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fiasKO [112]
2 years ago
5

The Animal World Safari Park is a rectangular piece of land with an area of 323 square miles. The length of the park is 17 miles

. What is its width?
Mathematics
2 answers:
ozzi2 years ago
8 0
The answer is 19 to be in fact
Charra [1.4K]2 years ago
6 0
The area of a rectangle is A = L * W.  We have the area as 323 and the length as 17.  Filling in our formula for area then, 323 = 17W.  Divide both sides by 17 to solve for the width.  W = 19
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A cone without a base is made from a half-circle of radius 10 cm. Determine the volume of the cone. Explain your reasoning.
DochEvi [55]

Answer:

  125π√3/3 cm³ ≈ 226.72 cm³

Step-by-step explanation:

The length of the circular edge of the half-circle is ...

  (1/2)C = (1/2)(2πr) = πr = 10π . . . . cm

This is the circumference of the circular edge of the cone, so the radius of the cone is found from ...

  C = 2πr

  10π = 2πr . . . . fill in the numbers; next, solve for r

  r = 5 . . . . cm

The slant height of the cone is the original radius, 10 cm, so the height of the cone from base to apex is found from the Pythagorean theorem.

  (10 cm)² = h² + r²

  h = √((10 cm)² -(5 cm)²) = 5√3 cm

And the cone's volume is ...

  V = 1/3·πr²h = (1/3)π(5 cm)²(5√3 cm)

  V = 125π√3/3 cm³ ≈ 226.72 cm³

5 0
2 years ago
Which of the following is the expansion of (3c + d2)6?
vovangra [49]

Answer: Option A) 729c^6 + 1,458c^5d^2 + 1,215c^4d^4 + 540c^3d^6 + 135c^2d^8 + 18cd^{10} + d^{12} is the correct expansion.

Explanation:

on applying binomial theorem,  (a+b)^n=\sum_{r=0}^{n} \frac{n!}{r!(n-r)!} a^{n-r} b^r

Here a=3c, b=d^2 and n=6,

Thus, (3c+d^2)^6=\sum_{r=0}^{6} \frac{6!}{r!(6-r)!} (3c)^{n-r} (d^2)^r

⇒ (3c+d^2)^6= \frac{6!}{(6-0)!0!} (3c)^{6-0}.(d^2)^0+\frac{6!}{(6-1)!1!} (3c)^{6-1}.(d^2)^1+\frac{6!}{(6-2)!2!} (3c)^{6-2}.(d^2)^2+\frac{6!}{(6-3)!3!} (3c)^{6-3}.(d^2)^3+\frac{6!}{(6-4)!4!} (3c)^{6-4}.(d^2)^4+\frac{6!}{(6-5)!5!} (3c)^{6-5}.(d^2)^5+\frac{6!}{(6-6)!6!} (3c)^{6-6}.(d^2)^6

⇒(3c+d^2)^6= \frac{6!}{(6-)!0!} (3c)^6.d^0+\frac{6!}{(5)!1!} (3c)^5.d^2+\frac{6!}{(4)!2!} (3c)^4.d^4+\frac{6!}{(6-3)!3!} (3c)^3.d^6+\frac{6!}{(2)!4!} (3c)^2.d^8+\frac{6!}{(1)!5!} (3c).d^{10}+\frac{6!}{(0)!6!} (3c)^0.d^{12}

⇒(3c+d^2)^6=(3c)^6.d^0+\frac{720}{120} (3c)^5.d^2+\frac{720}{48} (3c)^4.d^4+\frac{720}{36} (3c)^3.d^6+\frac{720}{48} (3c)^2.d^8+\frac{720}{120} (3c).d^{10}+.d^{12}

⇒(3c+d^2)^6=729c^6 + 1,458c^5d^2 + 1,215c^4d^4 + 540c^3d^6 + 135c^2d^8 + 18cd^{10} + d^{12}

3 0
2 years ago
Read 2 more answers
robin is making bead necklaces she want to use 717 beads to make 57 necklaces. if she wants each necklaces to have the same numb
EleoNora [17]

717=12\cdot684+33

<u>33 beads</u>

7 0
2 years ago
A fair coin is flipped twice. Drag letters to complete the tree diagram to represent the sample space
ankoles [38]

Answer:

Step-by-step explanation:

HH

HT

TH

TT

6 0
2 years ago
Manny is making 12 quarts of orange juice from concentrate and water. The number of quarts of water is 3 times the number of qua
trasher [3.6K]

Answer: There are 3 quarts of concentrate and 9 quarts of water.

Step-by-step explanation:

Since we have given that

Ratio of number of quarts of water to number of quarts of concentrate is

3:1

Number of quarts of orange juice from concentrate and water = 12 quarts

So, the number of quarts of concentrate would be

\dfrac{1}{4}\times 12\\\\=\dfrac{12}{4}\\\\=3\ quarts

the number of quarts of water would be

\dfrac{3}{4}\times 12\\\\=3\times 3\\\\=9\ quarts

Hence, there are 3 quarts of concentrate and 9 quarts of water.

8 0
2 years ago
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