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3 years ago

Given the table below for selected values of f(x), use 6 left rectangles to estimate the value of

Mathematics

2 answers:

Gnoma [55]3 years ago

8 0

Answer:

Step-by-step explanation:

Given is a table of x, f(x) as below

x 1 3 4 6 7 9 10

f(x) 4 8 6 10 10 12 16

Mid pt 6 7 8 10 11 14

width of

interval 2 1 2 1 2 1

dA1 12 7 16 10 22 14

area = area of all rectangles= 81 sq units.

IrinaVladis [17]3 years ago

3 0

Divide the area into 6 portions and find the sum of each one to find the value of the final integral:

f(x)dx = 2(8+4)/2 + 1 (8+6)/2 + 2 (6+10)/2 + 1(10+10)/2 + 2 (10+12)/2 + 1 (12+16)/2

= 12 + 7 + 16 + 10 + 22 + 14 = 81 sq units

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Write an equation that models this situation. At a sports banquet, 8 guests are seated at each of the 15 available tables. How m

leonid [27]

Answer:

The equation that models this situation is:

x = 15 × 8 or x ÷ 8 = 15

Step-by-step explanation:

Total number of available tables = 15

The number of guests who are seated at each of the 15 available tables = 8

Let 'x' be the total number of guests who are seated at the tables.

If have to determine how many guests (x) are seated at the tables, all we need is to multiply the 15 with 8.

so the equation becomes

x = 15 × 8 or x ÷ 8 = 15

Therefore, the equation that models this situation is:

x = 15 × 8 or x ÷ 8 = 15

5 0

3 years ago

Read 2 more answers

How to find the derivative of cos^2x? i seem to be confused.

slamgirl [31]

If you're using the app, try seeing this answer through your browser: brainly.com/question/2927231

————————

You can actually use either the product rule or the chain rule for this one. Observe:

• Method I:

y = cos² x

y = cos x · cos x

Differentiate it by applying the product rule:

$\mathsf{\dfrac{dy}{dx}=\dfrac{d}{dx}(cos\,x\cdot cos\,x)}\\\\\\
\mathsf{\dfrac{dy}{dx}=\dfrac{d}{dx}(cos\,x)\cdot cos\,x+cos\,x\cdot \dfrac{d}{dx}(cos\,x)}$

The derivative of cos x is – sin x. So you have

$\mathsf{\dfrac{dy}{dx}=(-sin\,x)\cdot cos\,x+cos\,x\cdot (-sin\,x)}\\\\\\
\mathsf{\dfrac{dy}{dx}=-sin\,x\cdot cos\,x-cos\,x\cdot sin\,x}$

$\therefore~~\boxed{\begin{array}{c}\mathsf{\dfrac{dy}{dx}=-2\,sin\,x\cdot cos\,x}\end{array}}\qquad\quad\checkmark$

—————

• Method II:

You can also treat y as a composite function:

$\left\{\!
\begin{array}{l}
\mathsf{y=u^2}\\\\
\mathsf{u=cos\,x}
\end{array}
\right.$

and then, differentiate y by applying the chain rule:

$\mathsf{\dfrac{dy}{dx}=\dfrac{dy}{du}\cdot \dfrac{du}{dx}}\\\\\\
\mathsf{\dfrac{dy}{dx}=\dfrac{d}{du}(u^2)\cdot \dfrac{d}{dx}(cos\,x)}$

For that first derivative with respect to u, just use the power rule, then you have

$\mathsf{\dfrac{dy}{dx}=2u^{2-1}\cdot \dfrac{d}{dx}(cos\,x)}\\\\\\
\mathsf{\dfrac{dy}{dx}=2u\cdot (-sin\,x)\qquad\quad (but~~u=cos\,x)}\\\\\\
\mathsf{\dfrac{dy}{dx}=2\,cos\,x\cdot (-sin\,x)}$

and then you get the same answer:

$\therefore~~\boxed{\begin{array}{c}\mathsf{\dfrac{dy}{dx}=-2\,sin\,x\cdot cos\,x}\end{array}}\qquad\quad\checkmark$

I hope this helps. =)

Tags: derivative chain rule product rule composite function trigonometric trig squared cosine cos differential integral calculus

3 0

4 years ago

(25-9)-5 and 25-(9-5)

Ymorist [56]

25-9=[16]-5 =-80
9-5=[4]-25 =-100

3 0

3 years ago

How does the circulatory system work at the tissue level? Please help!

soldi70 [24.7K]

Answer:

Blood cells carry nutrients

Step-by-step explanation:

blood cells carry oxygen and other nutrients with them and that's how things like oxygen are supplied to tissues

8 0

3 years ago

Complete function tables part 3 please help me

Paraphin [41]

Answer:

2 8 15 50

Step-by-step explanation:

h~mmmmm maybe im wrong

8 0

3 years ago