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castortr0y [4]
3 years ago
9

A 100 inch strip of sheet metal starting out 16 inches wide is to be made into a small open trough (open top and ends) by turnin

g up two sides at right angles to the base. The sides will be the same height, x. If the trough is to have maximum volume, how many inches should be turned up on each side?
Mathematics
1 answer:
daser333 [38]3 years ago
8 0

Answer:

4 inches should be turned up on both sides.

Step-by-step explanation:

In order to find this, create a situation in which we give the amount turned up on each side as x. Then give the amount that isn't turned up as 16 - 2x (since 2x is the amount turned up). Now we can find the area by multiplying the 3 measurements.

100 * x * (16 - 2x) = MAX

100 * (16x - 2x^2) = MAX

-200x^2 + 1600x = MAX

Now that we have a quadratic function, we can find the maximum value of x by using the vertex formula for x values (-b/2a).

x = -b/2a

x = -1600/2(-200)

x = -1600/-400

x = 4

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erastova [34]

Answer:

Step-by-step explanation:

Formula for calculating the surface area of the box S = 2(LW+LH+WH) where

L is the length of the box

W is the width of the box

H is the height of the box

If the box is square based with dimension 4 * 4in, then L = W = 4in. substituting this values given into the formula we will have;

S = 2(4(4)+4H + 4H)

S = 2(16+8H)

S = 32+16H

<em>Hence, The function that represents the surface area of this box as a </em>

<em>function of its height is S = 32+16H where H is the height of the box</em>

<em></em>

Given H = 6.5in, to evaluate the function, we will substitute h = 6.5in into the modeled equation;

S = 32+16H

S = 32+16(6.5)

S = 32+106

<em>S = 138in²</em>

<em>Hence the total surface area of the box is 138in²</em>

5 0
2 years ago
What is the missing reason in Step 7? Triangle angle sum theorem quadrilateral angle sum theorem definition of complementary con
Daniel [21]

Answer:

Hello your question is incomplete attached below is the complete question

Given: wxyz is a parallelogram, zx ≅ wy prove: wxyz is a rectangle what is the missing reason in step 7? a. triangle angle sum theorem. b. quadrilateral angle sum theorem. c. definition of complementary. d. consecutive ∠s in a ▱ are supplementary. 1. wxyz is a ▱; zx ≅ wy 1. given 2. zy ≅ wx 2. opp. sides of ▱ are ≅ 3. yx ≅ yx 3. reflexive 4. △zyx ≅ △wxy 4. sss ≅ thm. 5. ∠zyx ≅ ∠wxy 5. cpctc 6. m∠zyx ≅ m∠wxy 6. def. of ≅ 7. m∠zyx + m∠wxy = 180° 7. ? 8. m∠zyx + m∠zyx = 180° 8. substitution 9. 2(m∠zyx) = 180° 9. simplification 10. m∠zyx = 90° 10. div. prop. of equality 11. wxyz is a rectangle 11. rectangle ∠ thm.

answer: consecutive angles of any parallelogram are supplementary

Step-by-step explanation:

The missing reason in step 7 is : consecutive angles of any parallelogram are supplementary i.e. m∠ZYX + m∠WXY  = 180°

<u>Reason </u>:  ZY || WX also  XY is the transversal line hence ∠wyx and ∠wxy are the consecutive angles on lines ZY and WX therefore m∠ZYX + m∠WXY = 180°  ( sum of consecutive angles )

4 0
3 years ago
Read 2 more answers
Which symbol creates a true sentence when x equals 3?
kondaur [170]

Answer:

C

Step-by-step explanation:

8×3-4×2=16

7(10-3)=14

so 16 is greater

7 0
3 years ago
How many cubes with side lengths of 1/2 cm does it take to fill the prism? Height: 3/2 cm Width:1 cm length: 2 cm
Irina18 [472]

Answer:

24

Step-by-step explanation:

If we want to cover the base of the prism having dimensions 2 cm × 1 cm with \frac{1}{2} cm length of cube, then there will be (4 × 2) = 8 cubes that can occupy the base.

Width is 1 cm, so there can fit 2 cubes of length \frac{1}{2} cm and length is 2 cm, where 4 cubes of length \frac{1}{2} cm can fit. So, in total (4 × 2) = 8 cubes of \frac{1}{2} cm length.

Now, height of the prism is \frac{3}{2} cm where 3 cubes of length \frac{1}{2} cm can fit.

Therefore, in total there can be (8 × 3) = 24 cubes of \frac{1}{2} cm length. (Answer)

8 0
3 years ago
Customer arrivals at a bank are random and independent; the probability of an arrival in any one-minute period is the same as th
deff fn [24]

Answer:

a)0.2240

b)0.5768

Step-by-step explanation:

Given:

µ=3

Poison probability is given by :

f_k=\frac{\mu^ke^-^\mu}{k!}

a) Evaluating at k=3

f(3)=\frac{3^3e^-^3}{3!} \approx 0.2240

b)Evaluating at k=0,1,2:

f(0)=\frac{3^0e^-^3}{0!} \approx 0.0498

f(1)=\frac{3^1e^-^3}{1!} \approx 0.1494

f(2)=\frac{3^2e^-^3}{2!} \approx 0.2240

Use complement rule:

P(x≥3)= 1 - f(0) - f(1) - f(2)= 1- 0.0498 - 0.1494 - 0.2240 =0.5768

4 0
3 years ago
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