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3 years ago

If an Isosceles right triangle has an hypotenuse of the square root of 30, what is the length of the other two sides?

Mathematics

1 answer:

MariettaO [177]3 years ago

7 0

Answer:

For a right angled triangle, hypotenuse is equal to the root of the sum of the squares of the other two sides.

If the sides are ‘a’ and ‘b’ and the hypotenuse is ‘c’,

c = Square Root of (’a’ squared + ’b’ squared)

So, ‘c’ squared = ‘a’ squared + ‘b’ squared.

In the instant case, the triangle is a right angled isosceles triangle; as such the sides are equal, say ‘a’. Also it is given that the square of the hypotenuse is 98.

As such 98 = ‘a’ squared + ‘a’ squared, i.e 2 ‘a’ sq.

So ‘a’ squared = 98/2 = 49

Then ‘a‘ = Root of 49 = 7

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10 ft

Lelu [443]

Answer:

P = 40.56 ft

Step-by-step explanation:

The figure is composed of a rectangle and half circle

The perimeter of the figure = the length of the borders round the figure

= W + 2L + ½(perimeter of full circle)

W = 8 ft

L = 10 ft

½(perimeter of circle) = ½(πd) = ½(3.14*8)

= 12.56 ft

Plug in the values

Perimeter of the figure = 8 + 2(10) + 12.56

= 8 + 20 + 12.56

= 40.56 ft

3 0

2 years ago

Find the domain of the function (f/g)(x) given f (x)=x^2-4x-5 and g(x)=x^2-25

stealth61 [152]

Answer:

all real numbers except ±5.

Step-by-step explanation:

Each function (f(x), g(x)) has a domain that is all real numbers. Their quotient (f(x)/g(x)) must exclude values that make g(x) = 0. The quotient is undefined when the denominator is zero. Those excluded values are x = ±5.

The domain of (f/g)(x) is all real numbers except ±5.

___

Of course you recognize x^2 -25 = 0 has solutions x = ±√25 = ±5. You can get there two ways:

add 25 and take the square root: x^2=25; x=±√25.
factor the difference of squares and set the factors to zero: (x-5)(x+5)=0 has solutions x-5=0 and x+5=0, that is, x = ±5.

5 0

2 years ago

1. One rule of thumb for estimating crowds is that each person occupies 2.5 square feet. Use this value to

givi [52]

Answer:

216 people

Step-by-step explanation:

Given:

2.5 feet² is occupied by 1 person

Dimension of room = 216 in × 360 in

Required:

No. of people that would occupy the room

SOLUTION:

Step 1:

Convert the dimensions of the room from in to ft

Note: 1 foot = 12 inches

216 inches = $\frac{216}{12} = 18 ft$

360 inches = $\frac{360}{12} = 30 ft$

Step 2: calculate area of the room.

Area of the room = 30*18 = 540 ft²

Step 3: calculate the no. of people the room will contain.

2.5 ft² will contain one person

Therefore, 540 ft² will contain: $\frac{540}{2.5} = 216 people$

6 0

3 years ago

√(2x+1)<br> Evaluate the integral<br> 2<br> (2x + 1) In (2x + 1)<br> dx.

Crank

Substitute $y=\ln(2x+1)$ and $dy=\frac2{2x+1}\,dx$ , so that

$\displaystyle \int \frac2{(2x+1) \ln(2x+1)} \, dx = \int \frac{dy}y = \ln|y| + C = \boxed{\ln|\ln(2x+1)| + C}$

6 0

1 year ago

How many sides does a regular polygon have if each exterior angle measures 30 degree

Nataly [62]

As the exterior angles always add up to 360, you can find the number of sides by dividing 360 by the measure of your exterior angle, 30. This gives you 360/30=12, meaning your polygon has 12 sides.

5 0

3 years ago