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3 years ago

Use the cubic model y = 10x3 − 12x to estimate the value of y when x = 3.

Mathematics

1 answer:

Pani-rosa [81]3 years ago

7 0

To solve this problem you must apply the proccedure shown below:

1. You have the following function given in the problem above:

$y=10^{3}-12x$

2. To estimate the value of $y$ when $x=3$ , you only need to substitute this value of $x$ into the function, as following:

$y=10^{3}-12x\\y=10(3)^{3}-12(3)\\y=10(27)-36\\y=270-36\\y=234$

Therefore, the answer is: A) 234

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balandron [24]

2(x + 4) -3

2x + 8 (-3)

2x + -24

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3 years ago

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3 years ago

What is k if : k!+48=48((k+1)^m)

lys-0071 [83]

Answer:

The value of k is greater than or equal to 0, i.e. k≥7.

Step-by-step explanation:

The given equation is

$k!+48=48((k+1)^m)$

The value of k must be a positive integer because k! is defined for k≥0, where k∈Z.

Subtract 48 from both the sides.

$k!=48((k+1)^m)-48$

$k!=48((k+1)^m-1)$

$k!=48(k+1-1)(\frac{(k+1)^m-1}{(k+1)-1})$

Using $[\frac{r^m-1}{r-1}=r^{m-1}+r^{m-2}+...+1]$ , we get

$k!=48k((k+1)^{m-1}+(k+1)^{m-2}+...+1)$

Divide both sides by 48k.

$\frac{k!}{48k}=(k+1)^{m-1}+(k+1)^{m-2}+...+1$

$\frac{k(k-1)!}{48k}=(k+1)^{m-1}+(k+1)^{m-2}+...+1$

$\frac{(k-1)!}{48}=(k+1)^{m-1}+(k+1)^{m-2}+...+1$

Note: The value of m can be 0 or 1.

The value of k is positive integer, so the right hand side of the above equation must be a positive integer.

Since RHS of the equation is positive integer, therefore (k-1)! is completely divisible by 48.

$k-1\geq 6$

Add 1 on both sides.

$k\geq 6+1$

$k\geq 7$

Therefore the value of k is greater than or equal to 0.

4 0

4 years ago

A swimming pool has a length of 12 feet, a width of 8 feet, and a depth of 9 feet. What is the volume of the pool in cubic feet?

Umnica [9.8K]

Answer:

V=864 cubic feet

Step-by-step explanation:

Volume of a rectangular prism is Length x width x depth

So V=12x8x9

V=864 Cubic feet

6 0

3 years ago

If Lylah completes the square for f(x)=x^2-12x+7 in order to find the minimum, she must write f(x) in the general form f(x)=(x-a

Ber [7]

<span>f(x) = x^2 - 12x + 7

First, separate the first two terms from the constant

f(x) = (x^2 - 12x) + 7

Next, half the coefficient of second term in the parenthesis (12x) and square the result. Make sure to subtract outside the parenthesis what you added inside so that the equation stays equal.

f(x) = (x^2 - 12x + 36) + 7 - 36
f(x) = </span><span>(x^2 - 12x + 36) - 29

Now, just factor the trinomial inside the parenthesis, lemme know in a comment if you don't know how to do this and I'll explain.

f(x) = (x(x - 6) -6(x - 6)) - 29
f(x) = (x - 6)^2 - 29

The polynomial is now in vertex form, and the value of a, as you can see, is 6.
</span>

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4 years ago