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nadezda [96]
3 years ago
8

JL is a common tangent to circles M and K at point J. If angle MLK measures 61ᵒ, what is the length of radius MJ? Round to the n

earest hundredth. (Hint: Show that triangles LMJ and LKJ are right triangles, and then use right triangle trigonometry to solving for missing sides of the right triangles.)
Mathematics
1 answer:
Dvinal [7]3 years ago
3 0
In the problem of insufficient data quantities. I can get a general  solution.We know that tangent to a circle is perpendicular to the radius at the point of tangency. It's mean that triangles LJM and LJK are rights.

Let angle JLK like X.

So, angle JLM=61-x.

And it's mean that by using right triangle trigonometry 

Radius MJ = LM*cos(61-X)
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CAN SOMEONE PLEASE ANSWER THISS ASAP PLEASE
solong [7]

Answer:

Step-by-step explanation:

11.04 = 10(1.02)^n

1.104 = 1.02^n

ln 1.104 = ln 1.02^n

ln 1.104 = n ln 1.02

n = ln 1.104/ ln 1.02

n = 4.99630409516

4.99 can be rounded to 5.

So a reasonable domain would be 0 ≤ x < 5

PART B)

f(0) = 10(1.02)^0

f(0) = 10(1)

f(0) = 10

The y-intercept represents the height of the plant when they began the experiment.

f(1) = 10(1.02)^1

f(1) = 10(1.02)

f(1) = 10.2

(1, 10.2)

f(5) = 10(1.02)^5

f(5) = 10(1.1040808)

f(5) = 11.040808

f(1)=10(1.02)^1

f(1)=10.2

Average rate= (fn2-fn1)/(n2-n1)

                     =11.04-10.2/(5-1)

                    =0.22

the average rate of change of the function f(n) from n = 1 to n = 5 is 0.22.  

8 0
2 years ago
A 26' long painting is how many yards long
yaroslaw [1]
Three feet is 1 yard. 26 feet would be 26/3=8 2/3 yards long.
6 0
3 years ago
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valentinak56 [21]
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4 0
3 years ago
A pet store sells mice reptiles and birds
Vera_Pavlovna [14]

Answer:

P(A or B) represents the probability that a customer will buy either a mouse or a reptile at the pet store.  So, there is a 20%, or 1 out 5 chance that a customer will buy either one when they come in to purchase a pet.

Step-by-step explanation:

Probability represents the fraction of the desired number of outcomes over the total number of outcomes.  In the case of the pet store, their total outcomes can be the purchase of a mouse, reptile or bird.  We don't know how much of each animal they have, however, they tell us that the probability that a customer will buy either a mouse OR a reptile is 0.20.  This means that the probability of buying a mouse and the probability of buying a reptile are added together to equal 0.20 or 20% which is also 1/5.  

7 0
3 years ago
Read 2 more answers
50 points! I understand A. and B. but I would really appreciate help with C.
FromTheMoon [43]

Answer:

51.72\text{ cells per hour}

Step-by-step explanation:

So, the function, P(t), represents the number of cells after t hours.

This means that the derivative, P'(t), represents the instantaneous rate of change (in cells per hour) at a certain point t.

C)

So, we are given that the quadratic curve of the trend is the function:

P(t)=6.10t^2-9.28t+16.43

To find the <em>instanteous</em> rate of growth at t=5 hours, we must first differentiate the function. So, differentiate with respect to t:

\frac{d}{dt}[P(t)]=\frac{d}{dt}[6.10t^2-9.28t+16.43]

Expand:

P'(t)=\frac{d}{dt}[6.10t^2]+\frac{d}{dt}[-9.28t]+\frac{d}{dt}[16.43]

Move the constant to the front using the constant multiple rule. The derivative of a constant is 0. So:

P'(t)=6.10\frac{d}{dt}[t^2]-9.28\frac{d}{dt}[t]

Differentiate. Use the power rule:

P'(t)=6.10(2t)-9.28(1)

Simplify:

P'(t)=12.20t-9.28

So, to find the instantaneous rate of growth at t=5, substitute 5 into our differentiated function:

P'(5)=12.20(5)-9.28

Multiply:

P'(5)=61-9.28

Subtract:

P'(5)=51.72

This tells us that at <em>exactly</em> t=5, the rate of growth is 51.72 cells per hour.

And we're done!

7 0
3 years ago
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