Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$ABCD$ is a rectangle with $AD = 3$ and $CD = 4$ . $T$ is a point on the side $AB$ . find the position of $T$ on this sides so that angles $CTD$ is maximized

View step-by-step help

View step-by-step help

Write and solve direct variation equations

Full solution

Q.

ABCD

is a rectangle with

AD = 3

and

CD = 4

.

T

is a point on the side

AB

. find the position of

T

on this sides so that angles

CTD

is maximized

Choose optimal position for $T$ : To maximize angle $CTD$ , $T$ should be at the corner $A$ , because the angle opposite the longest side in a triangle is the largest.
Utilize properties of rectangle: Since $ABCD$ is a rectangle, $AD$ is parallel to $BC$ , and angle $CTD$ would be maximized when $T$ is at $A$ , making angle $CTD$ a right angle.
Position of T at end of AB: Therefore, the position of T is the same as point A, which is at the end of side $AB$ .

More problems from Write and solve direct variation equations

Question

In a direct variation,

y = 6

x = 2

. Write a direct variation equation that shows the relationship between

x

y

\newline

Write your answer as an equation with

y

first, followed by an equals sign.

Posted 3 months ago

Question

y

varies directly with

x

y = 12

x = 6

y

x = 4

\newline

Write and solve a direct variation equation to find the answer.

\newline

y =

Posted 2 months ago

Question

Which equation shows inverse variation?

\newline

\newline

(\frac{x}{36}) = y

\newline

yx = -74

Posted 3 months ago

Question

y

varies inversely with

x

y = 1

x = 4

y

x = 2

\newline

Write and solve an inverse variation equation to find the answer.

\newline

y =

Posted 2 months ago

Question

What is the value of

\frac{x^{2}}{y^{4}}

x=8

y=2

Posted 21 days ago

Question

(x+4)(2 x-a)=0

\newline

In the given equation,

a

is a constant. If the equation has the solutions

x=4

x=-4

, what is the value of

a

Posted 2 months ago

Question

(2 x+5)(-m x+9)=0

\newline

In the given equation,

m

is a constant. If the equation has the solutions

x=-\frac{5}{2}

x=\frac{3}{2}

, what is the value of

m

Posted 2 months ago

Question

(4 x+3)-(5 x-7)=a x+b

\newline

In the given equation,

b

is a constant. What is the value of

b

Posted 2 months ago

Question

y=\frac{29}{8} x-\frac{2}{3}

\newline

The given equation is graphed in the

x y

-plane. What is the slope of the line?

Posted 2 months ago

Question

a t^{2}+\frac{7}{2} t-4=0

\newline

The given equation has solutions at

t=-8

t=1

. What is the value of the constant

a

Posted 1 month ago