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2 years ago

What type of limacon is graphed by the polar equation r=4+2sinttheta?

Mathematics

2 answers:

sergiy2304 [10]2 years ago

8 0

The type of limacon graphed is a convex.

nydimaria [60]2 years ago

6 0

Answer:

The graph is a convex limacon.

Step-by-step explanation:

Polar equation is defined as

$r=b+a\sin \theta$ and $r=b+a\cos \theta$

Types of limacon:

1. If b < a, then graph is a limacon with and inner loop.

2. If a < b < 2a, then graph is a dimpled limacon.

3. If 2a ≤ b, then graph is a convex limacon.

The given equation is

$r=4+2\sin \theta$

Here b=4 and a=2.

$2a=2(2)=4=b$

$2a=4$

$2a=b$ $[\because b=4]$

Since 2a ≤ b, therefore the graph is a convex limacon.

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Help please logarithms

DochEvi [55]

Answer:

Simplified: 40

Step-by-step explanation:

To simplify this, we need to first separate the terms in this expression. There is a property of exponents that says: $x^{a+b} =x^ax^b$ We can do this same thing to simplify this expression. Next, we can simplify each of these terms. $2^2$ simply becomes 4. In the other term, the $2^{log_2}$ simply cancel each other and leave the 10. This means that we're left with 4*10, which is 40

$2^{2+log_210} \\\\2^2*2^{log_210} \\\\4*10\\\\40$

6 0

2 years ago

Given: ∠AOC, ∠BOC - complementary angles

34kurt

Answer:

30
COB . . . . or . . . . BOC

Step-by-step explanation:

The reason given on the line of interest is "substitution," so the problem boils down to determining what was substituted for what. The previous statement says ...

AOC + COB = 90

and the first part of the statement we're to complete has BOC + ___.

We see from the given statements that m∠AOC = m∠BOC + 30°, so it appears that is the substitution that has been made: AOC has been replaced by BOC + 30.

This means the first blank is filled with 30.

The second part of the previous statement is ...

AOC + COB = 90

so we believe this (COB) should go in the second blank.

Then the line of interest would read ...

BOC + 30 + COB = 90

_____

Comment on the problem

There is a curious mix of notations here. Usually, (as in the beginning of this problem) we refer to the measure of an angle using "m∠" in front of the angle designator, and we use a degree symbol to indicate the units of that measure. Part-way through the problem statement written here, those notations were dropped, and we're to assume they are intended. IMO, this is a poor way to demonstrate careful problem solving.

The substitution given for AOC is BOC+30, but the line into which that is substituted has AOC +COB = 90. This means the equation after substitution is ...

BOC +30 +COB = 90

Since BOC and COB are the same angle, we can sort of fudge the "algebra" to get to BOC=30, but if the problem were more carefully written, the angle would be referred to by consistent nomenclature:

m∠AOC + m∠BOC = 90° . . . . . . . . . preferred angle designations

(m∠BOC + 30°) + m∠BOC = 90° . . . . substitution for m∠AOC

2(m∠BOC) = 60° . . . . . . algebra (subtract 30°, collect terms)

m∠BOC = 30° . . . . . . . . algebra (divide by 2)

3 0

2 years ago

Santiago walked 500 m

N76 [4]

Answer:

500 X 7 = 3500, 3500m = 3.5 km

She walked 3.5 km in 1 week.

7 0