What is the measure of 78°

Jet001 [13]

Answer:

In a sporting event, the scoring area (shown here) consists of four concentric circles on the ice with radii of 6 inches, 4 feet, 6 feet, and 7 feet. If a team member lands a (43-pound) stone randomly within the scoring area, find the probability that it ends up centered on the given color. (a) red (b) white (c) blue (a) The probability that it ends up centered on red is (Type an integer or a simplified fraction.) (b) The probability that it ends up centered on white is (Type an integer or a simplified fraction.) (c) The probability that it ends up centered on blue is (Type an integer or a simplified fraction.) of the answer boxes

7 0

3 years ago

The school has a $500 budget for pizza. Pizza costs $15 per pie and the school orders 27 of them. How much money will be left in

Fynjy0 [20]

Step-by-step explanation:

27×15=405 which means there is 95$ left

3 0

3 years ago

Round 3/2/7 to the nearest half

mr Goodwill [35]

I don't think your question was worded properly

6 0

3 years ago

Let f(x) = 3 * sqrt(x) + 7. Define g$to be the inverse of f.

aliina [53]

By using the definition of inverse functions, we will see that:

g(g(f(f(f(36))))) = f(36) = 25.

<h3>What are inverse functions?</h3>

Two functions f(x) and g(x) are inverses if:

f( g(x) ) = x

g( f(x) ) = x

Then we can rewrite:

g(g(f(f(f(36)))))

First, we can see that:

g(f(f(f(36)))) = f(f(36))

Replacing that in our expression, we get:

g(g(f(f(f36))))) = g(f(f(36)))

And the above expression is equal to f(36), to be sure of that, let's replace:

u = f(36)

Then we can rewrite:

g(f(f(36))) = g(f(u))

And by definition, the above thing is equal to u:

g(f(u)) = u = f(36).

Finally, we conclude that:

g(g(f(f(f(36))))) = f(36) = 3*√36 + 7 = 3*6 + 7 = 25

If you want to learn more about inverse functions, you can read:

brainly.com/question/12220962

4 0

2 years ago

Find the directional derivative of the function at the given point in the direction of the vector v. h(r, s, t) = ln(3r + 6s + 9

vodka [1.7K]

Answer:

$D_\overrightarrow{\rm v}$ $h(r,s,t)=(\frac{2}{7}\overrightarrow{\rm i})*(\frac{1}{r+2s+3t})+(\frac{6}{7}\overrightarrow{\rm j})*(\frac{2}{r+2s+3t})+(\frac{3}{7}\overrightarrow{\rm k})*(\frac{3}{r+2s+3t})$

Step-by-step explanation:

First, let’s check to see if the direction vector is a unit vector:

$||v||=\sqrt{(14)^{2} +(42)^{2} +(21)^{2} } =\sqrt{2401} =49$

It’s not a unit vector. therefore let's divide the vector by its magnitude in order to convert it into a unit vector:

$\overrightarrow{\rm v}=(\frac{14}{49}\overrightarrow{\rm i})+(\frac{42}{49}\overrightarrow{\rm j})+(\frac{21}{49}\overrightarrow{\rm k})= (\frac{2}{7}\overrightarrow{\rm i})+(\frac{6}{7}\overrightarrow{\rm j})+(\frac{3}{7}\overrightarrow{\rm k})$

Now, the directional derivative is given by:

$D_\overrightarrow{\rm v}$ $h(r,s,t)=\frac{\partial h(r,s,t)}{\partial r}\overrightarrow{\rm i} + \frac{\partial h(r,s,t)}{\partial s}\overrightarrow{\rm j} + \frac{\partial h(r,s,t)}{\partial t}\overrightarrow{\rm k}$

So let's calculate the partial derivates:

$\frac{\partial }{\partial r} ln(3r+6s+9t)=\frac{3}{3r+6s+9t}=\frac{1}{r+2s+3t}$

$\frac{\partial }{\partial s} ln(3r+6s+9t)=\frac{6}{3r+6s+9t}=\frac{2}{r+2s+3t}$

$\frac{\partial }{\partial t} ln(3r+6s+9t)=\frac{9}{3r+6s+9t}=\frac{3}{r+2s+3t}$

Therefore:

$D_\overrightarrow{\rm v}$ $h(r,s,t)=(\frac{2}{7}\overrightarrow{\rm i})*(\frac{1}{r+2s+3t})+(\frac{6}{7}\overrightarrow{\rm j})*(\frac{2}{r+2s+3t})+(\frac{3}{7}\overrightarrow{\rm k})*(\frac{3}{r+2s+3t})$

3 0

4 years ago