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3 years ago

A skatepark charges $10 per person for an all-day admission to the park.

Mathematics

1 answer:

nirvana33 [79]3 years ago

7 0

Answer:

$60.00

Step-by-step explanation:

10n=y

so if 6 people are going then it will be 10×6=60

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Whoever says this sentence backward first will get brainlyest.

Blizzard [7]

Answer:

.tseylniarb teg lliw tsrif drawkcab ecnetnes siht syas reveohW

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3 years ago

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Abigail wrote the statements shown in the chart. . Statement. Description. . 1. If two lines intersect, then exactly one plane c

Lilit [14]

The correct answer is:

B) Statement 1 and Statement 2 are theorems because they can be proved with the help of appropriate postulates.

Explanation:

Statement 1 is the Line Intersection Theorem. To prove this, we use postulates about having only one plane passing through any 3 noncollinear points. We would choose two points from one line and one point from the second; they would be non-collinear points and be in one plane. This also works choosing the points the opposite way.

Statement 2 is the Point and Line Contained in Plane Theorem. Again, if two lines intersect, we can choose three points to define a plane. We have to prove that both lines are in the plane. We rely on previously proven postulates to do this.

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3 years ago

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Find all points on the curve x=4cos(t),y=4sin(t) that have the slope of 12.

Marianna [84]

Answer:

$\left (-\dfrac{4}{\sqrt{5}},\dfrac{8}{\sqrt{5}}\right )\text{ and }\left (\dfrac{4}{\sqrt{5}},-\dfrac{8}{\sqrt{5}}\right )$ .

Step-by-step explanation:

We need to find all the points on the curve x=4cos(t),y=4sin(t) that have the slope of 1/2.

$x=4cos (t)$

$\dfrac{dx}{dt}=-4sin (t)$

$y=4sin (t)$

$\dfrac{dy}{dt}=4cos (t)$

Now,

$\dfrac{dy}{dx}=\dfrac{dy}{dt}\times \dfrac{dt}{dx}$

$\dfrac{dy}{dx}=4cos (t)\times \dfrac{1}{-4sin (t)}$

$\dfrac{dy}{dx}=-\cot t$

So, slope of the curve is $-\cot t$ .

$-\cot t=\dfrac{1}{2}$

$-\tan t=2$

$\tan t=-2$ ...(1)

Using $\sec^2t=1+\tan^2t$ , we get

$\sec^2t=1+(-2)^2$

$\sec^2t=1+4$

$\sec t=\pm \sqrt{5}$

$\cos t=\pm \dfrac{1}{\sqrt{5}}$

Now,

$\sin^2t=1-cos^2t$

$\sin t=\pm \sqrt{1-\dfrac{1}{5}}$

$\sin t=\pm \sqrt{\dfrac{4}{5}}$

$\sin t=\pm \dfrac{2}{\sqrt{5}}$

It equation (1), tan(t) is negative. So, sin and cos have different signs.

If $\sin t= \dfrac{2}{\sqrt{5}}$ , then $\cos t=- \dfrac{1}{\sqrt{5}}$ .

$x=4cos (t)=-\dfrac{4}{\sqrt{5}}$

$y=4sin (t)=\dfrac{8}{\sqrt{5}}$

If $\sin t=- \dfrac{2}{\sqrt{5}}$ , then $\cos t= \dfrac{1}{\sqrt{5}}$ .

$x=4cos (t)=\dfrac{4}{\sqrt{5}}$

$y=4sin (t)=-\dfrac{8}{\sqrt{5}}$

Therefore, the two points are $\left (-\dfrac{4}{\sqrt{5}},\dfrac{8}{\sqrt{5}}\right )\text{ and }\left (\dfrac{4}{\sqrt{5}},-\dfrac{8}{\sqrt{5}}\right )$ .

5 0

3 years ago

Perform the operation and, if possible, simplify 21/20 - 4/15

Kazeer [188]

Answer:

47/60

Step-by-step explanation:

Find the LCM and multiply to get there.

LCM is 60

63/60-16/60

47/60

8 0

3 years ago

Solve the system of equations below 5x+2y=9 2×-3y=15

nirvana33 [79]

Answer:

The solution is (3, -3)

Step-by-step explanation:

5x + 2y = 9

2x - 3y = 15

Use elimination by addition/subtraction. Multiply the first equation by 3 and the second by 2, obtaining:

15x + 6y = 27

4x - 6y = 30

----------------------

19x = 57

This yields x = 3.

Substituting 3 for x into 5x + 2y = 9, we get 5(3) + 2y = 9, or

15 + 2y = 9, or

2y = -6

This yields y = -3.

The solution is (3, -3)

4 0

3 years ago