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2 years ago

Can someone help me figure out the answer?

Mathematics

1 answer:

olga_2 [115]2 years ago

8 0

Answer:

y = -2x +15

Step-by-step explanation:

The point-slope form of the equation for a line through (h, k) with slope m is ...

... y - k = m(x - h)

For your point (h, k) = (5, 5) and slope m = -2, the equation in point-slope form is ...

... y - 5 = -2(x - 5)

Simplifying, we get

... y - 5 = -2x +10

Adding 5 puts the equation into slope-intercept form, as you want.

... y = -2x +15

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Consider the function f(x)=xln(x). Let Tn be the nth degree Taylor approximation of f(2) about x=1. Find: T1, T2, T3. find |R3|

Fynjy0 [20]

Answer:

R3 <= 0.083

Step-by-step explanation:

f(x)=xlnx,

The derivatives are as follows:

f'(x)=1+lnx,

f"(x)=1/x,

f"'(x)=-1/x²

f^(4)(x)=2/x³

Simialrly;

f(1) = 0,

f'(1) = 1,

f"(1) = 1,

f"'(1) = -1,

f^(4)(1) = 2

As such;

T1 = f(1) + f'(1)(x-1)

T1 = 0+1(x-1)

T1 = x - 1

T2 = f(1)+f'(1)(x-1)+f"(1)/2(x-1)^2

T2 = 0+1(x-1)+1(x-1)^2

T2 = x-1+(x²-2x+1)/2

T2 = x²/2 - 1/2

T3 = f(1)+f'(1)(x-1)+f"(1)/2(x-1)^2+f"'(1)/6(x-1)^3

T3 = 0+1(x-1)+1/2(x-1)^2-1/6(x-1)^3

T3 = 1/6 (-x^3 + 6 x^2 - 3 x - 2)

Thus, T1(2) = 2 - 1

T1(2) = 1

T2 (2) = 2²/2 - 1/2

T2 (2) = 3/2

T2 (2) = 1.5

T3(2) = 1/6 (-2^3 + 6 *2^2 - 3 *2 - 2)

T3(2) = 4/3

T3(2) = 1.333

Since;

f(2) = 2 × ln(2)

f(2) = 2×0.693147 =

f(2) = 1.386294

Since;

f(2) >T3; it is significant to posit that T3 is an underestimate of f(2).

Then; we have, R3 <= | f^(4)(c)/(4!)(x-1)^4 |,

Since;

f^(4)(x)=2/x^3, we have, |f^(4)(c)| <= 2

Finally;

R3 <= |2/(4!)(2-1)^4|

R3 <= | 2 / 24× 1 |

R3 <= 1/12

R3 <= 0.083

5 0

2 years ago

What is 3/4 x -1/6 .

jarptica [38.1K]

Answer:

The answer to 3/4x-1/6 is -0.126

6 0

2 years ago

Read 2 more answers

Cuanto es 120% en fraccion

kow [346]

The answer is 6/5 (six over five) 100 divided by 20

4 0

2 years ago

A recent study at UGA (March 5, 2008) suggests that students with cell phones may take more risks than students that do not have

Ira Lisetskai [31]

Answer:

(a) -2.8

b) (1) Reject H0: p = 0.50 in favor of HA: p < 0.50; there is sufficient evidence to conclude that less than half of all UGA female students who, if they had a cell phone, would be willing to walk somewhere after dark that they would normally not go.

Step-by-step explanation:

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

H0: p = 0.50

This means that:

$\mu = 0.5, \sigma = \sqrt{0.5*0.5} = 0.5$

In a random sample of 305 UGA female students, 128 responded that, if they had a cell phone, they would be willing to walk somewhere after dark that they would normally not go.

This means that $n = 305, X = \frac{128}{305} = 0.4197$

a) Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.4197 - 0.5}{\frac{0.5}{\sqrt{305}}}$

$z = -2.8$

Pvalue:

We are testing the hypothesis that the proportion is less than 0.5, which means that the pvalue of the test is the pvalue of z = -2.81.

Looking at the z-table, z = -2.8 has a pvalue of 0.0026

(b) What is the correct conclusion for this hypothesis test at the 0.05 level of significance?

0.0026 < 0.05, which means that we reject the null hypothesis, that the proportion is 0.5, and accept the alternate hypothesis, that the proportion is less than 0.5, option (1).

6 0

2 years ago

Andrea claims that 2,899 rounded to the nearest hundred is 3,000. Zoe claims that 2,899 rounded to the nearest thousand is 3,000

dusya [7]

A) Only Zoe is correct.
2,899 rounded to the nearest hundredth would be 2,900

6 0

3 years ago