Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Please briefly explain why you feel this question should be reported.
Please briefly explain why you feel this answer should be reported.
Please briefly explain why you feel this user should be reported.
harmonic sequence
The nth term of a harmonic sequence is given by $T_n=\dfrac{1}{a+(n-1)d}$. Since the first term is 3, thus $\dfrac{1}{a}=3$, and the third term is $\dfrac{3}{5}$, thus $\dfrac{1}{a+2d}=\dfrac{3}{5}$. Taking the reciprocal gives that $a=\dfrac{1}{3}$ and $a+2d=\dfrac{5}{3}\Rightarrow\dfrac{1}{3}+2d=\Read more
The nth term of a harmonic sequence is given by
.
Since the first term is 3, thus
, and the third term is 
, thus 
. Taking the reciprocal gives that 
and 
.
Therefore, the 6th term is
.
See lessgeneral mathematics
A mapping is said to be one-to-one if every element in the range is mapped to exactly one element in the domain. Consider the mapping $X\rightarrow Y$, defined by the relation $y=2x-1$. If X = {1, 2, 8} and Y = {1, 3, 15}, then we say that the mapping is one-to-one as all elements in Y are mapped toRead more
A mapping is said to be one-to-one if every element in the range is mapped to exactly one element in the domain.
Consider the mapping
, defined by the relation 
.
If X = {1, 2, 8} and Y = {1, 3, 15}, then we say that the mapping is one-to-one as all elements in Y are mapped to exactly one element in X.
A horizontal line test is a test used to find out whether a function has an inverse.
See lessAll about geometry
The circumference of a circle is given by the formula $2\pi r$. Thus, $2\pi r=30\pi\Rightarrow r=15$. The area of a circle is given by $\pi r^2$. Thus, the area of the given circle is $\pi(15)^2=225\pi$.
The circumference of a circle is given by the formula
.
Thus,
.
The area of a circle is given by
.
Thus, the area of the given circle is
.
See lessMath question need answer agad
Given $\sqrt{x+5}-6=7$ Adding 6 to both sides, we have $\sqrt{x+5}-6+6=7+6\Rightarrow\sqrt{x+5}=13$. Squaring both sides, we have $(\sqrt{x+5})^2=13^2\Rightarrow x+5=169$. Subtracting 5 from both sides, we have $x+5-5=169-5\Rightarrow x=164$. Therefore, x = 164.
Given
Adding 6 to both sides, we have
.
Squaring both sides, we have
.
Subtracting 5 from both sides, we have
.
Therefore, x = 164.
See lessFinding the Common External Tangent
For your question, though the information provided is not complete. For this solution, as seen in the attached image, I assumed that the two circles are side by side, thus the distance between the centers of the two circles is the sum of the radii. We represent the lines with a right triangle with lRead more
For your question, though the information provided is not complete.
For this solution, as seen in the attached image, I assumed that the two circles are side by side, thus the distance between the centers of the two circles is the sum of the radii.
We represent the lines with a right triangle with legs 6 and
and hypotenuse, 10.
Thus, using the Pythagoras theorem, we have
.
Therefore, the length of an external tangent is 8.
See lessProving Theorem on the Different Kinds of Parallelogram
The best name of a quadrilateral whose diagonals bisect each other at right angles (perpendicular bisectors) is a rhombus. A rhombus is a quadrilateral with parallel opposite sides whose diagonals bisect each other at right angles. A square is a special type of rhombus with the additional property tRead more
The best name of a quadrilateral whose diagonals bisect each other at right angles (perpendicular bisectors) is a rhombus.
A rhombus is a quadrilateral with parallel opposite sides whose diagonals bisect each other at right angles. A square is a special type of rhombus with the additional property that the interior angles are right angles.
See lessProblem in algebra
To find the slope of a line from the equation, we first make $y$ the subject of the equation. Then, the coefficient of $x$ after making $y$ the subject is the slope. Thus, given $4x – 3y = 8$ Subtracting $4x$ from both sides gives $-3y = 8 - 4x$. And dividing through by -3 gives $\dfrac{-3y}{-3}=\dfRead more
To find the slope of a line from the equation, we first make
the subject of the equation. Then, the coefficient of 
after making 
the subject is the slope.
Thus, given
Subtracting
from both sides gives 
.
And dividing through by -3 gives
Therefore, the slope of the line is
.
See lessTwo angles are complementary and one of them is four times as big as the other. What is the size of the larger of the two angles?
Let one of the angles measure $x^o$. Since one of the angles is four times as big as the other, then the other angle measures $4x^o$, and since the angles are complementary, that means the sum of the angles gives $90^o$. Thus, $x^o + 4x^o = 90^o$ $\Rightarrow 5x = 90$ $\Rightarrow x = \dfrac{90}{5}Read more
Let one of the angles measure
. Since one of the angles is four times as big as the other, then the other angle measures 
, and since the angles are complementary, that means the sum of the angles gives 
.
Thus,
Therefore, the angles are
and 
.
See lessStatistics and Probability
Statistics is a branch of mathematics that deals with the collection, organization, interpretation, and presentation of data.
Statistics is a branch of mathematics that deals with the collection, organization, interpretation, and presentation of data.
See lessWhat is trigonometry
Trigonometry is a branch of mathematics that deals with angles and their applications.
Trigonometry is a branch of mathematics that deals with angles and their applications.
See less