All categories

3 years ago

In a square of a side length s, what is the length of a diagonal?

1 answer:

5 0

S - length of a square

d - length of a diagonal

d = s√2

why?

Use the Pythagorean theorem:

d² = s² + s²
d² = 2s²
d = √(2s²)
d = √2 · √s²
d = s√2

You might be interested in

a cargo ship arrived at Kingston Harbour carrying 403,172 kilograms of flour. All the flour was tranfered to 5 trains and 9 truc

IrinaVladis [17]

Each train carried 64141 kg of flour and each truck carried 9163 kg of flour.

Step-by-step explanation:

Let the no. of kg of flour carried by each train be 'a'

Let the no. of kg of flour carried by each truck be 'b'

Total flour = 403172 kg

No. Of trains = 5

No. of trucks = 9

a = 7(b)

5a + 9b = 403172

5(7b) + 9b = 403172

35b + 9b = 403172

44b = 403172

b = 403172/44

b = 9163

Each truck carried 9163 kg of flour.

a = 7b

a = 7(9163)

a = 64141

Each train carried 64141 kg of flour.

4 0

4 years ago

You want to get from a point A on the straight shore of the beach to a buoy which is 54 meters out in the water from a point B o

anyanavicka [17]

Answer:

$x =\dfrac{45 \sqrt{6}}{ 2}$

Step-by-step explanation:

From the given information:

The diagrammatic interpretation of what the question is all about can be seen in the diagram attached below.

Now, let V(x) be the time needed for the runner to reach the buoy;

∴ We can say that,

$\mathtt{V(x) = \dfrac{70-x}{7}+\dfrac{\sqrt{54^2+x^2}}{5}}$

In order to estimate the point along the shore, x meters from B, the runner should stop running and start swimming if he want to reach the buoy in the least time possible, then we need to differentiate the function of V(x) and relate it to zero.

i.e

The differential of V(x) = V'(x) =0

= $\dfrac{d}{dx}\begin {bmatrix} \dfrac{70-x}{7} + \dfrac{\sqrt{54^2+x^2}}{5} \end {bmatrix}= 0$

$-\dfrac{1}{7}+ \dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}=0$

$\dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}$

$\dfrac{5x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}$

$\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{\dfrac{7}{5}}$

$\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{5}{7}$

squaring both sides; we get

$\dfrac{x^2}{54^2+x^2}= \dfrac{5^2}{7^2}$

$\dfrac{x^2}{54^2+x^2}= \dfrac{25}{49}$

By cross multiplying; we get

$49x^2 = 25(54^2+x^2)$

$49x^2 = 25 \times 54^2+ 25x^2$

$49x^2-25x^2 = 25 \times 54^2$

$24x^2 = 25 \times 54^2$

$x^2 = \dfrac{25 \times 54^2}{24}$

$x =\sqrt{ \dfrac{25 \times 54^2}{24}}$

$x =\dfrac{5 \times 54}{\sqrt{24}}$

$x =\dfrac{270}{\sqrt{4 \times 6}}$

$x =\dfrac{45 \times 6}{ 2 \sqrt{ 6}}$

$x =\dfrac{45 \sqrt{6}}{ 2}$

8 0

3 years ago

Help -9x + 3.0 > 6.6 Group of answer choices x 0.4 x 2.4

Y_Kistochka [10]

Answer:

x 0.4

Step-by-step explanation:

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

3 0

3 years ago

Solve the system of equations y=9x+13 y=2x+48

MakcuM [25]

Both are equal y. So you can set them equal to each other

9x+13=2x+48

Subtract 2x from both sides

7x+13=48
Subtract 13 from both sides

7x= 35

X=5

7 0

3 years ago

In a long division exercise the divisor is 8x5−4x. What is the degree of the remainder for which the division process can be st

labwork [276]

Answer:

The degree of the remainder should be 4 for the division process to be stopped

Step-by-step explanation:

From the question, we have the degree of the divisor as 5

So, for the division process to be stopped, the degree of the remainder should be one less than the degree of the divisor

Once the degree of the remainder is less than the degree of the divisor, we have no option that to stop and not proceed further with the division

So in the case of the particular question, the degree of the remainder should be of degree 4

4 0

3 years ago