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3 years ago

Which choice could represent the volume of a cake pan

Mathematics

1 answer:

Sav [38]3 years ago

5 0

Answer:

3150^3

Step-by-step explanation:

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(x-5)^3 expand each binomial

Nina [5.8K]

Answer:

$x^{3} -15x^{2} + 75x-125$

Step-by-step explanation:

6 0

2 years ago

. Isabella buys a 1.75 litre carton of apple juice. What is the largest number of 200 millilitre glasses that she can have from

Free_Kalibri [48]

Answer:

<em>The largest number of glasses of juice Isabella can have from the carton is 8.</em>

Step-by-step explanation:

<u>Ratios</u>

Knowing the total capacity of the carton of apple juice Ct, and the capacity of each glass Co, we can calculate how many glasses can be taken from the carton by finding the ratio:

$\displaystyle n=\frac{Ct}{Co}$

There are 1,000 milliliters in one liter, thus the carton has a capacity of

C t= 1.75*1,000 = 1,750 milliliters

Thus,

$\displaystyle n=\frac{1,750}{200}$

n=8.75

Since we cannot have 8.75 glasses, we round to the previous integer, then:

The largest number of glasses of juice Isabella can have from the carton is 8.

6 0

2 years ago

If Vector u=(5,-7) and v=(-11,3), 2v-6u=_____ and ||2v-6u||≈_____

Sauron [17]

<h2>Answer:</h2>

$2\vec{v}-6\vec{u}=(-52,48) \\ \\ ||2\vec{v}-6\vec{u}||=75.28}$

<h2>Step-by-step explanation:</h2>

In this problem we have two vectors:

$\vec{u}=(5,-7) \ and \ \vec{v}=(-11,3)$

So we need to find two things:

$2\vec{v}-6\vec{u}$

and:

$||2\vec{v}-6\vec{u}||$

FIRST:

In this case we have the multiplication of vectors by scalars. A scalar is a simple number, so:

$2\vec{v}-6\vec{u} \\ \\ Replace \ \vec{v} \ and \ \vec{u} \ by \ the \ given \ vectors: \\ \\ 2(-11,3)-6(5,-7) \\ \\ Multiply \ each \ component \ by \ the \ corresponding \ scalar:\\ \\ (2\times (-11),2\times 3)+(-6\times 5,-6\times (-7)) \\ \\ (-22,6)+(-30,42) \\ \\ Sum \ of \ vectors: \\ \\ (-22-30,6+42) \\ \\ \therefore \boxed{(-52,48)}$

SECOND:

If we name:

$\vec{w}=2\vec{v}-6\vec{u}$

Then, $||2\vec{v}-6\vec{u}||$ is the magnitude of the vector $\vec{w}$ . Therefore:

$||\vec{w}||=||2\vec{v}-6\vec{u}|| \\ \\ ||\vec{w}||=||(-52,48)|| \\ \\ ||\vec{w}||=\sqrt{(-58)^2+48^2} \\ \\ ||\vec{w}||=\sqrt{3364+2304} \\ \\ ||\vec{w}||=\sqrt{5668} \\ \\ \boxed{||\vec{w}||=75.28}$