Basing on the question the volume of metal should be equal to the volume of the wire.
We already have the volume of the metal which is 1cm cube.
To get the volume of the wire, the equation is V=3.14 x r^2 x h
since the volume of the wire is same as the volume of the metal, we simply substitute.
1 cm^3 = 3.14 x r^2 x h
h is the length of the wire.
the diameter of the wire is 1 mm or 0.1 cm, to get the radius we divide it by 2, 0.1 cm / 2 is 0.05 cm, we substitute
1 cm^3= 3.14 x (0.05 cm)^2 x h
1 cm^3= 3.14 x 0.0025 cm^2 x h
h = 0.00785 cm^2 / 1 cm^3
h=0.00785 cm or 0.0785 mm.
The length of the rectangle is based on its width, so let's call width w and put the length in terms of the width. We are told that the width is 45 less than 4 times the width, so the length is 4w - 45. Area is found by multiplying length times width and we are given the area as 3325. So we will set up length times width and solve for w, which we will then use to solve for l. 3325 = (4w - 45)(w). Multiplying out we have
. Move the constant over by subtraction and then we will have a quadratic that can be factored to solve for w.
. We would put that through the quadratic formula to solve for w. When we do that we get that w = 35 and w = -23.75. The 2 things in math that will never EVER be negative is time and distance/length, so -23.75 is out. That means that the width is 35. The length is 4(35) - 45 which is 95. The dimensions of your rectangle are length is 95 and width is 35. There you go!
Answer:
$25.5
Step-by-step explanation:
To find 85% of $30, we can simply multiply the usual price, $30, by the decimal form of the percentage.
The decimal form of 85% is .85.
Now, multiply.
30*.85=25.5
The sale price of the backpack is $25.5.
Hope this helps!
Answer:
Step-by-step explanation:
I believe it is the 2nd one its the most logical
Answer:
60 miles
Step-by-step explanation:
let d = distance to the lake
Using: time = distance ÷ speed
Create expressions for the time it takes for each journey:
Drive: ![t_1=\dfrac{d}{30}](https://tex.z-dn.net/?f=t_1%3D%5Cdfrac%7Bd%7D%7B30%7D)
Walk: ![t_2=\dfrac{d}{4}](https://tex.z-dn.net/?f=t_2%3D%5Cdfrac%7Bd%7D%7B4%7D)
If total time = 17 hours
![\implies t_1+t_2=17](https://tex.z-dn.net/?f=%5Cimplies%20t_1%2Bt_2%3D17)
![\implies \dfrac{d}{30}+\dfrac{d}{4}=17](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7Bd%7D%7B30%7D%2B%5Cdfrac%7Bd%7D%7B4%7D%3D17)
![\implies \dfrac{17d}{60}=17](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B17d%7D%7B60%7D%3D17)
![\implies 17d=1020](https://tex.z-dn.net/?f=%5Cimplies%2017d%3D1020)
![\implies d=\dfrac{1020}{17}](https://tex.z-dn.net/?f=%5Cimplies%20d%3D%5Cdfrac%7B1020%7D%7B17%7D)
![\implies d=60](https://tex.z-dn.net/?f=%5Cimplies%20d%3D60)
Therefore she walked 60 miles