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3 years ago

Q is directly proportional to r. Q is 76 when r is 20. Work out q when r is 45

Mathematics

1 answer:

r-ruslan [8.4K]3 years ago

3 0

Answer:

171

Step-by-step explanation:

Q~r

find k (k is the constant)

Q=kr

76=k×20

76=20k divide 20 on both sides giving you

k=3.8

then Q=k×r

Q=3.8×45

Q=171

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Can anyone give me this answere

nika2105 [10]

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2 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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3 years ago

If A is nonsingular, then (AT )-1 =(A-1) T . (a) Verify this theorem for 2 × 2 matrices

kipiarov [429]

Answer:

Verified

Step-by-step explanation:

Let the 2x2 matrix A be in the form of:

$\left[\begin{array}{cc}a&b\\c&d\end{array}\right]$

Where det(A) = ad - bc # 0 so A is nonsingular:

Then the transposed version of A is

$A^T = \left[\begin{array}{cc}a&c\\b&d\end{array}\right]$

Then the inverted version of transposed A is

$(A^T)^{-1} = \frac{1}{ad - cb} \left[\begin{array}{cc}a&-c\\-b&d\end{array}\right]$

The inverted version of A is:

$A^{-1} = \frac{1}{ad - bc}\left[\begin{array}{cc}a&-b\\-c&d\end{array}\right]$

The transposed version of inverted A is:

$(A^{-1})^T = \frac{1}{ad - bc}\left[\begin{array}{cc}a&-c\\-b&d\end{array}\right]$

We can see that

$(A^T)^{-1} = (A^{-1})^T$

So this theorem is true for 2 x 2 matrices

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3 years ago

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solmaris [256]

The mean of a dataset is the all members of the dataset added together and then divided by the number of members in the set. From your description of the number line, I've created a list of members.

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Adding all members of this set up produces the value 273. There are 14 members in the set, so 273 / 14 = 19.5. Thus, the mean of the set is 19.5

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