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2 years ago

Use the circle to solve for the missing measures. Assume lines that appear tangent are tangent. Do NOT round any answers.

Mathematics

1 answer:

wlad13 [49]2 years ago

4 0

The given circle having two external tangents, according to circle

theorem, have the following values;

r = 3

m∠1 = 82°

m∠2 = 49°

x = 82°

<h3>How can the radial length and angles be found?</h3>

r² + 1.6² = (0.4 + r)²

(0.4 + r)² - (r² + 1.6²) = 0

0.8·r - 2.4 = 0

0.8·r = 2.4

r = 2.4 ÷ 0.8 = 3

r = 3

y = 49°

From the two tangent angle theorem, we have;

m∠1 = ((82 + 98 + 82) - (360 - ((82 + 98 + 82)))) ÷ 2 = 82

m∠1 = 82°

According to circle theorems, angle at the center is twice angle

subtended at the circumference.

m∠2 = (360 - (82 + 98 + 82)) ÷ 2 = 49°

m∠2 = 49°

The length of the chord subtended by the arc x is equal to the length of

the chord subtended by 89°, which gives;

x = 82°

Learn more about circle theorems applications here:

brainly.com/question/16879446

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For each of these relations on the set {21, 22, 23, 24}, decide whether it is reflexive, whether it is symmetric, whether it is

bonufazy [111]

Answer:

Step-by-step explanation:

I. { (22,22) , (22,23) , (22,24) , (23,22) , (23,23) , (23,24) }

Reflexive : True because we see the pairs (22,22) , (23,23)..

Symmetrix : NO, as we see the pairs (22,24) BUT NOT (24,22)

Transitive : YES, As we see (22,22 ) and (22, 24) , we see the pairs (22,24)

Antisymmetric : NO

II){ (21,21) , (21,22) , (22,21) , (22,22) , (23,23) , (24,24) }

Reflexive : True because we see the pairs (22,22) , (23,23) (21,21)

Symmetrix : Yes, as we see the pairs (21,22) AND (22,21)

Transitive : YES,

Antisymmetric : NO

7 0

3 years ago

Read 2 more answers

Find the second derivative y= x^2lnx

Dimas [21]

First we use product rule
y=x^2lnx
dy/dx = x^2 d/dx (lnx) + lnx d/dx (x^2)
dy/dx = x^2 (1/x) + lnx (2x)
dy/dx = x + 2xlnx

now taking second derivative:
d2y/dx2 = 1 + 2[x (1/x) + lnx (1)]
d2y/dx2 = 1 + 2[1+lnx]
1+2+2lnx
3+2lnx is the answer

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3 years ago

A can of soda is placed inside a cooler. As the soda cools, its temperature T(x) in degrees Celsius is given by the following ex

Lana71 [14]

Answer:

Ans: -21.87 ≅ -22°C

Step-by-step explanation:

T(x)=-22+44e^-0.03x

Initial temperature (x = 0):

T(0) = = -22 + 44e-0.03(0) = -22 + 44(1) = 22°C

After 18 minutes (x = 18):

T(18) = -22 + 44e-0.03(18) = -21.87°C ≅ -22°C

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2 years ago

Please help me with this geometry problem. :)

Reika [66]

Answer:

See below

Step-by-step explanation:

3 are congruent, 4 are supplementary

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6 0

3 years ago

write the given equation into vertex form and sketch the graph. Determine the domain and range f(x)=3x^2-6+2 plss help

LuckyWell [14K]

Answer: the range would thus be [-3, 1/3].)

Step-by-step explanation:

1. To sketch the function f(x) = (2/3)x - 3, we first need to find two points that we can later join to sketch the line, for example the x- and y-intercepts.

a) The x-intercept occurs when f(x) = 0, so if f(x) = 0, then:

f(x) = (2/3)x - 3

0 = (2/3)x - 3

3 = (2/3)x (Add three to both sides)

3*(3/2) = x (Multiply both sides by 3/2)

9/2 = x

We have now found the x-intercept at (9/2, 0)

b) The y-intercept occurs when x = 0, so:

f(x) = (2/3)x - 3

f(0) = (2/3)*0 - 3

f(0) = -3

Now we know that the y-intercept is at (0, -3)

c) All that's left is to sketch the graph axes and label them, plot the two points, join them together using a ruler and label their coordinates.

2. The Domain is the range of x-values for which the function exists, and the Range is the range of y-values for which the function exists.

Since there haven't been any constraints specified, we can say that both the Domain and Range are (-∞, ∞), since the graph continues forever both along the x- and y-axis.

(Note that this isn't always the case and would change if, for example, the question stipulated that there was a domain of [0, 5] and you had to find the range. Then, you would calculate the value of y at each end of the domain (if x = 0, y = -3 and if x = 5, y = 1/3) - in my example, the range would thus be [-3, 1/3].)

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3 years ago