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Jlenok [28]
2 years ago
9

Jayden uses the net below to design a box. A net with 4 rectangles and 2 squares. The rectangles measure 6 feet by 4 feet and th

e squares have side lengths of 4 feet. How much cardboard will Jayden need to make the box? A. 60 ft2 B. 96 ft2 C. 128 ft2 D. 144 ft2
Mathematics
1 answer:
goldfiish [28.3K]2 years ago
6 0

Answer:

C .128 ft²

Step-by-step explanation:

net with 4 rectangles and 2 squares.

The rectangles measure 6 feet by 4

Area of the rectangle=6*4

Area of the rectangle= 24.ft²

Total area of the rectangle= 4*24.

Total area of the rectangle= 96 ft²

the squares have side lengths of 4 feet.

Area of tge square= 4²

Area of the square= 16ft²

Total area of the square= 16*2

Total area of the square= 32 ft²

Total area of the cardboard needed

= Area of square + Are of rectangle

= 32+96

= 128 ft²

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A forest ranger is in a forest 2 miles from a straight road. A car is located c miles down the road. The forest ranger can walk
Tcecarenko [31]

Answer:

  • T(x) = (√(4+x^2))/2 +(c -x)/4
  • (a) x = 1.155 miles
  • (b) x = 1/2 mile

Step-by-step explanation:

The straight line distance from the starting point to the point x on the road is given by the Pythagorean theorem:

  d1 = √(2²+x²)

The time required to walk that distance in the woods (at 2 miles per hour) is ...

  time = distance / speed

  t1 = √(4+x²)/2

The remaining distance along the road to the car is ...

  d2 = c - x . . . . . for c > x

and the corresponding time at 4 mph is ...

  t2 = (c -x)/4

Then the total time is ...

  T(x) = t1 +t2

  T(x) = √(4+x²)/2 +(c -x)/4

__

(a) The value of x that minimizes total time is the one that makes the derivative zero.

  T'(x) = x/(2√(4+x²)) -1/4

  0 = (2x -√(4+x²))/(4√(4+x²))

  √(4+x²) = 2x . . . . . fraction is zero when numerator is zero; add radical

  4 +x² = 4x² . . . . . . square both sides

  4/3 = x² . . . . . . . . . subtract x², divide by 3

  x = (2/3)√3 ≈ 1.1547

If c = 9 miles, x = 1.1547 miles.

__

(b) For c < (2/3)√3, the shortest travel time will be along the straight-line path to the car.

If c = 1/2 mile, x = 1/2 mile.

8 0
2 years ago
Simplify sin θ / square root 1 - sin^2 θ
Soloha48 [4]

Recall that

\cos^2\theta+\sin^2\theta=1

which means

\dfrac{\sin\theta}{\sqrt{1-\sin^2\theta}}=\dfrac{\sin\theta}{\sqrt{\cos^2\theta}}

Now, \cos\theta could be positive or negative, which means \sqrt{\cos^2\theta}=|\cos\theta|. If we specifically knew the sign of \cos\theta was positive, then we can simplify and write

\dfrac{\sin\theta}{\sqrt{1-\sin^2\theta}}=\dfrac{\sin\theta}{\cos\theta}=\tan\theta

or if it's negative,

\dfrac{\sin\theta}{\sqrt{1-\sin^2\theta}}=\dfrac{\sin\theta}{-\cos\theta}=-\tan\theta

7 0
2 years ago
Zenaida is shopping and wants to purchase a $320 stereo system. The store is offering an incentive of 10 to 30 percent off when
lesantik [10]

The stereo system costs $256.

Step-by-step explanation:

Given:

Cost of the stereo system = $320.  

The discount Zenaida received = 20%.  

To Find:

Cost of the stereo system after the discount=?

Solution:

Step1:  Finding the discount amount:

Discount percentage =20

Discount amount = original cost × discount percent

Substituting the values,

\text { Discount amount }=320 \times 20 \%

\text { Discount amount }=320 \times \frac{20}{100}

\text { Discount amount }=320 \times \frac{1}{5}

\text { Discount amount }=320 \times 0.2

\text { Discount amount }=64

Step 2: Removing the discounted amount from the original price

Final cost of the stereo system =original cost of the stereo system –discount amount

Substituting the values we get,

Final cost=320-64

Final cost=256

Result:

Thus the cost of the stereo system after discount is $256

7 0
2 years ago
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Viefleur [7K]

Step-by-step explanation:

1.901

hope this helps.

8 0
2 years ago
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Simplify 4a³b² × 3a⁶b⁵​
Rasek [7]

Answer:

12a^9b^7

Step-by-step explanation:

Multiplying variables of the same base, will require you to add the exponents.

4a^3b^2 * 3a^6b^5

         4*3 =  12

a^3 * a^6 =   a^9

b^2 * b^5 =   b^7

12a^9b^7

4 0
2 years ago
Read 2 more answers
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