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2 years ago

Suppose that the height of the slide is 2 feet,

Mathematics

2 answers:

krok68 [10]2 years ago

8 0

Answer:

-3.9

Just got done with edge

Lena [83]2 years ago

5 0

$\bf \stackrel{\textit{average rate of change}}{slope = m\implies} \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{\stackrel{height}{2}}{\stackrel{width}{20}}\implies \cfrac{1}{10}$

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Two boats leave port at noon. Boat 1 sails due east at 12 knots. Boat 2 sails due south at 8 knots. At 2 pm the wind diminishes

Ivan

Answer:

14.86 knots.

Step-by-step explanation:

Given that:

The boats leave the port at noon.

Speed of boat 1 = 12 knots due east

Speed of boat 2 = 8 knots due south

At 2 pm:

Distance traveled by boat 1 = 24 units due east

Distance traveled by boat 2 = 16 units due south

Now, speed of boat 1 changes to 9 knots:

At 3 pm:

Distance traveled by boat 1 = 24 + 9= 33 units due east

Distance traveled by boat 2 = 16+8 = 24 units due south

Now, speed of boat 1 changes to 8+7 = 15 knots

At 5 pm:

Distance traveled by boat 1 = 33 + 2 $\times$ 9= 51 units due east

Distance traveled by boat 2 = 24 + 2 $\times$ 15 = 54 units due south

Now, the situation of distance traveled can be seen by the attached right angled $\triangle AOB$ .

O is the port and A is the location of boat 1

B is the location of boat 2.

Using pythagorean theorem:

$\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow AB^{2} = OA^{2} + OB^{2}\\\Rightarrow AB^{2} = 51^{2} + 54^{2}\\\Rightarrow AB^{2} = 2601+ 2916 = 5517\\\Rightarrow AB = 74.28\ units$

so, the total distance between the two boats is 74.28 units.

Change in distance per hour = $\dfrac{Total\ distance}{Total\ time}$

$\Rightarrow \dfrac{74.28}{5} = 14.86\ knots$

6 0

2 years ago

Solve the linear equation for x -4.8(6.3x-4.18) =-58.56 X=

lyudmila [28]

Answer:

x= 2.6

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

4 0

2 years ago

The base of a solid right pyramid is a regular hexagon with

cupoosta [38]

Answer: Last option.

Step-by-step explanation:

Observe the base of the pyramid, which is a regular hexagon. You can see that there is a right triangle.

The area of the triangle can be calculated with this formula:

$A_t=\frac{bh}{2}$

Where "b" is the base and "h" is the height.

You can say that the apothem is the height of the right triangle, then, you need to find the base applying the Pythagorean Theorem:

$(2x)^2=(x\sqrt{3})^2+b^2\\\\b=\sqrt{(2x)^2-(x\sqrt{3})^2} \\\\b=\sqrt{4x^2-3x^2}\\\\b=\sqrt{x^2}\\\\b=x$

Then, the area of the triangle is:

$A_t=\frac{x(x\sqrt{3})}{2}=\frac{x^2\sqrt{3})}{2}$

Since the base of the pyramid is a regular hexagon, then you can multiply by 12 the area of the right triangle calculated above, in order to find the area of the hexagon. Then you get:

$A_h=12(\frac{x^2\sqrt{3})}{2})=6x^2\sqrt{3}\ units^2$