Find the composite area of the shaded region. Use 3.14 for 11.

Four mathematicians, three physicists, and an engineer are to be seated equally spaced around a circular table. How many differe

Vesna [10]

First, we can choose the seats for the four mathematicians. Then we seat the physicits, then the engineer. There are 4! ways to seat the mathematicians, then 3! ways to seat the physicists, then 1! ways to seat the engineer. But then we must divide by 8, because we can rotate the table, so there are 8!*4!*3!/8 = 725760 ways to seat everyone.

3 0

3 years ago

The position equation for a particle is s of t equals the square root of the quantity t cubed plus 1 where s is measured in feet

vladimir1956 [14]

$\bf s(t)=\sqrt{t^3+1}
\\\\\\
\cfrac{ds}{dt}=\cfrac{1}{2}(t^3+1)^{-\frac{1}{2}}\cdot 3t^2\implies \boxed{\cfrac{ds}{dt}=\cfrac{3t^2}{2\sqrt{t^3+1}}}\leftarrow v(t)
\\\\\\
\cfrac{d^2s}{dt^2}=\cfrac{6t(2\sqrt{t^3+1})-3t^2\left( \frac{3t^2}{\sqrt{t^3+1}} \right)}{(2\sqrt{t^3+1})^2}\implies 
\cfrac{d^2s}{dt^2}=\cfrac{ \frac{6t(2\sqrt{t^3+1})-1}{\sqrt{t^3+1}} }{4(t^3+1)}$

$\bf \cfrac{d^2s}{dt^2}=\cfrac{6t[2(t^3+1)]-1}{4(t^3+1)\sqrt{t^3+1}}\implies 
\boxed{\cfrac{d^2s}{dt^2}=\cfrac{12t^4+12t-1}{4t^3+4\sqrt{t^3+1}}}\leftarrow a(t)\\\\
-------------------------------\\\\a(2)=\cfrac{215~ft^2}{44~sec}$

8 0

3 years ago

Read 2 more answers

The product of two consecutive positive integers is 56. Find the two integers

vredina [299]

Answer:

Two consecutive integers are of the form

x and x + 1

Their product is equal to 56

x(x + 1) = 56

Solve and find the two numbers x and x + 1. The above equation may be written as follows

x2 + x - 56 = 0

Factor and solve

(x - 7)(x + 8) = 0

solutions: x = 7 , x = -8

x= - 8 is not valid since the number sought must be positive. Hence

x = 7 and x + 1 = 8 are the two consecutive numbers.

Step-by-step explanation:

7 0

3 years ago

find the gradient of the line joining (3,7) and (6,9). Hence, find the acute angle it makes with the positive x-y axis

stiv31 [10]

Answer:

33.7 degrees

Step-by-step explanation:

As we go from (3,7) to (6,9), x increases by 3 and y increases by 2. Thus, the gradient (slope) of the line connecting these two points is

m = rise / run = 2/3. Using the slope-intercept formula y = mx + b, we obtain

7 = (2/3)(3) + b, or 7 = 2 + b, so we see that b = 5 and y = (2/3)x + 5. The y-intercept is (0, 5).

Next we find the x-intercept. We set y = (2/3)x + 5 = to 0 and solve for x:

(2/3)x = -5, or (3/2)(2/3)x = -5(3/2), or x = -15/2, so that the x-intercept is

(-15/2, 0). This line intersects the x-axis at (-15/2, 0).

Now look at the segment of this line connecting (-15/2, 0) and (0, 5). Here x increases by 15/2 and y increases by 5, and so the tangent of the acute angle in question is

tan Ф = 5 / (15/2) = 10 / 15 = 2/3.

Using the inverse tangent function, we get Ф = arctan 2/3, or approx.

33.7 degrees.

I believe you meant "the acute angle it makes with the positive x-axis."

3 0

3 years ago

katie has 4 grapes candies and 3 cherries candies. The ratio of the number of grapes candies to the total number of candie is

Tom [10]

Answer: 7 I think its adding but if its multiplying it is 12

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers