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Olegator [25]
3 years ago
8

If an angle of 96 degrees is rotated 90 degrees clockwise. what the measure?

Mathematics
1 answer:
Natali [406]3 years ago
3 0

Answer:

The measure is 6°.

Step-by-step explanation:

If an angle of 96 degrees is rotated 90 degrees clockwise then the measure of the new angle will be given by

= 96° - 90° = 6°

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The formula Upper A equals 23.1 e Superscript 0.0152 tA=23.1e0.0152t models the population of a US​ state, A, in​ millions, t ye
Wewaii [24]

Answer:

a) A(t=0)= 23.1 e^{0.0152(0)}=23.1e^0 =23.1

b) t = \frac{ln(\frac{28.3}{23.1})}{0.0152}=13.357 years

So for this case the answer would be 13.347 years, the population will be 28.3 million and ye year would be 2000+13.347 and that would be approximately in 2014

Step-by-step explanation:

For this case we assume the following model:

A(t)= 23.1 e^{0.0152 t}

Where t is the number of years after 2000/

Part a

For this case we want the population for 2000 and on this case the value of t=0 since we have 0 years after 2000. If we rpelace into the model we got:

A(t=0)= 23.1 e^{0.0152(0)}=23.1e^0 =23.1

So then the initial population at year 2000 is 23.1 million of people.

Part b

For this case we want to find the time t whn the population is 28.3 million.

So we need to solve this equation:

28.3= 23.1 e^{0.0152(t)}

We can divide both sides by 23.1 and we got:

\frac{28.3}{23.1}= e^{0.0152t}

Now we can apply natural log on both sides and we got:

ln(\frac{28.3}{23.1})= 0.0152 t

And then for t we got:

t = \frac{ln(\frac{28.3}{23.1})}{0.0152}=13.357 years

So for this case the answer would be 13.347 years, the population will be 28.3 million and ye year would be 2000+13.347 and that would be approximately in 2014

3 0
3 years ago
he price of oil recently went from ​$6.60 to ​$8.80 per case of 12 quarts. Find the ratio of the increase in price to the origin
Artist 52 [7]
It increased by $2.20, so the increase is 2.20. But out of ten dollars, it should be a 24% increase.
8 0
3 years ago
Find the absolute maximum and minimum values of f(x,y)=xy−4x in the region bounded by the x-axis and the parabola y=16−x2.
skad [1K]

Answer:

The absolute maximum and minimum is 20\; \text{and} -20.

Step-by-step explanation:

We first check the critical points on the interior of the domain using the

first derivative test.

f_x=y-4=0

f_y=x=0

The only solution to this system of equations is the point (0, 4), which lies in the domain.

f_{xx}=0, \;f_{yy}=0\; \text{and}\; f_{xy}=-1

\Rightarrow f_{xx}f_{yy}-f_{xy}=o-1=-1

\therefore (0,4) is a saddle point.

Boundary points -  (4,0),  (-4,0), (0,16)

Along boundary  y=16-x^2

   f=x(16-x^2)-4x

=16x-x^3-4x

\Rightarrow f^'=16-3x^2-4=0

\Rightarrow 3x^2=12

\Rightarrow x=\pm2,\;\;y=14

Values of f(x) at these points.

\begin{array}{}(4,0)=-16\\(-4,0)=16\\(0,16)=0\\(2,14)=20\\(-2,14)=-20\end{array}

Therefore, the absolute maximum and minimum is 20\; \text{and} -20.

6 0
3 years ago
Name the<br> alternate<br> interior angle<br> with angle 5.
const2013 [10]
<h3>Answer:  B) angle 4</h3>

==================================

Explanation:

We can think of lines L and M as sort of train tracks. Inside the train tracks we have the interior angles of: 3, 4, 5, 6

Angles 3 and 6 are one pair of alternate interior angles. They are on alternate sides of the transversal line N.

The other pair of alternate interior angles are 4 and 5

Alternate interior angles are only congruent when L and M are parallel.

5 0
3 years ago
Read 2 more answers
Simplify this expression 5a/11a
barxatty [35]
You could cross cancel the a and your final answer would be 5/11
6 0
3 years ago
Read 2 more answers
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