The distance between two points A(a_{1}, a_{2}, a_{3}) and B(b_{1}, b_{2}, b_{3}) is given by the following formula:
d=\sqrt{(a_{1}- b_{1})^2+(a_{2}- b_{2})^2+(a_{3}- b_{3})^2}
So, in our case...
Type: Posts; User: miranda
The distance between two points A(a_{1}, a_{2}, a_{3}) and B(b_{1}, b_{2}, b_{3}) is given by the following formula:
d=\sqrt{(a_{1}- b_{1})^2+(a_{2}- b_{2})^2+(a_{3}- b_{3})^2}
So, in our case...
This is a GDC (graphic display calculator) question.
For example in CASIO fx-9860 we have to do the following procedure in order to find the real roots (x-intercepts) of this graph....
This is a GDC (graphic display calculator) question.
For example in CASIO fx-9860 we have to do the following procedure in order to find the real roots (x-intercepts) of this graph....
The Factor Theorem states that a polynomial p(x) has a factor x-r if and only if f(r)=0.
From Factor theorem we have that P(4)=0.
So, P(4)=2(4)^4-4(4)^3+(k+1)(4)^2-k(4)+8=0 \Rightarrow
...
We know that for the imaginary unit i hold the following
i^2=-1,
i^3= i^2 \cdot i=(-1) \cdot i=-i
and i^4=(i^2)^2=(-1)^2=1.
Also, 2013 can be written as 4*503+1
So, i^{2013}=(i^4)^{503}...
For the imaginary unit i holds that i^2=-1
So, (x-i)(x+i)=x^2-(i)^2=x^2-(-1)= x^2+1
Therefore the correct answer is (C).
This is an easy SAT question using GDC and find the roots of the given quadratic equation.
Another way is to recognize the identity x^2+4x+4=(x+2)^2 and thus the equation has one double (repeated)...
The percentage decrease in TV price is given by the following formula:
\frac{\$\ 400-\$\ 450}{\$\ 450} \cdot 100 \%\ = 11\%
Therefore the correct answer is (B).
The axis of symmetry of the parabola is given by the equation x=-2. So f(-4)=9, since the -4 has equal distance from -2 as 0.
Therefore the correct answer is (C).
Hope these help!
The perimeter of triangle RST is P=2x+y=14
and we also know that \frac{x}{y}=\frac{4}{3} \Rightarrow x=\frac{4y}{3}
P=2\frac{4y}{3} +y=14\Rightarrow 8y+3y =42 \Rightarrow 11y =42 \Rightarrow...
The triangle DGF is equilateral since DG=DF as radii and we also know that DG=GF.
Therefore, each angle of the triangle DGF measures 60^o.
We’ ll use two formulas for areas.
The first one gives...
The sum of angles in a triangle is always 180^o
So, x+y+50=180 \Rightarrow x+y=130 (1)
2x-y=110 (2)
Solving the simultaneous equations (1), (2)
x+y=130 \Rightarrow x+2x-110=130 ...
Let x,y be the Jim’s and John’s age now respectively.
So, the proposition “Five years ago, Jim was half as old as John is now” can be written as
x-5=\frac{y}{2} (1)
and the proposition “John is...
This absolute value inequality can be solved as follows
|a+4|>5
a+4>5 \ or\ a+4<-5
a>1 \ or\ a<-9
Therefore the correct answer is (C).
From the given inequalities we deduce that a>0, b<0, \ and\ c>0 and the only NOT negative i.e. positive expression is ab^2c^3
Therefore the correct answer is (B).
First we transform the inequality as x^2<17 and then plug-in the values of (A)-(D) to find a choice which doesn’t satisfy the inequality.
Therefore the correct answer is (D).
We know that
(x+y)^2= x^2+2xy+y^2 =12+2(-\frac{3}{2})=12-3=9?
Therefore the correct answer is (A).
The ratio of the areas of two circles is 9:4 \frac{A_{1}}{ A_{2}}=\frac{\pi (r_{1})^2}{\pi (r_{2})^2}=\frac{ (r_{1})^2}{ (r_{2})^2}=\frac{9}{4} \Rightarrow \frac{ r_{1}}{ r_{2}}=\frac{3}{2}...
The circumference is given by the formula C=2\pi r=12\pi \Rightarrow r= 6 /units/
The area is given by the formula A=\pi r^2=\pi (6)^2=36 \pi /units/ ^{2}
Therefore the correct answer is (C).
...
4^{1}=4
4^{2}=16
4^{3}=64
4^{4}=256
……
We observe that when the power is even then the unit digit of the result is 6 and when the power is odd then the unit digit of the result is 4.
Therefore...
First we solve for x : z=x^7 \Rightarrow x=z^{\frac{1}{7}} in terms of z
then we solve for y : z=x^7 \Rightarrow x=z^{\frac{1}{4}} in terms of z
So, xy= z^{\frac{1}{7}} z^{\frac{1}{4}}=...
In this case we have permutations since the order matters. Additionally we must divide the number of permutations by 2! , 4!, 3! and 2! Since there are 2 black boxes, 4 white boxes, 3 blue boxes and...
In this case we have permutations since the order matters. Additionally we must divide the number of permutations by 2! Since the digit “1” appears twice.
Therefore the answer is ...
Every digit of the password can be chosen with 10 different ways. Therefore the number of possible passwords are 10*10*10*10*10=10^5.
The correct answer is (A)
The visitor can choose for his entry to the museum between 4 different ways and for his exit also between 4 different ways. Therefore the visitor can enter and leave the museum in 4*4=16 ways.
The...