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3 years ago

Engh

Mathematics

1 answer:

Gennadij [26K]3 years ago

7 0

Answer:

Step-by-step explanation: bc i said

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Find a cartesian equation for the curve and identify it. r = 10 tan(θ) sec(θ)

Vilka [71]

For a cartesian equation
$x=r\cos\theta \ and \ y=r\sin\theta \\ \\ \cos\theta=\frac{x}{r} \ and \ \sin\theta=\frac{y}{r} \\ \\ \tan\theta=\frac{\sin\theta}{\cos\theta}=\frac{y}{r}\cdot\frac{r}{x}=\frac{y}{x} \\ \\ \sec\theta=\frac{1}{\cos\theta}=\frac{r}{x}$

Given r = 10 tan(θ) sec(θ)
$r=10\tan\theta\sec\theta=10\cdot\frac{y}{x}\cdot\frac{r}{x} \\ \\ \Rightarrow10y=x^2 \\ \\ \Rightarrow y= \frac{1}{10} x^2$

Therefore,the curve is a parabola opening upward with vertex (0, 0).

3 0

3 years ago

(Tough day dividing polynomials and I'm still lost!) Please help me my hands are legit numb:)

N76 [4]

Answer:

Option D. 9

Step-by-step explanation:

There are two ways to obtain the answer to the question.

Method 1:

Let 2x + 1 = 0

Making x the subject, we have

2x + 1 = 0

Collect like terms

2x = –1

Divide both side by 2

x = –1/2

Now, put the value of x into the expression 4x³ – 6x² – 8x + 7, we have:

4x³ – 6x² – 8x + 7

x = –1/2

4(–1/2)³ – 6(–1/2)² – 8(–1/2) + 7

4(–1/8) – 6(1/4) – 8(–1/2) + 7

–1/2 – 3/2 + 4 +7

– 4/2 + 4 + 7

– 2 + 4 + 7

= 9

Method 2:

Divide 4x³ – 6x² – 8x + 7 by 2x + 1

Please see attached photo for explanation.

4 0

3 years ago

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

SashulF [63]

ANSWER

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

EXPLANATION

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

-3 1/2= 1/2x+1/2x+x A)-1 3/4 B)-5 1/2 C)-1 1/2 10points each

rosijanka [135]

Answer:

-1 3/4 =x

Step-by-step explanation:

-3 1/2= 1/2x+1/2x+x

Combine like terms

-3 1/2 = 2x

Change to an improper fraction

- ( 2*3+1)/2 = 2x

-7/2 = 2x

Multiply each side by 1/2

-7/2 *1/2 = 2x* 1/2

-7/4 = x

Changing to a mixed number

-4/4 -3/4 =x

-1 3/4 =x

4 0

3 years ago

Edward is taking a trip. The distance

Grace [21]

Answer:

67.5 miles

Step-by-step explanation:

If 1 cm represents 15 miles, then 4.5 cm represents 4.5 * 15 miles.

4.5 * 15 miles = 67.5 miles

Answer: 67.5 miles

3 0

3 years ago