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Solve f(x)= x2 when x = 5.

ira [324]

Answer:

10

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

(07.03 MC)

Umnica [9.8K]

The probability of pulling a blue marble and the coin landing tails up is 360/2500

<h3>How to determine the probability?</h3>

The tables of values are given as:

Color Times

Blue 18

Green 20

Yellow 12

Heads Tails

20 30

The probability of obtaining a blue marble is:

P(Blue) = 18/50

The probability of landing tails up is:

P(Tail) = 20/50

The required probability is:

P = P(Blue) * P(Tail)

This gives

P = 18/50 * 20/50

Evaluate the product

P = 360/2500

Hence, the probability of pulling a blue marble and the coin landing tails up is 360/2500

Read more about probability at:

brainly.com/question/25870256

#SPJ1

8 0

2 years ago

Consider F and C below. F(x, y, z) = 2xz + y2 i + 2xy j + x2 + 9z2 k C: x = t2, y = t + 3, z = 3t − 1, 0 ≤ t ≤ 1 (a) Find a func

Ray Of Light [21]

Answer:

a)∇f = 2y + 2x + 18z

b) $\int\limits^._C {F} \, dr$ =108

Step-by-step explanation:

Given:

f (x,y,z ) = $(2xz+ y^{2})i + (2xy) j +(x^{2} + 9z^{2})k$

The curve C :

$x=t^{2} ,\\y= t+3\\z= 3t-1$

where 0 ≤ t ≤ 1

Required:

(a) F = ∇f =? (F is a vector here)

(b) $\int\limits^._C {F} \, dr$ =?

Solution

First we will find the directional derivative F = ∇f

for that , we will use the formula :

∇f = $F_{x}i+ F_{y} j+F_{z}k$

Fx= δf/δx = δ/δx $(2xz+ y^{2})i$ = 2z i

Fy= δf/δy=δ/δy (2xy)j = 2x j

Fz= δf/δz=δ/δz $(x^{2} + 9z^{2})k$ = 18z k

∇f = (2z) i .i + (2x) j.j + (18z) k.k

∇f = 2z + 2x + 18z

<em>we will use line integral formula:</em>

$\int\limits^._C {F} \, dr$

to calculate dr, we will need the curve C:

r = x(t)+y(t)+z(t)

r= $(t^{2})i + (t+3) j +(3t-1) k$

$\frac{dr}{dt}=\frac{dx}{dt} +\frac{dy}{dt} + \frac{dz}{dt}$

$\frac{dx}{dt} = 2t$

$\frac{dy}{dt} = 1$

$\frac{dz}{dt} = 3$

$\int\limits^._C {F} \, dr$ = $\int\limits^1_0 {F_{x} } \, dx+ F_{y} dy +F_{z} dz$

= $\int\limits^1_0 {(2z(2t) + 2x(1) + 18z (3)} \, )$

put values of y, x and z

= $\int\limits^1_0 {2(3t-1) + 2(t^{2}) +18 (3) (3t-1)} \,$

= ${2t^{2} + 6t+162t -54-2}\, |^1_0$

= ${ 2t^{2}+ 168t - 56} \,|^1_0$ (Note : f(1)-f(0))

=2(1)+162(1)+2(0)+162(0)-56

= 2+162 -56

$\int\limits^._C {F} \, dr$ =108

3 0

3 years ago

Weights of statistics students were obtained by a teacher as part of an experiment conducted for the class. The last digit of th

nasty-shy [4]

Answer:

The height appear to be reported because there are disproportionately more 0s and 5s.

Step-by-step explanation:

Given the data :

0 0 0 0 0 0 0 0 0 1 2 3 3 3 4 5 5 5 5 5 5 5 5 5 5 5 6 8 8 8 9

Creating a frequency table :

Last digit ______ Frequency

0 ______________ 9

1 _______________ 1

2 _______________1

3 _______________3

4 _______________ 1

5 _______________11

6 _______________ 1

8 _______________ 3

9 ________________1

From the frequency distribution table, it could be seen that the volumeof 5's and 0's are far more than the volume of the other digits. We could infer from this numbers were reported and not measured.

3 0

3 years ago

If cos(θ) = 6/8 and θ is in the IV quadrant, then fine:

svetoff [14.1K]

Answer:

a) 1

b) $\frac{4}{3}$

c) = 1

Step-by-step explanation:

We are given the following in the question:

$\cos \theta = \dfrac{6}{8}$

θ is in the IV quadrant.

$\sin^2 \theta + \cos^2 \theta = 1\\\\\sin \theta = \sqrt{1-\dfrac{36}{64}} = -\dfrac{2\sqrt7}{8}\\\\\tan \theta = \dfrac{\sin \theta}{\cos \theta} = -\dfrac{2\sqrt7}{6}\\\\\csc \theta = \dfrac{1}{\sin \theta} = -\dfrac{8}{2\sqrt7}$