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svlad2 [7]
3 years ago
5

A point has a position vector given by

t)=(2t,t^2)" alt="r(t)=(2t,t^2)" align="absmiddle" class="latex-formula"> for all time t ≥ 0 seconds. Find the speed of the object at t = 1 seconds.
8
4
2
2\sqrt{2}
Mathematics
1 answer:
sertanlavr [38]3 years ago
3 0

Answer:

2√2

Step-by-step explanation:

r(t) = (2t, t²)

v(t) = dr/dt

v(t) = (2, 2t)

v(1) = (2, 2)

|v(1)| = √(2² + 2²)

|v(1)| = 2√2

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The angle of elevation from me to the top of a hill is 51 degrees. The angle of elevation from me to the top of a tree is 57 deg
julia-pushkina [17]

Answer:

Approximately 101\; \rm ft (assuming that the height of the base of the hill is the same as that of the observer.)

Step-by-step explanation:

Refer to the diagram attached.

  • Let \rm O denote the observer.
  • Let \rm A denote the top of the tree.
  • Let \rm R denote the base of the tree.
  • Let \rm B denote the point where line \rm AR (a vertical line) and the horizontal line going through \rm O meets. \angle \rm B\hat{A}R = 90^\circ.

Angles:

  • Angle of elevation of the base of the tree as it appears to the observer: \angle \rm B\hat{O}R = 51^\circ.
  • Angle of elevation of the top of the tree as it appears to the observer: \angle \rm B\hat{O}A = 57^\circ.

Let the length of segment \rm BR (vertical distance between the base of the tree and the base of the hill) be x\; \rm ft.

The question is asking for the length of segment \rm AB. Notice that the length of this segment is \mathrm{AB} = (x + 20)\; \rm ft.

The length of segment \rm OB could be represented in two ways:

  • In right triangle \rm \triangle OBR as the side adjacent to \angle \rm B\hat{O}R = 51^\circ.
  • In right triangle \rm \triangle OBA as the side adjacent to \angle \rm B\hat{O}A = 57^\circ.

For example, in right triangle \rm \triangle OBR, the length of the side opposite to \angle \rm B\hat{O}R = 51^\circ is segment \rm BR. The length of that segment is x\; \rm ft.

\begin{aligned}\tan{\left(\angle\mathrm{B\hat{O}R}\right)} = \frac{\,\rm {BR}\,}{\,\rm {OB}\,} \; \genfrac{}{}{0em}{}{\leftarrow \text{opposite}}{\leftarrow \text{adjacent}}\end{aligned}.

Rearrange to find an expression for the length of \rm OB (in \rm ft) in terms of x:

\begin{aligned}\mathrm{OB} &= \frac{\mathrm{BR}}{\tan{\left(\angle\mathrm{B\hat{O}R}\right)}} \\ &= \frac{x}{\tan\left(51^\circ\right)}\approx 0.810\, x\end{aligned}.

Similarly, in right triangle \rm \triangle OBA:

\begin{aligned}\mathrm{OB} &= \frac{\mathrm{AB}}{\tan{\left(\angle\mathrm{B\hat{O}A}\right)}} \\ &= \frac{x + 20}{\tan\left(57^\circ\right)}\approx 0.649\, (x + 20)\end{aligned}.

Equate the right-hand side of these two equations:

0.810\, x \approx 0.649\, (x + 20).

Solve for x:

x \approx 81\; \rm ft.

Hence, the height of the top of this tree relative to the base of the hill would be (x + 20)\; {\rm ft}\approx 101\; \rm ft.

6 0
3 years ago
Calculate the standard deviation. Variance = 107.76. Mean = 34.2
Llana [10]

Answer:

The standard deviation is 10.38

Step-by-step explanation:

Given;

Variance, v = 107.76

mean, x = 34.2

The standard deviation is given by;

standard deviation = √variance

standard deviation = √107.76

standard deviation =  10.381

standard deviation = 10.38 (two decimal places)

Therefore, the standard deviation is 10.38

8 0
3 years ago
A baker uses a coffee mug with a diameter of 8 cm 8 cm8, start text, space, c, m, end text to cut out circular cookies from a bi
horsena [70]

Answer:

Step-by-step explanation:

The diameter of the top of the coffee mug which the baker uses to cut out circular cookies from the big sheet of cookie dough is 8 cm.

Radius of the coffee mug is diameter of the coffee mug/2.

Radius of the coffee mug

= 8/2 = 4cm

The area of the circular mug is expressed as

Area = πr^2

Where π is a constant whose value is 3.14

Therefore,

Area of the top of the circular mug = 3.14 × 4^2 = 3.14 × 16 = 50.24 cm^2

The area of the top of the circular cup is the same as the area of each cookie. Therefore,

The area of each cookie is 50.24 cm^2

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fredd [130]

Replace x in the equation for f(x) with -5:

|2x +9| = |2(-5) +9| = |-10 +9| = |-1| = 1

Now find x 1 and see where the graph of G(x) crosses the Y :

It crosses ay Y = 5

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Lunna [17]

Answer:

Step-by-step explanation:

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3 years ago
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