Do anyone know this question?

Given:

z be inversely proportional to the cube root of y.

When y =0.064, then z =3.

To find:

a) The constant of proportionality k.

b) The value of z when y = 0.125.​

Solution:

a) It is given that, z be inversely proportional to the cube root of y.

[tex]z\propto \dfrac{1}{\sqrt[3]{y}}[/tex]

[tex]z=k\dfrac{1}{\sqrt[3]{y}}[/tex]              ...(i)

Where, k is the constant of proportionality.

We have, z=3 when y=0.064. Putting these values in (i), we get

[tex]3=k\dfrac{1}{\sqrt[3]{0.064}}[/tex]

[tex]3=k\dfrac{1}{0.4}[/tex]

[tex]3\times 0.4=k[/tex]

[tex]1.2=k[/tex]

Therefore, the constant of proportionality is [tex]k=1.2[/tex].

b) From part (a), we have [tex]k=1.2[/tex].

Substituting [tex]k=1.2[/tex] in (i), we get

[tex]z=1.2\dfrac{1}{\sqrt[3]{y}}[/tex]

We need to find the value of z when y = 0.125.​ Putting y=0.125, we get

[tex]z=1.2\dfrac{1}{\sqrt[3]{0.125}}[/tex]

[tex]z=\dfrac{1.2}{0.5}[/tex]

[tex]z=2.4[/tex]

Therefore, the value of z when y = 0.125 is 2.4.

Proportional quantities are either inversely or directly proportional. For the given relation between y and z, we have:

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

[tex]p = kq[/tex]

where k is some constant number called constant of proportionality.

This directly proportional relationship between p and q is written as

[tex]p \propto q[/tex]  where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n are two variables.

Then m and n are said to be inversely proportional to each other if

[tex]m = \dfrac{c}{n}[/tex]

or

[tex]n = \dfrac{c}{m}[/tex]

(both are equal)

where c is a constant number called constant of proportionality.

This inversely proportional relationship is denoted by

[tex]m \propto \dfrac{1}{n}\\\\or\\\\n \propto \dfrac{1}{m}[/tex]

As visible, increasing one variable will decrease the other variable if both are inversely proportional.

For the given case, it is given that:

[tex]z \propto \dfrac{1}{^3\sqrt{y}}[/tex]

Let the constant of proportionality be k, then we have:

[tex]z = \dfrac{k}{^3\sqrt{y}}[/tex]

It is given that when y = 0.064, z = 3, thus, putting these value in equation obtained above, we get:

[tex]k = \: \: ^3\sqrt{y} \times z = (0.064)^{1/3} \times (3) = 0.4 \times 3 = 1.2[/tex]

Thus,  the constant of proportionality k is 1.2. And the relation between z and y is:

[tex]z = \dfrac{1.2}{^3\sqrt{y}}[/tex]

Putting value y = 0.0125, we get:

[tex]z = \dfrac{1.2}{^3\sqrt{y}}\\\\z = \dfrac{1.2}{(0.125)^{1/3} } = \dfrac{1.2}{0.5} = 2.4[/tex]

Thus, for the given relation between y and z, we have:

Learn more about proportionality here:

https://brainly.com/question/13082482

Answer:

Slope of line B: 1/3

Step-by-step explanation:

To find a slope perpendicular to another slope, you take its negative reciprocal.

Therefore, line B will have a slope of 1/3 because -3 -> -1/3 -> 1/3

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

x² - 5xy + 6y² = x² - 3xy - 2xy + 6y²

                      = x(x  - 3y) - 2y(x - 3y)

                      = (x - 3y)(x -2y)

x² - 4xy + 3y² = x² -xy - 3xy + 3y²

                      = x(x - y) - 3y(x - y)

                      = (x - y)(x - 3y)

x² - 3xy + 2y² = x² - xy - 2xy + 2y²

                      = x(x - y) - 2y(x - y)

                     = (x - y)(x - 2y)

Least common denominator = (x-y)(x - 2y)(x - 3y)

