(a): How many calories is Ashley burning per?<br><br> (b): What is the slope of the graph?

Pls help I don't wanna get a bad grade

Katena32 [7]

Answer:

48.15

Step-by-step explanation:

60 * 75% = 45

45 * 107% = $48.15

I hope this helps!

8 0

3 years ago

Read 2 more answers

What’s h ? and how do you solve it and show the steps

zhenek [66]

Here are the steps to solve for h. Your final answer is h=4

7 0

4 years ago

Evaluate the integral ∫2032x2+4dx. Your answer should be in the form kπ, where k is an integer. What is the value of k? (Hint: d

faltersainse [42]

Here is the correct computation of the question;

Evaluate the integral :

$\int\limits^2_0 \ \dfrac{32}{x^2 +4} \ dx$

Your answer should be in the form kπ, where k is an integer. What is the value of k?

(Hint: $\dfrac{d \ arc \ tan (x)}{dx} =\dfrac{1}{x^2 + 1}$ )

k = 4

(b) Now, lets evaluate the same integral using power series.

$f(x) = \dfrac{32}{x^2 +4}$

Then, integrate it from 0 to 2, and call it S. S should be an infinite series

What are the first few terms of S?

Answer:

(a) The value of k = 4

(b)

$a_0 = 16\\ \\ a_1 = -4 \\ \\ a_2 = \dfrac{12}{5} \\ \\a_3 = - \dfrac{12}{7} \\ \\ a_4 = \dfrac{12}{9}$

Step-by-step explanation:

(a)

$\int\limits^2_0 \dfrac{32}{x^2 + 4} \ dx$

$= 32 \int\limits^2_0 \dfrac{1}{x+4}\ dx$

$=32 (\dfrac{1}{2} \ arctan (\dfrac{x}{2}))^2__0$

$= 32 ( \dfrac{1}{2} arctan (\dfrac{2}{2})- \dfrac{1}{2} arctan (\dfrac{0}{2}))$

$= 32 ( \dfrac{1}{2}arctan (1) - \dfrac{1}{2} arctan (0))$

$= 32 ( \dfrac{1}{2}(\dfrac{\pi}{4})- \dfrac{1}{2}(0))$

$= 32 (\dfrac{\pi}{8}-0)$

$= 32 ( (\dfrac{\pi}{8}))$

$= 4 \pi$

The value of k = 4

(b) $\dfrac{32}{x^2+4}= 8 - \dfrac{3x^2}{2^1}+ \dfrac{3x^4}{2^3}- \dfrac{3x^6}{2x^5}+ \dfrac{3x^8}{2^7} -... \ \ \ \ \ (Taylor\ \ Series)$

$\int\limits^2_0 \dfrac{32}{x^2+4}= \int\limits^2_0 (8 - \dfrac{3x^2}{2^1}+ \dfrac{3x^4}{2^3}- \dfrac{3x^6}{2x^5}+ \dfrac{3x^8}{2^7} -...) dx$

$S = 8 \int\limits^2_0dx - \dfrac{3}{2^1} \int\limits^2_0 x^2 dx + \dfrac{3}{2^3}\int\limits^2_0 x^4 dx - \dfrac{3}{2^5}\int\limits^2_0 x^6 dx+ \dfrac{3}{2^7}\int\limits^2_0 x^8 dx-...$

$S = 8(x)^2_0 - \dfrac{3}{2^1*3}(x^3)^2_0 +\dfrac{3}{2^3*5}(x^5)^2_0- \dfrac{3}{2^5*7}(x^7)^2_0+ \dfrac{3}{2^7*9}(x^9)^2_0-...$

$S= 8(2-0)-\dfrac{1}{2^1}(2^3-0^3)+\dfrac{3}{2^3*5}(2^5-0^5)- \dfrac{3}{2^5*7}(2^7-0^7)+\dfrac{3}{2^7*9}(2^9-0^9)-...$

$S= 8(2-0)-\dfrac{1}{2^1}(2^3)+\dfrac{3}{2^3*5}(2^5)- \dfrac{3}{2^5*7}(2^7)+\dfrac{3}{2^7*9}(2^9)-...$

$S = 16-2^2+\dfrac{3}{5}(2^2) -\dfrac{3}{7}(2^2) + \dfrac{3}{9}(2^2) -...$

$S = 16-4 + \dfrac{12}{5}- \dfrac{12}{7}+ \dfrac{12}{9}-...$

$a_0 = 16\\ \\ a_1 = -4 \\ \\ a_2 = \dfrac{12}{5} \\ \\a_3 = - \dfrac{12}{7} \\ \\ a_4 = \dfrac{12}{9}$

6 0

3 years ago

1-7x-7=15 Solve Please I don't know.

DIA [1.3K]

Answer:

Step-by-step explanation:

So first we combine like terms on the left

1-7=-6

then we have

-7x-6=15

next we add 6 both sides

-7x-6=15

+6 +6

-7x=21

then we divide -7 each side

we get

x=-3

4 0

3 years ago

Read 2 more answers

can someone please help me with this I'm failing this class and I need help please I'll mark you brainliest.

Murrr4er [49]

Answer:

1. 36 $m^{2}$

2. 333.125 $ft^{3}$

3. 210 $ft^{3}$

4. Yes, Martina's estimate is reasonable.

Step-by-step explanation:

Numbering the rectangular surfaces, we have:

Area of a rectangle = length x width

For surface 1: Area = 2 x 2.4

= 4.8 $m^{2}$

For surface 2: Area = 3 x 2.4

= 7.2 $m^{2}$

For surface 3: Area = 3 x 2

= 6.0 $m^{2}$

For surface 4: Area = 3 x 2.4

= 7.2 $m^{2}$

For surface 5: Area = 2 x 2.4

= 4.8 $m^{2}$

For surface 6: Area = 3 x 2

= 6.0 $m^{2}$

Total surface area of the rectangular prism = (2 x 4.8) + (2 x 7.2) + (2 x 6.0)

= 36 $m^{2}$

2. length = 10.25 ft

width = 5 ft

height = 6.5 ft

Thus,

volume = l x w x h

= 10.25 x 5 x 6.5

= 333.125 $ft^{3}$

3. length = 15 ft

width = 7 ft

height = 2 ft

So that,

volume = l x w x h

= 15 x 7 x 2

= 210 $ft^{3}$

4. For a rectangular prism, area of the opposite surfaces are equal. So that;

Area of rectangle = length x width

For surface 1: Area = 13.0 x 6

= 78.0 $ft^{2}$

For surface 2: Area = 13.0 x 8

= 104.0 $ft^{2}$

For surface 3: Area = 6 x 8

= 48 $ft^{2}$

Surface area of the prism = (2 x 78.0) + (2 x 104.0) + (2 x 48)

= 460.0 $ft^{2}$

Therefore, Martina's estimate is reasonable.

5 0

3 years ago

(a): How many calories is Ashley burning per? (b): What is the slope of the graph?