All categories

2 years ago

Anu's age exceeds Sumbo's age by 15 The sum of the square of their ages is 725. What are their ages?

Mathematics

1 answer:

Mrac [35]2 years ago

5 0

Answer:

Anita= 25 years old

Sumbo= 10 years old

Step-by-step explanation:

Start by forming 2 equations that represent the given information.

Let Anu's and Sumbo's ages be A and S respectively.

A= S +15 -----(1)

A² +S²= 725 -----(2)

Now, solve for A and S by substitution.

Substitute (1) into (2):

(S +15)² +S²= 725

Expand:

S² +2(S)(15) +15² +S²= 725

2S² +30S +225= 725

-725 on both sides:

2S² +30S -500= 0

Divide both sides by 2:

S² +15S -250= 0

Factorise:

(S +25)(S -10)= 0

S +25= 0 or S -10= 0

S= -25 (reject) or S= 10

Sumbo's age cannot be a negative value hence -25 is rejected.

Substitute S= 10 into (1):

A= S +15

A= 10 +15

A= 25

You might be interested in

Use DeMoivre's Theorem to find the indicated power of the complex number. Write the answer in rectangular form.

slava [35]

Answer:

After solving the power:

$\bold{2(cos60^\circ+isin60^\circ)}$

Rectangular form:

$\bold{1+i\sqrt3}$

Step-by-step explanation:

Given the complex number:

$2(cos20^\circ+isin20^\circ)^3$

To find:

The indicated power by using De Moivre's theorem.

The complex number in rectangular form.

Rectangular form of a complex number is given as $a+ib$ where a and b are real numbers.

Solution:

First of all, let us have a look at the De Moivre's theorem:

$(cos\theta+isin\theta )^n=cos(n\theta)+isin(n\theta )$

First of all, let us solve:

$(cos20^\circ+isin20^\circ)^3$

Let us apply the De Moivre's Theorem:

Here, n = 3

$(cos20^\circ+isin20^\circ)^3 = cos(3 \times 20)^\circ+isin(3 \times 20)^\circ\\\Rightarrow cos60^\circ+isin60^\circ$

Now, the given complex number becomes:

$2(cos60^\circ+isin60^\circ)$

Let us put the values of $cos60^\circ = \frac{1}{2}$ and $sin60^\circ = \frac{\sqrt3}{2}$

$2(\dfrac{1}{2}+i\dfrac{\sqrt3}2)\\\Rightarrow (2 \times \dfrac{1}{2}+i\dfrac{\sqrt3}2\times 2)\\\Rightarrow \bold{1 +i\sqrt3 }$

So, the rectangular form of the given complex number is:

$\bold{1+i\sqrt3}$

3 0

3 years ago

Which set of integers is included in (-1,3]?

denpristay [2]

Hello,

N={0,1,2,3,4,5,...}

(-1,3]={0,1,2,3}⊂N

Answer (1) no negative whole numbers.

6 0

4 years ago

Find the volume of the cylinder. Round your answer to the nearest tenth

valentinak56 [21]

I think it's 85 but Is this like a multiple choice question?

8 0

3 years ago

Read 2 more answers

please help me solve. Blank 1 I have the answer 9 and blank 2 I have the answer 5. Blank 2 is correct but not Blank 1

Sidana [21]

Amplifying,

$3\text{ }\sqrt[]{45}\rightarrow\sqrt[]{(3^2)\cdot45}\rightarrow\sqrt[]{9\cdot45}\rightarrow\sqrt[]{405}$

Now, let's simplify:

$undefined$

Blank 1:

405

Blank 2:

$undefined$

8 0

2 years ago

Which is larger, 3/7 or 5/7?

Wittaler [7]

Answer:

5/7

Step-by-step explanation:

4 0

3 years ago

Anu's age exceeds Sumbo's age by 15 The sum of the square of their ages is 725. What are their ages?​

Anu's age exceeds Sumbo's age by 15 The sum of the square of their ages is 725. What are their ages?