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3 years ago

0.1 meters long. 1/10 of 0.1

Mathematics

1 answer:

larisa [96]3 years ago

6 0

Hey mate u wrote the answer in the same question

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Solve the equation. StartFraction dy Over dx EndFraction equals5 x Superscript 4 Baseline (1 plus y squared )Superscript three h

dangina [55]

Answer:

Step-by-step explanation:

To solve the differential equation

dy/dx = 5x^4(1 + y²)^(3/2)

First, separate the variables

dy/(1 + y²)^(3/2) = 5x^4 dx

Now, integrate both sides

To integrate dy/(1 + y²)^(3/2), use the substitution y = tan(u)

dy = (1/cos²u)du

So,

dy/(1 + y²)^(3/2) = [(1/cos²u)/(1 + tan²u)^(3/2)]du

= (1/cos²u)/(1 + (sin²u/cos²u))^(3/2)

Because cos²u + sin²u = 1 (Trigonometric identity),

The equation becomes

[1/(1/cos²u)^(3/2) × 1/cos²u] du

= cos³u/cos²u

= cosu

Integral of cosu = sinu

But y = tanu

Therefore u = arctany

We then have

cos(arctany) = y/√(1 + y²)

Now, the integral of the equation

dy/(1 + y²)^(3/2) = 5x^4 dx

y/√(1 + y²) = x^5 + C

y - (x^5 + C)√(1 + y²) = 0

is the required implicit solution

5 0

3 years ago

Graph the line with the equation y = -x - 3.

larisa [96]

Answer:

Step-by-step explanation:

$y=-x-3$

This means a graph with a slope of -1, and a y-intercept of -3

8 0

2 years ago

Grace's car left four skid marks on the road surface during a highway accident. Two of the skid marks were each 52 feet and two

Mashcka [7]

Answer:

The skid distance to be used is 54 feet.

Step-by-step explanation:

Given:

Four skid marks on the highway.

$52,52,56,56$ in feet.

We have to find the skid distance.

The skid distance that will be used to further calculate the skid speed is actually the mean skid distance.

Mean skid distance (m) :

⇒ $(m)=\frac{Sum\ of \ the\ skid\ marks }{Number\ of\ skid\ marks}$

⇒ $(m) =\frac{52+52+56+56}{4}$

⇒ $(m) =\frac{216}{4}$

⇒ $(m)=54$ feet.

So the skid distance to be used is 54 feet.

7 0

3 years ago

7. Jen has a collection of 45 corn husk dolls that she wants to arrange in equal groups. Write a fact family that shows how Jen

Rainbow [258]

Answer:

9 × 5

5 × 9

3 × 15

15 × 3

1 × 45

45 × 1

Step-by-step explanation:

45 corn husk dolls can be arranged in equal groups

Number of husk by number of group

9 × 5

5 × 9

3 × 15

15 × 3

1 × 45

45 × 1

Facts family that shows how Jen could arrange her corn husk dolls is shown above

5 0

3 years ago

How much is 33 1/3% of $60,000?

EastWind [94]

33 1/3% of $60,000 = 20,000

8 0

3 years ago