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2 years ago

6w-19+k when w=8 and k=2

Mathematics

2 answers:

Ne4ueva [31]2 years ago

4 0

Substitute

6(8) - 19 + (2)

6(8) = 48

48 - 19

29 + 2 = 31

pychu [463]2 years ago

4 0

Answer:

Step-by-step explanation:

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Solve the equation <br> 3= x/6 + 1

dangina [55]

Answer:

x = 12

Step-by-step explanation:

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2 years ago

What is the area and perimeter?

luda_lava [24]

Answer:

Perimeter: 26 units

Area: 24 units²

Step-by-step explanation:

12 + 9 + 5 = 26

A = 1/2BH

A = 1/2 12(4)

A = 1/2 48

A = 24

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If dy dx equals cosine squared of the quantity pi times y over 4 and y = 1 when x = 0, then find the value of x when y = 3.

Afina-wow [57]

Answer: $x = -\frac{8}{\pi}$

Explanation: Note that

$\frac{dy}{dx} = \cos^2 \left ( \frac{\pi y}{4} \right )
\\
\\ \frac{dy}{\cos^2 \left ( \frac{\pi y}{4} \right )} = dx
\\
\\ \int{\frac{dy}{\cos^2 \left ( \frac{\pi y}{4} \right )}} = \int dx
\\
\\ \boxed{x = \int{\sec^2 \left ( \frac{\pi y}{4} \right )dy}}$

To evaluate the integral in the boxed equation, let $u = \frac{\pi y}{4}$ . Then,

$du = \frac{\pi}{4} dy 
\\ \Rightarrow \boxed{dy = \frac{4}{\pi}du}$

So,

$x = \int{\sec^2 \left ( \frac{\pi y}{4} \right )dy}
\\
\\ = \int{\sec^2 u \left ( \frac{4}{\pi}du \right )}
\\
\\ = \frac{4}{\pi}\int{\sec^2 u du}
\\
\\ = \frac{4}{\pi} \tan u + C
\\
\\ \boxed{x = \frac{4}{\pi} \tan \left ( \frac{\pi y}{4} \right ) + C}\text{ (1)}$

Since y = 1 when x =0, equation (1) becomes

$0 = \frac{4}{\pi} \tan \left ( \frac{\pi (1)}{4} \right ) + C 
\\ 
\\ 0 = \frac{4}{\pi} (1) + C 
\\
\\ \frac{4}{\pi} + C = 0
\\
\\ \boxed{C = -\frac{4}{\pi}}$

With the value of C, equation (1) becomes

$\boxed{x = \frac{4}{\pi} \tan \left ( \frac{\pi y}{4} \right ) -\frac{4}{\pi} }$

Hence, if y = 3,

$x = \frac{4}{\pi} \tan \left ( \frac{\pi y}{4} \right ) -\frac{4}{\pi} 
\\
\\ x = \frac{4}{\pi} \tan \left ( \frac{\pi (3)}{4} \right ) -\frac{4}{\pi} 
\\
\\ x = \frac{4}{\pi} (-1) -\frac{4}{\pi} 
\\
\\ \boxed{x = -\frac{8}{\pi}}$

6 0

3 years ago

An 80-foot rope from the top of a tree house to the ground forms a 45° angle of elevation from the ground. How high is the top o

lina2011 [118]

Answer:

56.6m

Step-by-step explanation:

Using SOH = opp/hyp

Where θ = 45°

Hpy = 80m

Opp = ?

Sin θ = opp/hpy

Sin 45 = opp/ 80

Sin 45 × 80 = opp

0.7071 × 80 = opp

Opp = 56.568

~ 56.6m

Hence the height of the top of the tree is 56.6m

4 0

3 years ago