What is the slope in the equation y=3/4x What is the y-intercept also?

6.4 Q3.) Use Simpson's rule to approximate and use the fundamental theorem of calculus to find the exact value of the definite i

Sav [38]

When we divide the interval from 1 to 5 into 4 subintervals, each has a width of 1. Simpson's rule has us evaluate the integral as

... integral = (1/3)(f(1) +4f(2) +2f(3) +4f(4) +f(5)) = (1/3)(10 +4·25 +2·46 +4·73 +106)

... integral = (1/3)(600) = 200 . . . . . by Simpson's rule

_____

The integral evaluates to

$\displaystyle \int_{1}^{5}{\left(3x^2+6x+1\right)}\,dx=\left[x^3+3x^2+x\right]\limits_{1}^{5}=(5^3-1^3)+3(5^2-1^2)+(5-1)\\=124+3*24+4=200$

_____

Simpson's rule uses a quadratic interpolation, so evaluates quadratics exactly.

5 0

3 years ago

F(x)=2x^2-x-6 g(x)=4-x (f+g)(x)

Semenov [28]

$\large \boxed{(f + g)(x) = f(x) + g(x)}$

The property above is distribution property where we distribute x-term in the function.

Substitute both f(x) and g(x) in.

$\large{ \begin{cases} f(x) = 2 {x}^{2} - x - 6 \\ g(x) = 4 - x \end{cases}} \\ \large{f(x) + g(x) = (2 {x}^{2} - x - 6) + (4 - x)} \\ \large{f(x) + g(x) = 2 {x}^{2} - x - 6 + 4 - x}$

Évaluate/Combine like terms.

$\large{f(x) + g(x) = 2 {x}^{2} - 2x - 2}$

The function can be factored so there are two answers. (Both of them work as one of them is factored form while the other one is not.)

$\large{(f + g)(x) = 2 {x}^{2} -2x -2}$

Alternative

$\large{(f + g)(x) = 2({x}^{2} -x - 1)}$

Answer

(f+g)(x) = 2x²-2x-2
(f+g)(x) = 2(x²-x-1)

Both answers work. The second answer is in factored form.

Let me know if you have any doubts!

8 0

2 years ago

I was having a hard time with this one as well. ASAP

matrenka [14]

Answer:

A

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

On the 40th birthday, Mr. Ramos decided to buy a pension plan for himself. This plan will allow him to claim

Mama L [17]

Answer:

The amount of one-time payment should he make on his 40th birthday to pay off his pension plan is P32,880.77.

Step-by-step explanation:

Step 1: Calculation of present value on 3 months after his 60th birthday

The present value on 3 months after his 60th birthday can be calculated using the formula for calculating the present value of an ordinary annuity as follows:

PV60 = Q * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

PV60 = present value on 3 months after his 60th birthday = ?

Q = quarterly claim = P10,000

r = quarterly interest rate = annual interest rate / 4 = 8% / 4 = 0.08 / 4 = 0.02

n = number of quarters = number of years * Number of quarters in a year = 5 * 4 = 20

Substitute the values into equation (1), we have:

PV60 = P10,000 * ((1 - (1 / (1 + 0.02))^20) / 0.02)

PV60 = P10,000 * 16.3514333445971

PV60 = P163,514.33

Step 2: Calculation of one-time payment on his 40th birthday

The one-time payment can be calculated using the formula the following formula:

PV = PV60 / (1 + r)^n ........................ (2)

Where;

PV = Present value or One-time payment = ?

PV60 = present value on 3 months after his 60th birthday = P163,514.33

r = quarterly interest rate = annual interest rate / 4 = 8% / 4 = 0.08 / 4 = 0.02

n = number of quarters from 40th to 3 months after his 60th birthday = (number of years * Number of quarters in a year) + One quarter = (20 * 4) + 1 = 81

Substitute the values into equation (2), we have:

PV = P163,514.33 / (1 + 0.02)^81 = P32,880.77

Therefore, the amount of one-time payment should he make on his 40th birthday to pay off his pension plan is P32,880.77.

7 0

3 years ago

Tim dug a hole that was 16 1/2 inches deep.He left a pile of dirt next to the hole that was 8 3/4 inches high.Show how you could

Viktor [21]

Answer:

14 inches

Step-by-step explanation:

Length of the hole = 16(½) inches

Length of the dirt = 8(¾)inches

The distance between the top of the pile to the bottom of the hole = ?

Since the dirt is beside the hole and not inside the hole, we can find it's length using addition.

Distance from the top to the bottom = length of dirt + length of the hole

Length of dirt = 8×¾ = 6 inches

Length of the hole = 16 × ½ = 8 inches

Distance from the top of the dirt to the bottom of the hole = (6 + 8) inches

Distance from the top of the dirt to the bottom of the hole = 14 inches

Note: the only way we can use subtraction here is if the hole was filled with dirt, what's the distance that's left

Distance left = length of hole - length of dirt

Distance left = 8 - 6 = 2 inches .

But what the question requested was the distance from the top of the dirt to the bottom of the hole

5 0

2 years ago