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Stels [109]
3 years ago
7

What is the rate and unit rate for 420 miles in 7 hours

Mathematics
1 answer:
lisabon 2012 [21]3 years ago
4 0
\frac{420mi}{7h}=\frac{420}{7}\ mi/h=60\ mph
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Determine the minimum value of f(x, y, z) = 2x 2 + y 2 + 2z 2 + 5 subject to the constraint 3x + 2y + 3z = 4. +
vlada-n [284]
<span>We want to optimize f(x,y,z)=x^2 y^2 z^2, subject to g(x,y,z) = x^2 + y^2 + z^2 = 289. 

Then, ∇f = λ∇g ==> <2xy^2 z^2, 2x^2 yz^2, 2x^2 y^2 z> = λ<2x, 2y, 2z>. 

Equating like entries: 
xy^2 z^2 = λx 
x^2 yz^2 = λy 
x^2 y^2 z = λz. 

Hence, x^2 y^2 z^2 = λx^2 = λy^2 = λz^2. 

(i) If λ = 0, then at least one of x, y, z is 0, and thus f(x,y,z) = 0 <---Minimum 
(Note that there are infinitely many such points.) 
(f being a perfect square implies that this has to be the minimum.) 

(ii) Otherwise, we have x^2 = y^2 = z^2. 
Substituting this into g yields 3x^2 = 289 ==> x = ±17/√3. 

This yields eight critical points (all signage possibilities) 
(x, y, z) = (±17/√3, ±17/√3, ±17/√3), and  
f(±17/√3, ±17/√3, ±17/√3) = (289/3)^3 <----Maximum 

I hope this helps! </span><span>
</span>
8 0
3 years ago
I attached a pic please help
umka2103 [35]
Function P: y intercept of 5 (0,5), no slope
Function Q: y=- \frac{1}{3} x+4, m=- \frac{1}{3}

A: Both functions do NOT have the same slope.
B: Both functions do NOT have negative slope.
C: Functions will NOT have same input when y=0
D. The functions will have different outputs when x=0 (Function P: (0, 5) and Function Q: (0, 4)
6 0
3 years ago
7207689984 !!!!!!!!!!!!!!
GarryVolchara [31]

Answer:

838494393928262829292928288!!!!!!!!!!!!!!!$

8 0
2 years ago
How do you graph this f(x)= -3/2|x|+5 if x≤4​
LenaWriter [7]

Answer:

  see below

Step-by-step explanation:

I enter the equation into a graphing calculator and let it do the graphing.

___

If you're graphing this by hand, you start by looking for the parent function. Here, it is |x|. That has a vertex of (0, 0) and a slope of +1 to the right of the vertex and a slope of -1 to the left of the vertex.

Here, the function is multiplied by -3/2, so will open downward and have slopes of magnitude 3/2 (not 1). The graph has been translated 5 units upward, so the vertex is (0, 5).

I'd start by plotting the vertex point at (0, 5), then identifying points with slope ±3/2 either side of it. To the left, it is left 2 and down 3 to (-2, 2). The points on the right of the vertex are symmetrically located about the y-axis, so one of them will be (2, 2).

Of course, you don't plot any function values for x > 4.

8 0
3 years ago
The quotient of a number and 6 decreased by 10 is equal to 2.​
Akimi4 [234]

Answer:

6

Step-by-step explanation:

x+6-10=2

x+6=12

x=12-6

<h2>x=6 </h2>

<h3>hence the number is 6</h3>
4 0
2 years ago
Read 2 more answers
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