Answer:
15 miles
Step-by-step explanation:
pythagorean theorem
9²+12²=x²
x=15 miles
Answer:
The ratio of seniors to the total team members is 7: 11
Step-by-step explanation:
Let us solve the question
∵ A varsity boy's basketball team has a ratio of seniors to juniors that is 7: 4
∴ seniors: juniors = 7: 4
→ That means seniors have 7 parts and juniors has 4 parts
∴ The seniors' members = 7 parts
∴ The juniors' members = 4 parts
→ Add them to find the total parts of the team
∴ The team's members = 7 + 4 = 11 parts
→ To find the ratio of the seniors' members to the total team's member
divide their parts
∵ The seniors ÷ The total = 
∵ The seniors' member : The team's members = 7: 11
∴ The ratio of seniors to the total team members is 7: 11
The points on the intersection of the ellipsoid with the plane that are respectively closest and furthest from the origin are
(2–√,−2–√,2−22–√)
(−2–√,2–√,2+22–√)
Using Lagrange multipliers we attempt to find the extrema of f(x,y,z)=x2+y2+z2 given that g(x,y,z)=x−y+z−2=0 and that h(x,y,z)=x2+y2−4=0.
Given,
∇f=⟨2x,2y,2z⟩
∇g=⟨1,−1,1⟩
∇h=⟨2x,2y,0⟩
Extrema satisfy the condition that ∇f=μ∇g+λ∇h for some λ,μ∈R.
This is to say,
2x=2λx+μ
2y=2λy−μ
2z=μ
If λ=1 then μ=0 and so z=0, the g constraint tells us that x=y+2, and the h constraint tells us that y2+(y+2)2=4, meaning that either y=0 or y=2. This provides us with two crucial points in addition to the g constraint:
(2,0,0)
(0,−2,0)
Now assume λ≠1, and so
x=μ2−2λ
y=−μ2−2λ=−x
Since x=−y, we have that x=±2–√, y=∓2–√. Using the g constraint, our two critical points are
(2–√,−2–√,2−22–√)
(−2–√,2–√,2+22–√)
And then it's east to determine which is the max and which is the min out of these four critical points.
To learn more about Lagrange multiplier
brainly.com/question/4609414
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First, assign two variables to the prices of the two appliances.
'w' will represent the price of a washer, and 'd' will represent the price of a dryer.
Because "the washer is three times the cost of the dryer," we can form this equation:
w = 3d
On top of that, we know the washer and dryer add up to 600, making another equation.
w + d = 600
Because we know the value of 'w,' we can input that into the equation 'w + d = 600'
(3d) + d = 600
Simplify:
4d = 600
d = 150
Since the washer is three times the price of the dryer:
w = 3(150) = 450
The dryer costs $150, and the washer costs $450.
-T.B.
I am not sure, but my answer is (a). However, I also think its (c), but mainly (a). Please tell me if I was incorrect. I'm sorry. Hope I helped.
