Given that 8 x − 5 y = 16 Find x when y = 8

A hot air balloon is flying at a constant speed of 20 mi/h at a bearing of N 36° E. There is a 10mi/h cross wind blowing due eas

Ksju [112]

Answer:

The actual speed = 27.12 mi/h

Direction = 36.5° in NE(north of east)

Step-by-step explanation:

As given , A hot air balloon is flying at a constant speed of 20 mi/h at a bearing of N 36° E.

⇒θ = 36°

Let v₀ be the constant speed, then v₀ = 20

Let vₓ be the speed in East direction

$v_{y}$ be the speed in North direction

So,

vₓ = v₀ sin(θ) = 20 sin(36°) + 10 ( As given, There is a 10mi/h cross wind blowing due east.)

⇒vₓ = 20(0.588) + 10 = 11.76 + 10 = 21.76 mi/h

and $v_{y}$ = v₀ cos(θ) = 20 cos(36°) = 20(0.809) = 16.18 mi/h

Now,

the actual speed = √(vₓ)² + ( $v_{y}$ )²

= √(21.76)² + (16.18)²

= √473.498 + 261.792

= √735.29 = 27.12

⇒The actual speed = 27.12 mi/h

Now,

Direction = θ = $tan^{-1}(\frac{v_{y} }{v_{x} } ) = tan^{-1}(\frac{16.18 }{21.76 } ) = tan^{-1}(0.74) = 36.5$

⇒ Direction = 36.5° in NE(north of east)

7 0

3 years ago

Help with number 7. we just started this unit so i'm clueless.. please help!

crimeas [40]

You first need to isolate the y
4x+9y=-108
9y=-4x-108 (subtract 4x from both sides)
y=-4/9x-12 (divide both sides by 9)
Then, by using the y=mx+b form, we can tell that the y-intercept is -12 so A

Hope this helps

7 0

3 years ago

Read 2 more answers

Mason is planning to buy a car two years from now. He currently has $400 saved up to buy the car. From all the cars Mason is con

Goshia [24]

Answer:150 dollars

Step-by-step explanation:

3600 (cost of car) divided by 24 (months)

8 0

3 years ago

Applying the Procedure

Verizon [17]

Answer:

15 Square Inches

Step-by-step explanation:

Volume of the cone=40 cubic inches

Height of the cone=8 Inches

Step 1: Applying the formula for the volume of a cone

Volume of a Cone $=\frac{1}{3}\pi r^2 h=\frac{1}{3} X $Base Area X Height$

Step 2: Substituting values for the variables

$40=\frac{1}{3} X $Base Area X 8$

Step 3: Simplifying the right side

$40=\frac{8}{3} X $Base Area$

Step 4: Multiplying by the reciprocal

$40X\frac{3}{8}=\frac{8}{3} X\frac{3}{8} X $Base Area\\$

Therefore, Base Area of the Cone=15 Square Inches

8 0

3 years ago

There is a positive correlation between drinking coconut milk and eating potato chips. What does this correlation mean? What are

faltersainse [42]

Answer with explanation:

It is given that, there is positive correlation between drinking coconut milk and eating potato chips.

→Correlation coefficient is denoted by r.

→The value of r lies between , -1 and 1 which is represented as , -1 ≤r≤1.

→Correlation that is relation between two variables is said to be strongly positive, if r is equal to 1, and it is said to be strongly weak, if it is equal to -1 , and said to have no association if r=0.

→ The meaning of positive correlation is that value of r, is greater than >0.8 but less than 1.

The two variables which are positively correlated ,can have following relationship.

1. With increase in one other increases.

2.With decrease in one other decreases.

3. Slope will be a linear that is a straight line not passing through origin.

3 0

3 years ago