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soldi70 [24.7K]

3 years ago

6

you own seven travel books and are taking five of them on vacation. in how many ways can you select the five books you will take

?

1 answer:

Ipatiy [6.2K]3 years ago

8 0

It depends on how many options you have
You multiply the total number of books you have time 5 because you can choose 5

You might be interested in

-3x^2 – 24x – 13 = -13

Fudgin [204]

$\begin{gathered} -3x^2-24x-13=-13 \\ \text{ Express it as:} \\ 3x^2+24x+26=0 \\ 3x^2+24x=-26 \\ 3(x^2+8x+16)=?-26 \\ 3(x+4)^2=48-26 \\ 3(x+4)^2=22 \end{gathered}$

oh,

3 0

1 year ago

Given the quadratic function g(x)=x^2, find g(3x-2).

maxonik [38]

Answer:

$g(3x-2) = (3x-2)^{2}$

Step-by-step explanation:

$g(x)=x^{2}$

To do this, you must substitute $3x-2$ for x in the equation g(x)

$g(3x-2) = (3x-2)^{2}$

Simplified this would be

$9x^{2} -12x+4$

7 0

2 years ago

(c). It is well known that the rate of flow can be found by measuring the volume of blood that flows past a point in a given tim

aleksklad [387]

(i) Given that

$V(R) = \displaystyle \int_0^R 2\pi K(R^2r-r^3) \, dr$

when R = 0.30 cm and v = (0.30 - 3.33r²) cm/s (which additionally tells us to take K = 1), then

$V(0.30) = \displaystyle \int_0^{0.30} 2\pi \left(0.30-3.33r^2\right)r \, dr \approx \boxed{0.0425}$

and this is a volume so it must be reported with units of cm³.

In Mathematica, you can first define the velocity function with

v[r_] := 0.30 - 3.33r^2

and additionally define the volume function with

V[R_] := Integrate[2 Pi v[r] r, {r, 0, R}]

Then get the desired volume by running V[0.30].

(ii) In full, the volume function is

$\displaystyle \int_0^R 2\pi K(R^2-r^2)r \, dr$

Compute the integral:

$V(R) = \displaystyle \int_0^R 2\pi K(R^2-r^2)r \, dr$

$V(R) = \displaystyle 2\pi K \int_0^R (R^2r-r^3) \, dr$

$V(R) = \displaystyle 2\pi K \left(\frac12 R^2r^2 - \frac14 r^4\right)\bigg_0^R$

$V(R) = \displaystyle 2\pi K \left(\frac{R^4}2- \frac{R^4}4\right)$

$V(R) = \displaystyle \boxed{\frac{\pi KR^4}2}$

In M, redefine the velocity function as

v[r_] := k*(R^2 - r^2)

(you can't use capital K because it's reserved for a built-in function)

Then run

Integrate[2 Pi v[r] r, {r, 0, R}]

This may take a little longer to compute than expected because M tries to generate a result to cover all cases (it doesn't automatically know that R is a real number, for instance). You can make it run faster by including the Assumptions option, as with

Integrate[2 Pi v[r] r, {r, 0, R}, Assumptions -> R > 0]

which ensures that R is positive, and moreover a real number.

5 0

2 years ago

The sum of three numbers is 113 . The second number is 3 times the third. The first number is 7 less than the third . What are t

OLga [1]

Number 1 = 17
number 2 = 72
number 3 = 24

work:

the three numbers are symbolized as x, y, and z

x + y + z = 113

number 2 (y) is 3 times the third number (z) so

y = 3z

so x + 3z + z = 113

the first number (x) is 7 less than than the third number (z) so

x = z - 7

so z -7 + 3z + z = 113

5z - 7 = 113
5z = 120

z = 24

x = 17
y = 72

Hope this helped :)

8 0

2 years ago

Can anybody help me please

vagabundo [1.1K]

Answer:

Not entirely positive of about the answers, but all of the values would equal 15

First Y = 5

First X = 15

Second X = -3

6 0

2 years ago

Read 2 more answers