Answer:
11.6 Inches
Step-by-step explanation:
Let the dimensions of the box be l,w and h
The length of a box is four-and-a-half inches more than its height; written as:
The width of the box is seven inches more than it’s height; written as:
Making h the subject of the formula, we have:
Volume of the box = 4981.5 cubic inches
Volume of a cuboid =lwh
Substituting the given values above:
![(w+4.5)(w)(w-7)=4981.5\\$Expanding\\w^3-2.5w^2-31.5w=4981.5\\w^3-2.5w^2-31.5w-4981.5=0\\$Solving the resulting cubic equation using a calculator\\w=18.6 inches (Every other value of w is in the complex plane)](https://tex.z-dn.net/?f=%28w%2B4.5%29%28w%29%28w-7%29%3D4981.5%5C%5C%24Expanding%5C%5Cw%5E3-2.5w%5E2-31.5w%3D4981.5%5C%5Cw%5E3-2.5w%5E2-31.5w-4981.5%3D0%5C%5C%24Solving%20the%20resulting%20cubic%20equation%20using%20a%20calculator%5C%5Cw%3D18.6%20inches%20%28Every%20other%20value%20of%20w%20is%20in%20the%20complex%20plane%29)
Therefore,
Height of the box, h=w-7=18.6-7=11.6 Inches
Step-by-step explanation:
Notice that tan (75) can be written as sin(75)/cos(75) = sin(30 + 45) / cos(30 + 45)
And using a couple of trig identities, we have
[sin 30 cos 45 + sin 45 cos 30 ] / [cos 30 cos 45 -sin 30 sin 45] =
[ (1/2)(1/√2) +(1/√2))(√3/2)] / [ (√3/2) (1/√2) -(1/2) (1/√2) ] =
([1 + √3)] / [2 √2]) / ([√3 - 1] / [2 √2]) =
[ 1 + √3] / [√3 - 1] rationalizing the denominator, we have
[ 1 + √3] * [√3 + 1] / 2 =
[ 1 + √3 ] [ 1 + √3 ] / 2 =
[1 + 2√3 + 3] / 2 =
[4 + 2√3 ] / 2 =
2 + √3 so this is the exact value
Answer:
Step-by-step explanation:
150 ft in 30 seconds
150/30=5 we have 5 ft per second
in 10 seconds 5*10=50 ft
choice C
Answer:
What is the equation i would love to help you.
Answer:
Imagine if your friend is 3ft, and he is scaled down into the drawing. If he's scaled down into the drawing, he would be 1 inch in the drawing. If your cat were 1.5ft, it would be half of your friend, so in the drawing it would be 0.5 inch. Now the table is 9ft, how many 3ft is in 9ft? That's 3 times of 3ft, so 1 inch would be multiplied 3 times, = 3 inches. Or there's a shortcut way in the pic.