Two adjacent angles form a right angle. The larger angle is 3 times the measure of the smaller angle. Which is the measure of the larger angle?This means the angles are in a ratio of 1:3.

A. 67.5°
B. 30°
C. 22.5°
D. 45°

Answers

Answer 1
Answer: The angles is B: 30 degrees
Answer 2
Answer:

Answer:

B. 30

Step-by-step explanation:


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Can you help me please

Answers

I believe the correct answer is 18
the answer to your problem is 5 ☺️

Consider the parabola r​(t)equalsleft angle at squared plus 1 comma t right angle​, for minusinfinityless thantless thaninfinity​, where a is a positive real number. Find all points on the parabola at which r and bold r prime are orthogonal.

Answers

Given:-   r(t)=< at^2+1,t>  ; -\infty < t< \infty , where a is any positive real number.

Consider the helix parabolic equation :  

                                              r(t)=< at^2+1,t>

now, take the derivatives we get;

                                            r{}'(t)=<2at,1>

As, we know that two vectors are orthogonal if their dot product is zero.

Here,  r(t) and r{}'(t)  are orthogonal i.e,   r\cdot r{}'=0

Therefore, we have ,

                                  < at^2+1,t>\cdot < 2at,1>=0

< at^2+1,t>\cdot < 2at,1>=<at^2+1\cdot\left(2at\right), t\cdot \left(1)>

                                              =2a^2t^3+2at+t

2a^2t^3+2at+t=0

take t common in above equation we get,

t\cdot \left (2a^2t^2+2a+1\right )=0

t=0 or 2a^2t^2+2a+1=0

To find the solution for t;

take 2a^2t^2+2a+1=0

The numberD = b^2 -4ac determined from the coefficients of the equation ax^2 + bx + c = 0.

The determinant D=0-4(2a^2)(2a+1)=-8a^2\cdot(2a+1)

Since, for any positive value of a determinant is negative.

Therefore, there is no solution.

The only solution, we have t=0.

Hence, we have only one points on the parabola  r(t)=< at^2+1,t> i.e <1,0>




                                               




You are hiking up a mountain peak. You begin hiking at a trailhead whose elevation is about 9400 feet. The trail ends near the summit at 14,255 feet. The horizontal distance between these two points is about 17,625 feet. Estimate the angle of elevation from the trailhead to the summit.

Answers

Answer:

Estimate angle of elevation = 15.4°

Step-by-step explanation:

Given:

Start elevation = 9,400 ft

Ends near the summit = 14,255 ft

horizontal distance = 17,625 ft

Find:

Estimate angle of elevation.

Computation:

⇒ Total elevation distance = Ends near the summit - Start elevation

⇒ Total elevation distance = 14,255 - 9,400

⇒ Total elevation distance = 4,855 ft

⇒ Tan A = 4,855 / 17,625

⇒ Tan A = 0.2754

⇒ Tan A = 15.4°

Estimate angle of elevation = 15.4°

the volume of a 15oz cereal box is 180.4in cube. the length of the box is 3.2 in. less than the height and the width is 2.3 in. find the height and length of the box to the nearest tenth.

Answers

The height and length of the box to the nearest tenth will be 10.6 inch and 7.4 inch respectively.

Explanation

Suppose, the height of the box is h inch

As the length of the box is 3.2 in. less than the height, so the length will be: (h-3.2) inch

Given that, the width of the box is 2.3 inch. and the volume is 180.4 inch³

Formula for Volume of a box:  V= length*width*height

So, the equation will be....

(h-3.2)*2.3*h = 180.4\n \n 2.3h^2 -7.36h=180.4\n \n 2.3h^2-7.36h-180.4=0

Now using quadratic formula......

h=(-b+/-√(b^2-4ac))/(2a)\n \n h= (-(-7.36)+/-√((-7.36)^2-4(2.3)(-180.4)))/(2(2.3))\n \n h= (7.36+/-√(1713.8496))/(4.6) \n \n h=(7.36+/-41.398...)/(4.6) \n \n h= 10.599... or -7.399...

(Negative value of h is ignored as the height can't be negative)

So, the height to the nearest tenth will be 10.6 inch and the length will be: (10.6-3.2)inch= 7.4 inch

The fraction 24/28 In simplest form is____.
12/14
48/56
6/9
6/7

Answers

Answer:

6/7

Step-by-step explanation:

Answer:

6/7

Step-by-step explanation:

divide it by 4

One urn contains 8 blue balls and 12 white balls, and a second urn contains 14 blue balls and 5 white balls. An urn is selected at random, and a ball is chosen from the urn. (Round your answers to one decimal place.) (a) What is the probability (as a %) that the chosen ball is blue? (b) If the chosen ball is blue, what is the probability (as a %) that it came from the first urn? Need Help? Read It Talk to a Tutor

Answers

Answer:

a) The probability that the chosen ball is blue is 56.84%

b) If the chosen ball is blue, there is a 35.19 probability that it came from the first urn.

Step-by-step explanation:

a) What is the probability (as a %) that the chosen ball is blue?

First the urn is chosen, then the ball. There can be a blue ball from urn 1 and from urn 2.

-The probability of a blue ball being chosen from urn 1 is:

40%(8 blue balls among 20 in urn 1, 8 of 20 is 40%) of 50%(the chance of urn 1 being chosen is 50%)

So P_(1) = 0.4*0.5 = 0.20

-The probability of a blue ball being chosen from urn 2 is:

73.68%(14 blue balls among 20 in urn 2, 14 of 19 is 73.68%) of 50%(the chance of urn 2 being chosen is 50%)

So P_(2) = 0.7368*0.5 = 0.3684

The probability that the chosen ball is blue is P = P_(1) + P_(2) = 0.20 + 0.3684 = 0.5684 = 56.84%.

b) If the chosen ball is blue, what is the probability (as a %) that it came from the first urn?

This item can be formulated as the following problem:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

P(B/A) = (P(B).P(A/B))/(P(A))

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

In this item, A(what has happened) is the ball being blue. In item a), we found that P(A) = 0.5684.

B is the blue ball coming from the first urn. P(B), the probability of the first urn being chosen, is 50% = 0.5.

P(A/B), the probability of the blue ball being chosen from the first urn is 40% = 0.4.

So:

P(B/A) = (0.5*0.4)/(0.5684) = 0.3519 = 35.19%

If the chosen ball is blue, there is a 35.19 probability that it came from the first urn.