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3 years ago

Is the following relation a function ?

Mathematics

2 answers:

Dafna11 [192]3 years ago

6 0

No, it is not a function. It fails the vertical line test (VLT). VLT state that if you draw a vertical line, it must only intersect the graph one time. If it intersections more than once, then it is not a function.

Hoochie [10]3 years ago

5 0

No because it fails the vertical line test. Note that a vertical line can be drawn through the graph which passes through 2 points. If it was a function any vertical line would pass through only one point on the graph.

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Among all right triangles whose hypotenuse has a length of 12 cm, what is the largest possible perimeter?

Veronika [31]

Answer:

Largest perimeter of the triangle =

$P(6\sqrt{2}) = 6\sqrt{2} + \sqrt{144-72} + 12 = 12\sqrt{2} + 12 = 12(\sqrt2 + 1)$

Step-by-step explanation:

We are given the following information in the question:

Right triangles whose hypotenuse has a length of 12 cm.

Let x and y be the other two sides of the triangle.

Then, by Pythagoras theorem:

$x^2 + y^2 = (12)^2 = 144\\y^2 = 144-x^2\\y = \sqrt{144-x^2}$

Perimeter of Triangle = Side 1 + Side 2 + Hypotenuse.

$P(x) = x + \sqrt{144-x^2} + 12$

where P(x) is a function of the perimeter of the triangle.

First, we differentiate P(x) with respect to x, to get,

$\frac{d(P(x))}{dx} = \frac{d(x + \sqrt{144-x^2} + 12)}{dx} = 1-\displaystyle\frac{x}{\sqrt{144-x^2}}$

Equating the first derivative to zero, we get,

$\frac{dP(x))}{dx} = 0\\\\1-\displaystyle\frac{x}{\sqrt{144-x^2}} = 0$

Solving, we get,

$1-\displaystyle\frac{x}{\sqrt{144-x^2}} = 0\\\\x = \sqrt{144-x^2}}\\\\x^2 = 144-x^2\\\\x = \sqrt{72} = 6\sqrt{2}$

Again differentiation P(x), with respect to x, using the quotient rule of differentiation.

$\frac{d^2(P(x))}{dx^2} = \displaystyle\frac{-(144-x^2)^{\frac{3}{2}}-x^2}{(144-x)^{\frac{3}{2}}}$

At x = $6\sqrt{2}$ ,

$\frac{d^2(V(x))}{dx^2} < 0$

Then, by double derivative test, the maxima occurs at x = $6\sqrt{2}$

Thus, maxima occurs at x = $6\sqrt{2}$ for P(x).

Thus, largest perimeter of the triangle =

$P(6\sqrt{2}) = 6\sqrt{2} + \sqrt{144-72} + 12 = 12\sqrt{2} + 12 = 12(\sqrt2 + 1)$

7 0

3 years ago

I would really appreciate help with the following, along with work shown so I can understand how these were solved.

Alja [10]

First, you have to know the double angle formula:

sin 2A = 2 sin A cos A

cos 2A = cos² A − sin² A = 2 cos² A − 1 = 1 − 2 sin² A

tan 2A = 2 tan A / (1 − tan² A)

Next, find the other leg: 17^2-15^=64, √64 is 8, so the unknown leg length is 8.

sinα=15/17, cosα=8/17, tanα=15/8

sinβ=8/17, cosβ15/17, tanβ=8/15

Plug these values in the above formula, you'll have your answers.

For the half angles, know the half-angle formula:

sin(B/2) = ± √(1 − cos B)/2

cos(B/2) = ± √(1 + cos B)/2

tan(B/2) = (1 − cos B) / sin B = sin B / (1 + cos B)

refer to this website for details:

https://brownmath.com/twt/double.htm

For the power reduction formula, please search for it. I tried to copy and paste here, but it wouldn't paste.

for number 4, factor the quadratic equation into (cscx-8)(cscx+1)=0

cscx=8 or cscx=-1

You may not have the csc button on your calculator. Recall that csc is 1/sin, so sinx=1/8 or sinx=-1, so x is either 7.18 or 270 degrees

6 0

3 years ago

A soccer team sold raffle tickets to raise money for the upcoming season. They sold three different types of tickets: premium fo

lesya692 [45]

Answer:

45 premium tickets were sold

Step-by-step explanation:

p = premium

d = deluxe

r = regular

p+d+r = 273

6p+4d + 2r = 836

118+d = r

Replace r with 118+d

p+d+118+d = 273

p +2d = 273-118

p+2d = 155

6p+4d + 2(118+d) = 836

6p+4d + 236+2d = 836

6p +6d = 836-236

6p + 6d = 600

Divide by 6

p+d = 100

d = 100-p

Replace d in p +2d= 155

p +2(100-p) = 155

p+200-2p = 155

-p = 155-200

-p =-45

p =45

45 premium tickets were sold

3 0

3 years ago

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For Anya's birthday her father gave out colorful birthday hats that were cone shaped. Anya was very happy that day. The opening

Darya [45]

Anya will have 5cm of candy sorry if it’s
Wrong

6 0

3 years ago

What is the value of c so that 9x^2 + 15x + c = 0 has one rational solution

valentinak56 [21]

Answer:

c=-9x^2-15x

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers