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3 years ago

Write an equation in slope-intercept form of the line through point P(–3, 6) with slope –2.

Mathematics

1 answer:

faust18 [17]3 years ago

8 0

Answer:

Step-by-step explanation:

An equation in point-slope form of the line passing through point <em>P(x₁, y₁)</em> with slope <em>m</em>: y - y₁ = m(x - x₁)

m = -2

P(-3, 6) ⇒ x₁ = -3, y₁ = 6

y - 6 = -2(x - (-3))

y - 6 = -2(x + 3) ← point-slope form

y - 6 = -2x - 6 {add 6 to both sides}

y = - 2x ← slope-intercept form {intercept=0}

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Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints of each subinterval as your

Veronika [31]

The expression of integral as a limit of Riemann sums of given integral $\int\limits^5_b {1} \, x/(2+x^{3}) dx$ is 4 $\lim_{n \to \infty}$ ∑ $n(n+4i)/2n^{3}+(n+4i)^{3}$ from i=1 to i=n.

Given an integral $\int\limits^5_b {1} \, x/(2+x^{3}) dx$ .

We are required to express the integral as a limit of Riemann sums.

An integral basically assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinite data.

A Riemann sum is basically a certain kind of approximation of an integral by a finite sum.

Using Riemann sums, we have :

$\int\limits^b_a {f(x)} \, dx$ = $\lim_{n \to \infty}$ ∑f(a+iΔx)Δx ,here Δx=(b-a)/n

$\int\limits^5_1 {x/(2+x^{3}) } \, dx$ =f(x)= $x/2+x^{3}$

⇒Δx=(5-1)/n=4/n

f(a+iΔx)=f(1+4i/n)

f(1+4i/n)= $[n^{2}(n+4i)]/2n^{3}+(n+4i)^{3}$

$\lim_{n \to \infty}$ ∑f(a+iΔx)Δx=

$\lim_{n \to \infty}$ ∑ $n^{2}(n+4i)/2n^{3}+(n+4i)^{3}4/n$

=4 $\lim_{n \to \infty}$ ∑ $n(n+4i)/2n^{3}+(n+4i)^{3}$

Hence the expression of integral as a limit of Riemann sums of given integral $\int\limits^5_b {1} \, x/(2+x^{3}) dx$ is 4 $\lim_{n \to \infty}$ ∑ $n(n+4i)/2n^{3}+(n+4i)^{3}$ from i=1 to i=n.

Learn more about integral at brainly.com/question/27419605

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2 years ago

Will eight be less or more than 2/4

daser333 [38]

Step-by-step explanation:

8 is more than 2/4 because the answer of 2/4 is 0.5 so 8 is more than 2/4

5 0

3 years ago

Pipe A can fill 3 tanks in 8 minutes. Pipe B can fill 5 tanks in 10 minutes. How long will it take for them to fill a single tan

weqwewe [10]

Answer:

8/7 min = $1 \frac{1}{7} minutes$

Step-by-step explanation:

A rate 2 2/3 = 8/3 min per tank

B rate 2 min per tank

thus:

A rate = 3/8 tank per min

B rate = 1/2 tank per min

A+ B = 3/8 + 4/8 = 7/8 tank per min

7/8 x = 1

x = 8/7 min

6 0

3 years ago

F(x) = x2. What is g(x)?

uranmaximum [27]

Answer:

g(x) = 1/2x^2

Step-by-step explanation:

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2 years ago

A population increases 3% each year. If the city is now 5 million, what will the population be in 5 years?

Step2247 [10]

5 million x 3% = 150,000
1 Year = 5,150,000

5.15 million x 3% = 154,500
2 Years = 5,304,500

5,304,500 x 3% = 159,135
3 Years = 5,463,635

5,463,635 x 3% = 163,909.05
4 Years = 5,627,544.05

5,627,544.05 x 3% = 168,826.322
5 Years = 5,796,370.37

After 5 years, the population will be 5,796,370.37

8 0

3 years ago