What is the value of the expression below?<br><br> -4(2)

Convert the Cartesian equation (x 2 + y 2)2 = 4(x 2 - y 2) to a polar equation.

SashulF [63]

<u>ANSWER</u>

${r}^{2} = 4 \cos2\theta$

<u>EXPLANATION</u>

The Cartesian equation is

${( {x}^{2} + {y}^{2} )}^{2} = 4( {x}^{2} - {y}^{2} )$

We substitute

$x = r \cos( \theta)$

$y = r \sin( \theta)$

and

${x}^{2} + {y}^{2} = {r}^{2}$

This implies that

${( {r}^{2} )}^{2} = 4(( { r \cos\theta) }^{2} - {(r \sin\theta) }^{2} )$

Let us evaluate the exponents to get:

${r}^{4} = 4({ {r}^{2} \cos^{2}\theta } - {r}^{2} \sin^{2}\theta)$

Factor the RHS to get:

${r}^{4} = 4{r}^{2} ({ \cos^{2}\theta } - \sin^{2}\theta)$

Divide through by r²

${r}^{2} = 4 ({ \cos^{2}\theta } - \sin^{2}\theta)$

Apply the double angle identity

$\cos^{2}\theta -\sin^{2}\theta= \cos(2 \theta)$

The polar equation then becomes:

${r}^{2} = 4 \cos2\theta$

7 0

3 years ago

Evaluate the function below for x=2. F(x)=x^4+6x^3+3

Nitella [24]

Answer:
f(2)=67
Step-by-step explanation:
In order to evaluate the function f(x)=x^4+6x^3+3 for x=2, you must replace all of the x's with the number two and then simplify:
f(2)=2^4+6(2)^3+3
f(2)=16+6(8)+3
f(2)=16+48+3
f(2)=16+51
f(2)=67

7 0

3 years ago

2. There are some benches in a classroom. If 4 students sit on each bench then 3 benches

NARA [144]

Answer: There are 48 students in the class.

Step-by-step explanation:

Let the number of students = S

Let the number of benches = B

<em>If 4 students sit on each bench, 3 benches are left vacant.</em>

S = 4(B - 3)

S = 4·B - 12 } Equation 1

<em>If 3 students sit on each bench, 3 students still standing.</em>

S = 3·B + 3 } Equation 2

We can match the two equations because they both indicate the same number of students.

4B - 12 = 3·B + 3

on solving this

4·B - 3·B = 3 + 12

B = 15 → number of benches

That is the number of benches, therefore substituting the value for B in equation 1

S = 4·B - 12 Equation 1

S = 4·15 -12

S = 60 - 12 = 48 → number of students

Answer: There are 48 students in the class.

<h3>Verification</h3>

There are 48 students and 15 benches.

<em>If 4 students sit on each bench, 3 benches are left vacant.</em>

48students ÷ 4students/bench = 12 benches are occupied and left 3 vacant benches.

<em>If 3 students sit on each bench, 3 students still standing.</em>

<h3 />

15benches * 3 students/bench = 45 students are sitting and 3 students remain standing.

<h3>Checked!!</h3>

$\textit{\textbf{Spymore}}$

8 0

3 years ago

Write the equation of the circle in standard form with the center located at

Alex787 [66]

Answer:

(x+2)^2 + (y-5)^2 = 9

Step-by-step explanation:

The equation of a circle is given by

(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius

(x- -2)^2 + (y-5)^2 = 3^2

(x+2)^2 + (y-5)^2 = 9

4 0

3 years ago

Can you answer (a,b)?

Alex

Answer:

a) 11.283 dollars

b) 1.435 hour

Step-by-step explanation:

1 kilo watt of electricity used for 1 hour

Charges of electricity per unit = $0.05224

Laura uses 5 heaters to warm her house. The electricity consumed by each use 1800 wats or 1.8 kilo wats

a) Charges in one day = 5 heaters * 1.8 kilo wats per hour * 24 hour* $0.05224 per kilowats per hour

= 11.283 dollars

b) 75 wat light bulb consumes 0.075 kilo wats per hour

Charge per kilowat per hour = $0.05224

In order to cost 1 $, the 75 wat bulb need to be on for 1.435 hour

6 0

3 years ago

What is the value of the expression below? -4(2)