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2 years ago

Find the domain of the function. (Enter your answer using interval notation.) f(x) = 9x² + 6x – 1

Mathematics

1 answer:

GuDViN [60]2 years ago

7 0

Answer: (-infty, infty)

Step-by-step explanation:

The domain of a quadratic function is the set of real numbers.

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Mark has a piece of wood 4 1/4 feet long. Tony has a piece of wood 1 2/4 feet long. How much wood do the boys have altogether. p

Alona [7]

They have 5 3/4 ft

4+1=5
1/4+2/4=3/4

but hey, its not the length of your wood that matters, its how you use it XD

8 0

4 years ago

Apply Gaussian quadrature with n = 4 to approximate integrate sin x^2dx from 1 to 5

maks197457 [2]

First, recall that Gaussian quadrature is based around integrating a function over the interval [-1,1], so transform the function argument accordingly to change the integral over [1,5] to an equivalent one over [-1,1].

$x=2t+3\iff t=\dfrac x2-\dfrac32\implies2\mathrm dt=\mathrm dx$
$x=1\implies t=\dfrac{2-6}4=-1$
$x=5\implies t=\dfrac{10-6}4=1$

So,

$\displaystyle\int_{x=1}^{x=5}\sin x^2\,\mathrm dx=\displaystyle2\int_{t=-1}^{t=1}\sin(2t+3)^2\,\mathrm dt$

Let $f(t)=2\sin(2t+3)^2$ . With $n=4$ , we're looking for coefficients $c_i$ and nodes $x_i$ , with $1\le i\le4$ , such that

$\displaystyle\int_{-1}^1f(t)\,\mathrm dt\approx c_1f(x_1)+\cdots+c_4f(x_4)$

You can either try solving for each with the help of a calculator, or look up the values of the weights and nodes (they're extensively tabulated, and I'll include a link to one such reference).

Using the quadrature, we then have

$\displaystyle\int_{-1}^1f(t)\,\mathrm dt\approx0.3749f(-0.8611)+0.6521f(-0.3400)+0.6521f(0.3400)+0.3749f-0.8611)$
$\displaystyle\int_{-1}^1f(t)\,\mathrm dt\approx0.5790$

4 0

3 years ago

What is the numerical coefficient of the first term

Ira Lisetskai [31]

Answer:

the number before the first variable (first term)

Step-by-step explanation:

this appears to be an incomplete question. The numerical coefficient of a term is the number before the variable.

the constant is the number without a variable.

4 0

3 years ago

Read 2 more answers

Jenny is baking 56 cookie sandwiches for her friend’s birthday party. She plans to transport the cookie sandwiches in the same f

Shtirlitz [24]

Answer:

Part A: 5 inches³.

Part B: 302 inches³.

Part C: Yes. Explanation below.

Step-by-step explanation:

Part A: The cookie sandwiches appear to be flat cylinders. The volume for a cylinder is pi * r^2 * h.

In this case, the h = 1 inch and r = 1.25 inches.

pi * 1.25^2 * 1

= pi * 1.5625

= 3.14 * 1.5625

= 4.90625.

So, the volume of a single cookie sandwich is about 5 inches³.

Part B: As stated before, the volume of a cylinder is pi * r^2 * h.

In this case, the r = 4.5 inches, and the h = 4.75 inches.

pi * 4.5^2 * 4.75

= 3.14 * 20.25 * 4.75

= 63.585 * 4.75

= 302.02875.

So, the volume of the food storage container is about 302 inches³.

Part C: Given the calculations from Parts A and B, Jenny will be able to transport all the cookie sandwiches in the food storage container. This is because there are 56 cookie sandwiches, each with a volume of 5 cubic inches. That means that the cookie sandwiches will take up 5 * 56 = 280 cubic inches of space. There is about 302 cubic inches of space in the container, so there will still be 22 cubic inches of air inside the container after the cookies are inside.

Hope this helps!

4 0

3 years ago

Read 2 more answers

5. Which statement is true?

sveta [45]

All rectangles are quadrilaterals because a quadrilateral has 4 sides and all rectangles have 4 sides so that one is correct

8 0

4 years ago

Read 2 more answers

Find the domain of the function. (Enter your answer using interval notation.) f(x) = 9x² + 6x – 1​

Find the domain of the function. (Enter your answer using interval notation.) f(x) = 9x² + 6x – 1