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3 years ago

Help and explain please?

Mathematics

1 answer:

Natali5045456 [20]3 years ago

8 0

Square root of 160.

Use Pythagorean’s Theorem.
a^2+b^2=c^2
(12)^2+(4)^2=c^2
144+16=c^2
160=c^2
C=square root of 160

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Two equations for the constant of proportionality equal to 1/2

NemiM [27]

y=kx and y= $\frac{k}{x}$ are two equations of constant of proportionality

Step-by-step explanation:

There are two equations for the constant of proportionality. That is

(i) Direct proportion

(ii) Inverse proportion

In direct proportion y=kx, Now

if x increases, then y also increases and if x decreases, then y also decreases. So, k is a constant proportionality.

In Inverse proportion y= $\frac{k}{x}$ , Now

if x increases then y decreases and if x decreases, then y increases and k is a constant proportionality.

In direct proportion, we put y=1 and x=2, So k= $\frac{1}{2}$ .

So, the equations y=kx and y= $\frac{k}{x}$ are two equations of constant of proportionality.

5 0

3 years ago

Suppose that you are to make a rectangular box with a square base from two different materials. The material for the top and fou

saw5 [17]

Answer:

height = 14.5 ft

width = length = 3.2 ft

Step-by-step explanation:

Let the side of the square base is a and the height of the box is h.

The material required to make the box is equal to the total surface area of the box.

Area of base = a²

Cost of square base is $ 2 per ft²

So, the cost of making base = 2a²

Area of four walls + area of top = 2 (a² + ah + ah) + a² = 3a² + 2ah

Cost of making walls and the top is $ 1 per ft²

So, the cost of making walls and the top = 1 x ( 3a² + 2ah)

Total cost of making the box = 2a² + 3a² + 2ah = 5a² + 2ah

According to the question

144 = 5a² + 2ah

$h = \frac{144-5a^{2}}{2a}$ .... (1)

The volume of the box is V = length x width x height

V = a x a x h

V = 72 a - 2.5 a³ from equation (1)

Differentiate both sides with respect to a.

dV/da = 72 - 7.5 a²

Put, it equal to zero for maxima and minima

7.5 a² = 72

a = 3.2 ft

Put in equation (1)

$h = \frac{144-5\times 3.2\times 3.2}{2\times 3.2}$

h = 14.5 ft

So, the dimensions of the box are

height = 14.5 ft

width = length = 3.2 ft

6 0

3 years ago

Frank was skiing down big bear mountain. He finished 22% of his skiing in the morning. Then he still had 23.4 miles left. How ma

gtnhenbr [62]

Answer: 6.6 miles

Step-by-step explanation:

Since he finished 22% of his skiing in the morning, that means he still has 78% (100% - 22%) of his skiing left.

The remaining 78% is equivalent to 23.4 miles. We need to know the total miles of the skiing. This will be:

78% of x = 23.4

0.78 × x = 23.4

0.78x = 23.4

x = 23.4 / 0.78

x = 30 miles

Since the total skiing is 30 miles and he has 23.4 miles left, the miles covered in the morning will be:

= 30 - 23.4

= 6.6 miles

8 0

3 years ago

-9 – 9u = -3u + 9 last one for today

Yakvenalex [24]

-9u + 3u = 9 + 9
-6u = 18
u = -18/6
u = -3
Thus, u is equal to -3

6 0

3 years ago

Read 2 more answers

You randomly select an integer from 0 to 19 (inclusively) and then randomly select an integer from 0 to 24 (inclusively). What

Mila [183]

Answer:

The probability of selecting 5 both times is 0.002.

Step-by-step explanation:

We are given that you randomly select an integer from 0 to 19 (inclusively) and then randomly select an integer from 0 to 24 (inclusively).

And we have to find the probability of selecting 5 both times.

As we know that the probability of an event is given by;

Probability = $\frac{\text{Favorable number of outcomes}}{\text{Total number of outcomes}}$

Now, here between integer from 0 to 19 (inclusively);

Number of times 5 comes = 1

Total number of integers = 20

Similarly, between integer from 0 to 24 (inclusively);

Number of times 5 comes = 1

Total number of integers = 25

So, the required probability = $\frac{1}{20}\times \frac{1}{25}$

= $\frac{1}{500}$ = 0.002

Hence, the probability of selecting 5 both times is 0.002.

5 0

3 years ago