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3 years ago

Divide 3.7÷0.006 round the answer the nearest hundredth?

1 answer:

6 0

First divide 3.7 by 0.006
Which is 616.666
The last 6 is the thousandths place. If it is 5 or bigger then the number to the left is rounded up. If its lower than 5 you round down

Since 6 is over 5 we tound up
616.67

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Which expression is equivalent to Left-bracket log 9 + one-half log x + log (x cubed + 4) Right-bracket minus log 6? log StartFr

dybincka [34]

Answer:

$\log{\dfrac{3\sqrt{x}(x^3+4)}{2}}$

Step-by-step explanation:

$\log{9}+\dfrac{1}{2}\log{x}+\log{(x^3+4)}-\log{6}=\log{\left(\dfrac{9x^{\frac{1}{2}}(x^3+4)}{6}\right)}\\\\=\boxed{\log{\dfrac{3\sqrt{x}(x^3+4)}{2}}}\qquad\text{matches choice A}$

The applicable rules of logarithms are ...

log(ab) = log(a) +log(b)

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3 years ago

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liq [111]

Answer:

...

against the wind, an airplane travels 3640 km in 7 hours.

with the wind, the same plane travels 6000 km in 6hrs.

...

let speed of plane in still air be x mph

speed of wind be y mph.

t=d/r

against wind speed = x-y mph

with wond speed = x=y mph

...

3640/(x-y)=7

3640 = 7x-7y

520=x-y.....................1

...

6000/x+y = 6

6000 = 6x+6y

1000=x+y.....................2

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Add (1) & (2)

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8 0

3 years ago

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dedylja [7]

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3 years ago

Math IIIB Performance Task: Piecewise-Defined Functions

meriva

9514 1404 393

Explanation:

a) see the attachment for a graph (red curve)

b) The piecewise defined function can be ...

$\displaystyle C(x)=\begin{cases}0&0\le x\le 1\\5&1$

c) The new cost function is ...

$\displaystyle C(x)=\begin{cases}10&0\le x\le5\\x+5&5$

The charge is a flat $10 for any period up to 5 hours, then $1 per additional hour after that, prorated for partial hours. There is apparently no upper limit on parking time as there was with the original function. (The graph shown goes beyond 15 hours; the domain of the original C(x) is 0 to 12 hours.) For reference, the new cost structure is shown in blue in the attachment.

_____

Additional comment

Under the new structure, costs are significantly higher for short-term parking, and lower once the term exceeds 6 hours.

7 0

3 years ago

What is the binomial expansion of (x + 2)4? x4 + 4x3 + 6x2 + 4x + 1 8x3 + 24x2 + 32x x4 + 8x3 + 24x2 + 32x + 16 2x4 + 8x3 + 12x2

Margaret [11]

Answer-

$\boxed{\boxed{(x+2)^4=x^4+8x^3+24x^2+32x+16}}$

Solution-

Given expression is $(x+2)^4$

Applying Binomial Theorem

$\left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i$

Here,

a = x, b = 2 and n = 4

So,

$\left(x+2\right)^4=\sum _{i=0}^4\binom{4}{i}x^{\left(4-i\right)}\cdot \:2^i$

Expanding the summation

$=\dfrac{4!}{0!\left(4-0\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(4-1\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(4-2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(4-3\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(4-4\right)!}x^0\cdot \:2^4$

$=\dfrac{4!}{0!\left(4\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(3\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(1\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(0\right)!}x^0\cdot \:2^4$

$=1\cdot x^4\cdot \:1+4\cdot x^3\cdot \:2+6x^2\cdot \:4+4\cdot x\cdot \:8+1\cdot 1\cdot \:16$

$=x^4+8x^3+24x^2+32x+16$

4 0

4 years ago

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