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3 years ago

What does x mean and why is y involved too

Mathematics

1 answer:

lora16 [44]3 years ago

8 0

well, it could mean many things like a variable, x axis on a graph, and a letter in the alphabet.

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Any help with this greatly appreciated.

Anestetic [448]

Put the equation in standard linear form.

$x'(t) + \dfrac{x(t)}{t + 5} = 5e^{5t}$

Find the integrating factor.

$\mu = \exp\left(\displaystyle \int \frac{dt}{t+5}\right) = e^{\ln|t+5|} = t+5$

Multiply both sides by $\mu$ .

$(t+5) x'(t) + x(t) = 5(t+5)e^{5t}$

Now the left side the derivative of a product,

$\bigg((t+5) x(t)\bigg)' = 5(t+5)e^{5t}$

Integrate both sides.

$(t+5) x(t) = \displaystyle 5 \int (t+5) e^{5t} \, dt$

On the right side, integrate by parts.

$(t+5) x(t) = \dfrac15 (5t+24) e^{5t} + C$

Solve for $x(t)$ .

$\boxed{x(t) = \dfrac{5t+24}{5t+25} e^{5t} + \dfrac C{t+5}}$

3 0

2 years ago

PLEASE HELP I HAVE NO IDEA HOW TO ANSWER THIS :(

dolphi86 [110]

The other 2 angles of given right angles are 61.93° and 28.072°, if a triangle with side lengths 8, 15, and 17 is a right triangle by the converse of the Pythagorean Theorem.

Step-by-step explanation:

The given is,

Right angled triangle,

Side lengths are 8, 15, and 17

Step:1

The given triangle is right angle triangle by the converse of Pythagorean theorem, so the trigonometric ratio,

Ref the attachment,

For angle a,

...................................................(1)

Where, Opp - 8

Hyp - 17

From equation (1),

= 0.470588

(0.470588)

a = 28.072°

For angle b,

...................................................(1)

Where, Opp - 15

Hyp - 17

From equation (1),

= 0.882352

(0.882352)

b = 61.93°

Step:2

Check for solution for right angle triangle,

90 ° = Other 2 angles

90 ° = a + b

90 ° = 28.072° + 61.93°

90 ° = 90 °

Result:

The other 2 angles of given right angles are 61.93° and 28.07°, if a triangle with side lengths 8, 15, and 17 is a right triangle by the converse of the Pythagorean Theorem.

7 0

3 years ago

(4,2);slope=3<br><br>help me out

ivolga24 [154]

We have a point and a slope, so let's use the point slope formula!

$(y - y1) = m(x - x1)$
where
x1=4
y1=2
and m=3

$(y - 2) = 3(x - 4) \\ y - 2 = 3x - 12 \\ y = 3x - 10$

8 0

3 years ago

I. Daska is situated at a distance of 15 miles from both Gujranwala and Sialkot. A bus travels from Gujranwala to Daska at an av

son4ous [18]

Answer:

The average speed of the entire trip is 8.5 miles per hour.

Step-by-step explanation:

Speed = Total Distance / Total Time

So we have to find the total distance and the total time taken .

1) From Gujranwala to Daska

speed= 25miles/hour distance = 15miles

Time taken = distance / speed

= 15/25= 0.6 hours

2) From Daska to Sialkot

speed= 40miles/hour distance = 15miles

Time taken = distance / speed

= 40/15= 2.67 hours

3 ) From Sialkot to Daska

speed= 30miles/hour distance = 15miles

Time taken = distance / speed

= 30/15= 2 hours

The total distance traveled to three places is = 15+ 15+15= 45miles

The Total time taken is = 0.6+ 2.67+ 2= 5.267=5.3 hours

Speed = Total Distance / Total Time

Speed= 45/ 5.3

= 8.49=8.5 miles per hour

The average speed of the entire trip is 8.5 miles per hour.

7 0

3 years ago

A student makes money by watching the neighbors' dog. The situation is modeled in the graph below. Money Made 130 120 110 100 90

saul85 [17]

Answer:

A student makes money by watching the neighbors' dog. The situation is modeled in the graph below. Money Made 130 120 110 100 90 80 Fee (dollars) 70 60 50 40 30 20 10 0 1 2 3 7 8 9 4 5 6 Time (days) 10 Select the statement that describes the relationship between the amount of money the student makes and time in days. The student charges $11 plus an additional $20 per day, The student charges $20 plus an additional $11 per day. The student charges $20 plus an additional $10 per day.

Step-by-step explanation:

4 0

3 years ago