 - 5/6 = 31/6

The answer is 31/6!

8 0

3 years ago

Jim dan and David share some sweets in the ratio 5:4:5. Jim gets 65 sweets. How many did dan get?

Elodia [21]

Answer:

Step-by-step explanation:

I'm pretty sure the answer is 52.

In Jim and Dave each got 5 and David got 4 then :

65/5 = 13

65 - 13 = 52

5 4 5

10 8 10

15 12 15

20 16 20

25 20 25

30 24 30

35 28 35

40 32 40

45 36 45

50 40 50

55 44 55

60 48 60

65 52 65

8 0

2 years ago

A rectangular carpet has a perimeter of 244 inches. The length of the carpet is 90 inches more than the width. Determine the dim

RSB [31]

Answer:

The dimensions of rectangle are:

Width = 16 inches

Length = 106 inches

Step-by-step explanation:

Perimeter of rectangle = 244 inches

Let Width of rectangle = w

Length of rectangle = w+90

We need to find the dimensions (length and width) of the carpet

The formula used will be: $Perimeter=2(length+width)$

Putting values and making equation:

$244=2w+2(w+90)\\Solving:\\244=2w+2w+180\\244=4w+180\\Switching\:sides\\4w+180=244\\Subtracting\:180\:from\:both\:sides\\4w=244-180\\4w=64\\Dividing\:both\:sides\:by\:4\\\frac{4w}{4} =\frac{64}{4}\\w=16$

So, we get w = 16

The width w = 16 inches

Now, finding length = w+ 90 = 16+90 = 106 inches

Therefore the dimensions of rectangle are:

Width = 16 inches

Length = 106 inches

4 0

3 years ago

Please help!!!!!!!!!!!!

Rashid [163]

9514 1404 393

Answer:

Step-by-step explanation:

The external angle at P is half the difference of the intercepted arcs:

P = (90° -58°)/2 = 32°/2

P = 16°

4 0

3 years ago