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4 years ago

Consider the function f(x) = 10x2 + 20. – 11 What is the vertex of the function

Mathematics

1 answer:

kogti [31]4 years ago

5 0

Answer:

Step-by-step explanation:

hello :

f(x) = 10x²+20x-11 Completing The Square

f(x) = 10(x²+2x)-11 = 10((x²+2x+1)-1)-11

f(x) =10((x+1)²-1)-11

f(x)= 10(x+1)²-21...vertex form when the vertex is : (-1 ; -21)

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3 years ago

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Need help question #1. Show steps please

SSSSS [86.1K]

Answer:

Step-by-step explanation:

We want to integrate:

$\displaystyle \int\frac{4x^4+3}{4x^5+15x+2}\,dx$

Notice that the expression in the denominator is quite similar to the expression in the numerator. So, we can try performing u-substitution. Let u be the function in the denominator. So:

$u=4x^5+15x+2$

By differentiating both sides with respect to x:

$\displaystyle \frac{du}{dx}=20x^4+15$

We can "multiply" both sides by dx:

$du=20x^4+15\,dx$

And divide both sides by 5:

$\displaystyle \frac{1}{5}\, du=4x^4+3\,dx$

Rewriting our original integral yields:

$\displaystyle \int \frac{1}{4x^5+15x+2}(4x^4+3\, dx)$

Substitute:

$\displaystyle =\int \frac{1}{u}\Big(\frac{1}{5} \, du\Big)$

Simplify:

$\displaystyle =\frac{1}{5}\int \frac{1}{u}\, du$

This is a common integral:

$\displaystyle =\frac{1}{5}\ln|u|$

Back-substitute. Of course, we need the constant of integration:

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3 years ago

Matching: Connect the correct statement with the corresponding picture. There are multiple correct statements per picture.

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Answer:

Figure 1: A , D

Figure 2: B, E

Figure 3: C, F

Hope that helps!

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3 years ago

Cube-shaped blocks are packed into a cube-shaped storage container. The edge length of the storage container is 212 feet. The

igor_vitrenko [27]

Answer:

The volume of cube-shaped block is 0.125 cubic feet.

Step-by-step explanation:

We are given the following in the question:

Edge length of storage container =

$2\dfrac{1}{2}\text{ feet}$

Edge length of block =

$\dfrac{1}{5}\times \text{Edge length of container}$

Putting value we get,

Edge length of block =

$\dfrac{1}{5}\times 2\dfrac{1}{2}\\\\=\dfrac{1}{5}\times \dfrac{5}{2}\\\\=\dfrac{1}{2}\text{ feet}$

Volume of cube-shaped block = Volume of cube

$V = \text{(Edge)}^3\\\\V =(\dfrac{1}{2})^3\\\\V = \dfrac{1}{8}\text{ cubic feet}\\\\V = 0.125\text{ cubic feet}$

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7 0

3 years ago