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3 years ago

Find n(a) for the set

Mathematics

1 answer:

elixir [45]3 years ago

6 0

Answer:

Step-by-step explanation:

n(A) means the number of elements in set A

Element 1=-10

Element 2=-9

Element 3=-8

Follow the pattern

Element 4=-7

Element 5=-6

Element 6=-5

Element 7=-4

Element 8=-3

Element 9=-2

Element 10=-1

Element 11=0

There are 11 elements in set A.

Also this has the same number of elements as {0,1,2,...,8,9,10} which has (10+1) elements.

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What is x in the expression 7x - 6

Eva8 [605]

Answer:

Variable

Step-by-step explanation:

I just know. You can search it up if you'd like!

7 0

3 years ago

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What is the answer??? Please help me! <br> 16% of 40 =

Murrr4er [49]

Answer:

16/100*40

32/2

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3 years ago

Write the slope-intercept form of the equation of the line described.

Genrish500 [490]

Answer:

The slope-intercept form is y = 7x + 3

Step-by-step explanation:

Remember: Perpendicular lines slope are negative reciprocals of each other.

y = -1/7x + 4.

Now you know the slope of the given line is -1/7.

So the slope of the perp line is 7/1 = 7 .

Use the given point (-1, -4) and the perp slope = 7 into y =mx + b and solve for "b".

y = mx + b

-4 = 7(-1) + b

-4 = -7 + b

-4 + 7 = b

3 = b

The slope-intercept form is y = 7x + 3

4 0

3 years ago

..Please simplify ..

Ket [755]

Answer:

3/2 * square root of 2

This is the correct answer

Step-by-step explanation:

3/14 * square root 98 =

= square root of 98 * 3/14^2 =

= square root of 98 * 9/196 =

= square root of 9/2

3/2 * square root of 2 =

= square root of 2 * 9/4 =

= square root of 9/2

square root of 9/2 = square root of 9/2

4 0

3 years ago

Use calculus to find the absolute maximum and minimum values of the function. (round all answers to three decimal places.) f(x)

Allisa [31]

Part A:

Given the function $f(x)=x+2\cos(x)$ , the absolute maximum or minimum occurs when $f'(x)=0$ .

$f'(x)=0 \\ \\ \Rightarrow1-2\sin{x}=0 \\ \\ \Rightarrow2\sin{x}=1 \\ \\ \Rightarrow\sin{x}= \frac{1}{2} \\ \\ \Rightarrow x=\sin^{-1}{\frac{1}{2}}= \frac{\pi}{6}$

Using the second derivative test,

$f''(x)=-2cosx \\ \\ \Rightarrow f''\left( \frac{\pi}{6} \right)=-2\cos{\left( \frac{\pi}{6} \right)}=-1.732$

Since the second derivative gives a negative number, the given function has a maximum point at $x=\frac{\pi}{6}$ .

And the maximum point is given by:

$f\left( \frac{\pi}{6} \right)=\frac{\pi}{6}+2\cos\left( \frac{\pi}{6} \right) \\ \\ =0.5236+2(0.8660)=0.5236+1.732 \\ \\ =\bold{2.256}$

i.e. $\left(\frac{\pi}{6},\ 2.256\right)$

Part B:

Given the function $f(x)=e^{-x}-e^{-2x}$ , the absolute maximum or minimum occurs when $f'(x)=0$ .

$f'(x)=0 \\ \\ \Rightarrow-e^{-x}+2e^{-2x}=0 \\ \\ \Rightarrow2e^{-2x}=e^{-x} \\ \\ \Rightarrow2e^{-x}=1 \\ \\ \Rightarrow e^{-x}=\frac{1}{2} \\ \\ \Rightarrow-x=\ln \frac{1}{2}=-0.6931 \\ \\ \Rightarrow x=0.6931$

Using the second derivative test,

$f''(x)=e^{-x}-4e^{-2x} \\ \\ \Rightarrow f''(0.6931)=e^{-0.6931}-4e^{-2(0.6931)} \\ \\ =0.5-4e^{-1.386}=0.5-4(0.25)=0.5-1 \\ \\ =-0.5$

Since the second derivative gives a negative number, the given function has a maximum point at $x=0.6931$ .

And the maximum point is given by:

$f(0.6931)=e^{-0.6931}-e^{-2(0.6931)} \\ \\ =0.5-e^{-1.386}=0.5-0.25=\bold{0.25}$

i.e. (0.693, 0.25)

3 0

3 years ago