Geometry question plz help

Find the length of a rectangle with a diagonal of 10 and a height of 8.

Answer:

The length of the rectangle is 6.

Step-by-step explanation:

Given: The diagonal of a rectangle is 10 and the height is 8.

Please understand, that a diagonal, divides the rectangle into two tringles.

To find the length of the rectangle, you can use Pythagoras on one of the right sided triangles, because the length of the triangle, is also the length of the rectangle!

EXTRA:

If you know the special 3 4 5 triangle, a so called Pythagorean Triple, then you can "see" the simularity between the numbers.

Instead of 5, a diagonal of 10 is given (factor of 2 bigger).

Instead of 4, the height of 8 is given (factor of 2 bigger). By scaling the Pythagorean Triple 3 4 5 by a factor of 2, you get the numbers 6 8 10. Could it be, that the number we need to find, is six?

Try to verify, by calculating the missing number (which is the length of the rectangle we are looking for).

a² + b² = c²

a = length (and is unknown)

b = height = 8

c = hypothenusa/diagonal = 10

Substitute the numbers given:

a² + 8² = 10²

Subtract 8² left and right of the = sign.

a² +8² -8² = 10² - 8²

a² + 0 = 100 - 64

a² = 36

a = + - √36

a = + - 6

EXTRA:

You can ignore the -√36 = -6 part of the solution, because a length of -6 has no meaning here.

a = 6

So, the length of the triangle is 6 and thus, the length of the rectangle is also 6.

8 0

3 years ago

You borrow $1200 at a rate of 4.5% for a period of 2 years. how much will you.repay at the end of two years?

tresset_1 [31]

54,00 is the answer............

4 0

3 years ago

Read 2 more answers

The pair of points lies on the same line with the given slope. Find x. (4,6). (x, 12); slope = 2

uysha [10]

Answer:

x=7

Step-by-step explanation:

I got this because it is rise over run

$\frac{rise}{run} =\frac{6}{?} =2$

The missing number would be 3, and if you add that three to 4 you get 7. which means that the answer is...

(7,12)

<h2>Hope this helps you!!!</h2>

6 0

3 years ago

The temperature at a point (x,y,z) is given by t(x,y,z)=200e−x2−y2/4−z2/9t(x,y,z)=200e−x2−y2/4−z2/9, where tt is measured in deg

yulyashka [42]

First find the gradient by using partial derivatives.

$T_x = (-2x)200 e^{(-x^2 -y^2/4 -z^2/9)} \\ \\ T_y = (-\frac{1}{2}y)200 e^{(-x^2 -y^2/4 -z^2/9)} \\ \\ T_z = (-\frac{2}{9}z)200 e^{(-x^2 -y^2/4 -z^2/9)}$

Sub in given point (0,-1,2) for x,y,z
∨ $T = (T_x, T_y,T_z) = (0,100e^{-25/36, \frac{-800}{9} e^{-25/36})$

Next, find unit vector from directional vector (0,-1,2) --> (-3,4,-3)
$v = (-3-0, 4-(-1), -3-2) = (-3,5,-5) \\ \\ ||v|| = \sqrt{(-3)^2 + 5^2 + (-5)^2} = \sqrt{59} \\ \\ u = (\frac{-3}{\sqrt{59}}, \frac{5}{\sqrt{59}},\frac{-5}{\sqrt{59}})$

Finally, use dot product on gradient and unit vector to get directional rate of change.
Answer is approx 61.398

8 0

3 years ago

MCHS sold 150 tickets at the last basketball game. Student tickets cost $3 and adult tickets cost $5. If they sold $580 worth of

Tanya [424]

Answer:the number of student tickets that were sold is 85

the number of adult tickets that were sold is 65

Step-by-step explanation:

Let x represent the number of student tickets that were sold.

Let represent the number of adult tickets that were sold.

MCHS sold 150 tickets at the last basketball game. This means that

x + y = 150

Student tickets cost $3 and adult tickets cost $5. If they sold $580 worth of tickets, it means that

3x + 5y = 580 - - - - - - - - - - -1

Substituting x = 150 - y into equation 1, it becomes

3(150 - y) + 5y = 580

450 - 3y + 5y = 580

- 3y + 5y = 580 - 450

2y = 130

y = 130/2 = 65

Substituting y = 65 into x = 150 - y, it becomes

x = 150 - 65 = 85

7 0

4 years ago