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3 years ago

What is the difference in temperature between 50°C and 30°C?

Mathematics

2 answers:

snow_lady [41]3 years ago

7 0

Answer:

B. 20

Step-by-step explanation:

qaws [65]3 years ago

3 0

Answer:

20'C

Step-by-step explanation:

50-30= 20

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Y''+y'+y=0, y(0)=1, y'(0)=0

mars1129 [50]

Answer:

$y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

Step-by-step explanation:

A second order linear , homogeneous ordinary differential equation has form $ay''+by'+cy=0$ .

Given: $y''+y'+y=0$

Let $y=e^{rt}$ be it's solution.

We get,

$\left ( r^2+r+1 \right )e^{rt}=0$

Since $e^{rt}\neq 0$ , $r^2+r+1=0$

{ we know that for equation $ax^2+bx+c=0$ , roots are of form $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ }

We get,

$y=\frac{-1\pm \sqrt{1^2-4}}{2}=\frac{-1\pm \sqrt{3}i}{2}$

For two complex roots $r_1=\alpha +i\beta \,,\,r_2=\alpha -i\beta$ , the general solution is of form $y=e^{\alpha t}\left ( c_1\cos \beta t+c_2\sin \beta t \right )$

i.e $y=e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

Applying conditions y(0)=1 on $e^{\frac{-t}{2}}\left ( c_1\cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$ , $c_1=1$

So, equation becomes $y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

On differentiating with respect to t, we get

$y'=\frac{-1}{2}e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+c_2\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )+e^{\frac{-t}{2}}\left ( \frac{-\sqrt{3}}{2} \sin \left ( \frac{\sqrt{3}t}{2} \right )+c_2\frac{\sqrt{3}}{2}\cos\left ( \frac{\sqrt{3}t}{2} \right )\right )$

Applying condition: y'(0)=0, we get $0=\frac{-1}{2}+\frac{\sqrt{3}}{2}c_2\Rightarrow c_2=\frac{1}{\sqrt{3}}$

Therefore,

$y=e^{\frac{-t}{2}}\left ( \cos\left ( \frac{\sqrt{3}t}{2} \right )+\frac{1}{\sqrt{3}}\sin \left ( \frac{\sqrt{3}t}{2} \right ) \right )$

3 0

2 years ago

I rlly don’t understand due today please help!

tatuchka [14]

Answer:

a) 2x+4

b)x=8

Step-by-step explanation:

a) x+x+4 =2x +4

b) 2x+4= 20

2x = 16

x=8

Jay bought 8 packets of Chips

c) Jay: 8 x 60

=£4,80

Lauren : 12 × 60

= £7,2

7 0

2 years ago

Rhombus A has a base of 7 inches and an area of 35 square inches. Rhombus B has a base and height that are three times the base

STALIN [3.7K]

For rhombus A:
base = 7 in
area = 35 in²

Area of rhombus = b * h
⇒ 35 = 7 * h
⇒ h = 35/7
⇒ h = 5 in

Rhombus B:
height = 3*5 = 15 in
base = 7*3 = 21 in
Area = 15 * 21 = 315 in²

Area of rhombus B is 9 times area of rhombus A. When the dimensions are increased to 3 times the initial dimension, area became 9 times.

8 0

3 years ago

Read 2 more answers

Lake Victoria surface area is 26,828 square miles. Lake Superior surface area is 31,700 square miles. How much larger is the sur

alekssr [168]

4,872 square miles larger

5 0

3 years ago

If one pie is shared equally by 6 people, then each person will get<br> what fraction of the pie?

amid [387]

Answer: Each person will take $\dfrac{1}{6}$ of the pie.