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Lesechka [4]
3 years ago
13

List the elements of the set, then indicate the cardinality of the set. HINT [See Example 2.] (Enter your answers as a comma-sep

arated list. Enter your answers from smallest to largest.) A = {k | k is a positive integer and 8 < k < 16}.
Mathematics
1 answer:
Gnom [1K]3 years ago
7 0

Answer:

Elements of the set: 9,10,11,12,13,14,15

Cardinality of the set: 7

Step-by-step explanation:

Firstly the set describes that A contains the values of k which are positive integers only.

Secondly it limits the values of k to be between 8 and 16, exclusive of both upper and lower limits.

Therefore we list all positive integers between 8 and 16 i.e. 9,10,11,12,13,14,15

Finally, we count the numbers of elements in the set which is also known as cardinality of the set i.e. 7 for our given set.

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Solve (X + 6)(x - 4) = -16<br> O {-4, 6)<br> O {-4, 2]<br> O (-12, 22)
masya89 [10]

Answer:

x=2 or x=−4

Step-by-step explanation:

Let's solve your equation step-by-step.

(x+6)(x−4)=−16

Step 1: Simplify both sides of the equation.

x2+2x−24=−16

Step 2: Subtract -16 from both sides.

x2+2x−24−(−16)=−16−(−16)

x2+2x−8=0

Step 3: Factor left side of equation.

(x−2)(x+4)=0

Step 4: Set factors equal to 0.

x−2=0 or x+4=0

x=2 or x=−4

6 0
3 years ago
Find an equation of the tangent to the curve x =5+lnt, y=t2+5 at the point (5,6) by both eliminating the parameter and without e
svet-max [94.6K]

ANSWER

y = 2x -4

EXPLANATION

Part a)

Eliminating the parameter:

The parametric equation is

x = 5 +  ln(t)

y =  {t}^{2}  + 5

From the first equation we make t the subject to get;

x - 5 =  ln(t)

t =  {e}^{x - 5}

We put it into the second equation.

y =  { ({e}^{x - 5}) }^{2}  + 5

y =  { ({e}^{2(x - 5)}) }  + 5

We differentiate to get;

\frac{dy}{dx}  = 2 {e}^{2(x - 5)}

At x=5,

\frac{dy}{dx}  = 2 {e}^{2(5 - 5)}

\frac{dy}{dx}  = 2 {e}^{0}  = 2

The slope of the tangent is 2.

The equation of the tangent through

(5,6) is given by

y-y_1=m(x-x_1)

y - 6 = 2(x - 5)

y = 2x - 10 + 6

y = 2x -4

Without eliminating the parameter,

\frac{dy}{dx}  =  \frac{ \frac{dy}{dt} }{ \frac{dx}{dt} }

\frac{dy}{dx}  =  \frac{ 2t}{  \frac{1}{t} }

\frac{dy}{dx}  =  2 {t}^{2}

At x=5,

5 = 5 +  ln(t)

ln(t)  = 0

t =  {e}^{0}  = 1

This implies that,

\frac{dy}{dx}  =  2 {(1)}^{2}  = 2

The slope of the tangent is 2.

The equation of the tangent through

(5,6) is given by

y-y_1=m(x-x_1)

y - 6 = 2(x - 5) =

y = 2x -4

5 0
3 years ago
Consider the lengths of the sides of a triangle as listed. Triangle A: 3, 4, 5 Triangle B: 5, 12, 13 Triangle C: 10, 12, 15 Tria
insens350 [35]

Answer:

Triangle E or D

Step-by-step explanation:

Is not the right one

6 0
3 years ago
What is the value of (4xy)^0
VMariaS [17]
Its1.  every number/variable that has a power to the zero, its goin to turn out to be just one
4 0
3 years ago
What happens to the interval as the level of confidence is​ changed? Explain why this is a logical result.
Elan Coil [88]

Answer with explanation:

A x% confidence interval interprets the percentage of certainty that a person can believe that the true population parameter.

It is also represented as Point estimate ± Margin of error

Confidence level is proportional to the Margin of error.

  • As confidence level increases the error bound increases that makes the confidence interval broader.
  • As confidence level decreases the error bound decreases , making the confidence interval narrower.
6 0
3 years ago
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