A line going through the points (30,45) and (60,30)

Mathematics

1 answer:

sdas [7]3 years ago

5 0

Oh what you mean by this is all because this can mean like four different so explain more

You might be interested in

A large soft drink costs one and a half times as much as small soft drink. If a small drink costs n dollars, write an expression

ASHA 777 [7]

A) 1.5n................................

5 0

4 years ago

Read 2 more answers

Greg is a novice cook trying to perfect his baked potato recipe. He decides to put

Sergio039 [100]

2.079 I think? I’m sorry if I’m wrong I haven’t done this in years and I just wanna help….

4 0

3 years ago

Find the constant difference for a hyperbola with foci (-3.5, 0) and (3.5, 0) and a point on the hyperbola (3. 5, 24).

Solnce55 [7]

Answer:

2a=1

Step-by-step explanation:

The constant difference for a hyperbola $\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1$ is $2a.$

1. Since hyperbola has foci (-3.5, 0) and (3.5, 0), then $c=3.5.$ Note that $c=\sqrt{a^2+b^2},$ then

$\sqrt{a^2+b^2}=3.5\Rightarrow a^2+b^2=3.5^2.$

2. Since point (3.5,24) lies on the hyperbola, then

$\dfrac{3.5^2}{a^2}-\dfrac{24^2}{b^2}=1.$

3. Solve the system of two equations:

$\left\{\begin{array}{l}a^2+b^2=3.5^2\\\dfrac{3.5^2}{a^2}-\dfrac{24^2}{b^2}=1\end{array}\right.$

From the 1st equation,

$b^2=3.5^2-a^2,$

then

$\dfrac{3.5^2}{a^2}-\dfrac{24^2}{3.5^2-a^2}=1,\\ \\\dfrac{3.5^2(3.5^2-a^2)-24^2a^2}{a^2(3.5^2-a^2)}=1,\\ \\3.5^4-3.5^2a^2-24^2a^2=3.5^2a^2-a^4,\\ \\a^4-a^2(2\cdot 3.5^2+24^2)+3.5^4=0,\\ \\a^4-600.5a^2+150.0625=0,\\ \\D=(-600.5)^2-4\cdot 150.0625=360000,\\ \\a^2_{1,2}=\dfrac{600.5\pm 600}{2}=\dfrac{1}{4},600\dfrac{1}{4}.$