a park is in the shape of a rectangle 8 miles long and 6 miles wide. how much shorter is your walk if you walk diagonally across the park than along two sides of it?

Answers

Answer 1

Answer: you need to use this particular formula
a^2 + b^2 = c^2
this allows you to solve for the sides of a triangle which is what the diagonal would look like if u were to draw it. a equals the width of the park and b equals the height of the park.
6^2 + 8^2 = c^2
next you need to multiply 6 by the power of 2
36 + 8^2 = c^2
then the same for the 8
36 + 64 = c^2
then add the numbers together.
100 = c^2
after you add you get the square root of 100 which is 10. a square root is 2 numbers that multiply together to equal a particular number. square root is what you do to cancel out a power of 2
so if you walk diagonally you go 10 miles instead of 14 miles leaving a difference of a whole 4 miles.

hope I helped

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Prove the identity: cos(3x) + cos(x) = 2cos(2x)cos(x)I'm almost done with my homework, just got stuck on this one.

Answers

$cos \alpha +cos \beta =2\cdot cos ( \alpha + \beta )/(2) \cdot cos ( \alpha - \beta )/(2)\n-----------------\n\n \alpha =3x\ \ \ and\ \ \ \beta =x\n\n$

$L=cos \alpha +cos \beta =cos(3x)+cos(x)\n\n\Rightarrow\ \ \ 2\cdot cos ( \alpha + \beta )/(2) \cdot cos ( \alpha - \beta )/(2)=2\cdot cos (3x+x)/(2) \cdot cos (3x-x)/(2) =\n\n.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =2\cdot cos (4x)/(2) \cdot cos (2x)/(2) =\n\n.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =2\cdot cos(2x)\cdot cos (x)=R$

What are the possible values for x in the equation 4x²=641) x=0
2) x=4
3) x=4,-4
4) x=0,4,-4

Answers

$4x^2=64\n \n4x^2-64 =0 \ \ /:4 \n \n x^2-16 =0 \n \nx^2-4^2=0 \n \n (x-4)(x+4)=0 \n \n x-4=0 \ \ or \ \ x+4 =0 \n \n x=4 \ \ or \ \ x= -4 \n \nAnswer : \ 3) \ \ x=4,-4$

The ratio of apples to bananas in a bowl of fruit is 2 to3. If there are 12 apples in the bowl, then how many
bananas are there?

Answers

We know that the ratio of apples to bananas is 2 to 3, which can also be written as 2/3.

Let's use a proportion to solve for the number of bananas:

2/3 = 12/x

Here, x represents the number of bananas in the bowl.

To solve for x, we can cross-multiply:

2x = 3 * 12

2x = 36

x = 18

Therefore, there are 18 bananas in the bowl.

Answer:

18 bananas

Step-by-step explanation:

for every 2 apples, there are 3 bananas.

So, if there are 12 apples then the original ratio of number of apples is being multiplied by 6

To prove this, 2 is the original ratio of apples and when 2 is multiplied by 6, you get 12 apples

To ensure the ratio of apples to bananas is the same, you multiply the original ratio of bananas by 3 as well. This leaves us with 18 bananas for every 12 apples (3*6 = 18)

To check if you are correct, you divide both the number of apples and the number of bananas by 6 and you get the original ratio, 2 to 3.

The ratio is essentially the same throughout except when you increase it by a constant ratio, it is no longer simplified but it is the same.

I tried explaining this the best I could and I really hope this made sense and helped!

help ! Find the volume of cylinder with a diameter of 8 inches and a height that is three times the radius. Use 3.14 for pi and round your answer to the nearest hundredth.( only numerical answers ! )

Answers

diameter(d)=8 in.
radius(r)= d/2= 4 in.
height(h)= 3r = 3(4) = 12 in.

Volume= $\pi$ r ² h
=(3.14)(4)²(12)
=(3.14)(16)(12)
=602.88 in.

Therefore, the volume of the cylinder is 602.88 in.

Let me get some help real quick big fella

Answers

Answer:

cos B = 9/41

Step-by-step explanation:

Using trig functions, since we have a right angle,

cos theta = adjacent side/ hypotenuse

Cos B = 18/82

Dividing the right side by 2

cos B = 9/41

The answer is A
You have to use the trigonometric ratio as it is a right angle triangle.

125% of what number is 0.08?

Answers

Answer:

0.06

Step-by-step explanation:

125% × ? = 0.08

? =

0.08 ÷ 125% =

0.08 ÷ (125 ÷ 100) =

(100 × 0.08) ÷ 125 =

8 ÷ 125 =

0.064 ≈

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