Share £747 in the ratio 2:7 between Tom and Ben

- If 2x2 + 8y = 121.5 and x2 - 8y = 121.5, then x =<br> 9<br> 6.36<br> 16<br> 7

Natalija [7]

Step-by-step explanation:

2x² + 8y = 121.5

x² - 8y = 121.5

Add the equations together to eliminate the y terms.

3x² = 243

x² = 81

x = 9

4 0

2 years ago

Find the cube roots of 8(cos 216° + i sin 216°).

Tomtit [17]

$z^3=8(\cos216^\circ+i\sin216^\circ)$
$z^3=2^3(\cos(6^3)^\circ+i\sin(6^3)^\circ)$
$\implies z=8^{1/3}\left(\cos\left(\dfrac{216+360k}3\right)^\circ+i\sin\left(\dfrac{216+360k}3\right)^\circ\right)$

where $k=0,1,2$ . So the third roots are

$z=\begin{cases}2(\cos72^\circ+i\sin72^\circ)\\2(\cos192^\circ+i\sin192^\circ)\\2(\cos312^\circ+i\sin312^\circ)\end{cases}$

5 0

2 years ago

in the drawing six out of every 10 tickets are winning tickets of the winning tickets one out of every three awards is a larger

Dafna11 [192]

$Answer: P(\text{a ticket is randomly chosen will award a large prize)}=\frac{2}{21}$

Since we have given that

Total number of tickets =10

Number of winning tickets =6

$\text {Possibility of getting a winning ticket }=^{10}C_6$

In which one out of every three awards is a large prize

so,

$\text{ Possibility of getting a large prize }=^6C_3$

Now,

$P(\text{a ticket is randomly chosen will award a large prize)}=\frac{^6C_3}{^{10}C_6}\\\\=\frac{20}{210}\\\\=\frac{2}{21}$

$P(\text{a ticket is randomly chosen will award a large prize)}=\frac{2}{21}$

8 0

2 years ago

Read 2 more answers

The greatest common divisor of two positive integers less than $100$ is equal to $3$. Their least common multiple is twelve time

tangare [24]

Answer:

129

Step-by-step explanation:

Let a and b be two numbers.

We have been given that the greatest common divisor of two positive integers less than 100 is equal to 3. We can represent this information as $GCD(a,b)=3$ .

Their least common multiple is twelve times one of the integers. We can represent this information as $LCM(a,b)=12a$ .

Now, we will use property $GCD(x,y)*LCM(x,y)=xy$ .

Upon substituting our given values, we will get:

$3*12a=ab$

$36a=ab$

Switch sides:

$ab=36a$

$\frac{ab}{a}=\frac{36a}{a}$

$b=36$

Now, we need to find a number less than 100, which is co-prime with 12 after dividing by 3.

The greatest multiple of 3 less than 100 is 99, but it is not co-prime with 12 after dividing by 3.

Similarly 96 is also not co-prime with 12 after dividing by 3.

We know that greatest multiple of 3 (less than 100), which is co-prime with 12, is 93.

Let us add 36 and 93 to find the largest possible sum of the required two integers as:

$36+93=129$

Therefore, the required largest possible sum of the two integers is 129.

3 0

2 years ago

Sarah begins at a negative position along the x-axis. Sarah moves in the positive x-direction, turns around and then moves in th

a_sh-v [17]

Answer:

he magnitude of Sarah's displacement is less than the distance she travels

Step-by-step explanation:

Hi!

The magnitude of her displacement is just the difference between her final and initial state, however the distance she traveled is two times the distance she moved in the positive x-direction until she turned around, since she had to move back, plus her displacement.

So:

$displacement = |x_{final} -x_{initial}| \\distanceTraveled = 2|x_{return}-x_{initial}| + displacement\\$

Since all the terms are positive:

$x_{displacement}$

3 0

2 years ago