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3 years ago

What is the initial value.

Mathematics

1 answer:

GrogVix [38]3 years ago

6 0

The function shown in the graph is a linear function, for a given linear function, the initial value is obtained at y-intercept. The y-intercept is the point where the graph cuts the y-axis. At this point the value of x is zero. Thus from the graph given, the point x=0 at y=2, hence the initial value is y=2.
Answer: y=2

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Find the surface area of the solid generated by revolving the region bounded by the graphs of y = x2, y = 0, x = 0, and x = 2 ab

Nikitich [7]

Answer:

See explanation

Step-by-step explanation:

The surface area of the solid generated by revolving the region bounded by the graphs can be calculated using formula

$SA=2\pi \int\limits^a_b f(x)\sqrt{1+f'^2(x)} \, dx$

If $f(x)=x^2,$ then

$f'(x)=2x$

and

$b=0\\ \\a=2$

Therefore,

$SA=2\pi \int\limits^2_0 x^2\sqrt{1+(2x)^2} \, dx=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx$

Apply substitution

$x=\dfrac{1}{2}\tan u\\ \\dx=\dfrac{1}{2}\cdot \dfrac{1}{\cos ^2 u}du$

Then

$SA=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx=2\pi \int\limits^{\arctan(4)}_0 \dfrac{1}{4}\tan^2u\sqrt{1+\tan^2u} \, \dfrac{1}{2}\dfrac{1}{\cos^2u}du=\\ \\=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0 \tan^2u\sec^3udu=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0(\sec^3u+\sec^5u)du$

Now

$\int\limits^{\arctan(4)}_0 \sec^3udu=2\sqrt{17}+\dfrac{1}{2}\ln (4+\sqrt{17})\\ \\ \int\limits^{\arctan(4)}_0 \sec^5udu=\dfrac{1}{8}(-(2\sqrt{17}+\dfrac{1}{2}\ln(4+\sqrt{17})))+17\sqrt{17}+\dfrac{3}{4}(2\sqrt{17}+\dfrac{1}{2}\ln (4+\sqrt{17}))$

Hence,

$SA=\pi \dfrac{-\ln(4+\sqrt{17})+132\sqrt{17}}{32}$

3 0

3 years ago

BRAINLIEST AND MAX PTS<br><br> CONVERT y = 40x + 600 to point-slope form

IRISSAK [1]

Answer:

The answer to your question is y - 0 = 40(x - 15)

Step-by-step explanation:

y = 40x + 600

Convert to y - y₁ = m(x - x₁)

Process

1.- Factor 40 in the right side of the equation

y = 40(x - 15)

2.- Give the form of the point slope form

y - 0 = 40(x - 15)

where

y₁ = 0

m = 40

x₁ = 15

3 0

3 years ago

Read 2 more answers

Suppose that a recent poll found that 49% of adults believe that the overall state of moral values is poor. Complete parts (a)

Lunna [17]

Answer:

The mean of X is 122.5 and the standard deviation is 7.9.

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they believe that the overall state of moral values is poor, or they do not believe this. The probability of an adult believing this is independent of other adults. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

$E(X) = np$