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2 years ago

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Which Property Is Shown? k(7-9)=(k7)-(k*9) a. Commutative Property of Multiplication b. Multiplicative Property c. Multiplicat

ive Inverse Property d. Distributive Property

1 answer:

Gnesinka [82]2 years ago

6 0

D. Distributive Property

The distributive property allow you to multiply a sum by multiplying each addend separately.

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How do you write triple a quantity more than nine

vladimir2022 [97]

3x+9 is the answer x is the quantity and its tripled and more than 9

3 0

2 years ago

PQRS is a trapezoid with a right angle. What are the coordinates of S

Brrunno [24]

Answer: (a, 0)

<u>Step-by-step explanation:</u>

Notice that S is on the x-axis, therefore the y-coordinate is "0".

Notice that S has the same x-value of R. The x-value of R is "a".

8 0

2 years ago

A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require

Aleksandr-060686 [28]

Answer:

$r\approx 1.084\ feet$

$h\approx 1.084\ feet$

$\displaystyle A=11.07\ ft^2$

Step-by-step explanation:

<u>Optimizing With Derivatives </u>

The procedure to optimize a function (find its maximum or minimum) consists in :

Produce a function which depends on only one variable
Compute the first derivative and set it equal to 0
Find the values for the variable, called critical points
Compute the second derivative
Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum

We know a cylinder has a volume of 4 $ft^3$ . The volume of a cylinder is given by

$\displaystyle V=\pi r^2h$

Equating it to 4

$\displaystyle \pi r^2h=4$

Let's solve for h

$\displaystyle h=\frac{4}{\pi r^2}$

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

$\displaystyle A=\pi r^2+2\pi rh$

Replacing the formula of h

$\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )$

Simplifying

$\displaystyle A=\pi r^2+\frac{8}{r}$

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

$\displaystyle A'=2\pi r-\frac{8}{r^2}=0$

Rearranging

$\displaystyle 2\pi r=\frac{8}{r^2}$

Solving for r

$\displaystyle r^3=\frac{4}{\pi }$

$\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet$

Computing h

$\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet$

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

$\displaystyle A''=2\pi+\frac{16}{r^3}$

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.

The minimum area is

$\displaystyle A=\pi(1.084)^2+\frac{8}{1.084}$

$\boxed{ A=11.07\ ft^2}$

8 0

2 years ago

Se corta una manzana en 12 partes, se comen ocho partes. Qué fracción simplificada a su mínima expresión representa la cantidad

lakkis [162]

Answer:

A. 1/3

Step-by-step explanation:

Dado que:

una manzana se corta en 12 partes y se comen ocho partes.

La fracción de manzanas consumidas = 8/12

= 2/3

La fracción de manzanas que quedan = valor original de la manzana que se corta - la fracción de la manzana que se come

La fracción de manzanas que quedan $=1- \dfrac{8}{12}$

La fracción de manzanas que quedan $=\dfrac{12-8}{12}$

La fracción de manzanas que quedan $=\dfrac{4}{12}$

A la fracción más baja; obtenemos = 1/3

6 0

2 years ago

Solve the following exponential equation:<br><br>5^x=2 <br><br>e^x=10

olya-2409 [2.1K]

Number 1.

$5^x=2$ , first we will take the $log$ of both of these numbers getting us,

$x=\frac{log(2)}{log(5)}$ , which then gives us that $x=0.4306777777....$

Number 2

$e^x=10$ , solve for our exponent, $2.718282^x=10$ , use the logarithmic formula, and we get,

$x=\frac{log(10)}{log(2.718282)}$ , which then we get that $x=2.302585$

3 0

2 years ago