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3 years ago

What are three collinear points on line l?

Mathematics

1 answer:

PtichkaEL [24]3 years ago

8 0

Answer:

Points A, F, and G are three collinear points on line l.

Step-by-step explanation:

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A sheet of paper 90 cm-by-66 cm is made into an open box (i.e. there's no top), by cutting x-cm squares out of each corner and f

NNADVOKAT [17]

Answer:

$26 - \sqrt{181}$ cm

Step-by-step explanation:

The volume of the box is:

V = height * length * width

V = x*(66 - 2*x)*(90 - 2*x)

V = (66*x - 2*x^2)*(90 - 2*x)

V = 5940*x - 132*x^2 - 180*x^2 + 4*x^3

V = 4*x^3 - 312*x^2 + 5940*x

where x is the length of the sides of the squares, in cm.

The mathematical problem is :

Maximize: V = 4*x^3 - 312*x^2 + 5940*x

subject to:

x > 0

2*x < 66 <=> x < 33

In the maximum, the first derivative of V, dV/dx, is equal to zero

dV/dx = 12*x^2 - 624*x + 5940

From quadratic formula

$x = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)}$

$x = \frac{624 \pm \sqrt{(-624)^2 - 4(12)(5940)}}{2(12)}$

$x = \frac{624 \pm \sqrt{104256}}{24}$

$x = \frac{624 \pm \sqrt{2^6*3^2*181}}{24}$

$x = \frac{624 \pm 8*3*\sqrt{181}}{24}$

$x_1 = \frac{624 + 24*\sqrt{181}}{24}$

$x_1 = 26 + \sqrt{181}$

$x_2 = \frac{624 - 24*\sqrt{181}}{24}$

$x_2 = 26 - \sqrt{181}$

But $x_1 > 33$ , then is not the correct answer.

5 0

3 years ago

I don't understand this question

kotegsom [21]

Answer: The correct answer is the third choice.

Step-by-step explanation: The question is asking you to look at pieces of data from the graph. The best way to do this question is to look at each question to determine whether the statement is true or false.

In looking at the each choice:

First one - The statement is true. Looking at the graph, a 40 and 50 year old person has the same average rate.

Second - The statement is true. Looking at the graph, you can see a steady decline from a 10 year old to a 20 year old person.

Third - The statement is false. A 10 year old and 20 year old do not have the same rate.

Fourth - The statement is true. A 20 and 30 year old have the same heart rate.

6 0

3 years ago

Find the missing sides.

love history [14]

Answer:

Part 3)

$x=6\ units$

$y=3\ units$

Part 4) $x=18\sqrt{2}\ units$

Step-by-step explanation:

Part 3)

step 1

Find the value of x

In the right triangle of the figure we know that

The cosine of angle of 30 degrees is equal to the adjacent side to angle of 30 degrees divide by the hypotenuse

$cos(30\°)=\frac{3\sqrt{3}}{x}$

and remember that

$cos(30\°)=\frac{\sqrt{3}}{2}$

substitute

$\frac{\sqrt{3}}{2}=\frac{3\sqrt{3}}{x}$

Simplify

$x=(2*3)=6\ units$

step 2

Find the value of y

In the right triangle of the figure we know that

The sine of angle of 30 degrees is equal to the opposite side to angle of 30 degrees divide by the hypotenuse

$sin(30\°)=\frac{y}{x}$

and remember that

$sin(30\°)=\frac{1}{2}$

substitute

$\frac{1}{2}=\frac{y}{6}$

$y=6/2=3\ units$

Part 4) Find the value of x

Applying the Pythagoras Theorem

$x^{2} =18^{2} +18^{2} \\ \\x^{2} = 324+324\\ \\x^{2}=648\\ \\x=\sqrt{648}\ units$

Simplify

$x=18\sqrt{2}\ units$

6 0

3 years ago

Aliun [14]

The answer:

according to the image, the main theorem concerning right triangle similarity is as follow:
the altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and each other,

in our case, KL is the altitude, and by applying theorem, we get three triangles that are similar:
therefore:
△JKL ~ △JKM
△JKM ~ △JKM
△JMK ~ △KML

5 0

3 years ago

Read 2 more answers

What is the solution for 13.2 = t 4.4? I'm super like spazzed out right now and can't think.

Olegator [25]

Answer:

4.4 t = 13.2

t = 13.2 / 4.4 = 3

t = 3

Step-by-step explanation:

5 0

3 years ago