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Ugo [173]
3 years ago
12

A committee is formed consisting of one representative from each of the 4 departments (CS-IS-IT-SW) in the computer science coll

ege, where the representative from a department is either the president or one of the two representatives from that department. How many ways are there to form this committee?
Mathematics
1 answer:
alexandr1967 [171]3 years ago
7 0

Step-by-step explanation:

each department has 3 options for their representative.

and each of these options can be associated with the 3 options of the next department. and so on.

so, we have

3×3×3×3 = 3⁴ = 81

possibilities to firm that committee overall.

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Answer choice A. The function moves left 4 units, and 2 units up.
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3 years ago
The edges of a cube are 5 centimeters each and the diagonal of a face is approximately 7 centimeters. What is the approximate ar
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Answer:

C. 35sqcm

Step-by-step explanation:

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2 years ago
Prove algebraically that the straight line with equation x=2y+5 is a tangent to the circle with equation x^2+y^2=5
zmey [24]

Differentiate both sides of the equation of the circle with respect to x, treating y=y(x) as a function of x:

x^2+y^2=5\implies2x+2y\dfrac{\mathrm dy}{\mathrm dx}=0\implies\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac xy

This gives the slope of any line tangent to the circle at the point (x,y).

Rewriting the given line in slope-intercept form tells us its slope is

x=2y+5\implies y=\dfrac12x-\dfrac52\implies\mathrm{slope}=\dfrac12

In order for this line to be tangent to the circle, it must intersect the circle at the point (x,y) such that

-\dfrac xy=\dfrac12\implies y=-2x

In the equation of the circle, we have

x^2+(-2x)^2=5x^2=5\implies x=\pm1\implies y=\mp2

If x=-1, then -1=2y+5\implies y=-3\neq2, so we omit this case.

If x=1, then 1=2y+5\implies y=-2, as expected. Therefore x=2y+5 is a tangent line to the circle x^2+y^2=5 at the point (1, -2).

7 0
3 years ago
Read 2 more answers
Rewrite using Radicals
Gre4nikov [31]

Answer:

cannot be put into radical form, sorry!

Step-by-step explanation:

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