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3 years ago

The formula for the volume of this rectangular prism is:

Mathematics

1 answer:

juin [17]3 years ago

8 0

Answer:

Step-by-step explanation: Explanation:

and

represent the length, height and width of the prism, then the volume of the rectangular prism is :

............. (1)

Given :

−

;

............... (2)

(

−

)

;

(

)

Let

(

)

be the expression for the length, then the RHS of equation (1) becomes

(

−

)

(

)

(

−

)

(

)

(

−

)

(

)

(

−

)

(

)

(

−

)

−

..... (3)

Comparing this to the LHS of equation (1), we get the following set of equations to solve for

;

−

;

Therefore

(

)

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If 6^4x = 82, what is the value of x?<br> Round your answer to three places.

neonofarm [45]

Answer:

$x=0.61485921$

Step-by-step explanation:

The given equation is in exponential form:

$6^{4x} =82$

To find $x$ we need to write it in logarithmic form:

$b^{a} =n$ ⇒ $log_{b} n=a$

$6^{4x} =82$ ⇒ $log_{ 6 } 82=4x$

$2.45943684 = 4x$

$\frac{2.45943684}{4} = x$

$0.61485921 =x$

To prove this, we can substitute the value into the given equation

$6^{4x} =82$

$6^{4(0.61485921)} =82$

$82=82$

Therefore, the answer is $x=0.61485921$

6 0

3 years ago

Tobias sent a chain letter to his friends, asking them to forward the letter to more friends. The number of people who receive t

malfutka [58]

Answer:

$P(t)=37\times (4)^{(t/9.1)}$

Explanation:

The number of emails is multiplied by <em>4</em> every <em>9.1 weeks.</em>

Thus, since <em>Tobias initially sent the chain letter to 37 friends</em>, the number of letters will grow as per this geometric series:

Start: 37 letters

In 9.1 weeks: 37 × 4

In 2 × 9.1 weeks: 37 × (4)²

In 3 × 9.1 weeks: 37 × (4)³

As you see, the exponent is the number of weeks divided by 9.1

Thus, if your variable is the number of weeks, t, then the exponent is t/9.1

And the exponential function, P(t) will be:

$P(t)=37\times (4)^{(t/9.1)}$

3 0

3 years ago

Simplify the following expression (62)4

bija089 [108]

Answer:

$3^{0} =1$

Step-by-step explanation:

7 0

3 years ago

Which table shows a function whose range has exactly three elements

Rudik [331]

<h2>Answer:</h2>

The table which shows that a function's range has exactly three elements is:

x y

3 8

4 6

5 12

6 8

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

<u>Domain of a function--</u>

The domain of a function is the set of all the x-values i.e. the value of the independent variable for which a function is defined.

<u>Range of a function--</u>

It is the set of all the y-value or the values which are obtained by the independent variable i.e. the values obtained by the function in it's defined domain.

x y

1 4

2 4

3 4

Domain: {1,2,3}

Range: {4}

Hence, the range has a single element.

x y

3 8

4 6

5 12

6 8

Domain: {3,4,5,6}

Range: {6,8,12}

Hence, the range has three element.

x y

0 5

2 9

0 15

This relation is not a function.

because 0 has two images.

0 is mapped to 5 and 0 is mapped to 15.

x y

1 4

3 2

5 1

3 4

This relation is not a function.

because 3 has two images.

3 is mapped to 2 in the ordered pair (3,2) and 3 is mapped to 4 in the ordered pair (3,4)

5 0

3 years ago

Read 2 more answers

Two-thirds of the T-shirts in a T-shirt shop are blue. Three-fifths of those T-shirts are on sale. One-half of the blue T

katrin2010 [14]

Let, total number of T-shirts are x.

Number of blue T-shirts = (2/3)x = 2x/3 .

Number of blue shirts on sale = (3/5)(2x/3) = 2x/5 .

Number of medium sized blue shirts on sale = (1/5)(2x/5) = 2x/25 .

Fraction of the shop's T-shirts are blue T-shirts that are on sale and are size medium = $\dfrac{2x/25}{x}$ = 2/25 . ( Number of medium sized blue shirts on sale divided by total number of T-shirts )

Hence, this is the required solution.

5 0

3 years ago