[tex]RHS = \frac{1*(x-y)}{(x-3y)(x-2y)*(x-y)}+\frac{a*(x-2y)}{(x-y)(x-3y)*(x-2y)}+\frac{1*(x-3y)}{(x-y)(x-2y)*(z-3y)}\\\\= \frac{x- y + ax - 2ay +x -3y}{(x-y)(x-2y)(x-3y)}\\\\= \frac{2x -4y +ax - 2ay}{ x^{3}-5x^{2}y+8xy^{2}-4y^{3}}[/tex]

Answer:

ANSWER IS B

Step-by-step explanation:

5x - 3 = 3x + 1

5x - 3x = 1 + 3

2x = 4

x = 4/2

x = 2

Answer:

B. 2

Step-by-step explanation:

The sides 5x - 3 and 3x + 1 are the same length, so you can put an equal sign: 5x - 3 = 3x + 1, x = 2:

5(2) - 3 = 3(2) + 1

10 - 3 = 6 + 1

7 = 7

So x is 2

Answer:

It is true

Step-by-step explanation:

Hopes this help

Answer:

a) (4,7/2)

Step-by-step explanation:

Midpoint Formula:

[(-1+9)/2], [(2+5)/2]

(8/2, 7/2) = (4, 7/2)

Answer:

242/48

Step-by-step explanation:

Answer:

Toney buys the coat for $ 14.8.

Step-by-step explanation:

Cost of coat =$ 22

Mark up by 75 %

discount = 10 %

Let toney pay $ R for the coat.

So, according to the question

R + 75 % R = 1.75 R

Now the cost is

1.75 R - 15 % of 1.75 R = 22

1.75 R - 0.2625 R = 22

R = 14.8

So, he buy the coat for $ 14.8.  

16

Step-by-step explanation:

10x+2=9x+18

-2 -2

10x=9x+16

-9x -9x

x=16

Hope this helps! :)

Answer:

x = 16°

Step-by-step explanation:

(10x + 2)° = (9x + 18)°

10x + 2 = 9x + 18

10x + 2 - 2 = 9x + 18 - 2

10x = 9x + 16

10x - 9x = 9x - 9x + 16

x = 16°

Answer:

3x

Step-by-step explanation:

You multiply the pervious number with 3 to get the next number

For example 2 times 3 = 6

6 times 3 = 18

18 times 3 =54

54 times 3= 162

So on and so forth

Answer:

90 students.

Step-by-step explanation:

279-9=270, and 270 divided by 9 is 90.

Answer:

yellow = 5 bags

red = 4 bags

Step-by-step explanation:

two equations can be derived from the question

x + y = 9 equation 1

6x + 7y = 59 equation 2

where x = number of red onion bags

y =  number of yellow onion bags

Multiply equation 1 by 6

6x + 6y = 54 equation 3

subtract equation 3 from 2

y = 5

substitute for y in equation 1

x + 5 = 9

x = 9 - 5

x = 4

Answer:

1695.6 cubic feet

Step-by-step explanation:

Given that,

The corn fills 25% of the height of the silo.

The diameter of silo, d = 12 feet

Radius, r = 6 feet

Height, h = 60 feet

The volume of the part of the silo that is filled with corn is given by :

[tex]V=25\%\ of\ \pi r^2 h\\\\=\dfrac{25}{100}\times 3.14\times 6^2\times 60\\\\V= $$1695.6\ feet^3[/tex]

So, the required volume is equal to 1695.6 cubic feet.

Answer:

x = 23

Step-by-step explanation:

Sum of 25 and x = 48

25 + x = 48

Subtract 25 from both sides

25 - 25 cancels out

48 - 25 = 23

We would be left with x = 23

Answer:

[tex]x =23[/tex]

Step-by-step explanation:

Sum of 25 and x

[tex]25 + x[/tex]

Sum of 25 and x is 48

[tex]25 + x = 48[/tex]

Now lets simply Solve the equation

[tex]25 + x = 48 \\ x = 48 - 25 \\ x =23[/tex]

Hope this helps you.

Have a nice day!

