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2 years ago

What is g(3) please help

Mathematics

1 answer:

ioda2 years ago

7 0

Answer:

g(3) = 0

Step-by-step explanation:

g(3) → x = 3 , in interval x≥ 3 , thus g(3) = - x + 3, that is

g(3) = - 3 + 3 = 0

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Suppose you need to know an equation of the tangent plane to a surface S at the point P(4, 1, 4). You don't have an equation for

Alex777 [14]

Answer:

$15x-8y+9z=88$

Step-by-step explanation:

We are given that

Equation of curves

$r_1(t)=$

$r_2(u)=$

Both curves lie on S.

We have to find the equation of tangent plane at P(4,1,4).

$r'_1(t)=,r'_2(u)=$

$r_1(0)=, r_2(1)=$

Hence, t=0 and u then it satisfied the given point.

Substitute the values in the derivatives

$r'_1(0)=,r'_2(1)=$

$r'_1(0)\times r'_2(1)=\times =$

The equation of tangent at point P(4,1,4) is given by

$30(x-4)-16(y-1)+18(z-4)=0$

$30x-120-16y+16+18z-72=0$

$30x-16y+18z=176$

$15x-8y+9z=88$

5 0

3 years ago

Bill needs to find the area of the ground covered by a conical tent. The tent is 12 feet tall and makes a 70° angle with the gro

Pie

Answer:

Step-by-step explanation:

To get the area of the cone we need to find the radius first.

tan 70=r/12

r=12tan 70

area of a circle is given by:

A=πr²

thus the area of the ground covered by the tent will be:

A=π(12tan70)²

The answer is

A] A=π(12tan70°)²

3 0

2 years ago

Tom throws a ball into the air. The ball travels on a parabolic path represented by the equation , where represents the height o

tigry1 [53]

Answer:

2.5 second

Step-by-step explanation:

The equation is missing in the question.

The equation is, $h=-8t^2+40t$ , where 'h' is the height and 't' is time measured in second.

Now we know to reach its maximum height, h in t seconds, the derivative of h with respect to time t is given by :

$\frac{dh}{dt} =0$

Now the differentiating the equation with respect to time t, we get

$\frac{dh}{dt}=\frac{d}{dt}(-8t^2+40t)$

$\frac{dh}{dt}=-16t+40$

For maximum height, $\frac{dh}{dt} =0$

So, $-16t+40=0$

$\Rightarrow 16t=40$

$\Rightarrow t=\frac{40}{16}$

$\Rightarrrow t = 2.5$

Therefore, the ball takes 2.5 seconds time to reach the maximum height.

7 0

2 years ago

The water under a draw bridge was 15 feet deep at midnight. As the tide went out, the

Vsevolod [243]

Answer:

80 minutes or 1 h 20 minutes

Step-by-step explanation:

15-13=2

2/0.025=80

So we can conclude that it takes 80 minutes till it reaches 13 feet.

7 0

3 years ago

NO LINKS!!! Part 2: Find the Lateral Area, Total Surface Area, and Volume. Round your answer to two decimal places.

slava [35]

Answer:

<h3><u>Question 7</u></h3>

<u>Lateral Surface Area</u>

The bases of a triangular prism are the triangles.

Therefore, the Lateral Surface Area (L.A.) is the total surface area excluding the areas of the triangles (bases).

$\implies \sf L.A.=2(10 \times 6)+(3 \times 6)=138\:\:m^2$

<u>Total Surface Area</u>

Area of the isosceles triangle:

$\implies \sf A=\dfrac{1}{2}\times base \times height=\dfrac{1}{2}\cdot3 \cdot \sqrt{10^2-1.5^2}=\dfrac{3\sqrt{391}}{4}\:m^2$

Total surface area:

$\implies \sf T.A.=2\:bases+L.A.=2\left(\dfrac{3\sqrt{391}}{4}\right)+138=167.66\:\:m^2\:(2\:d.p.)$

<u>Volume</u>

$\sf \implies Vol.=area\:of\:base \times height=\left(\dfrac{3\sqrt{391}}{4}\right) \times 6=88.98\:\:m^3\:(2\:d.p.)$

<h3><u>Question 8</u></h3>

<u>Lateral Surface Area</u>

The bases of a hexagonal prism are the pentagons.

Therefore, the Lateral Surface Area (L.A.) is the total surface area excluding the areas of the pentagons (bases).

$\implies \sf L.A.=5(5 \times 6)=150\:\:cm^2$

<u>Total Surface Area</u>

Area of a pentagon:

$\sf A=\dfrac{1}{4}\sqrt{5(5+2\sqrt{5})}a^2$

where a is the side length.

Therefore:

$\implies \sf A=\dfrac{1}{4}\sqrt{5(5+2\sqrt{5})}\cdot 5^2=43.01\:\:cm^2\:(2\:d.p.)$

Total surface area:

$\sf \implies T.A.=2\:bases+L.A.=2(43.01)+150=236.02\:\:cm^2\:(2\:d.p.)$

<u>Volume</u>

$\sf \implies Vol.=area\:of\:base \times height=43.011193... \times 6=258.07\:\:cm^3\:(2\:d.p.)$

8 0

1 year ago