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3 years ago

How do we change from radians to degrees?

Mathematics

1 answer:

posledela3 years ago

4 0

Answer:

To convert radians to degrees, the key is knowing that 180 degrees is equal to pi radians. Then multiply the measurement in radians by 180 divided by pi

Step-by-step explanation:

For example, pi over 3 radians would be equal to 60 degrees.

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the height h(t) of a trianle is increasing at 2.5 cm/min, while it's area A(t) is also increasing at 4.7 cm2/min. at what rate i

nekit [7.7K]

Answer:

The base of the triangle decreases at a rate of 2.262 centimeters per minute.

Step-by-step explanation:

From Geometry we understand that area of triangle is determined by the following expression:

$A = \frac{1}{2}\cdot b\cdot h$ (Eq. 1)

Where:

$A$ - Area of the triangle, measured in square centimeters.

$b$ - Base of the triangle, measured in centimeters.

$h$ - Height of the triangle, measured in centimeters.

By Differential Calculus we deduce an expression for the rate of change of the area in time:

$\frac{dA}{dt} = \frac{1}{2}\cdot \frac{db}{dt}\cdot h + \frac{1}{2}\cdot b \cdot \frac{dh}{dt}$ (Eq. 2)

Where:

$\frac{dA}{dt}$ - Rate of change of area in time, measured in square centimeters per minute.

$\frac{db}{dt}$ - Rate of change of base in time, measured in centimeters per minute.

$\frac{dh}{dt}$ - Rate of change of height in time, measured in centimeters per minute.

Now we clear the rate of change of base in time within (Eq, 2):

$\frac{1}{2}\cdot\frac{db}{dt}\cdot h = \frac{dA}{dt}-\frac{1}{2}\cdot b\cdot \frac{dh}{dt}$

$\frac{db}{dt} = \frac{2}{h}\cdot \frac{dA}{dt} -\frac{b}{h}\cdot \frac{dh}{dt}$ (Eq. 3)

The base of the triangle can be found clearing respective variable within (Eq. 1):

$b = \frac{2\cdot A}{h}$

If we know that $A = 130\,cm^{2}$ , $h = 15\,cm$ , $\frac{dh}{dt} = 2.5\,\frac{cm}{min}$ and $\frac{dA}{dt} = 4.7\,\frac{cm^{2}}{min}$ , the rate of change of the base of the triangle in time is:

$b = \frac{2\cdot (130\,cm^{2})}{15\,cm}$

$b = 17.333\,cm$

$\frac{db}{dt} = \left(\frac{2}{15\,cm}\right)\cdot \left(4.7\,\frac{cm^{2}}{min} \right) -\left(\frac{17.333\,cm}{15\,cm} \right)\cdot \left(2.5\,\frac{cm}{min} \right)$

$\frac{db}{dt} = -2.262\,\frac{cm}{min}$

The base of the triangle decreases at a rate of 2.262 centimeters per minute.

6 0

2 years ago

A car travels 322 miles on 11.5 gallons of gas. What is the cars miles per gallon

kolbaska11 [484]

28 miles per gallon. To find miles per gallon you do miles divided by gallons which in this case is 322/11.5=28.

If you need any more help feel free to message me.

6 0

3 years ago

Researchers have discovered a new genetic marker for a form of cancer. Twelve percent of the overall population carry this marke

In-s [12.5K]

Answer:

The probability that a person with the marker develops cancer is 0.0725.

Step-by-step explanation:

Let's denote the events as follows:

A = a person has cancer

B = a person carries the marker.

Given:

P (A) = 0.03

P (B) = 0.12

P (B|A) = 0.29

The conditional probability of an event X provided that another event Y has already occurred is:

$P(X|Y)=\frac{P(Y|X)P(X)}{P(Y)}$

Use the conditional probability formula to compute the probability that a person with the marker develops cancer.

$P(A|B)=\frac{P(B|A)P(A)}{P(B)} =\frac{0.29\times0.03}{0.12}=0.0725$

Thus, the probability that a person with the marker develops cancer is 0.0725.

3 0

3 years ago

A standard deck of playing cards has 52 cards: 13 spades, 13 clubs, 13 hearts, and 13 diamonds. What is the probability of drawi

Vaselesa [24]

13 spades, 52 cards total

probability of drawing a single spade = 13/52 = 1/4

If we replace that card, then the probability of drawing of drawing a spade is still 1/4 as nothing has changed

Overall, the probability of getting two spades in a row is (1/4)*(1/4) = 1/16

note: the two events are independent because of the replacement happening

---------

The answer as a fraction is 1/16

As a decimal, that would be 0.0625 which converts to 6.25%

5 0

3 years ago

as part of a grand opening an arcade gave out free tokens to the first 100 customers the graph shows the number of tokens custom

Anna [14]

Customers get 5 tokens per 1.00 time's
100 customers equal 500 tokens.
tokens equal 25 cents
5 tokens per dollar
25 cents times 100 equal 25.00
the arcade gave out 125.00 total.

6 0

3 years ago