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USPshnik [31]
3 years ago
14

An office and apartment building is made up of modules. Each module is a rectangular prism. The building has 150 modules, and is

15 stories high. If all of the modules were divided evenly among the number of stories, how many modules would be on each floor? How many different rectangular prisms could be made from that number? If all of the modules were divided evenly there would be modules on each floor. different rectangular prisms could be made from the number of modules on each floor: × 1 × 1 and 2 × × 1.
Mathematics
1 answer:
In-s [12.5K]3 years ago
3 0

Answer:

Part 1. 10 modules per floor

Part 2. Two different rectangular prism

Step-by-step explanation:

Let

x ----> the number of modules

y ---> the number of stories

we have

x=150\ modules\\y=15\ stories

Divide the number of modules by the number of stories

so

\frac{x}{y}=\frac{150}{15}=10\ \frac{modules}{floor}

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nadezda [96]

Answer:

The answer is B.

Step-by-step explanation:

3< x _<5

3 0
3 years ago
T(z)= sin^2(z/4), {-3 ≤ z ≤ 8}
Usimov [2.4K]

Answer:

T´(z)=n^2s/4*i

Step-by-step explanation:

T(z)=d/dz(sin^2*z/4)

T´(z)=d/dz(sn^2zi/4)

T´(z)=d/dz(sn^2z/4*i)

T´(z)i*d/dz(sn^2z/4)

T´(z)=n^2s/4*i

Simplify

3 0
3 years ago
The following function represents the profit P(n), in dollars, that a concert promoter makes by selling tickets for n dollars ea
Gre4nikov [31]
A) zeroes

P(n) = -250 n^2 + 2500n - 5250

Extract common factor:

P(n)= -250 (n^2 - 10n + 21)

Factor (find two numbers that sum -10 and its product is 21)

P(n) = -250(n - 3)(n - 7)

Zeroes ==> n - 3 = 0  or n -7 = 0
Then n = 3 and n = 7 are the zeros.

They rerpesent that if the promoter sells tickets at 3  or 7 dollars the profit is zero.

B) Maximum profit

Completion of squares

n^2 - 10n + 21 = n^2 - 10n + 25 - 4 = (n^2 - 10n+ 25) - 4 = (n - 5)^2 - 4

P(n) = - 250[(n-5)^2 -4] = -250(n-5)^2 + 1000

Maximum ==> - 250 (n - 5)^2 = 0 ==> n = 5 and P(5) = 1000

Maximum profit =1000 at n = 5

C) Axis of symmetry

Vertex = (h,k) when the equation is in the form A(n-h)^2 + k

Comparing A(n-h)^2 + k with - 250(n - 5)^2 + 1000

Vertex = (5, 1000) and the symmetry axis is n = 5.



8 0
3 years ago
Find the measures of the angles of the triangle whose vertices are A = (-3,0) , B = (1,3) , and C = (1,-3).A.) The measure of ∠A
alekssr [168]

Answer:

\theta_{CAB}=128.316

\theta_{ABC}=25.842

\theta_{BCA}=25.842

Step-by-step explanation:

A = (-3,0) , B = (1,3) , and C = (1,-3)

We're going to use the distance formula to find the length of the sides:

r= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}

AB= \sqrt{(-3-1)^2+(0-3)^2}=5

BC= \sqrt{(1-1)^2+(3-(-3))^2}=9

CA= \sqrt{(1-(-3))^2+(-3-0)^2}=5

we can use the cosine law to find the angle:

it is to be noted that:

the angle CAB is opposite to the BC.

the angle ABC is opposite to the AC.

the angle BCA is opposite to the AB.

to find the CAB, we'll use:

BC^2 = AB^2+CA^2-(AB)(CA)\cos{\theta_{CAB}}

\dfrac{BC^2-(AB^2+CA^2)}{-2(AB)(CA)} =\cos{\theta_{CAB}}

\cos{\theta_{CAB}}=\dfrac{9^2-(5^2+5^2)}{-2(5)(5)}

\theta_{CAB}=\arccos{-\dfrac{0.62}}

\theta_{CAB}=128.316

Although we can use the same cosine law to find the other angles. but we can use sine law now too since we have one angle!

To find the angle ABC

\dfrac{\sin{\theta_{ABC}}}{AC}=\dfrac{\sin{CAB}}{BC}

\sin{\theta_{ABC}}=AC\left(\dfrac{\sin{CAB}}{BC}\right)

\sin{\theta_{ABC}}=5\left(\dfrac{\sin{128.316}}{9}\right)

\theta_{ABC}=\arcsin{0.4359}\right)

\theta_{ABC}=25.842

finally, we've seen that the triangle has two equal sides, AB = CA, this is an isosceles triangle. hence the angles ABC and BCA would also be the same.

\theta_{BCA}=25.842

this can also be checked using the fact the sum of all angles inside a triangle is 180

\theta_{ABC}+\theta_{BCA}+\theta_{CAB}=180

25.842+128.316+25.842

180

6 0
3 years ago
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Sergio [31]
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3 years ago
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