Ask question

Ask question

All categories

1 year ago

9

Is the square root of 65 rational or irrational?

1 answer:

wlad13 [49]1 year ago

3 0

Step-by-step explanation:

$\sqrt{65}$

As it can't be expressed in the form p/q, where q is not equal to 0,

<em><u>Hence</u></em><em><u>,</u></em>

<em><u>square</u></em><em><u> </u></em><em><u>root</u></em><em><u> </u></em><em><u>65</u></em><em><u> </u></em><em><u>is</u></em><em><u> </u></em><em><u>an</u></em><em><u> </u></em><em><u>irrational</u></em><em><u> </u></em>

You might be interested in

Suppose a and b are both non zero real numbers. Find real numbers c and d such that 1/a+ib= c+id

Thepotemich [5.8K]

$\begin{gathered} c=\frac{a}{a^2+b^2} \\ d=\frac{-b}{a^2+b^2} \end{gathered}$

Explanation

$\frac{1}{a+bi}=c+di$

Step 1

multiplicate by the conjugate

$\begin{gathered} \frac{1}{a+bi}\cdot\frac{a-bi}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2-(bi)^2} \\ \frac{1}{a+bi}\cdot\frac{a-bi}{a+bi}=\frac{a-bi}{(a+bi)(a-bi)}=\frac{a-bi}{a^2-(-b^2)}=\frac{a-bi}{a^2+b^2} \end{gathered}$

notice that

$\begin{gathered} \frac{1}{a+bi}=\frac{a-bi}{a^2+b^2}=\frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i \\ \frac{a}{a^2+b^2}-\frac{b}{a^2+b^2}i=c+di \\ so \\ \end{gathered}$ $\begin{gathered} c=\frac{a}{a^2+b^2} \\ d=\frac{-b}{a^2+b^2} \end{gathered}$

I hope this helsp you

6 0

8 months ago

17. Solve for<br> for x.<br> M<br> (10x - 45)<br> N<br> R<br> Р<br> (6x - 1)

Mashutka [201]

Looks confusing in the way you put it.

4 0

2 years ago

FIRST ONE TO ANSWER GETS BRAINLIEST!!!!

-Dominant- [34]

Answer:

The maximum distance traveled is 4.73 meters in 0.23 seconds.

Step-by-step explanation:

We have that the distance traveled with respect to time is given by the function,

$d(t) = 4.9t^2-2.3t+5$ .

Now, differentiating this function with respect to time 't', we get,

d'(t)=9.8t-2.3

Equating d'(t) by 0 gives,

9.8t - 2.3 = 0

i.e. 9.8t = 2.3

i.e. t = 0.23 seconds

Substitute this value in d'(t) gives,

d'(t) = 9.8 × 0.23 - 2.3

d'(t) = 2.254 - 2.3

d'(t) = -0.046.

As, d'(t) < 0, we get that the function has the maximum value at t = 0.23 seconds.

Thus, the maximum distance the skateboard can travel is given by,

$d(t) = 4.9\times 0.23^2-2.3\times 0.23+5$ .

i.e. $d(t) = 4.9\times 0.0529-2.3\times 0.23+5$ .

i.e. $d(t) = 0.25921-0.529+5$ .

i.e. $d(t) = 0.25921-0.529+5$ .

i.e. d(t) = 4.73021

Hence, the maximum distance traveled is 4.73 meters in 0.23 seconds.

5 0

2 years ago

Given a right triangle with legs a, b and hypotenuse c, solve for b if a= 72 and c= 75

kotykmax [81]

Answer:

The answer is a. 21.

Step-by-step explanation:

We solve this question by using Pythagoras theorem to relate the sides of a right angled triangle.

Here,

Hypotenuse of the given triangle(c)=75

Two sides of right angled triangle are:

a=72

b=?

Then,

for a given right angled triangle abc,

Using Pythagoras theorem,

$c=\sqrt{a^{2} +b^{2} }$

Squaring on both sides,

$c^{2} =a^{2}+b^{2}$

or, $75^{2}=72^{2}+b^{2}$

or, $b^{2}=75^{2}-72^{2}$

or, $b^{2}=5625- 5184$

or, $b^{2} =441$

∴ $b=21$

So, the value of b is obtained to 21 by the use of Pythagoras theorem.

7 0

2 years ago

What type of triangle is pictured?

Evgen [1.6K]

Answer:

I think it is either A or D

5 0

2 years ago

Read 2 more answers