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Fantom [35]
3 years ago
9

Describe the graph of the function. y = 9x2 + 18x – 6

Mathematics
2 answers:
Vika [28.1K]3 years ago
5 0
The graph of the function y = 9x^2 + 18x - 6 is a parabola facing up with vertex at (-1, -5), x-intercepts at (-2.29, 0) and (0.29, 0) and y-intercept at (0, -4).
Lina20 [59]3 years ago
4 0

Answer: Roots: 0.3 and -2.3

              y-intercetpt (0,-6)

              vertex (-1,-15)              

Step-by-step explanation: it's a parabola.

As a = 9 and it is > 0, it is facing up.

To find the roots:

9x² + 18x - 6 = 0

a = 9; b = 18; c = -6

Δ = b² - 4ac = 18² - 4.9.(-6)

Δ = 324 + 216 = 540

√Δ = √540 = 23.24

x = -b <u>+</u> √Δ /2a = -18 <u>+</u> 23.24/18

x₁ = -18 + 23.24/18 = 0.3

x₂ = -18 - 23.24/18 = -2.3

So, it intercepts x (0.3;0) and (-2.3;0)

For the y-intercept → x = 0

9.0² + 18.0 - 6 = -6

So, it intercepts y on (0,-6)

For the vertex

xv = -b/2a = -18/18 = -1

yv = -Δ/4a = -540/36 = -15

So, the vertex is (-1,-15)

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Find a closed form expression for the nth right Riemann sum of this integral?
DIA [1.3K]
Partitioning the interval [6,11] into n equally-spaced subintervals gives n rectangles of width \Delta x=\dfrac{11-6}n=\dfrac5n and of heights determined by the right endpoints of each subinterval.

If a=x_1=6, then x_2=6+\dfrac5n, x_3=6+2\dfrac5n, and so on, up to b=x_{n+1}=6+n\dfrac5n=11. Because we're using the right endpoints, the approximation will consider x_2,\ldots,x_{n+1}

The definite integral is then approximated by

\displaystyle\int_6^{11}(1-5x)\,\mathrm dx\approx\sum_{i=2}^{n+1}f(x_i)\Delta x=\sum_{i=2}^{n+1}\left(1-\left(6+(i-1)\dfrac5n\right)\dfrac5n

You have

\displaystyle\sum_{i=2}^{n+1}\left(1-5\left(6+(i-1)\dfrac5n\right)\dfrac5n=\sum_{i=2}^{n+1}\left(-29-\dfrac{25}n(i-1)\right)\dfrac5n
=\displaystyle-{145}n\sum_{i=2}^{n+1}1-\dfrac{125}{n^2}\sum_{i=2}^{n+1}(i-1)
=-145-\dfrac{125(n^2+n)}{2n^2}
=-\dfrac{145}2-\dfrac{125}{2n}

To check that this is correct, let's make sure the sum converges to the exact value of the definite integral. As n\to\infty, you have the sum converging to -\dfrac{145}2.

Meanwhile,

\int_6^{11}(1-5x)\,\mathrm dx=\left[x-\dfrac52x^2\right]_{x=6}^{x=11}=-\dfrac{415}2

so we're done.
4 0
3 years ago
Every Thursday, Matt and Dave's Video Venture has "roll-the-dice" day. A customer may choose to roll two fair dice and rent a se
Vesnalui [34]

Answer:

c. 0.14

Step-by-step explanation:

Generally, for a given normal distribution, we can estimate the probability of the normal distribution using the equation below:

P (x greater than x_{min}) = pnorm(x_{min}, mean, sd, lower tail=FALSE)

The following variables are provided in the question:

x_{min} = 15

n = 30

Therefore:

Mean: E(30*X) = 30(0.47)

Standard deviation: 0.15*\sqrt{30}

P (y greater than 15) = 1 - pnorm (15, 30*0.47, 0.15*\sqrt{30})

P (y greater than 15) = 1 - pnorm (15, 14.1, 0.822) = 0.137

The approximate probability is 0.14

7 0
2 years ago
Gavin goes to the market and buys one rectangle shape board. The length of the board is 16 cm and width of board is 10cm . If he
Elanso [62]

Answer:

280cm squared

Step-by-step explanation:

By adding a 2cm wooden board, Gavin is adding 4 cm to each side, os the new sides would be 14 and 20. 14*20=280 cm squared.

7 0
3 years ago
It rained r inches on Saturday. On Sunday it rained 0.15 inches less than twice Saturday’s amount.
soldier1979 [14.2K]
The answer is

0.15r - 2x

hope this helps 

5 0
3 years ago
Read 2 more answers
What is the surface area of this<br> square pyramid?
Otrada [13]

Answer:

33 ft²

Step-by-step explanation:

The formula for the surface area of a square pyramid is:

SA = b² + 2bs

Where b is the measure of the base and s is the slant height

Let's substitute into this equation:

SA = b² + 2bs

SA = 3² + 2(3)(4)

Solve:

SA = 3² + 2(3)(4)

Square 3:

SA = 3² + 2(3)(4)

SA = 9 + 2(3)(4)

Multiply:

SA = 9 + 2(3)(4)

SA = 9 + (6)(4)

SA = 9 + 24

Add:

SA = 9 + 24

SA = 33

Therefore, the surface area is 33 square feet.

8 0
3 years ago
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