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3 years ago

A suitcase measures 24 inches long and -8 i aches high. What is the diagonal length of the suitcase? (Pythagorean Theorem)

Mathematics

1 answer:

BartSMP [9]3 years ago

7 0

Answer:

Diagonal Length = $8\sqrt{10}$ inches

Step-by-step explanation:

The suitcase is a rectangle with one side being 24 and another side being 8.

The diagonal is the line through the middle connecting two opposite corners.

If we draw the diagonal, it creates a triangle with one leg being 24 and another being 8.

The diagonal is the "hypotenuse" of the triangle.

Now, the pythagorean theorem:

leg^2 + another leg^2 = hypotenuse^2

So, we substitute the values known and find the hypotenuse (which is length of the diagonal). Shown below:

$24^2+8^2=h^2\\640=h^2\\h=\sqrt{640}\\h=\sqrt{64*10}\\h=\sqrt{64}\sqrt{10}\\h=8\sqrt{10}$

We have written the answer in exact form (with radical in simplified term).

We also use the radical property $\sqrt{a*b}=\sqrt{a}\sqrt{b}$

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The water from a fire hose follows a path described by y equals 2.0 plus 0.9 x minus 0.10 x squared (units are in meters). If

Alecsey [184]

Answer:

The resultant velocity is 12.21 m/s.

Step-by-step explanation:

We are given that the water from a fire hose follows a path described by y equals 2.0 plus 0.9 x minus 0.10 x squared (units are in meters).

Also, v Subscript x is constant at 10.0 m/s.

The water from a fire hose follows a path described by the following equation below;

$y=2.0 + 0.9x-0.10x^{2}$

The velocity of the $x$ component is constant at = $v_x=10.0 \text{ m/s}$

and the point at which resultant velocity has to be calculated is (9.0,2.0).

Let the velocity of x and y component be represented as;

$v_x=\frac{dx}{dt} \text{ and } v_y=\frac{dy}{dt}$

Now, differentiating the above equation with respect to t, we get;

$y=2.0 + 0.9x-0.10x^{2}$

$\frac{dy}{dt} =0 + 0.9\frac{dx}{dt} -(0.10\times 2)\frac{dx}{dt}$

$\frac{dy}{dt} = 0.9\frac{dx}{dt} -0.2\frac{dx}{dt}$

$v_y = 0.9v_x -0.2v_x$

$v_y = 0.7v_x$

Now, putting $v_x=10.0 \text{ m/s}$ in the above equation;

$v_y = 0.7 \times 10.0$ = 7 m/s

Now, the resultant velocity is given by = $v=\sqrt{v_x^{2}+v_y^{2} }$

$v=\sqrt{10^{2}+7^{2} }$

= $\sqrt{149}$ = 12.21 m/s

5 0

3 years ago

George is twice as old as Edward, and Edward’s age exceeds Robert’s age by 4 years. If the sum of the three ages is at least 56

vova2212 [387]

Answer:

Step-by-step explanation:

if george is 30 than edward would be 15 as he is twice younger than george

and robert would be 11 as he is 4 year younger than edward.

4 0

3 years ago

Why 13/4hr and 4hr are equal ?

zmey [24]

Answer:

they are not equal

Step-by-step explanation:

13/4 hour is 3hour and 15 minutes

7 0

3 years ago

a section in a stained glass window is shaped like a trapezoid. The top base is 4 centimeters and the bottom base is 2.5 centime

dem82 [27]

Hello, so the equation for the area of a trapezoid is A = (a+b)*(h/2)

In which, a is one of the bases, b is the other base, and h is the height. A is the Area. If you wanna solve for height, rearrange the equation to what h equals.

First divide (a+b) from both sides
A/(a+b) = h/2

Now multiply 2 on both sides

2(A/(a+b)) = h

Now you have it rearranged equal to just h. Plug in the values now.

2(3.9/(4+2.5)) = h

2(3.9/(6.5)) = h

2(.6) = h

1.2 = h

The section is 1.2 centimeters tall.

5 0

3 years ago

An antelope can run at a speed of 61 miles per hour. What is this speed in yards per second? Round to the nearest hundredth.

andrew11 [14]

Answer:

20.3 yards per second.

Step-by-step explanation:

I THINK, IM NOT 100% SURE

6 0

3 years ago

Read 2 more answers