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4 years ago

For what value of x would the expression

Mathematics

1 answer:

Zarrin [17]4 years ago

8 0

Answer:

x = 7/10 + sqrt(409)/10 or x = 7/10 - sqrt(409)/10

Step-by-step explanation by completing the square:

Solve for x:

5 x - 7 - 18/x = 0

Bring 5 x - 7 - 18/x together using the common denominator x:

(5 x^2 - 7 x - 18)/x = 0

Multiply both sides by x:

5 x^2 - 7 x - 18 = 0

Divide both sides by 5:

x^2 - (7 x)/5 - 18/5 = 0

Add 18/5 to both sides:

x^2 - (7 x)/5 = 18/5

Add 49/100 to both sides:

x^2 - (7 x)/5 + 49/100 = 409/100

Write the left hand side as a square:

(x - 7/10)^2 = 409/100

Take the square root of both sides:

x - 7/10 = sqrt(409)/10 or x - 7/10 = -sqrt(409)/10

Add 7/10 to both sides:

x = 7/10 + sqrt(409)/10 or x - 7/10 = -sqrt(409)/10

Add 7/10 to both sides:

Answer: x = 7/10 + sqrt(409)/10 or x = 7/10 - sqrt(409)/10

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B) The number of volume of a cylinder is half of its number of the total surface area.

faust18 [17]

Answer:

$V=179.6cm^3$

Step-by-step explanation:

the volume of a cylinder is given by:

$V=\pi r^2h$

where r is the radius and h is the height.

and the surface area:

$SA=2\pi r^2+2\pi rh$

the first term is the area of the circles and the second term is the area of the body.

since "The number of volume of a cylinder is half of its number of the total surface area." we will have that:

$V=\frac{1}{2}SA$

substitutig the equivalent expressions on each side:

$\pi r^2 h = \frac{1}{2} (2\pi r^2+2\pi r h)$

and we simplify and solve for the height (since is the value we don't know of the cylinder):

$\pi r^2 h = \pi r^2+\pi r h\\\pi r^2h-\pi rh=\pi r^2\\h(\pi r^2-\pi r)=\pi r^2\\h=\pi r^2/(\pi r^2-\pi r)$

we substitute the value of the radius $r=7cm$ , and we get:

$h=\pi (7cm)^2/(\pi (7cm)^2-\pi (7cm))\\h=153.938/(153.938-21.991)\\h=153.938/131.947\\h=1.1666cm$

thus the volume is:

$V=\pi r^2h$

$V=\pi (7cm)^2(1.1666cm)\\V=179.6cm^3$

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3 years ago

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You buy milk in 1 gallon containers. One portion of waffles requires 0.4 ounces of milk. How many portions can be made with one

xenn [34]

320 portions of waffles can be made with one container.

Step-by-step explanation:

Given,

Milk is bought in 1 gallon container.

One portion of waffles require = 0.4 ounces of milk

We know that;

1 gallon = 128 ounces

Now;

No. of portions of waffles = $\frac{Total\ ounces\ of\ milk}{Milk\ used\ per\ waffle}$

No. of portions of waffles = $\frac{128}{0.4}$

No. of portions of waffles = 320

320 portions of waffles can be made with one container.

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fgiga [73]

The Answer is 524 meters

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Damm [24]

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3 years ago

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Alina [70]

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