Answer:
Dimensions are;
2.5 inches height
Base: 10 inches by 10 inches
Max volume; 250 Sq.in
Step-by-step explanation:
Let each side of the square that's cut-off from each corner be represented by x.
This means that the base of the box will be of dimension of the side 15−2x while the height of the box will be x.
Thus;
Volume of box is:
V = (15 − 2x)(15 − 2x)x
V = (15 − 2x)²x
V = (4x² - 60x + 225)x
V = 4x³ - 60x² + 225x
Let's differentiate with respect to x to get;
dV/dx = 12x² - 120x + 225
Maximum value of x is at dV/dx = 0
12x² - 120x + 225 = 0
Using quadratic formula, we arrive at;
x = 2.5 or 7.5
Now, let's find the second derivative of the volume;
d²V/dx² = 24x - 120
Putting x = 2.5 gives;
d²V/dx² = 24(2.5) - 120
d²V/dx² = -60
Thus, V is maximum at x = 2.5, since d²V/dx² is negative
At x = 7.5;
d²V/dx² = 24(7.5) - 120
d²V/dx² = 60
Thus, V is minimum at x = 7.5, since d²V/dx² is negative
Thus,we will use x = 2.5
Maximum volume; V = (15 − 2(2.5))(15 − 2(2.5))(2.5)
V = 10 × 10 × 2.5
V = 250 Sq.inches
Dimensions are;
(15 − 2x) = 15 - 2(2.5) = 10 inches
(15 − 2x) = 15 - 2(2.5) = 10 inches
x = 2.5 inches
q + 12 - 2(q - 22) > 0 |use distributive property
q + 12 +(-2)(q) + (-2)(-22) > 0
q + 12 - 2q + 44 > 0 |combine like terms
(q - 2q) + (12 + 44) > 0
-q + 56 > 0 |subtract 56 from both sdies
-q > -56 |change the signs
<h3>q < 56</h3>
Answer:
<em>The shop made a profit about $40.</em>
<em>Step-by-step explanation:</em>
<em>Now, According to the question We know that :</em>
<em>The shop marked the $200 price up by 60%.</em>
<em>60% of $200 is = $120. </em>
<em>Now, the price is = $320 because, 200 + 120 = 320. </em>
<em />
<em>Joseph bought the tennis racket at 25% off.</em>
<em>25% of $320 is = $80.</em>
<em>Now, the discount price is = $240 Because, 320 - 80 = 240.</em>
<em />
<em>So, Joseph bought the racket for = $240.</em>
<em />
<em>Now we know that the original price from the factory was $200.</em>
<em>Joseph bought it for $240.</em>
<em>So, the shop made a profit of $40.</em>
Answer:
C
Step-by-step explanation:
Therefore, the answer is C. Hope this helps!
Answer:
if it were an equation it would be y = mx + b and B would be the y intercept and mx is slope.
Step-by-step explanation:
