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zlopas [31]
3 years ago
9

A straw is placed inside a rectangular box that is 10 inches by 8 inches by 2 inches, as

Mathematics
1 answer:
scoundrel [369]3 years ago
8 0

Answer:

2\sqrt{42}

Step-by-step explanation:

Given

l = 10in --- Length

w = 8in --- Width

h = 2in --- Height

Required: Determine the length of the straw

<em>Since the straw fits the diagonal of the box, the length of the straw is equivalent of the length of the diagonal.</em>

The length of the diagonal is calculated as:

\displaystyle d = \sqrt{w^{2} + l^{2} + h^{2}}

\displaystyle d = \sqrt{8^{2} + 10^{2} + 2^{2}}

\displaystyle d = \sqrt{64 + 100 + 4}

\displaystyle d = \sqrt{168}

\displaystyle d = \sqrt{4*42}

Split

\displaystyle d = \sqrt{4}*\sqrt{42}

\displaystyle d = 2*\sqrt{42}

\displaystyle d = 2\sqrt{42}

Hence, the straw length is: 2\sqrt{42}

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A carpenter wants to build a rectangular box with square sides in which to put round things. the material for the bottom costs $
alexira [117]

Answer:1.627\times 1.627\times 1.88\ ft^3

Step-by-step explanation:

Given

Suppose side face have a dimension of l\times l

and width of h

volume V=l^2\cdot h

h=\frac{V}{l^2}

volume V=5 ft^3

Area of side wall is A_s=l^2

Area of top Wall A_t=l\times h

Area of bottom A_b=l\times h

Cost of bottom wall c_b=20\times l\times h=20lh

Cost of top wall c_t=50\times l\times h=50lh

Cost of side walls c_s=4\times l^2\times 10=40l^2

total cost C=c_s+c_t+c_b=20lh+50lh+40l^2

C=70lh+40l^2

C=70\times l\times \frac{5}{l^2}+40l^2

differentiate C w.r.t l to get minima or maxima

\frac{\mathrm{d} C}{\mathrm{d} l}=0

-\frac{350}{l}+80l^2=0

l^3=\frac{350}{80}

l=1.627 ft

h=\frac{5}{2.648}

h=1.88 ft

Dimension of Box is 1.627\times 1.627\times 1.88\ ft^3

5 0
3 years ago
10.Adrienne is going to deposit $8,500 in an account that earns 2.5% interest for 360 months. How much more interest will she ea
suter [353]

Answer:

Difference= $3,090.15 in favor of compounded interest

Step-by-step explanation:

Giving the following information:

Present value (PV)= $8,500

Ineterest (i)= 0.025/12= 0.00208

Number of periods (n)= 360 months

<u>We will calculate the future value of each option and determine the difference:</u>

<u>Simple interest:</u>

FV= (PV*i*n) + PV

FV= (8,500*0.00208*360) + 8,500

FV= $14,864.8

<u>Compounded interest:</u>

FV= PV*(1+i)^n

FV= 8,500*(1.00208^360)

FV= $17,958.95

Difference= $3,090.15

6 0
2 years ago
Dan has five times as many $1 bills as $5 bills. he has a total of 48 bills. how many of each does he have?
Sholpan [36]
Let the number of $1 bill be x and $5 bill be y
x=5y
5y+y=48
6y=48
x=40
y=8

number of $1 bill= 40
number of $5 bill = 8
6 0
3 years ago
The floor of a concert venue is 100 3/4 feet by 75 1/2 feet. What is the area of the floor
Anettt [7]
3/4 = 0.75 1/2 = 0.5 Area = l * w 100.75 * 75.5 = 7,606.625 Answer = 7,606.625 ft
5 0
3 years ago
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If 7x-2y=z then -14x+4y+3z
creativ13 [48]
I'm confused what are you suppose to do
8 0
3 years ago
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