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natali 33 [55]
3 years ago
13

Convert 50 grains to milligrams

Mathematics
1 answer:
Tasya [4]3 years ago
3 0

Answer:

3239.95

Step-by-step explanation:

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Find dy/dx by implicit differentiation for ycos(x)=xcos(y)
alekssr [168]

Answer:

dy/dx = (cos y + y sin x) / (cos x + x sin y)

Step-by-step explanation:

y cos x = x cos y

y (-sin x) + dy/dx cos x = x (-sin y dy/dx) + cos y

-y sin x + dy/dx cos x = -x sin y dy/dx + cos y

dy/dx (cos x + x sin y) = cos y + y sin x

dy/dx = (cos y + y sin x) / (cos x + x sin y)

5 0
3 years ago
Find the surface area of the prism.
Maurinko [17]

Answer:

326m²

Step-by-step explanation:

Find the area of each side and find the total sum from each individual area:

2(15*4)+2(7*4)+2(7*15)=2(60)+2(28)+2(105)=2(163)=326

So the surface area of the prism is 326m²

5 0
2 years ago
Hey can someone please help explain and answer this 1 question. There's a picture. Thank you!
zmey [24]
//You can substitute some values in to find out, for example (1, -5) and (5, -5) are good.
Using this method, you can deduce that it would be A
3 0
2 years ago
I need the answer to a parts I-iii and the answer to b
fomenos

Answer:

a)

i) Mean = 72

ii) Median = 72

iii) Mode = 72

b)

69, 70, 71, 72, 72, 72, 73, 74, 75

Step-by-step explanation:

<u>a. To find mean, median and mode</u>

It is given that all the 9 students get 72 marks.

Therefore the data set be,

72, 72, 72, 72, 72, 72, 72, 72 72

<u>i) mean </u>= (sum of data)/(total number of data)

 = (9 * 72)/9 = 9

<u>ii) Median </u>- Central data in the data set when arranging ascending or descending order

72, 72, 72, 72, 72, 72, 72, 72 72

Median = 72

<u>iii) Mode </u>- Most repeating data in the data set

Here mode = 72

<u>b). To find a data set</u>

69, 70, 71, 72, 72, 72, 73, 74, 75

Here Mean, mode and median are all 72

3 0
3 years ago
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
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