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2 years ago

In a cylindrical wooden block with a radius of 7 cm and a height of 14 cm, hemispherical blocks with

Mathematics

1 answer:

Sunny_sXe [5.5K]2 years ago

4 0

9514 1404 393

Answer:

1372π/3 cm^3 ≈ 1436.8 cm^3

Step-by-step explanation:

The diameter and height of the cylinder are both 14 cm. The resulting solid will be a 14 cm sphere. Its volume is ...

V = 4/3πr^3 = 4/3π(7 cm)^3 = 1372π/3 cm^3 ≈ 1436.8 cm^3

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Find domain of y=rad20-6x

Evgesh-ka [11]

Domain, on an "even root" context, means, an even root cannot have a negative radicand, since say for example $\bf \sqrt{-25}\ne -5\qquad why?\implies (-5)(-5)=25$

so... you end up with an "imaginary value"

so... for the case of 20-6x
"x", the domain, or INPUT
can afford to have any value, so long it doesn't make the radicand negative

to check for that, let us make the expression to 0, and see what is "x" then

$\bf 20-6x=0\implies 20=6x\implies \cfrac{20}{6}=x\implies \cfrac{10}{3}=x$

now, if "x" is 10/3, let's see $\bf \sqrt{20-6\left( \frac{10}{3} \right)}\implies \sqrt{20-20}\implies \sqrt{0}\implies 0$

now, 0 is not negative, so the radicand is golden

BUT, if "x" has a value higher than 10/3, the radicand turns negative
for example $\bf x=\frac{11}{3}
\\\\\\

\sqrt{20-6\left( \frac{11}{3} \right)}\implies \sqrt{20-22}\implies \sqrt{-2}$

so.. that's not a good value for "x"

thus, the domain, or values "x" can safely take on, are all real numbers from 10/3 onwards, or to infinity if you wish

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3 years ago

The length of the longer leg of a right triangle is 4 inches more than twice the length of the shorter leg. the length of the hy

Serjik [45]

The Pythagorean's Theorem for our situation would look like this:

$shortleg^2+longleg^2=hypotenuse^2$

So let's call the short leg s, the long leg l and the hypotenuse h. It appears that all our measurements are based on the measurement of the short leg. The long leg is 4 more than twice the short leg, so that expression is l=2s+4; the hypotenuse measure is 6 more than twice the short leg, so that expression is h=2s+6. And the short leg is just s. Now we can rewrite our formula accordingly:

$s^2+(2s+4)^2=(2s+6)^2$

And of course we have to expand. Doing that will leave us with

$s^2+4s^2+8s+8s+16=4s^2+12s+12s+36$

Combining like terms we have

$5s^2+16s+16=4s^2+24s+36$

Our job now is to get everything on one side of the equals sign and solve for s

$s^2-8s-20=0$

That is now a second degree polynomial, a quadratic to be exact, and it can be factored several different ways. The easiest is to figure what 2 numbers add to be -8 and multiply to be -20. Those numbers would be 10 and -2. Since we are figuring out the length of the sides, AND we know that the two things in math that will never EVER be negative are time and distance/length, -2 is not an option. That means that the short side, s, measures 10. The longer side, 2s+4, measures 2(10)+4 which is 24, and the hypotenuse, 2s+6, measures 2(10)+6 which is 26. So there you go!

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3 years ago

Simplify. -22-10) - 92

Rzqust [24]

Answer:

2944

Step-by-step explanation:

(-22-10)-92

(-32)-92

2944

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3 years ago

20 POINTS!!!!!!!! A picture is photocopied by using a scale factor of 2. Each side of the photocopy of the picture is

LUCKY_DIMON [66]

Answer:

Each side of the photocopy of the picture is enlarged by a factor of 2 so it would be A.

Step-by-step explanation:

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2 years ago

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ddd [48]

Answer:

x = 2/3

Step-by-step explanation:

combine -3 and 1. We get -2 there, and now have:

-2 + 10x = x + 4.

Combining the x terms, we get 9x = 6, so that x = 6/9, or x = 2/3

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3 years ago

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