Consider the limaçon with equation r = 3 4cos(θ). how does the quotient of a and b relate to the existence of an inner loop?

Answer:

see image

Step-by-step explanation:

I did two different problems depending on whether the 4 beside the log is a base or not.

If the log IS the base, I got x = 1 as you did. But if the 4 is not the base then there is no base written and that means the base is 10.

For log problems that have log on one side of the equation only, then a good strategy is to change the equation from logarithmic form to exponential form. See image for work. Hope this helps.

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:x = -16 [/tex]

[tex]\qquad \tt \rightarrow \: y =4 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: 27 + yi = 11 - x + 4i[/tex]

[tex]\qquad \tt \rightarrow \: yi + x = 11 + 4i - 27[/tex]

[tex]\qquad \tt \rightarrow \: x + yi = - 16 + 4i[/tex]

By equating both equations we get :

[tex]\qquad \tt \rightarrow \: x = - 16[/tex]

[tex]\qquad \tt \rightarrow \: y = 4[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The graph of the exponential function in discuss whose base is; e would have a y-intercept t at point (0, 1), with a domain as the set of all real numbers and its range as the set of all positive numbers.

It follows from the task content that the function in discuss can be written as;

y = e^x.

Consequently, the y-intercept of the graph which corresponds to x= 0 is; (0, 1).

The domain and range of the graph as with other exponential functions are therefore given as the set of all real numbers and all real positive numbers respectively.

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Answer: 8 pieces

Step-by-step explanation:

- if there are 24 pieces of sushi in 6 packages then 24/6 = 4 so there’s 4 pieces of sushi in each package

- since there’s 4 pieces of sushi in each pack just do 4 x 2 = 8

- so there’s 8 pieces of sushi in 2 packages

hope this helps :)

The function that is a  tangent to the graph of f is [tex]f(x) = (5/4)x^4+60[/tex]

The definite integral can be interpreted as the resulting area of a region. In addition, it is a value in its result, that is, it does not depend on the variable x, which can be exchanged for any other variable without changing the value of the integral.

Knowing that :

therefore, f'(x)|x=a = -40, so only look for a we have:

[tex]5a^3 = -40\\a^3 = -8\\a = -2[/tex]

if, x = -2, then y = 80 (since, 40x + y = 0), therefore, f(x) passes through (-2,80), so in the equation:

[tex]f'(x) = 5x^3\\f(x) = (5/4)x^4 + c\\80 = (5/4)(-2)^4 + c\\c = 60[/tex]

Therefore,

[tex]f(x) = (5/4)x^4+60[/tex]

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According to the empirical rule, the percent of the data points that are above 76 is; 2.28%

We are given;

Mean; μ = 88

Standard deviation; σ = 6

Sample mean; x' = 76

Formula for z-score is;

z = (x' -  μ)/σ

z = (76 - 88)/6

z = -2

Now, from the empirical rule of normal distribution graph attached, we see that at z = -2, the percentage is 95.44%. However, we want to find the percentage that lie above 27. Thus, this is (100% - 95.44%)/2 = 2.28%

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Answer:

the x value is 13 and the y value is 10. x=13 and y=10

Answer:

2 miles

Step-by-step explanation:

6X + 10 = 22

X = (22-10)/6 = 12/6 = 2 miles

Step-by-step explanation:

[tex]\sqrt{35} =\sqrt{5} *\sqrt{7};[/tex]

all the details are in the attachment.

We can simplify the given rational function into a linear one, the graph is below.

Here we have the rational function:

[tex]f(x) = \frac{4x^2 - 16}{2x - 4}[/tex]

Factorization the numerator, we get:

4x² - 16 = 0

4x² = 16

x² = 16/4 = 4

x = ±√4 = ±2

Then the numerator can be written as:

4*(x - 2)*(x + 2)

And the denominator can be rewritten as:

2x - 4 = 2*(x - 2)

Then the function becomes:

[tex]f(x) = \frac{4*(x + 2)*(x - 2)}{2*(x - 2)} \\\\f(x) = 2*(x + 2) = 2x + 4[/tex]

So we have just a linear equation, so the graph that represents the function is the graph of a line, the one you can see below.

