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rodikova [14]
3 years ago
5

How to find the measure of an exterior angle?

Mathematics
1 answer:
MariettaO [177]3 years ago
4 0
180 -internal angel good luck
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Yuki walked for 1 3/4 hours at 4 miles per hour. how far did she walk?
Rzqust [24]
She walked 7 miles. If it takes her one hour to walk four miles, then it will take 45 minutes to walk 3 miles.
8 0
3 years ago
Read 2 more answers
Reservation fee of 47.00 and additional fee of 7.40 per hour. Spend less than 91.40. Possible about if time for room
KIM [24]

Answer:

The room can be rented for 6 hours with $91.4

Step-by-step explanation:

If my guess was correct, there was a reservation fee of $47, and there was another fee of $7.4 per hour and the question is asking for how many hours can be rented with $91.4 and the variable t to represent the time.

First, $91.4-$47 as that is the reservation fee. $91.4-$47 = $44.4

Next, we figure out how many hours can we rent with $44.4. Since one hour of rental costs $7.4, t = 44.4/7.4

Finally, we just divide. This is a relatively simple question when thinking about how straightforward this is.

44.4/7.4 = 6

Recheck:

7.4*6 = 44.4

t = 6

5 0
2 years ago
Please help me with these I’ve been stuck and don’t know what to do
Olenka [21]
First, x intercepts are (-1,0) and (-3,0). y intercept is(0,2)

second, left side is a function because there are no x-values paired with two different y-values. right side is not a function because the x-value 3 is paired with two different y-values values

third, slope is ride over run, or the difference in y values divided by difference in x values. slope is 1/2. intercept is at (0,2). the equation is then y=1/2*x + 2
3 0
3 years ago
Let f be the function defined by f(x) = e^(x) cos x.
Pavel [41]
(a)

The average rate of change of f on the interval 0 ≤ x ≤ π is

   \displaystyle
f_{avg\Delta} = \frac{f(\pi) - f(0)}{\pi - 0} =\frac{-e^\pi-1}{\pi}

____________

(b)

f(x) = e^{x} cos x \implies f'(x) = e^x \cos(x) - e^x \sin(x) \implies \\ \\
f'\left(\frac{3\pi}{2} \right) = e^{3\pi/2} \cos(3\pi/2) - e^{3\pi/2} \sin(3\pi/2) \\ \\
f'\left(\frac{3\pi}{2} \right) = 0 - e^{3\pi/2} (-1) = e^{3\pi/2}

The slope of the tangent line is e^{3\pi/2}.

____________

(c)

The absolute minimum value of f occurs at a critical point where f'(x) = 0 or at endpoints.

Solving f'(x) = 0

f'(x) = e^x \cos(x) - e^x \sin(x) \\ \\
0 = e^x \big( \cos(x) - \sin(x)\big)

Use zero factor property to solve.

e^x \ \textgreater \  0\forall x \in \mathbb{R} so that factor will not generate solutions.
Set cos(x) - sin(x) = 0

\cos (x) - \sin (x) = 0 \\
\cos(x) = \sin(x)

cos(x) = 0 when x = π/2, 3π/2, but x = π/2. 3π/2 are not solutions to the equation. Therefore, we are justified in dividing both sides by cos(x) to make tan(x):

\displaystyle\cos(x) = \sin(x) \implies 0 = \frac{\sin (x)}{\cos(x)} \implies 0 = \tan(x) \implies \\ \\
x = \pi/4,\ 5\pi/4\ \forall\ x \in [0, 2\pi]

We check the values of f at the end points and these two critical numbers.

f(0) = e^1 \cos(0) = 1

\displaystyle f(\pi/4) = e^{\pi/4} \cos(\pi/4) = e^{\pi/4}  \frac{\sqrt{2}}{2}

\displaystyle f(5\pi/4) = e^{5\pi/4} \cos(5\pi/4) = e^{5\pi/4}  \frac{-\sqrt{2}}{2} = -e^{\pi/4}  \frac{\sqrt{2}}{2}

f(2\pi) = e^{2\pi} \cos(2\pi) = e^{2\pi}

There is only one negative number.
The absolute minimum value of f <span>on the interval 0 ≤ x ≤ 2π is
-e^{5\pi/4} \sqrt{2}/2

____________

(d)

The function f is a continuous function as it is a product of two continuous functions. Therefore, \lim_{x \to \pi/2} f(x) = f(\pi/2) = e^{\pi/2} \cos(\pi/2) = 0

g is a differentiable function; therefore, it is a continuous function, which tells us \lim_{x \to \pi/2} g(x) = g(\pi/2) = 0.

When we observe the limit  \displaystyle \lim_{x \to \pi/2} \frac{f(x)}{g(x)}, the numerator and denominator both approach zero. Thus we use L'Hospital's rule to evaluate the limit.

\displaystyle\lim_{x \to \pi/2} \frac{f(x)}{g(x)} = \lim_{x \to \pi/2} \frac{f'(x)}{g'(x)} = \frac{f'(\pi/2)}{g'(\pi/2)}

f'(\pi/2) = e^{\pi/2} \big( \cos(\pi/2) - \sin(\pi/2)\big) = -e^{\pi/2} \\ \\&#10;g'(\pi/2) = 2

thus

\displaystyle\lim_{x \to \pi/2} \frac{f(x)}{g(x)} = \frac{-e^{\pi/2}}{2}</span>

3 0
3 years ago
Are some integers whole numbers?
horrorfan [7]
Yes,  all whole numbers are integers, no matter negative or positive.
6 0
3 years ago
Read 2 more answers
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