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zhuklara [117]
2 years ago
14

Evaluate 7p+6(p/q)2 q if p = 6 and q = 3. show your work and give an explanation for each step .

Mathematics
1 answer:
Degger [83]2 years ago
6 0

Answer:

63 is the required value.

Step-by-step explanation:

We need to find the value if p = 6 and q = 3 in the below expression i.e.

7p+6(\dfrac{p}{q})^2-q

Put p = 6 and q = 3 in the above expression.

=7(6)+6(\dfrac{6}{3})^2-3\\\\=42+6(2)^2-3\\\\=42+24-3\\\\=63

So, the value of the given expression is 63.

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The sides of a triangle are 1, x, and x2. what are possible values of x?
Whitepunk [10]
The sides of the triangle are given as 1, x, and x².

The principle of triangle inequality requires that the sum of the lengths of any two sides should be equal to, or greater than the third side.

Consider 3 cases
Case (a):  x < 1,
      Then in decreasing size, the lengths are 1, x, and x².
      We require that x² + x ≥ 1
      Solve x² + x - 1 = 
      x = 0.5[-1 +/- √(1+4)] = 0.618 or -1.618.
      Reject the negative length.
     Therefore, the lengths are 0.382, 0.618 and 1.

Case (b): x = 1
   This creates an equilateral triangle with equal sides
    The sides are 1, 1 and 1.

Case (c): x>1
  In increasing order, the lengths are 1, x, and x².
  We require that x + 1 ≥ x²
  Solve x² - x - 1 = 0
  x = 0.5[1 +/- √(1+4)] = 1.6118 or -0.618
  Reject the negative answr.
 The lengths are 1, 1.618 and 2.618.

Answer:
The possible lengths of the sides are
(a) 0.382, 0.618 and 1
(b) 1, 1 and 1.
(c) 2.618, 1.618 and 1.

7 0
3 years ago
Please help me solve
mihalych1998 [28]

Answer:

x = 36.3°

using tane rule:

\sf tan(x)= \dfrac{opposite}{adjacent}

Here!

  • x = missing angle
  • opposite = 22
  • adjacent = 30

=============

\hookrightarrow \sf tan(x) = \dfrac{22}{30}

\hookrightarrow \sf x= tan^{-1}(\dfrac{22}{30} )

\hookrightarrow \sf x= 36.253^{\circ \:}

\hookrightarrow \sf x= 36.3^{\circ \:}        ( rounded to nearest tenth of a degree)

3 0
3 years ago
Read 2 more answers
40% of the students in a school band play brass instruments while 4 students play strings instruments
MaRussiya [10]
10 students (brass)=40% of band
4 students (strings)=16% of band 
? students (other)=44% rest of band
14/56%=?/44%
(cross multiply to find ?){don't forget to turn percents into decimals}
?=11
There are 25 students in total in the band.

5 0
4 years ago
A tree trunk is pulled with a force of 3200 pounds by a truck's cable that makes an angle of 25° with the horizontal. What is th
elena-s [515]

Answer:

The vertical component of the force is 1352 pounds.

Step-by-step explanation:

Given that,

Force acting on the tree trunk, F = 3200 pounds

The truck's cable makes an angle of 25 degree with the vertical. We need to find the vertical component of the force. We know that the force is a vector quantity. The vertical component is given by :

F_y=F\sin\theta\\\\F_y=3200\times \sin (25)\\\\F_y=1352.37\ \text{pounds}

F_y=1352\ \text{pounds}

Hence, the vertical component of the force is 1352 pounds.

7 0
3 years ago
Max has 3 fiction books and 6 nonfiction books to donate to the community center. He wants to package them so that there is an e
frutty [35]

Answer:

Each group has 1 fiction book and 2 nonfiction book(s).

7 0
3 years ago
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