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3 years ago

Please answer this question

Mathematics

2 answers:

Murrr4er [49]3 years ago

7 0

I am not sure but I think the answer is of second one.

Llana [10]3 years ago

7 0

Answer:

I think it would be B but im not completly sure.

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a new statue with a circular base is being unveiled in a downtown park. the statue base has a radius of 8 feet. round your answe

fiasKO [112]

I believe you are asking for the area of the statue base.

r^2x3.14 = area of a circle

8 x 8 = 64

64 x 3.14 = 200.96
200.96 rounded = 201

The area of the statue base is 201 square feet.

5 0

2 years ago

Write an exponential function in the form y=ab^x that goes through points (0,9) and (3, 576)

sineoko [7]

Answer:

An exponential function in the form y=9(4ˣ)

Step-by-step explanation:

Step(i):-

Given that exponential function

y = a bˣ ...(i)

The equation (i) passes through the point (0,9)

9 = a (b )⁰ = a

a =9

Step(ii):-

The equation (i) passes through the point (3,576)

576 = 9(b)³

⇒ $\frac{576}{9} = b^{3}$

⇒ 64 = b³

⇒ 4³ = b³

$(4^{3} )^{\frac{1}{3} } = (b^{3} )^{\frac{1}{3} }$

b = 4

Final answer:-

An exponential function in the form y=abˣ

An exponential function in the form y=9(4ˣ)

6 0

2 years ago

A hiker is hiking in a valley. The height of the valley is h(x,y)=4x2+y2 where x and y are the east-west and north-south distanc

Ainat [17]

Answer:

A. $\frac{\partial{h}}{\partial{t}}=0$

Step-by-step explanation:

A. The problems asked for 2 ways to solve it, expanding the equation with the substitution x(t)=2 cos(t) and y(t)=4 sin(t) to differentiate it . The other way is by chain rule.

Expanding and differentiating:

We start by substituting x(t)=2 cos(t) and y(t)=4 sin(t) in h(x,y)=4x2+y2:

$h(x,y)=4x^{2}+y^{2}= 4(2cos(t))^{2}+(4sin(t))^{2}\\h(x,y)=4(4cos^{2}(t))+(16sen^{2}(t))\\h(x,y)=16cos^{2}(t)+16sen^{2}(t)=16(sen^{2}(t)+cos^{2}(t))\\h(x,y)=16$

So, in the path that the hiker chose:

$\frac{\partial{h}}{\partial{t}}=0$

Chain rule:

We start differentiating h(x,y) using chain rule as follows:

$\frac{\partial{h}}{\partial{t}}= \frac{\partial{h}}{\partial{x}}\frac{\partial{x}}{\partial{t}}+\frac{\partial{h}}{\partial{y}}\frac{\partial{y}}{\partial{t}}$

Now, it´s easy to find all these derivatives:

$\frac{\partial{h}}{\partial{x}}=8x\\\frac{\partial{x}}{\partial{t}}=-2sin(t)\\\frac{\partial{h}}{\partial{y}}=2y\\\frac{\partial{y}}{\partial{t}}=4cos(t)$