Ask question

Ask question

All categories

3 years ago

5

A cube has an edge if 4 feet. The edge is increasing at a rate of 2 feet per minute. Express the volume of the cube as a functio

n

1 answer:

GarryVolchara [31]3 years ago

7 0

Volume=a^3
so 16^3=4096

You might be interested in

Find the 2th term of the expansion of (a-b)^4.

vladimir1956 [14]

The second term of the expansion is $-4a^3b$ .

Solution:

Given expression:

$(a-b)^4$

To find the second term of the expansion.

$(a-b)^4$

Using Binomial theorem,

$(a+b)^{n}=\sum_{i=0}^{n}\left(\begin{array}{l}n \\i\end{array}\right) a^{(n-i)} b^{i}$

Here, a = a and b = –b

$$(a-b)^4=\sum_{i=0}^{4}\left(\begin{array}{l}4 \\i\end{array}\right) a^{(4-i)}(-b)^{i}$

Substitute i = 0, we get

$$\frac{4 !}{0 !(4-0) !} a^{4}(-b)^{0}=1 \cdot \frac{4 !}{0 !(4-0) !} a^{4}=a^4$

Substitute i = 1, we get

$$\frac{4 !}{1 !(4-1) !} a^{3}(-b)^{1}=\frac{4 !}{3!} a^{3}(-b)=-4 a^{3} b$

Substitute i = 2, we get

$$\frac{4 !}{2 !(4-2) !} a^{2}(-b)^{2}=\frac{12}{2 !} a^{2}(-b)^{2}=6 a^{2} b^{2}$

Substitute i = 3, we get

$$\frac{4 !}{3 !(4-3) !} a^{1}(-b)^{3}=\frac{4}{1 !} a(-b)^{3}=-4 a b^{3}$

Substitute i = 4, we get

$$\frac{4 !}{4 !(4-4) !} a^{0}(-b)^{4}=1 \cdot \frac{(-b)^{4}}{(4-4) !}=b^{4}$

Therefore,

$$(a-b)^4=\sum_{i=0}^{4}\left(\begin{array}{l}4 \\i\end{array}\right) a^{(4-i)}(-b)^{i}$

$=\frac{4 !}{0 !(4-0) !} a^{4}(-b)^{0}+\frac{4 !}{1 !(4-1) !} a^{3}(-b)^{1}+\frac{4 !}{2 !(4-2) !} a^{2}(-b)^{2}+\frac{4 !}{3 !(4-3) !} a^{1}(-b)^{3}+\frac{4 !}{4 !(4-4) !} a^{0}(-b)^{4}$ $=a^{4}-4 a^{3} b+6 a^{2} b^{2}-4 a b^{3}+b^{4}$

Hence the second term of the expansion is $-4a^3b$ .

3 0

2 years ago

1. Writing an equation for an exponential function by

Naya [18.7K]

Answer: 1) $t(n)=0.6(2)^n$

2) $f(x)=10(5)^x$

Step-by-step explanation:

1) Let the function that shows the thickness of the paper after n folds,

$t(n) = ab^n$ ---------(1)

Since, According to the question,

Initially the thickness of the paper = 0.6

That is, at n = 0, t(0) = 0.6

By equation (1),

$0.6 = a(b)^0\implies 0.6 = a$

Hence the function that shows the given situation,

$t(n) = 0.6 b^n$ -----------(2)

Again when we fold the paper the thickness of the paper will be doubled.

Thus, at n = 1, t(1) = 1.2

By equation (2),

$1.2 = 0.6 b^1\implies 2 = b$

Thus, the complete function is,

$t(n) = 0.6 (2)^n$

2) Let the function that is passing through the points (-2, 2/5) and (-1,2),

$f(x) = ab^x$ ---------(1)

For f(x) = 2, x = -1

By equation (1),

$2= ab^{-1}$ ---------(2)

Also, For f(x) = 2/5, x = -2

Again, By equation (1),

$\frac{2}{5}= a(b)^{-2}$

$\implies \frac{2}{5}=ab^{-1}b^{-1}=2b^{-1}$

$\implies \frac{2}{5}=\frac{2}{b}$

$\implies 2b=10$

$\implies b = 5$

By substituting this value in equation (2),

We get, a = 10

Hence, from equation (1), the function that is passing through the points (-2, 2/5) and (-1,2),

$f(x) = 10(5)^x$

5 0

2 years ago

Royce has 4 green pens, 2 blue pens and 6 red pens in a box. He will randomly choose 1 pen from the box. What is the probability

Archy [21]

Answer:

2/12

Step-by-step explanation:

4 + 2 = 6 + 6 = 12

there is 2 blue pens

so 2 out of 12

CAN I HAVE BRAINLEIST PLEASE?????

6 0

3 years ago

Read 2 more answers

Help with question 5,9, and 13. It would be a big help.

solniwko [45]

I am using "x" but alphabet letter does not matter.

#9

Words: x is greater than or equal to -4
Algebra: x ≥ -4
Possible solutions: 0,1,2

#13

Words: x is greater than 0
Algebra: x > 0
Possible solutions: 1,2,3

3 0

2 years ago

About 8% of the U.S. population catches the flu each season. Assuming everyone has equal probability of catching the flu, about

avanturin [10]

Answer:

<u>The odds are 2 : 23, or about 0.09 : 1 (0.09 to 1).</u>

Explanation:

The <em>odds </em>of an event is the ratio of occurrence to non-occurrence of the event.

When you know the <em>probability</em> of an event, then you can calculate the odds by dividing the probability of occurence by the probability of non-occurrence.

Calling p the probability that an event will happen, 1 - p is the probability that it will not happen and the odds will be:

Odds = p / ( 1 - p)

You have p = 8% = 0.08, and 1 - p = 1 -0.08 = 0.92.

Therefore:

Odds = 0.08 / 0.92 = 8 : 92 = 2 : 23 ≈ 0.09 : 1 (0.09 to 1)

8 0

2 years ago