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2 years ago

Find the altitude of a kite where 120 feet of string makes a 64 degree angle to the ground

Mathematics

1 answer:

Mekhanik [1.2K]2 years ago

4 0

Answer:

107.86 to 2 d.p.

Step-by-step explanation:

makes a triangle. 120 feet is the hypotenuse.

we want to find the opposite so we will use sine.

sin(x) = opp/hyp which means opp = sin(x)hyp.

opp = sin(64)120

opp = 107.86 to 2d.p.

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Which sequences of transformations will map circle M onto circle N?

sergiy2304 [10]

Answer:

1: Reflect M across the x-axis

2: Dilate about the center by 3/2

Step-by-step explanation:

Given

See attachment for M and N

Required

Which maps M to N

The coordinates of the radius of the circles are:

$M = (5,5)$

$N = (5,-5)$

And the radius of circles are:

$r_M=2$

$r_N=3$

The first transformation from M to M' is:

- Reflect across the x-axis

The rule is:

$(x,y) \to (x,-y)$

$M(5,5) \to M'(5,-5)$

At this point, M' and N now have the same center but different radius.

The second transformation from M' to N is:

- Dilate about the center by dividing the radius of N by the radius of M

i.e.

$k =\frac{r_N}{r_M}$

$k =\frac{3}{2}$

At this point, M has been completely mapped to N.

4 0

3 years ago

7x+2y=-28 Help write slope-intercept form pls

kap26 [50]

Answer:

y = - $\frac{7}{2}$ x - 14

Step-by-step explanation:

Slope intercept form: y = mx + b

Isolate the y:

7x + 2y = -28

2y = -7x - 28

y = - $\frac{7}{2}$ x - 14

3 0

3 years ago

A hot air balloon rising vertically is tracked by an observer located 5 miles from the lift-off point. At a certain moment, the

Zigmanuir [339]

Answer:

Step-by-step explanation:

aThe person and the hot air balloon form a right triangle, with the lift-off point as the vertex that form the right angle. If you were to try to solve for the height of the balloon, you would need to use tangent to do so:

tanθ = opp/adj = y/x

y = xtanθ

What this problem ultimately wants to know, is how the distance of the balloon is changing with respect to time: dy/dt. So we need to take the derivative of the above equation (you need to product rule to do so):

dy/dt = (dx/dt)tanθ + xsec2θ(dθ/dt)

We need to find out values for all of the variables:

The observer is not moving, therefore dx/dt = 0.

The observer is standing 4 miles away from the lift-off point, so x = 4.

The angle between the horizontal and the observer's line of sight is π/3, therefore θ = π/3.

The rate of change for the angle, dθ/dt, is 0.1.

Just plug all the numbers in:

dy/dt = (0)tan(π/3) + (4)sec2(π/3)(0.1)

dy/dt = 0 + 1.6

dy/dt = 1.6 mi/min

5 0

2 years ago

I need help QUICKLY on this algebra question!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Luda [366]

Answer:

x = -1

Step-by-step explanation:

to find axis of symmetry, use the following equation:

x = -b/2a

in this problem, a = 3, b = 6, c = -12

x = -6/2(3)

x = -6/6

x = -1

8 0

3 years ago

What is the value of y?

Nataliya [291]

Answer:

B. 85

Step-by-step explanation:

I haven't taken Geometry in 2 years So I don't remember how to explain it.

5 0

3 years ago