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3 years ago

11

Consider the differential equation y prime left parenthesis t right parenthesisequalst squared minus 6 y squared and the solutio

n curve that passes through the point (3,1). What is the slope of the curve at (3,1)?

1 answer:

White raven [17]3 years ago

6 0

Answer:

The slope of the curve at (3,1) is 3.

Step-by-step explanation:

The given differential equation is

$y'(t)=t^2-6y^2$

It is given that the solution curve is passing through the point (3,1).

The slope of a curve y(t) at a point (a,b) is the value of y'(t) at (a,b).

We need to find the slope of the curve at (3,1).

$m=[y'(t)]_{(3,1)}$

$m=[t^2-6y^2]_{(3,1)}$

Substitute t=3 and y=1 in the above equation, to find the slope.

$m=(3)^2-6(1)^2$

$m=9-6$

$m=3$

Therefore the slope of the curve at (3,1) is 3.

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A line segment is partitioned with a ratio 2:5, how many total parts has the segment been split into

schepotkina [342]

Answer:

7 parts

Step-by-step explanation:

To get the answer to this, we only simply to know the number of times in which the division was made.

This means that the total ratio of the lines is 2 +5 = 7. Meaning we have 7 different divisions.

The first division carries 2/7 while the second division carrues 5/7

7 0

4 years ago

Help -8(9n-10) -20 a. 90n+54 b. -72n+60 c. -17n – 80 d. -160n

Anna [14]

Answer:

1) -8(9n-10) - 20

-72n + 80 - 20

-7n + 60

Can't factor

2) 90n+54

18(5n+3)

3) -72n+60

-12(6n-5)

4) -17n - 80

Can't factor

5) -160n

Can't factor

3 0

3 years ago

Read 2 more answers

Is 247 divided by 18<br>who will answer first they will be marked as brainliest

Andrew [12]

Answer:

13.7

Step-by-step explanation:

Hope this helps

3 0

4 years ago

A ball is tossed between three friends. The first toss is 8.6 feet, the second is 5.8 feet, and the third toss is 7.5 feet, whic

Rainbow [258]

angles formed by these tosses are $79.45, 59.02$ and $41.53$ degrees to the nearest hundredth.

<u>Step-by-step explanation:</u>

Here , We have a triangle with sides of length 8.6 feet, 5.8 feet and 7.5 feet.

The Law of Cosines (also called the Cosine Rule) says:

$c^2 = a^2 + b^2 - 2ab (cosx)$

Using the Cosine Rule to find the measure of the angle opposite the side of length 8.6 feet:

⇒ $c^2 = a^2 + b^2 - 2ab (cosx)$

⇒ $c^2 -a^2 - b^2 = -2ab (cosx)$

⇒ $(cosx) =\frac{ c^2 -a^2 - b^2}{ -2ab}$

⇒ $(cosx) =\frac{(8.6^2 - 5.8^2 - 7.5^2)}{ ( -2(5.8)7.5)}$

⇒ $(cosx) =0.18310$

⇒ $cos^{-1}(cosx) = cos^{-1}(0.18310)$

⇒ $x = 79.45$

The Law of Sines (or Sine Rule) is very useful for solving triangles:

$\frac{a}{sin A} = \frac{ b}{sin B} = \frac{c}{sin C}$

We can now find another angle using the sine rule:

⇒ $\frac{ 8.6 }{ sin 79.45} = \frac{7.5}{ sin Y}$

⇒ $sin Y = \frac{(7.5 (sin 79.45))}{ 8.6}$

⇒ $Y = 59.02 degrees$

So, the third angle = $180 - 79.45 - 59.02 = 41.53 degrees.$

Therefore, angles formed by these tosses are $79.45, 59.02$ and $41.53$ degrees to the nearest hundredth.

4 0

4 years ago

5 is subtracted from one-fourth part of the product of 12 and 3 and multiplied by 2.

elena-14-01-66 [18.8K]

Step-by-step explanation:

<h3>One fourth Part of Product of 12 and 3 </h3>

<h3>: 36 = 1/4 = 9</h3><h3>5 subtract from this = 9 - 5 = 4</h3>

<h3>Multiply by 2 = 2×4 = 8</h3>

3 0

3 years ago