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The interest rate Cindy will be charged with money factor 0.00354 is approximately 8.5% which is option b.

Given The factor included in lease is 0.00354.

Interest is the amount that a bank or person who gives loan charges from loan taker.

Money factor is a method for finding the financing charges on a lease with monthly payments. The money factor can be translated into the annual percentage rate by multiplying the money factor by 2400.

Money factor=0.00354.

So the interest rate that Cindy will charge is equal to 2400*0.00354

The interest rate Cindy will be charged =8.496%

=8.5%

Hence the interest rate charged is approximately 8.5%.

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Answer:

  k ≠ -14/3

Step-by-step explanation:

A square matrix is invertible if and only if its determinant is not zero.

The determinant of a 2×2 matrix is the difference of the products of the diagonal terms and the off-diagonal terms:

  det = (6)(k) -(-7)(4) = 6k +28

The requirement that the determinant is not zero places a restriction on k.

  6k +28 ≠ 0

  k +14/3 ≠ 0 . . . . . . divide by 6

  k ≠ -14/3 . . . . . . . . subtract 14/3

For the matrix to be invertible, the value of k must not be -14/3.

Answer:

480 Hectares potatoes, 340 Hectares corn

Step-by-step explanation:

Let x be the land used to plant potatoes in hectares.

Let y be the land used to plant corn in hectares.

Given the information from the question, we know that:

x + y = 820 - Equation 1

and

x - y = 140 - Equation 2

as you can see here we have 2 equations, means we can solve them simulteanously to solve for both. We will use elimination method.

We will use Equation 1 - Equation 2.

x-x+y-(-y)=820-140

2y = 680

y = 680 ÷ 2 = 340 hectares

We substiture y into equation 1 to find x

x + 340 = 820

x = 820 - 340

= 480 hectares

Therefore, 480 hectares of potatoes and 340 hectares of corn were planted.

Answer:

Answer:

a.) P(HH|C)=2/5

Explanation:

Given following:

Solving steps:

[tex]\sf P(HH|C) = \dfrac{P(HH \cap C) }{P(C)}[/tex]

[tex]\sf P(HH|C) = \dfrac{4 }{10}[/tex]

[tex]\sf P(HH|C) = \dfrac{2 }{5}[/tex]

Answer: 4

Step-by-step explanation:

[tex]f(4)=\frac{1}{4} \cdot 2^{4}=\frac{1}{4} \cdot 16=4[/tex]

Answer:

Ordinal, 3,355th. This number as US currency, three thousand three hundred fifty-five dollars ... 3355 is NOT a triangle number ... Base 6

The transformation was a 180° rotation about the origin.

We can solve this question by plotting the points R (1, 1)

S (3, 1) T (1, 6) and R' (–1, –1) S' (–3, –1) T' (–1, –6) on the graph as shown below.

As we can see from the graph, the original triangle RST which was in quadrant 1, now becomes triangle R’S’T’ in quadrant 3. Thus, when triangle RST was transformed using the rule (x, y) → (–x, –y), from quadrant 1 to quadrant 3 it is a 180° rotation about the origin.

Hence, the transformation was a 180° rotation about the origin.

Your question was incomplete. Please check below for full content.

Triangle RST was transformed using the rule (x, y) → (–x, –y). The vertices of the triangles are shown. R (1, 1) S (3, 1) T (1, 6) R' (–1, –1) S' (–3, –1) T' (–1, –6)

Which best describes the transformation?

The transformation was a 90° rotation about the origin.

The transformation was a 180° rotation about the origin.

The transformation was a 270° rotation about the origin.

The transformation was a 360° rotation about the origin.

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It takes 1.7 x 10 ^4 for light from the sun to reach the comet.

