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3 years ago

5

In a city, the bus route numbers consist of a positive number less than 100, followed by one of the letters a,b,c,d,e and f. how

many different bus routes are possible?

1 answer:

Phantasy [73]3 years ago

8 0

Abcdef,bcdefa,ecbdfa,fabedf,cabedf,badfe,and more.

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The sum of the square root of a number and 6

Anna007 [38]

Answer:

36

Step-by-step explanation:

4 0

3 years ago

Show that the equation x^3+6x-5=0 has a solution between x=0 and x=1

Mnenie [13.5K]

Answer:

Since the value of f(0) is negative and the value of f(1) is positive, then there is at least one value of x between 0 and 1 for which f(x) =0.

Step-by-step explanation:

The equation f(x) given is:

$f(x) = x^3+6x-5$

For x = 0. the value of the expression is:

$f(0) = 0^3+0-5\\f(0) = -5$

For x = 1, the value of the expression is:

$f(1) = 1^3+6-5\\f(1)=2$

Since the value of f(0) is negative and the value of f(1) is positive, then there is at least one value of x between 0 and 1 for which f(x) =0.

In other words, there is at least one solution for the equation between x=0 and x=1.

6 0

3 years ago

A piece of cardboard is 15 inches by 30 inches. A square is to be cut from each corner and the sides folded up to make an open-t

solmaris [256]

Answer:

Maximum volume = 649.519 cubic inches

Step-by-step explanation:

A rectangular piece of cardboard of side 15 inches by 30 inches is cut in such that a square is cut from each corner. Let x be the side of this square cut. When it was folded to make the box the height of box becomes x, length becomes (30-2x) and the width becomes (15-2x).

Volume is given by

V = $V = Length\times Width\times Height\\V = (30 - 2x)(15-2x)x= 4x^3-90x^2+450x\\So,\\V(x) = 4x^3-90x^2+450x$

First, we differentiate V(x) with respect to x, to get,

$\frac{d(V(x))}{dx} = \frac{d(4x^3-12x^2+9x)}{dx} = 12x^2 - 180x +450$

Equating the first derivative to zero, we get,

$\frac{d(V(x))}{dx} = 0\\\\12x^2 - 180x +450 = 0$

Solving, with the help of quadratic formula, we get,

$x = \displaystyle\frac{5(3+\sqrt{3})}{2}, \frac{5(3-\sqrt{3})}{2}$ ,

Again differentiation V(x), with respect to x, we get,

$\frac{d^2(V(x))}{dx^2} = 24x - 180$

At x =

$\displaystyle\frac{5(3-\sqrt{3})}{2}$ ,

$\frac{d^2(V(x))}{dx^2} < 0$

Thus, by double derivative test, the maxima occurs at

x = $\displaystyle\frac{5(3-\sqrt{3})}{2}$ for V(x).

Thus, largest volume the box can have occurs when $x = \displaystyle\frac{5(3-\sqrt{3})}{2}}$ .

Maximum volume =

$V(\displaystyle\frac{5(3-\sqrt{3})}{2}) = (30 - 2x)(15-2x)x = 649.5191\text{ cubic inches}$

8 0

3 years ago

Victor is y years old. His 9-year-old sister Marsha is 4 years younger than he is. Write an equation to represent this situation

Maurinko [17]

Victor = y years old
Marsha = 9 years old
Marsha is 4 years younger than Victor.

Answer: y = 9 + 4

7 0

3 years ago

-3•e^(2m-5)-3=-27 how to solve

zzz [600]

Answer:

m = 3.53972077085

Step-by-step explanation:

-3 × $e^{2m - 5}$ - 3 = -27

Subtracting -3 from both sides of the equation gives;

-3 × $e^{2m - 5}$ = -24

Dividing by -3 on both sides of the equation gives;

$e^{2m - 5}$ = 8

Let 2m - 5 = x

xloge = 3log2

x = $\frac{3log2}{loge}$ = 2.0794415417

So,

2m - 5 = 2.0794415417

2m = 2.0794415417 + 5

2m = 7.0794415417

Dividing by 2 on both sides of the equation gives:

m = 3.53972077085

3 0

3 years ago