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4 years ago

3 inches of reason in 6 hours

1 answer:

4 0

OK, if you say so.

3 inches of reason in 6 hours = (3/6) inch/hour = 1/2 inch of reason per hour.

The statement is meaningless, but the math is air-tight and bullet-proof.

(By any chance, could it be 'rain' after not proofreading ?)

You might be interested in

Find the value of the variable and BC, if B is between A and C. AB = 5x, BC = 3x-1, AC = 47

schepotkina [342]

Answer:

Step-by-step explanation:

AC = AB + BC

Since we know what each variable equals, we can write out the equation as shown:

47 = 5x + 3x - 1

Combining like terms:

47 = 8x - 1

Add 1 on both sides:

48 = 8x

Divide 8 on both sides:

X = 6

Now that we know what X equals, we can solve BC.

BC = 3(6) - 1

BC = 18 - 1

BC = 17

Therefore BC = 17.

4 0

3 years ago

Danielle earns a 8.25% commission on everything she sells at the electronics store where she works. She also earns a base salary

Mariulka [41]

Answer: her sales last week was $4300.

Step-by-step explanation:

Let x represent her her sales in a week.

Danielle earns a 8.25% commission on everything she sells at the electronics store where she works. This means that the commission she gets if she makes sales of $x is 0.0825x

She also earns a base salary of $675 per week. The expression for the total earnings for a week in which she made sales of $x would be

0.0825x + 675

if her total earnings for last week were $1,029.75, it means that

0.0825x + 675 = 1029.75

0.0825x = 1029.75 - 675

0.0825x = 354.75

x = 354.75/0.0825

x = $4300

3 0

3 years ago

Evaluate Dx / ^ 9-8x - x2^

Solnce55 [7]

It depends on what you mean by the delimiting carats "^"...

Since you use parentheses appropriately in the answer choices, I'm going to go out on a limb here and assume something like "^x^" stands for $\sqrt x$ .

In that case, you want to find the antiderivative,

$\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}$

Complete the square in the denominator:

$9-8x-x^2=25-(16+8x+x^2)=5^2-(x+4)^2$

Now substitute $x+4=5\sin y$ , so that $\mathrm dx=5\cos y\,\mathrm dy$ . Then

$\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\int\frac{5\cos y}{\sqrt{5^2-(5\sin y)^2}}\,\mathrm dy$

which simplifies to

$\displaystyle\int\frac{5\cos 
y}{5\sqrt{1-\sin^2y}}\,\mathrm dy=\int\frac{\cos y}{\sqrt{\cos^2y}}\,\mathrm dy$

Now, recall that $\sqrt{x^2}=|x|$ . But we want the substitution we made to be reversible, so that

$x+4=5\sin y\iff y=\sin^{-1}\left(\dfrac{x+4}5\right)$

which implies that $-\dfrac\pi2\le y\le\dfrac\pi2$ . (This is the range of the inverse sine function.)

Under these conditions, we have $\cos y\ge0$ , which lets us reduce $\sqrt{\cos^2y}=|\cos y|=\cos y$ . Finally,

$\displaystyle\int\frac{\cos y}{\cos y}\,\mathrm dy=\int\mathrm dy=y+C$

and back-substituting to get this in terms of $x$ yields

$\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\sin^{-1}\left(\frac{x+4}5\right)+C$

4 0

3 years ago

What is the range of arcsinx

Aleonysh [2.5K]

Y= arcsin(x) is equivalent to sin(y) = x

we know that -1≤x+1, hence the range of y is: -π/2≤y≤+π/2

3 0

3 years ago

-0.5 = -4/7 True False

taurus [48]

Answer:

Step-by-step explanation:

false