Answer:

they are equal

Step-by-step explanation:

The triangle with sides 5, 12, 13 is a right triangle because

a^2+b^2 = c^2

5^2+12^2 = 13^2

25+144 = 169

169 = 169

I'm using the pythagorean theorem converse.

Answer:

Option C

Step-by-step explanation:

same logic as in 2D problems. if C wasn't true, then the two planes couldn't be parallel

Answer:

[tex](x-4)^2+(y+1)^2=29[/tex]

Step-by-step explanation:

We want to find a circle whose diameter has the endpoints (6, 4) and (2, -6).

Since this is the diameter, its midpoint will be the center of the circle. Find the midpoint:

[tex]\displaystyle M=\left(\frac{6+2}{2}, \frac{4+(-6)}2}\right)=(4, -1)[/tex]

So, the center of our circle is (4, -1).

Next, to find the radius, we can find the length of the diameter and divide it by half.

Using the distance formula, find the length of the diameter:

[tex]\begin{aligned} d&=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\ &=\sqrt{(2-6)^2+(-6-4)^2}\\\\&=\sqrt{(4)^2+(-10)^2}\\\\&=\sqrt{116}\\\\&=2\sqrt{29}\end{aligned}[/tex]

So, the radius will be:

[tex]\displaystyle r=\frac{1}{2}d=\frac{1}{2}\left(2\sqrt{29}\right)=\sqrt{29}[/tex]

The equation for a circle is given by:

[tex]\displaystyle (x-h)^2+(y-k)^2=r^2[/tex]

Substitute:

[tex](x-4)^2+(y+1)^2=29[/tex]

Answer:

$127.75

Step-by-step explanation:

Multiply the cost by the area to find the total cost

Answer:

diagonal, congruent triangles

Step-by-step explanation:

Answer:

x = 5.1

Step-by-step explanation.

Our first step is to find all the angles. If b = 91 degree and c is 38, a. has to be 51 because all triangles add up to 180 degree. Because we have both B and b, we can use sine law.

a/A     13/sin91      c/38

we can use b in this situation.

The legnth  of a is 10.1.

So,  x-5 would be 5.1

Answer:

Step-by-step explanation:

OMG! Don't do that! I am so sorry this is happening to you. Look I don't know how to comfort you. IF he keeps doing this tell your mom or litterally call 911. If he did it just on that day then try confronting him on it. And ask him why he did that! Don't self-harm you deserve so much more than that! You are awesome!

Answer:

y - 41°

x - ?

Step-by-step explanation:

use method of Z equation

Z 41° so y is 41° too

make sense

Answer:

306 square inches.

Step-by-step explanation:

All surfaces of the cubes are exposed to the outside except 2 ( where 2 of the cubes join).

6 separate cubes have 6 * 6 faces exposed so this object has 36 - 2 = 34 surfaces exposed.

Each face of one cube = 3*3 = 9 in^2.

Therefore the surface area =  9 * 34 = 306 in^2.

Answer:

[tex]slope = \frac{2 - ( - 1)}{0 - ( - 1)} \\ = 3 \\ y = mx + c \\ 2 = (0 \times 3) + c \\ c = 2 \\ { \boxed{y = 3x + 2}}[/tex]

Answer:

x=35 this is your answer

Answer:

28800 square feet

Step-by-step explanation:

We solve this using the Heron's formula

Area of a Triangle = √s(s - a)(s - b)(s - c)

s = a + b + c/2

s = 100 + 580 + 600/2 = 640

Area of the land(Triangle) = √640 × (640 - 100)(640 - 580)(640 - 600)

= √640 × (540) ×( 60) × (40)

= √(829440000)

= 28800 square feet

Therefore, the approximate the area of the land is 28800 square feet.

Answer:

256 ft

Step-by-step explanation:

cross multiply

4x = 32(32)

4x = 1024

x =256

256 ft

Answer:

Ten thousands

Step-by-step explanation:

Replace all other digits with zero

This gives 40,000

Ten thousand (10,000) has the same amount of digits