The number is written in the form  [tex]a \times 10^b[/tex] where we have [tex]1 \leq a < 10[/tex]

Scientific notations have some of the profits as:

Better readability due to compact representation

Its value in terms of the power of 10 is known, which helps in the easy comparison of quantities differing by a large value.

A comet is about  [tex]5.1 \times 10 ^9[/tex] km from the sun.

Light travels at about [tex]3.0 \times 10 ^5[/tex] km per second.

[tex]\dfrac{5.1 \times 10 ^9}{3.0 \times 10 ^5}[/tex]

= [tex]1.7 \times 10 ^4[/tex]

Hence, It takes 1.7 x 10 ^4 for light from the sun to reach the comet.

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Answer:

Actual distance=187.5miles

Step-by-step explanation:

1cm=30miles

6.25cm=6.25*30miles

=187.5miles

The distance between the two towns using the map scale is 187.5 miles.

A measurement unit is a unit to measure certain quantities.

For example, the mass can be measured in kilograms, length can be measured in meter and time can be measured in seconds.

To find the measurement of a new quantity known units can be used in operation. As to find the unit for speed we use m/s as a unit, where, m is the unit of distance and s is the unit of time.

Given that,

The distance between the towns on map is 1 cm.

And, the scale of map is 1 cm = 30 miles.

As per the problem the actual distance can be found by using the scale of the map as follows,

The distance between two towns is 6.25 × 30 = 187.5 miles.

Hence, the actual distance between the two towns is 187.5 miles.

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Answer:

(x-4)² + y² = 100

Step-by-step explanation:

The only circles that have a center at (4 , 0) are :

(x-4)² + y² = 100

(x-4)² + y² = 10

……………………

•  (-2 - 4)² + 8² = (-6)² + 64 = 36 + 64 = 100 ≠ 10

Then

The circle (x-4)² + y² = 10 doesn’t contain the point (-2, 8)

•  (-2 - 4)² + 8²  = 100

Then

The circle (x-4)² + y² = 100 contains the point (-2, 8)

Answer:

(x/0.2)(7)-2.8=-499.8

x=-14.2

Step-by-step explanation:

(x/0.2)(7)-2.8=-499.8

7x/0.2 -2.8 = -499.8

35x -2.8 = -499.8

35x = -499.8 +2.8

35x = -497

35x/35 = -497/35

x = -14.2

you probably already got it solved, but at least this can help anyone else!

The first three terms of the sequence are 10, 20, and 30.

The function given is 10n. In this case, the terms will be:

First term = 10n = 10 × 1 = 10

Second term = 10 × 2 = 40

Third term = 10 × 3 = 30

In this case, the first three terms of the sequence are 10, 20, and 30.

It an arithmetic sequence as there is a common difference of 10.

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The point that is labeled H on this graph is the point where Chana's and Josiah's distance from the starting line at the time when Chana catches up with Josiah.

At the point H, there is an intersection between the distance covered by both of these individuals.

This point is the point where we are shown that Chana has caught up with Josiah as they are skating.

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Answer:

t = 4.0

Step-by-step explanation:

1.) P(t) = 1578

2.) Divide both sides by 1400

3.) Take the natural log of both sides (to remove the "e")

4.) Divide both sides by 0.03

5.) Properly round to the 1st decimal place

Answer:

[tex]57[/tex]

Step-by-step explanation:

You just plug in 8 as a, and 7 as b. This gives you the following equation: [tex](8)^2-7[/tex] which becomes [tex]64-7[/tex] by squaring the 8, Then subtract 7 and you get [tex]57[/tex]

Answer:

57

Step-by-step explanation:

a = 8

b = 7

a² - b

= 8² - 7

= (8*8) - 7

= 64 - 7

= 57

Answer: [tex]f(x) > 0[/tex]

Step-by-step explanation:

The range of all exponential functions without a vertical shift is the set of positive real numbers.