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IRISSAK [1]
3 years ago
9

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

Is

y/√(1 + y²) = x^5 + C

So

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
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