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3 years ago

Solve the equation by completing the square. Round to the nearest hundredth if necessary. X^2-5x=12

Mathematics

1 answer:

Reptile [31]3 years ago

3 0

Answer:

x = -1.77, 6.77.

Step-by-step explanation:

x^2 - 5x = 12

(x - 2.5)^2 - 6.25 = 12

(x - 2.5)^2 = 18.25

x - 2.5 = +/- √18.25

x = 2.5 +/- √18.25

x = -1.77, 6.77.

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3 years ago

A space telescope on a mountaintop is housed inside of a cylindrical building with a hemispheric dome. If the circumference of t

Vlad1618 [11]

Answer:

$185553.7\text{ feet}^3$

Step-by-step explanation:

GIVEN: A space telescope on a mountaintop is housed inside of a cylindrical building with a hemispheric dome. If the circumference of the dome is $84\text{ feet}$ , and the total height of the building up to the top of the dome is $91\text{ feet}$ .

TO FIND: what is the approximate total volume of the building.

SOLUTION:

let the height of the mountaintop be $h\text{ feet}$

As the dome hemispherical.

circumference of a hemisphere $=\frac{1}{2}\times2\pi\times radius$

$=\pi\times radius$

$\frac{22}{7}\times radius=84$

$radius=26.75\text{ feet}$

total height of the building up to the top of the dome $=\text{radius of hemisphere}+\text{height of mountaintop}$

$=26.75+h=91$

$h=64.25\text{ feet}$

Volume of building $=\text{volume of cylindrical mountaintop}+\text{volume of dome}$

$=\pi(radius)^2h+\frac{2}{3}\pi(radius)^3$

as radius of mountain top is same as dome

putting values

$=3.14(26.75)^264.75+\frac{2}{3}3.14(26.75)^3$

$=145484.6+40069.1$

$185553.7\text{ feet}^3$

Hence the total volume of the building is $185553.7\text{ feet}^3$

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4 years ago

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lubasha [3.4K]

Answer:

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Step-by-step explanation:

Given

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3 years ago

Recall the experiment comparing patients 4 weeks after surgery for carpal

dimulka [17.4K]

Answer:

4. H0: u1= u2 Ha; u1≠ u2

5. The smaller value of p supports the null hypothesis.

Step-by-step explanation:

4. The null and alternate hypotheses are

H0: u1= u2 i.e there no difference between the mean pinch strengthof the two surgeries

against the claim

Ha; u1≠ u2 i.e there a difference between the mean pinch strengthof the two surgeries

It can be written like this as well

H0: u1 -u2= 0 i.e there no difference between the mean pinch strengthof the two surgeries

against the claim

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3 years ago