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Semmy [17]
3 years ago
11

Analyze the graph below to identify the key features of the logarithmic function. The x-intercept is y = 2, and the graph approa

ches a vertical asymptote at y = 3.
The x-intercept is x = 2, and the graph approaches a vertical asymptote at x = 3.
The x-intercept is y= -2, and the graph approaches a vertical asymptote at y = -3.
The x-intercept is x = -2, and the graph approaches a vertical asymptote at x = -3.

Mathematics
1 answer:
Mamont248 [21]3 years ago
7 0

Answer:

The x-intercept is x = -2, and the graph approaches a vertical asymptote at x = -3.

Step-by-step explanation:

The given graph is a transformed logarithm function.

The graph is obtained by shifting the parent function three units left.

The vertical asymptote is now

x =  - 3

The x-intercept is where the graph intersect the x-axis, which is x=-2

Therefore the last option is correct.

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PLZ HELP!!! Use limits to evaluate the integral.
Marrrta [24]

Split up the interval [0, 2] into <em>n</em> equally spaced subintervals:

\left[0,\dfrac2n\right],\left[\dfrac2n,\dfrac4n\right],\left[\dfrac4n,\dfrac6n\right],\ldots,\left[\dfrac{2(n-1)}n,2\right]

Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,

r_i=\dfrac{2i}n

where 1\le i\le n. Each interval has length \Delta x_i=\frac{2-0}n=\frac2n.

At these sampling points, the function takes on values of

f(r_i)=7{r_i}^3=7\left(\dfrac{2i}n\right)^3=\dfrac{56i^3}{n^3}

We approximate the integral with the Riemann sum:

\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{112}n\sum_{i=1}^ni^3

Recall that

\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4

so that the sum reduces to

\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{28n^2(n+1)^2}{n^4}

Take the limit as <em>n</em> approaches infinity, and the Riemann sum converges to the value of the integral:

\displaystyle\int_0^27x^3\,\mathrm dx=\lim_{n\to\infty}\frac{28n^2(n+1)^2}{n^4}=\boxed{28}

Just to check:

\displaystyle\int_0^27x^3\,\mathrm dx=\frac{7x^4}4\bigg|_0^2=\frac{7\cdot2^4}4=28

4 0
3 years ago
PLEASE HELP ASAP WILL MARK BRAINLIEST
nikdorinn [45]

Answer: 314 mm

Step-by-step explanation:

Area of a circle is π*r^2

r is radius and π is 3.14

here the radius is 10

3.14 * 10^2 = 3.14 * 100 = 314

3 0
2 years ago
Please solve the following Factor. 9w2-49
romanna [79]

Answer:

(3w - 7)(3w + 7)

Step-by-step explanation:

The expression is a difference of squares and factors in general as

a² - b² = (a - b)(a + b)

Thus

9w² - 49

= (3w)² - 7²

= (3w - 7)(3w + 7)

5 0
3 years ago
I am VERY confused on this question. Can someone help me?
Iteru [2.4K]
Answer: z=67-at
————
a-45
6 0
3 years ago
WILL GIVE BRAINLIEST!!!
Natalka [10]
Volume of a cylinder= (height) x area of the base (circle)

We know the height = 160 cm (given), let's find the radius of the base.

The circumference of the base = 87.92 = 2πR==> R=87.92/(2π) =13.993 cm

Area of circle = πR²=π(13.993)² = 615.128 cm²

Hence the volume of the cylinder = 615.128 x 160 = 92,420.48 cm³
4 0
3 years ago
Read 2 more answers
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