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Problem-solving
Let the age of John's father, Steve, be $x$, then John's age is $\dfrac{1}{3}x$ and their combined age is $x+\dfrac{1}{3}x=68\Rightarrow\dfrac{4}{3}x=68$. Multiplying both sides by 3 gives $4x=3\times68=204$. And dividing both sides by 4 gives $x=\dfrac{204}{4}=51$. Therefore, Steves age is 51 yearsRead more
Let the age of John’s father, Steve, be , then John’s age is and their combined age is .
Multiplying both sides by 3 gives .
And dividing both sides by 4 gives .
Therefore, Steves age is 51 years and John’s age is years.
See lessCompound Interest
The value (Fv) of an investment (P) made at an annual interest rate (r) compounded t times annually for a period of n years is given by $Fv=P\left(1+\dfrac{r}{t}\right)^{nt}$. Here, Fv = ₱67,500, P = ₱42,950, n = 5 years and 3 months = 5 + 3/12 years = 5.25 years, t = 12 because it is compounded monRead more
The value (Fv) of an investment (P) made at an annual interest rate (r) compounded t times annually for a period of n years is given by .
Here, Fv = ₱67,500, P = ₱42,950, n = 5 years and 3 months = 5 + 3/12 years = 5.25 years, t = 12 because it is compounded monthly, that is 12 times a year. We want to find the rate, r.
Thus, .
First, we divide both sides by 42950 to get
Taking the log of both sides, we have .
Next, we divide both sides by 63 to get .
Next, we remove the log by taking the exponential of both sides to get .
Next, we subtract 1 from both sides to get .
Finally, we multiply both sides by 12 to get .
Therefore, the rate of interest is 8.64%.
See lessQUESTION OF THE DAY 04/07/21
Let the tens digit be $a$ and the ones/units digit be $b$, then the number is given by $10\times a+1\times b=10a+b$. "The sum of the 2-digit number is 8" means $a+b=8$ . . . . . (1). If the digits are reversed, then $b$ becomes the tens digit and $a$ becomes the ones/units digit and the new number bRead more
Let the tens digit be and the ones/units digit be , then the number is given by .
“The sum of the 2-digit number is 8” means . . . . . (1).
If the digits are reversed, then becomes the tens digit and becomes the ones/units digit and the new number becomes .
When the digits are reversed, “the new number is 36 more than the original number” means . . . . . (2).
Dividing (2) through by 9 gives . . . . . (3)
Adding (1) and (3) gives .
From (1), .
Therefore, the original number is , while the new number is 62.
See lessHow to find and solve the limits of a function?
The limit, $L$, of a function, $f$, is the value to which the function approaches as the independent variable approaches a certain point. For instance, $\lim_{x\rightarrow a}f(x)=L$ means that as the variable, $x$, approaches the point, $a$, the function, $f(x)$, approaches the value, $L$. For the lRead more
The limit, , of a function, , is the value to which the function approaches as the independent variable approaches a certain point.
For instance, means that as the variable, , approaches the point, , the function, , approaches the value, .
For the limit of a function to exist, must be equal as approaches both from the left and from the right.
The method used in evaluating the limit of a function at a point depends on the type of function, however, we usually start (especially for polynomial functions) by substituting for in the function.
For example, to evaluate , we substitute 1 for to get .
Therefore,
See lessMathematics Questions
A linear equation is an equation in which the highest power of the variable is 1. A linear equation is of the form $y=ax+c$, where $a\ne0$. Thus, the equation $2x+5$ is a linear equation since the highest exponent of the variable, $x$, is 1.
A linear equation is an equation in which the highest power of the variable is 1. A linear equation is of the form , where .
Thus, the equation is a linear equation since the highest exponent of the variable, , is 1.
See lessIs a square a rectangle?
A rectangle is a parallelogram whose interior angles are right angles. A square is a type of rectangle with the additional property that the four sides are congruent. Therefore, a square is a rectangle.
A rectangle is a parallelogram whose interior angles are right angles.
A square is a type of rectangle with the additional property that the four sides are congruent.
Therefore, a square is a rectangle.
See lessMathematics questions
Total distance = 1750 m + 250 m = 2000 m Time = 12 minutes = 12 x 60 = 720 seconds Velocity = $\dfrac{\text{Total distance}}{\text{time}}=\dfrac{2000}{720}\approx2.78m/s$
Total distance = 1750 m + 250 m = 2000 m
Time = 12 minutes = 12 x 60 = 720 seconds
Velocity =
See lessMath Question for Senior Secondary School Students
The surface area of a cube is given by $A=6l^2$. Thus, $6l^2=54\Rightarrow l^2=\dfrac{54}{6}=9\Rightarrow l=\sqrt{9}=3$. The volume of a cube is given by $V=l^3$. Thus, $l^3=3^3=27$. Therefore the volume of the cube is 27.
The surface area of a cube is given by .
Thus, .
The volume of a cube is given by .
Thus, .
Therefore the volume of the cube is 27.
See less16 – 2t = 5t + 9
We solve for $t$ by isolating $t$. First, we add $2t$ to both sides to get $16-2t+2t=5t+9+2t\Rightarrow16=7t+9$. Next, we subtract 9 from both sides to get $16-9=7t+9-9\Rightarrow7=7t$. Finally, we divide both sides by 7 to get $\dfrac{7}{7}=\dfrac{7t}{7}\Rightarrow1=t$. Therefore, $t=1$.
We solve for by isolating .
First, we add to both sides to get .
Next, we subtract 9 from both sides to get .
Finally, we divide both sides by 7 to get .
Therefore, .
See lessProblem Solving
The vertex form of the equation of a parabola with vertex at (h, k) is given by $y=a(x-h)^2+k$. Given the parabola $y – 2x² = 8x + 5\Rightarrow y=2x^2+8x+5$ Using the method of completing the square, we convert the equation into vertex form to have $y=2(x^2+4x)+5=2(x^2+4x+4)+5-2(4)=2(x+2)^2+5-8=2(x+Read more
The vertex form of the equation of a parabola with vertex at (h, k) is given by .
Given the parabola
Using the method of completing the square, we convert the equation into vertex form to have
Thus, the vertex of the given parabola is at (-2, -3).
Translating the vertex 3 units to the left and 2 units up gives the new vertex (-2 – 3, -3 + 2) = (-5, -1).
See less