Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

find the area of the figure bonded by $y=2x$ , $y=5x$ , $x=3$

View step-by-step help

View step-by-step help

Unions and intersections of sets

Full solution

Q. find the area of the figure bonded by

y=2x

,

y=5x

,

x=3

Identify Intersection Points: Identify the points of intersection between the lines $y=2x$ , $y=5x$ , and the line $x=3$ .
$y=2x$ and $y=5x$ intersect when $2x=5x$ , which never happens, so they don't intersect.
The lines $y=2x$ and $x=3$ intersect when $y=2(3)$ , so $y=6$ .
The lines $y=5x$ and $x=3$ intersect when $y=5x$ $2$ , so $y=5x$ $3$ .
Plot Points on Coordinate Plane: Plot the points of intersection on a coordinate plane. $\newline$ The points are $(3,6)$ and $(3,15)$ .
Draw Triangle with Lines: Draw the lines $y=2x$ , $y=5x$ , and $x=3$ to form a triangle. $\newline$ The base of the triangle is on the $x$ -axis from $x=0$ to $x=3$ . $\newline$ The height of the triangle is from $y=6$ (intersection with $y=2x$ ) to $y=15$ (intersection with $y=5x$ ).
Calculate Triangle Height: Calculate the height of the triangle. $\newline$ Height = $y$ at $x=3$ on $y=5x$ - $y$ at $x=3$ on $y=2x$ . $\newline$ Height = $15 - 6 = 9$ .
Calculate Triangle Base: Calculate the base of the triangle. $\newline$ Base = $x=3 - x=0 = 3$ .
Calculate Triangle Area: Calculate the area of the triangle. $\newline$ Area = $\frac{1}{2} \times$ base $\times$ height. $\newline$ Area = $\frac{1}{2} \times 3 \times 9$ . $\newline$ Area = $\frac{1}{2} \times 27$ . $\newline$ Area = $13.5$ .

More problems from Unions and intersections of sets

Question

R = \{-4, 4, 14\}

S = \{2, 12\}

R \cup S

\newline

\newline

\{-4,2,4,12,14\}

\newline

\Phi

\newline

\{2, 4, 12\}

\newline

\{-4, 2\}

Posted 2 months ago

Question

Which is the set of integers greater than or equal to

0

and less than or equal to

6

\newline

\newline

(A)\{1,2,3,4,5,6\}

\newline

(B)\{0,1,2,3,4,5,6\}

\newline

(C)\{\text{null set}\}

\newline

(D)\{1,6\}

Posted 2 months ago

Question

Which is the set of numbers less than

-13

\newline

\newline

\{x|x = -13\}

\newline

\{x|x < -13\}

\newline

\{x|x > -13\}

\newline

\{x|x \leq -13\}

Posted 2 months ago

Question

What interval does this inequality represent?

\newline

\newline

[A](-3,\infty)

\newline

[B](-3,\infty)

\newline

[C](-\infty,-3)

\newline

[D](-\infty,-3]

Posted 2 months ago

Question

Which of the following expressions is equivalent to

\newline

106 \times 3.7

\newline

1

\newline

106 \times 37 \div 10

\newline

106 \times 37 \div 100

\newline

106 \times 37 \div 1,000

\newline

106 \times 37 \div 10,000

Posted 4 months ago

Question

What is the value of

x^{6}+y^{2}

x=1

y=9

Posted 1 month ago

Question

What is the value of

y^{2}-x^{2}

x=5

y=6

Posted 2 months ago

Question

What is the value of

y^{2}-x^{4}

y=8

x=2

Posted 4 months ago

Question

A physicist measures the energies of atoms

A

B

to be the positive values

a

b

respectively. He determines that the energy of atom

B

is between one percent more than and one percent less than twice the energy of atom

A

. Which of the following systems of inequalities best models the possible range of values for the energies of atoms

A

B

\newline

1

\newline

\left\{\begin{array}{l}a<2.02 b \\ a>1.98 b\end{array}\right.

\newline

\left\{\begin{array}{l}a<2 b+0.02 \\ a>2 b-0.02\end{array}\right.

\newline

\left\{\begin{array}{l}b<2.02 a \\ b>1.98 a\end{array}\right.

\newline

\left\{\begin{array}{l}b<2 a+0.02 \\ b>2 a-0.02\end{array}\right.

Posted 1 month ago

Question

2+2(8347-4783)=-2 j

, then what is the value of

-j

Posted 6 days ago