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3 years ago

B (t)= 80t -16t^2 + 3.5

1 answer:

8 0

Whats the answer whats the answer whats the answer whats the answer whats the answer whats the answer whats the answer whats the answer whats the answer

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the Millers drove 105 miles on 4 gallons of gas. at this rate, how many miles can they drive on 6 gallons of gas.

Alinara [238K]

Answer:

157.5 miles with 6 gallons

Step-by-step explanation:

105miles / 4gallons = 26.25miles per gallon

26.25miles per gallon * 6miles = 157.5 miles

5 0

3 years ago

Read 2 more answers

Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S.

sweet-ann [11.9K]

Answer:

2.794

Step-by-step explanation:

Recall that if G(x,y) is a parametrization of the surface S and F and G are smooth enough then

$\bf \displaystyle\iint_{S}FdS=\displaystyle\iint_{R}F(G(x,y))\cdot(\displaystyle\frac{\partial G}{\partial x}\times\displaystyle\frac{\partial G}{\partial y})dxdy$

F can be written as

F(x,y,z) = (xy, yz, zx)

and S has a straightforward parametrization as

$\bf G(x,y) = (x, y, 3-x^2-y^2)$

with 0≤ x≤1 and 0≤ y≤1

$\bf \displaystyle\frac{\partial G}{\partial x}= (1,0,-2x)\\\\\displaystyle\frac{\partial G}{\partial y}= (0,1,-2y)\\\\\displaystyle\frac{\partial G}{\partial x}\times\displaystyle\frac{\partial G}{\partial y}=(2x,2y,1)$

we also have

$\bf F(G(x,y))=F(x, y, 3-x^2-y^2)=(xy,y(3-x^2-y^2),x(3-x^2-y^2))=\\\\=(xy,3y-x^2y-y^3,3x-x^3-xy^2)$

and so

$\bf F(G(x,y))\cdot(\displaystyle\frac{\partial G}{\partial x}\times\displaystyle\frac{\partial G}{\partial y})=(xy,3y-x^2y-y^3,3x-x^3-xy^2)\cdot(2x,2y,1)=\\\\=2x^2y+6y^2-2x^2y^2-2y^4+3x-x^3-xy^2$

we just have then to compute a double integral of a polynomial on the unit square 0≤ x≤1 and 0≤ y≤1

$\bf \displaystyle\int_{0}^{1}\displaystyle\int_{0}^{1}(2x^2y+6y^2-2x^2y^2-2y^4+3x-x^3-xy^2)dxdy=\\\\=2\displaystyle\int_{0}^{1}x^2dx\displaystyle\int_{0}^{1}ydy+6\displaystyle\int_{0}^{1}dx\displaystyle\int_{0}^{1}y^2dy-2\displaystyle\int_{0}^{1}x^2dx\displaystyle\int_{0}^{1}y^2dy-2\displaystyle\int_{0}^{1}dx\displaystyle\int_{0}^{1}y^4dy+\\\\+3\displaystyle\int_{0}^{1}xdx\displaystyle\int_{0}^{1}dy-\displaystyle\int_{0}^{1}x^3dx\displaystyle\int_{0}^{1}dy-\displaystyle\int_{0}^{1}xdx\displaystyle\int_{0}^{1}y^2dy$

=1/3+2-2/9-2/5+3/2-1/4-1/6 = 2.794

5 0

3 years ago

A book contains pages from 1-48. A student picks a page at random. What is the probability that the page contains a 3

Nutka1998 [239]

1/48

Since there is only 1 page labeled “3,” the probability of picking page 3 is 1/48.

6 0

2 years ago

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A kite is flying 70 feet above the ground and is attached to a string tied to a stake on the ground. The angle of elevation form

rosijanka [135]

Taking the length of the string to be the hypothenuse and the vertical height above the ground to be the 'opposite' side,
the length of the string
= 70/sin(40°)
= 109 feet

3 0

3 years ago

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How much would $500 invested at 6% interest compounded monthly be

neonofarm [45]

Answer:

i think it is b

Step-by-step explanation:

4 0

2 years ago