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3 years ago

Which expression is equivalent to \large 4x^3+x^2-3?

Mathematics

1 answer:

vovikov84 [41]3 years ago

3 0

Answer:

$22222222 { { { { { { { { { { { { { { { { { { { { { { { { { { { { { { { { { { { { { { { { {?}^{2} }^{2} }^{2} }^{2} }^{2} }^{2} }^{2} }^{2} }^{2} }^{2} }^{2} }^{2} }^{2} }^{2} }^{2} }^{2} }^{2} }^{2} }^{2} }^{2} }^{2} }^{2} }^{2} }^{2} }^{2} }^{2} }^{2} }^{2} }^{2} }^{?} }^{?} }^{?} }^{?} }^{?} }^{?} }^{?} }^{?} }^{?} }^{?} }^{?} }^{?}$

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A home gardener estimates that 24 apple trees will have an average yield of 104 apples per tree. But because of the size of the

d1i1m1o1n [39]

Answer:

The farmer should plant 14 additional trees, for maximum yield.

Step-by-step explanation:

Given

$Trees = 24$

$Yield = 104$

$x \to additional\ trees$

So, we have:

$Trees = 24 + x$

$Yield = 104 - 2x$

Required

The additional trees to be planted for maximum yield

The function is:

$f(x) = Trees * Yield$

$f(x) = (24 + x) * (104 - 2x)$

Open bracket

$f(x) = 24 * 104 + 104x - 24 * 2x - x * 2x$

$f(x) = 2796 + 104x - 48x - 2x^2$

$f(x) = 2796 + 56x - 2x^2$

Rewrite as:

$f(x) = - 2x^2 + 56x + 2796$

Differentiate

$f'(x) = -4x + 56$

Equate $f'(x) = -4x + 56$ to 0 and solve for x to get the maximum of x

$-4x + 56 = 0$

$-4x =- 56$

Divide by -4

$x =14$

The farmer should plant 14 additional trees, for maximum yield.

5 0

3 years ago

What is the answer to -5(6+9k)

anzhelika [568]

Answer: The answer is -30 - 45 k

Step-by-step explanation:

8 0

2 years ago

I need to find the derivative. I’m not very good at this so I am answer asap would be sosososo helpful

Bingel [31]

Answer:

See below.

Step-by-step explanation:

First, notice that this is a composition of functions. For instance, let's let $f(x)=\sqrt{x}$ and $g(x)=7x^2+4x+1$ . Then, the given equation is essentially $f(g(x))=\sqrt{7x^2+4x+1}$ . Thus, we can use the chain rule.

Recall the chain rule: $\frac{d}{dx}[f(g(x))]=f'(g(x))\cdot g'(x)$ . So, let's find the derivative of each function:

$f(x)=\sqrt{x}=x^\frac{1}{2}$

We can use the Power Rule here:

$f'(x)=(x^\frac{1}{2})'=\frac{1}{2}(x^{-\frac{1}{2} })=\frac{1}{2\sqrt{x}}$

Now:

$g(x)=7x^2+4x+1$

Again, use the Power Rule and Sum Rule

$g'(x)=(7x^2+4x+1)'=(7x^2)'+(4x)'+(1)'=14x+4$

Now, we can put them together:

$y'=f'(g(x))\cdot g'(x)=\frac{1}{2\sqrt{g(x)}} \cdot (14x+4)$

$y'=\frac{14x+4}{2\sqrt{7x^2+4x+1} } =\frac{7x+2}{\sqrt{7x^2+4x+1} }$

5 0

3 years ago

The measure of an interior angle of a regular polygon is 140°140°. find the number of sides of the polygon.

MA_775_DIABLO [31]

$\alpha = \cfrac{180(n-2)}{n} \ \ \ \ \ [ \alpha =interior \ angle, \ \ n=number \ of 
 \ sides] \\ \\ \\ 140 = \cfrac{180(n-2)}{n} \\ \\ 140n = 180(n-2) \\ \\ 140n=180n-360 \\ \\ 40n=360 \\ \\ n= \frac{360}{40}=9 \ \ sides$

4 0

3 years ago

Read 2 more answers

160% of what number is 19.2

riadik2000 [5.3K]

Answer:

The number is 12

Step-by-step explanation:

Let x be the number

160/100 = 1.6

1.6 x = 19.2

x = 19.2 / 1.6

x = 12

7 0

2 years ago