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3 years ago

Find the polar equation of the conic with the focus at the pole, directrix x = 4, and eccentricity 1.

Mathematics

1 answer:

BabaBlast [244]3 years ago

6 0

Answer:

Choice D is correct

Step-by-step explanation:

The eccentricity of the conic section is 1, implying we are looking at a parabola. Parabolas are the only conic sections with an eccentricity of 1.

Next, the directrix of this parabola is located at x = 4. This implies that the parabola opens towards the left and thus the denominator of its polar equation contains a positive cosine function.

Finally, the value of k in the numerator is simply the product of the eccentricity and the absolute value of the directrix;

k = 1*4 = 4

This polar equation is given by alternative D

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The expression sin 57° is equal to

ValentinkaMS [17]

Answer:

$cos(33^{\circ})$

Step-by-step explanation:

Given

$sin(57^{\circ})$

Required

Determine an equivalent expression

In trigonometry:

$sin(\theta)= cos(90^{\circ} - \theta)$

In $sin(57^{\circ})$

$\theta=57^{\circ}$

Substitute $57^{\circ}$ for $\theta$

in $sin(\theta)= cos(90^{\circ} - \theta)$

$sin(57^{\circ})= cos(90^{\circ} - 57^{\circ})$

$sin(57^{\circ})= cos(33^{\circ})$

Hence, the equivalent expression is: $cos(33^{\circ})$

5 0

3 years ago

1/3(m-1)=-5<br> Please help

dezoksy [38]

Answer:

m=-14 I hope this helps u

Step-by-step explanation:

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4 years ago

Malik grills a steak 45 minutes longer than he grills a serving of fish. The fish takes twice as long as the asparagus to grill.

stellarik [79]

Vasellasar26,

Penso che tu parli italiano, quindi ecco la risposta alla domanda in italiano. Malik griglia una bistecca 45 minuti in più rispetto a u.na porzione di pesce. Il pesce impiega il doppio del tempo per grigliare gli asparagi. Malik griglia i pomodori tagliati a metà per 3 minuti, che è 3 minuti in più rispetto a quando griglia gli asparagi. 3 33 Questa domanda è composta da 3 parti. Assicurati di completare tutte le parti. A Indicazioni: digita la tua risposta nella casella. Scrivi un'espressione che rappresenti il tempo durante il quale Malik griglia la bistecca se gli asparagi grigliano x minuti.

3 0

3 years ago

Given that these simultaneous equations

Tatiana [17]

The value of k is $(3\sqrt{ 10})/2$

<h3>How to solve the simultaneous equation?</h3>

Given:

x-y=k.............(eq i)

2x²+y²-15..............(eq ii)

We would make y the subject formula in eq ii

2x²+y²-15= 0

2x² + y²= 15

y²= 15-2x²

y= $\sqrt{15-2x^2}$ ...........(eq iii)

Substitute the value of y into eq i

x-( $\sqrt{15-2x^2}$ = k

x- ( $\sqrt{15} - 2x$ = k

k= $(3\sqrt{ 10})/2$

Read more about simultaneous equations here:

brainly.com/question/16863577

#SPJ1

3 0

2 years ago

What is the sum of a geometric sequence 1, 3, 9, ... if there are 12 terms?

attashe74 [19]

We know that
a1=1
a2=3
a3=9
a2/a1=3/1----> 3
a3/a2=9/3----> 3
<span>common ration r is equal to 3
number of terms n is 12

The </span><span>Sum of geometric series is given by the formula
</span>Sum=a1*[1-r<span>^n]/[1-r]
</span>Sum=1*[1-3^12]/[1-3]-----> Sum=[1-3^12]/[1-3]----> [3^12-1]/[3-1]
<span>Sum=531440/2-----> 265720

the answer is
265720

</span>

4 0

4 years ago