The difference of a number x and 9 is fewer then 4

F(x)=1/2x+3; Find f(8)

Shtirlitz [24]

Answer:

7

Step-by-step explanation:

1/2(8)+3

4+3

f(8)=7

8 0

3 years ago

Use the Divergence Theorem to evaluate the following integral S F · N dS and find the outward flux of F through the surface of t

Xelga [282]

Answer:

Result;

$\int\limits\int\limits_S { \textbf{F}} \, \cdot \textbf{N} d {S} = 32\pi$

Step-by-step explanation:

Where:

F(x, y, z) = 2(x·i +y·j +z·k) and

S: z = 0, z = 4 -x² - y²

For the solid region between the paraboloid

z = 4 - x² - y²

div F

For S: z = 0, z = 4 -x² - y²

We have the equation of a parabola

To verify the result for F(x, y, z) = 2(x·i +y·j +z·k)

We have for the surface S₁ the outward normal is N₁ = -k and the outward normal for surface S₂ is N₂ given by

$N_2 = \frac{2x \textbf{i} +2y \textbf{j} + \textbf{k}}{\sqrt{4x^2+4y^2+1} }$

Solving we have;

$\int\limits\int\limits_S { \textbf{F}} \, \cdot \textbf{N} d {S} = \int\limits\int\limits_{S1} { \textbf{F}} \, \cdot \textbf{N}_1 d {S} + \int\limits\int\limits_{S2} { \textbf{F}} \, \cdot \textbf{N}_2 d {S}$

Plugging the values for N₁ and N₂, we have

$= \int\limits\int\limits_{S1} { \textbf{F}} \, \cdot \textbf{(-k)}d {S} + \int\limits\int\limits_{S2} { \textbf{F}} \, \cdot \frac{2x \textbf{i} +2y \textbf{j} + \textbf{k}}{\sqrt{4x^2+4y^2+1} } d {S}$

Where:

F(x, y, z) = 2(xi +yj +zk) we have

$= -\int\limits\int\limits_{S1} 2z \ dA + \int\limits\int\limits_{S2} 4x^2+4y^2+2z \ dA$

$= -\int\limits^2_{-2} \int\limits^{\sqrt{4-y^2}} _{-\sqrt{4-y^2}} 2z \ dA + \int\limits^2_{-2} \int\limits^{\sqrt{4-y^2}} _{-\sqrt{4-y^2}} 4x^2+4y^2+2z \ dA$

$= \int\limits^2_{-2} \int\limits^{\sqrt{4-y^2}} _{-\sqrt{4-y^2}} 4x^2+4y^2 \ dxdy$

$= \int\limits^2_{-2} \frac{(16y^2 +32)\sqrt{-(y^2-4)} }{3} dy$

= 32π.

6 0

4 years ago

Pls help me in these two little exercises about the slope.

den301095 [7]

Answer:

3) $y=\dfrac35x+\dfrac25$

4) a) $y=-2x+7$

b) $y=\dfrac12x+\dfrac92$

Step-by-step explanation:

<u>Exercise 3</u>

$-3x + 5y = 2$

$\implies 5y = 3x + 2$

$\implies y=\dfrac35x+\dfrac25$

<u>Exercise 4</u>

a) If L2 is parallel to L1, it has the same slope (gradient) ⇒ $m = -2$

If L2 passes through point (3, 1):

$y-y_1=m(x-x_1)$

$\implies y-1=-2(x-3)$

$\implies y=-2x+7$

So L2 = L1

b) If L3 is perpendicular to L1, then the slope of L3 is the negative reciprocals of the slope of L1 ⇒ $m = \dfrac12$

If L3 passes through point (-5, 2):

$y-y_1=m(x-x_1)$

$\implies y-2=\dfrac12(x+5)$

$\implies y=\dfrac12x+\dfrac92$

4 0

3 years ago

Read 2 more answers

Which distribution is used to test the claim that women have a higher mean resting heart rate than men?

xeze [42]

This question is incomplete, the complete question is;

Assume that two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Which distribution is used to test the claim that women have a higher mean resting heart rate than men?

A.t

B.F

C.Normal

D. Chi-square

Answer:

A) t test

Step-by-step explanation:

A t-test uses sample information to assess how plausible it is for the population means μ1 and μ2 to be equal.

The formula for a t-statistic for two population means (with two independent samples), with unknown population variances shows us how to calculate t-test with mean and standard deviation and it depends on the assumption of having an equal variance or not.

If the variances are assumed to be not equal,

he formula is:

t = (bar X₁ - bar X₂) / √( s₁²/n₁ + s₂²/n₂ )

If the variances are assumed to be equal, the formula is:

t = (bar X₁ - bar X₂) / √ (((n₁ - 1)s₁² + (n₂ - 1)s₂²) / (n₁ + n₂ - 2)) ( 1/n₁ + 1/n₂)

it called t-test for independent samples because the samples are not related to each other, in a way that the outcomes from one sample are unrelated from the other sample.

hence option A is correct. t test

4 0

3 years ago

SUMMARY: how can you use mapping rules to find rotations of objects at 90, 180, and 270 degrees?

Levart [38]

A rotation is an isometric transformation that turns every point of a figure through a specified angle and direction about a fixed point.

To describe a rotation, you need three things:

Direction (clockwise CW or counterclockwise CCW)

Angle in degrees

Center point of rotation (turn about what point?)

The most common rotations are 180° or 90° turns, and occasionally, 270° turns, about the origin, and affect each point of a figure as follows:

Mark me as brainliest! :D Hope it helps

6 0

3 years ago