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2 years ago

- Owen is helping his Dad get the cabana ready for summer. He has two pieces of wood, one is 6 feet long

Mathematics

1 answer:

Anton [14]2 years ago

6 0

Answer:

Step-by-step explanation:

6 ft + 4 ft = 10 ft

Easy: 6 is 3+3

4 is 2+2

Now do (3+2)+(3+2)= 5+5= 10 = 6+4

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Twelve members of a band purchase one beverage each during a break at practice. Exactly 5 of the 12 members bought bottled water

Hoochie [10]

Answer:

Step-by-step explanation:

You have to use ratios. If 5 of 12 members bought water, then x of 168 members will buy water.

$\frac{5}{12} = \frac{x}{168}\\12x = 840\\x = 70$

70 members will buy bottled water.

8 0

3 years ago

Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that

Helga [31]

Answer:

$\sum^\infty_{n=0} -5 (\frac{x+2}{2})^n$

Step-by-step explanation:

Rn(x) →0

f(x) = 10/x

a = -2

Taylor series for the function f at the number a is:

$f(x) = \sum^\infty_{n=0} \frac{f^{(n)}(a)}{n!} (x - a)^n$

$f(x) = f(a) + \frac{f'(a)}{1!}(x-a)+\frac{f"(a)}{2!} (x-a)^2 + ...$ ............ equation (1)

Now we will find the function f and all derivatives of the function f at a = -2

f(x) = 10/x f(-2) = 10/-2

f'(x) = -10/x² f'(-2) = -10/(-2)²

f"(x) = -10.2/x³ f"(-2) = -10.2/(-2)³

f"'(x) = -10.2.3/x⁴ f'"(-2) = -10.2.3/(-2)⁴

f""(x) = -10.2.3.4/x⁵ f""(-2) = -10.2.3.4/(-2)⁵

∴ The Taylor series for the function f at a = -4 means that we substitute the value of each function into equation (1)

So, we get $\sum^\infty_{n=0} - \frac{10(x+2)^n}{2^{n+1}}$ Or $\sum^\infty_{n=0} -5 (\frac{x+2}{2})^n$

4 0

3 years ago

If the radius of mars is about 13.7% of neptune's radius, what is the radius of neptune?

Marianna [84]

The volumetric mean radius of Mars is about 3389.5 km. We know that it's 13.7% of Neptune's mean radius, so we can write it down as:

3389.5 = 13.7% of x (where x is Neptune's radius)
3389.5 = 13.7% x
3389.5 = 137/1000x / * 1000 (both sides)
3389500 = 137x / ÷ 137 (both sides)
x = 24740.87591240876
x ≈ 24740.88

Answer: The mean radius of Neptune is about 24740.88 km.

6 0

3 years ago

In another survey, Jane found that 25% of the total number of teenagers surveyed like sandwiches. If 50 teenagers like sandwiche

34kurt

Set up a proportion: 25/100 = 50/n where n = # of teens surveyed
Simplify fraction: 1/4 = 50/n
Cross multiply: n = 200
So 200 teens were surveyed.

7 0

3 years ago

Convert y =(x+1)(x-9) to vertex form

IgorC [24]

Answer:

y = (x - 4)² - 25

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square.

Given

y = (x + 1)(x - 9) ← expand factors using FOIL, thus

y = x² - 8x - 9

To complete the square

add/subtract ( half the coefficient of the x- term )² to x² - 8x

y = x² + 2(- 4)x + 16 - 16 - 9

= (x - 4)² - 25 ← in vertex form

5 0

3 years ago