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crimeas [40]
3 years ago
11

A company buys pens at the rate of $7.50 per box for the first 10 boxes, $5.50 per box for the next 10 boxes, and $4.50 per box

for any additional boxes. how many boxes of pens can be bought for $148.00?
Mathematics
1 answer:
photoshop1234 [79]3 years ago
4 0

So it is really easy to solve firstly we can see how much does the first 10 boxes make which makes around 75$ obviously. Secondly 55$ for the next 10 boxes.

So for now we can simply calculate that we have spent around 130$ which means 20 boxes. The remaining money left is 18$ so we can buy 18/4.5 = 4 only 4 boxes with that money. Hence a total of 24 boxes.

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Find the directional derivative of the function at the given point in the direction of the vector v. f(x, y, z) = xyz , (3, 3, 9
Anna [14]

The derivative of f(x,y,z) in the direction of a vector \mathbf u is

\nabla_{\mathbf u}f=\nabla f\cdot\dfrac{\mathbf u}{\|\mathbf u\|}

With f(x,y,z)=xyz, we get

\nabla f=(yz,xz,xy)

and \mathbf u=(-1,-2,2),

\|\mathbf u\|=\sqrt{(-1)^2+(-2)^2+2^2}=3

Then

\nabla_{(-1,-2,2)}f(3,3,9)=(27,27,9)\cdot\dfrac{(-1,-2,2)}3=-21

8 0
3 years ago
1.) What is the equation of the path of firework #1? Write your equation in general form.
valina [46]

1. I'm assumig that the paths are perfect parabolas

this means that their general forms can be written in y=ax^2+bx+c

it's easier to find vertex form first then expand to get general form

vertex form is y=a(x-h)^2+k where the vertex is (h,k) and a is a constant


firework #1

vertex is (10,50), so (h,k)=(10,50) and h=10, k=50

h_1=a(t-10)^2+50

to find the value of a, subsitute another point

(0,0)

0=a(0-10)^2+50)

0=100a+50

a=\frac{-1}{2}

so the equation in vertex form is h_1=\frac{-1}{2}(t-10)^2+50

expand to get general form

h_1=\frac{-1}{2}(t^2-20t+100)+50

h_1=\frac{-1}{2}t^2+10t-50+50

h_1=\frac{-1}{2}t^2+10t





2.

same as last time

vertex is (10,72) so (h,k)=(10,72) so h=10 and k=72

equation is h_2=a(t-10)^2+72

find a

use another point

(0,22)

22=a(0-10)^2+72

22=100a+72

-50=100a

a=\frac{-1}{2}

so the equation in vertex form is h_2=\frac{-1}{2}(t-10)^2+72




3.

range is the numbers that h is allowed to be

think about what h represents. it represents the height of the rocket

from the graph, we can see that the lowest possible height is 0yd and the highest height is 50yd

so range is 0 to 50 or 0≤h≤50


domain is the numbers that t is allowed to be

think about what t represents. it represents how long the rocket has been flying

it will stop flying when it hits the ground or at t=20

it starts flying at t=0

so domain is from 0 to 20 or 0≤t≤20

3 0
3 years ago
I'm giving branliest 2X - 3y = 12 in a standard and point slope form ​
iogann1982 [59]
In slope intercept form it is y=2/3x-4
In point slope form it is 2/3x-y-4 :)
5 0
3 years ago
100pts Help rounding!
Semmy [17]

Answer:

5

Step-by-step explanation:

5 158/559

= 5 + 158/559

= 5 + 0.28264758

= 5.28264758

= 5 (rounded to nearest whole number)

4 0
2 years ago
Read 2 more answers
What is an equation of the line that passes through the points (-6, 2)and (−6,6)?
monitta

Answer:

x=-6

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(6-2)/(-6-(-6))

m=4/(-6+6)

m=4/0

undefined

x=-6

4 0
2 years ago
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