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3 years ago

*Use the Area formula

Mathematics

1 answer:

Artist 52 [7]3 years ago

4 0

Answer:

5ft

Step-by-step explanation:

Given parameters:

Length of the pool = 25ft

Width of the pool = 15ft

Volume of water the pool can hold = 1875ft³ of water

Unknown:

Depth of the pool = ?

Solution:

The pool is in the shape of a cuboid.

The volume of a cuboid is given as;

Volume of a cuboid = L x width x depth

Insert the parameters and solve for the depth;

1875 = 25 x 15 x depth

depth = $\frac{1875}{25 x 15}$ = 5ft

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If y=8 when x=3 when x=45

Veronika [31]

Answer:

The value of y for x = 45 is 120 .

Step-by-step explanation:

Given as :

Let The variables y and x are proportional to each others

I,e y ∝ x

Now , y = k x

So, for x = 3 , y = 8

I.e 8 = k × 3 ........1

∴ k = $\frac{8}{3}$

Similarly

for x = 45 , y = k × 3

I.e y = k × 45 ..........2

Now, putting the value of k in eq 2

So, y = $\frac{8}{3}$ × 45

I.e y = $\frac{8\times 45}{3}$

Or, y = 8 × 15

∴ y = 120

So, for x = 45 , y = 120

Hence The value of y for x = 45 is 120 . Answer

5 0

3 years ago

Write an inequality for this situation

Rainbow [258]

Answer: $E \ge 31$

Reason:

"at least 31 points" means "31 or more".

So either E = 31 or E > 31 (meaning Embiid scored 31 points or he scored more than 31 points).

Choice A looks like the closest match assuming the inequality sign is $\ge$

Saying E > 31 instead of $E \ge 31$ would be false because it leaves out the case E = 31.

6 0

2 years ago

Problems 2.21, 2.22, 2.23

RoseWind [281]

Statements can be proved by contrapositive, contradiction or by induction.

2.21 and 2.23 are proved by contrapositive
2.22 is proved by induction

2.21: If $n^3$ is even, then n is even (By contrapositive)

The contrapositive of the above statement is that:

If n is odd, then $n^3$ is odd

Represent the value of n as:

$n = 2k + 1$ , where $k \ge 0$

Take the cube of both sides

$n^3 = (2k + 1)^3$

Expand

$n^3 = 8k^3 + 6k^2 + 6k + 1$

Group

$n^3 =[ 8k^3 + 6k^2 + 6k] + 1$

Factor out 2

$n^3 =2[4k^3 + 3k^2 + 3k] + 1$

Assume w is an integer; where:

$w =4k^3 + 3k^2 + 3k$

So, we have:

$n^3 =2w + 1$

The constant term (i.e. 1) means that $n^3$ is odd.

Hence, the statement has been proved by contrapositive.

i.e. If n is odd, then $n^3$ is odd

2.22 $3n + 4$ is even, if and only if n is even

We have: $3n + 4$

Assume that: $n = 2k + 2$ for $k \ge 0$

So, we have:

$3n + 4 = 3(2k + 2) + 4$

Open bracket

$3n + 4 = 6k + 6 + 4$

$3n + 4 = 6k + 10$

Factorize

$3n + 4 = 2(3k + 5)$

The factor of 2 means that $3n + 4$ is even.

Hence, $3n + 4$ is even, if and only if n is even

2.22: $s \ne -1$ and $t \ne -1$ , then $s + t + st \ne -1$

To do this, we prove by contrapositive.

The contrapositive of the above statement is:

If $s = -1$ and $t=-1$ , then $s + t + st = -1$

We have:

$s + t + st = -1$

Substitute the values of s and t in: $s + t + st = -1$

$-1 -1 -1 \times -1 = -1$

$-1 -1 + 1 = -1$

$-1 = -1$

Hence, by contrapositive:

If $s = -1$ and $t=-1$ , then $s + t + st = -1$