All categories

3 years ago

Find the differential equation of the family of tangent lines to the parabola y^2 = 2x

Mathematics

1 answer:

dusya [7]3 years ago

5 0

$\bf 
y^2=2x\implies y=\sqrt{2x}\implies y=x^{\frac{1}{2}}
\\ \quad \\
\cfrac{dy}{dx}=\boxed{?}$

You might be interested in

Students at Hampton Middle School sold T-shirts as a school fundraiser. Sylvie asked 12 random seventh-grade students how many T

natulia [17]

Answer:

4.1 shirts

Step-by-step explanation:

Mean can be found by adding all data points and dividing that by the total amount of data points.

There are 12 students selling shirt, which gives you 12 data points.

So (3+4+8+5+2+5+0+5+3+4+3+7)/12 = 4.083...

Which rounds to 4.1 shirts

6 0

3 years ago

What is a solution to (x + 6)(x + 2) = 60?

Reika [66]

Solution of the equation $(x+6)(x+2)=60$ is x=4 and x=-12

Step-by-step explanation:

We need to solve the equation: $(x+6)(x+2)=60$

Solving:

$(x+6)(x+2)=60$

Multiplying terms on the left hand side

$x(x+2)+6(x+2)=60$

$x^2+2x+6x+12=60$

$x^2+8x+12=60$

$x^2+8x+12-60=0$

$x^2+8x-48=0$

Now factorizing:

$x^2+12x-4x-48=0$

$x(x+12)-4(x+12)=0$

$(x-4)(x+12)=0$

$(x-4)=0\,\,and\,\,(x+12)=0$

$x=4\,\,and\,\,x=-12$

So, solution of the equation $(x+6)(x+2)=60$ is x=4 and x=-12

Keywords: Solving Equations

Learn more about Solving Equations at:

#learnwithBrainly

5 0

3 years ago

Can someone find the expression for h in terms of x.

PilotLPTM [1.2K]

The volume of the cylinder is equal to the sum of all spheres
the volume of 1 sphere is V1=4/3×pi×(1/2 x)³
simplified V1=1/6×pi×x²
we conclude that the volume of the cylinder is V2=270V1
V2=45×pi×x³
also the V2 can be calculated from the cylinder
V2= base(circle)×height
V2=(3x)²×pi×h=9x²×h
so we have
9x²×pi×h=45×pi×x³
simplified h=5x

7 0

4 years ago

it takes 45 pounds of seeds to completely plant a 5 acre field how many acres can be planted per pound of seed

Travka [436]

1/9 acres. It's 9lbs/acre so you dive that by 9 and get 1/9 acres/lbs.

6 0

3 years ago

Read 2 more answers

8+7×6/3x3 please help me with the question.

Leto [7]

Answer:

Step-by-step explanation:

must use PEMDAS (order of operations)

step 1: multiply 7 and 6

8 + 42 / 3 x 3

step 2: divide 42 by 3

8 + 14 x 3

step 3: multiply 14 and 3

8 + 42

Add to get 50

7 0

3 years ago

Read 2 more answers