In triangle ABC, the measure of angle B is 50 degrees.

Metal Fabrication If an open box is made from a tin sheet 10 in. square by cutting out identical squares from each corner and be

MrRa [10]

Answer:

ength (l) : (10-2*5/3) = 20/3
width(w): (10 - 2*5/3) = 20/3
height(h): 5/3

Step-by-step explanation:

Let x is the side of identical squares

By cutting out identical squares from each corner and bending up the resulting flaps, the dimension are:

length (l) : (10-2x)
width(w): (10-2x)
height(h): x

The volume will be:

V = (10-2x) (10-2x) x

<=> V = (10x-2 $x^{2}$ ) (10-2x)

<=> V = 100x -20 $x^{2}$ - 20 $x^{2}$ + 4 $x^{3}$

<=> V = 4 $x^{3}$ - 40 $x^{2}$ + 100x

To determine the dimensions of the largest box that can be made, we need to use the derivative and and set it to zero for the maximum volume

dV/dx = 12 $x^{2}$ -80x + 100

<=> 12 $x^{2}$ -80x + 100 =0

<=> x = 5 or x= 5/3

You know 'x' cannot be 5 , because if we cut 5 inch squares out of the original square, the length and the width will be 0. So we take x = 5/3

=>

length (l) : (10-2*5/3) = 20/3
width(w): (10 - 2*5/3) = 20/3
height(h): 5/3

6 0

3 years ago

Jimmy's Bakery sold 950 donuts last week. This week , the number of donuts sold increased 12%. How many more donuts were sold th

Mkey [24]

Step 1: Find 12% of 950
114
Step 2: Add the result to the original number
950 + 114 = 1064
Answer = 114

5 0

2 years ago

store announced that their $500 appliances were on sale for $475 what is the percent discount on the appliances

Aleks04 [339]

Answer:

We are given that a store announced that their $500 appliances were on sale.

The price of the appliances after discount is $475.

We are required to find the percent discount on the appliances.

To find the percent discount, we have to use the below formula:

$\frac{(Actual-discounted)}{Actual} \times 100\%$

$\frac{500-475}{500}\times 100\%$

$\frac{25}{500} \times 100\%$

$0.05 \times 100\%$

$5\%$

Therefore, the percent discount on the appliances is 5%

6 0

3 years ago

What is the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (-2, 4)?

Korolek [52]

Answer:

y=-5/2x-1

Step-by-step explanation:

first find the gradient whereas since the two lines are parallel they hav the same gradient. y=mx+c whereas m is the gradient. 5x+2y=12

2y=-5x+12

y=-5/2x+12(so the gradient is -5/2x..... gradient=-5/2

y-4=-5/2

x+2

y-4=-5/2(x+2)

y-4=-5/2x-5

y=-5/2x-5+4

y=-5/2x-1

6 0

3 years ago

Four friends each purchased a hat for $12.50

mrs_skeptik [129]

Answer:

$70 each

Step-by-step explanation:

If 4 friends each buy a hat, that would be $50 because that is $12.50X4=%50.00. Then, Since the total is $190 and $50 is off the chart, you would be left with $140 to spend on two t-shirts. Finally, since they are the same price, you divide $140/2=$70. Each t-shirt is $70.

Let me know if you need clarification and I will help the best I can. Have a nice day. :)

8 0

3 years ago