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2 years ago

Express the radical using the imaginary unit i

Mathematics

1 answer:

valentinak56 [21]2 years ago

7 0

Answer:

$=\pm i\sqrt{66}$

Step-by-step explanation:

So we have:

$\pm\sqrt{-66}$

This is the same as:

$=\pm\sqrt{66\cdot-1}$

Separate:

$=\pm\sqrt{66}\cdot\sqrt{-1}$

Replace the second term with i:

$=\pm i\sqrt{66}$

The square root of 66 cannot be simplified.

So, this is our answer :)

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Draw an example of a composite figure that has a volume between 750 cubic inches and 900 cubic inches

grigory [225]

Volume:

$V \approx 888.02in^3 \\ \\ And, \ 750in^3$

<h2>Explanation:</h2>

A composite figure is formed by two or more basic figures or shapes. In this problem, we have a composite figure formed by a cylinder and a hemisphere as shown in the figure below, so the volume of this shape as a whole is the sum of the volume of the cylinder and the hemisphere:

$V_{total}=V_{cylinder}+V_{hemisphere} \\ \\ \\ V_{total}=V \\ \\ V_{cylinder}=V_{c} \\ \\ V_{hemisphere}=V_{h}$

So:

$V_{c}=\pi r^2h \\ \\ r:radius \\ \\ h:height$

From the figure the radius of the hemisphere is the same radius of the cylinder and equals:

$r=\frac{8}{2}=4in$

And the height of the cylinder is:

$h=15in$

So:

$V_{c}=\pi r^2h \\ \\ V_{c}=\pi (4)^2(15) \\ \\ V_{c}=240\pi in^3$

The volume of a hemisphere is half the volume of a sphere, hence:

$V_{h}=\frac{1}{2}\left(\frac{4}{3} \pi r^3\right) \\ \\ V_{h}=\frac{1}{2}\left(\frac{4}{3} \pi (4)^3\right) \\ \\ V_{h}=\frac{128}{3}\pi in^3$

Finally, the volume of the composite figure is:

$V=240\pi+\frac{128}{3}\pi \\ \\ V=\frac{848}{3}\pi in^3 \\ \\ \\ V \approx 888.02in^3 \\ \\ And, \ 750in^3$

<h2>Learn more:</h2>

Volume of cone: brainly.com/question/4383003

#LearnWithBrainly

4 0

2 years ago

I WILL AWARD BRAINLIEST!!!! PLEASE HELP!!!!!

Dahasolnce [82]

as AB || DE then

angle BAE = angle AED

so angle AED = 70

as AD = AE then

angle AED = angle ADE = 70

now in a triangle

angle DAE + Angle ADE + angle AED = 180

angle DAE + 70 + 70 = 180

angle DAE = 180 - 140 = 40

4 0

2 years ago

For every $3.00 the 5th grade raise, the 6th grade raises $5.00. If the 5th grades raises $36.00, how much does the 6th grade ra

frutty [35]

The sixth graders raised $60

7 0

2 years ago

Read 2 more answers

a Carnival charges $5 to enter, and $2 per ride. If you paid a total of $23, how many rides did you go at the carnival

IrinaK [193]

Answer : 8$

you have 1$ left

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1 year ago

A rectangle is twice as long as it is wide. If its length and width are both

puteri [66]

Answer:

a rectangle is twice as long as it is wide . if both its dimensions are increased 4 m , its area is increaed by 88 m squared make a sketch and find its original dimensions of the original rectangle

Step-by-step explanation:

Let l = the original length of the original rectangle

Let w = the original width of the original rectangle

From the description of the problem, we can construct the following two equations

l=2*w (Equation #1)

(l+4)*(w+4)=l*w+88 (Equation #2)

Substitute equation #1 into equation #2

(2w+4)*(w+4)=(2w*w)+88

2w^2+4w+8w+16=2w^2+88

collect like terms on the same side of the equation

2w^2+2w^2 +12w+16-88=0

4w^2+12w-72=0

Since 4 is afactor of each term, divide both sides of the equation by 4

w^2+3w-18=0

The quadratic equation can be factored into (w+6)*(w-3)=0

Therefore w=-6 or w=3

w=-6 can be rejected because the length of a rectangle can't be negative so

w=3 and from equation #1 l=2*w=2*3=6

I hope that this helps. The difficult part of the problem probably was to construct equation #1 and to factor the equation after performing all of the arithmetic operations.

5 0

2 years ago