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2 years ago

What is the area of the square that shares a side with the third side of the triangle?

Mathematics

1 answer:

disa [49]2 years ago

3 0

Step-by-step explanation:

Cuz sides of square are same, we just find hypotenusa side of triangle (use Phytagoras Theorem) :

c² = a² + b²

c² = 2² + 4²

c² = 4 + 16

c² = 20

c = √20

Side of square is √20 units.

The area of square :

A = s²

= √20²

= √20 × √20

= 20 units²

So, the area of square is 20 units²

Hope it helpful and useful :)

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The length of a Train A is 480 m and it takes 2 minutes to cross a tunnel of length 1,320 m. The length of a Train B, which is s

nasty-shy [4]

Answer: 52.94

Step-by-step explanation:

Length of train A = 480m

Tunnel length = 1320m

Time taken to cross tunnel = 2 mins = 120sec

Length of train B = 420m

Train B is slower than train A

Difference between their speed = 18km/hr

18km/hr = (18×1000)/3600 = 5m/s

Speed of train A :

Speed = distance / time

Speed = 1320 / 120 = 11m/s

Therefore, speed of train B :

(11 - 5)m/s = 6m/s

Relative speed of the two trains is therefore;

(Speed of A + speed of B)

Note : they are moving in opposite direction

( 11 + 6)m/s = 17m/s

Therefore time taken to cross each other :

(Sum of the length of both trains / relative speed of the trains)

Time taken = (480m + 420m) / (17m/s)

Time taken = 900m / 17m/s

Time taken = 52.94s

4 0

2 years ago

There are twice as many gray kittens than white

Marianna [84]

Answer:

8 gray kittens

Step-by-step explanation:

There are double the amount of grey kittens compared to white kittens so, you would do 4 × 2 which is 8. There are 8 grey kittens.

Hope this helps!

7 0

2 years ago

Paloma ran 3 3/4 miles around the school track. If each lap is 1/2 mile, how many laps did she run?

Ratling [72]

Answer:

Step-by-step explanation:

It is 9 because 1/2 goes into 3, 6 times, and then 3/4 divided by 1/2 is 1 1/2 so 1/2 goes into 3/4 1/12 times, so then figure out how mnay 1/2 is in 1 1/2 and youll get 3 so 6 plus 3 equals 9 :)

7 0

2 years ago

What is the answer to this

Softa [21]

Answer:

5 f

Re-order terms so that constants are on the left

. 5

5 f

solution

5 f

7 0

2 years ago

PLZ HELP!!! Use limits to evaluate the integral.

Marrrta [24]

Split up the interval [0, 2] into n equally spaced subintervals:

$\left[0,\dfrac2n\right],\left[\dfrac2n,\dfrac4n\right],\left[\dfrac4n,\dfrac6n\right],\ldots,\left[\dfrac{2(n-1)}n,2\right]$

Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,

$r_i=\dfrac{2i}n$

where $1\le i\le n$ . Each interval has length $\Delta x_i=\frac{2-0}n=\frac2n$ .

At these sampling points, the function takes on values of

$f(r_i)=7{r_i}^3=7\left(\dfrac{2i}n\right)^3=\dfrac{56i^3}{n^3}$

We approximate the integral with the Riemann sum:

$\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{112}n\sum_{i=1}^ni^3$

Recall that

$\displaystyle\sum_{i=1}^ni^3=\frac{n^2(n+1)^2}4$

so that the sum reduces to

$\displaystyle\sum_{i=1}^nf(r_i)\Delta x_i=\frac{28n^2(n+1)^2}{n^4}$

Take the limit as n approaches infinity, and the Riemann sum converges to the value of the integral:

$\displaystyle\int_0^27x^3\,\mathrm dx=\lim_{n\to\infty}\frac{28n^2(n+1)^2}{n^4}=\boxed{28}$

Just to check:

$\displaystyle\int_0^27x^3\,\mathrm dx=\frac{7x^4}4\bigg|_0^2=\frac{7\cdot2^4}4=28$

4 0

2 years ago

What is the area of the square that shares a side with the third side of the triangle?​

What is the area of the square that shares a side with the third side of the triangle?