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4 years ago

Reflect (-8, -9) over the Y-axis. Where does it end up?

Mathematics

1 answer:

mina [271]4 years ago

8 0

Answer:

(8, - 9 )

Step-by-step explanation:

Under a reflection in the y- axis

a point (x, y ) → (- x, y ) , then

(- 8, - 9 ) → (8, - 9 )

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A surveyor sights the far bank of a river at an angle of 110° to the near bank. She then moves 75 feet upriver and sights the sa

Leya [2.2K]

Answer:

Correct answer is 54.82 ft.

Step-by-step explanation:

First of all, let us label the diagram and do the construction as per the attached answer image.

Let us consider $\triangle ABC$ :

$\angle B = 90^\circ\\\angle ACB = 180-110 = 70^\circ$

Let side AB = d ft and let side BC = x ft

We need to find AB to find the shortest distance across the river.

Using trigonometric identity of tangent:

$tan\theta = \dfrac{Perpendicular}{Base}$

$tan 70 = \dfrac{d}{x}\\\Rightarrow x = \dfrac{d}{tan70} = 0.36d ..... (1)$

Now, let us have a look at another right angled triangle ABD:

Let us consider $\triangle ABC$ :

$\angle B = 90^\circ\\\angle ADB = 180-150 = 30^\circ$

side AB = d ft and side BD = x+75 ft

Using trigonometric identity of tangent:

$tan\theta = \dfrac{Perpendicular}{Base}$

$tan 30 = \dfrac{d}{x+75}\\\text{Using equation (1)}:\\0.577 = \dfrac{d}{0.36d+75}\\\Rightarrow 0.207d + 43.27 = d\\\Rightarrow 0.793d = 43.27\\\Rightarrow d \approx 54.82\ ft$

Correct answer is 54.82 ft.

7 0

4 years ago

Find the gradient of the line segment between the points (-2,2) and (0,6).<br> I

liberstina [14]

Answer:

rise 4, run -2. the gradiant is 2

Step-by-step explanation:

(X1,Y1)___(X2,Y2)

| | | |

(-2,2)_____(0,6)

X1-X2, Y1-Y2.

-2-0= -2= (-2,_)

2-6= 4= (_,4)

(-2,4)

3 0

3 years ago

Zoe is a chemistry teacher earning a salary of $38,000 per year. She also tutors part-time, charging $20 per session. Which of t

rjkz [21]

Earned Income because she is working full time, but also adds the extra 20$ for when she tutors in her free time<span />

8 0

4 years ago

Read 2 more answers

F ind the volume under the paraboloid z=9(x2+y2) above the triangle on xy-plane enclosed by the lines x=0, y=2, y=x

olga nikolaevna [1]

Answer:

The answer is 48 units³

Step-by-step explanation:

If we simply draw out the region on the x-y plane enclosed between these lines we realize that,if we evaluate the integral the limits all in all cannot be constants since one side of the triangular region is slanted whose equation is given by y=x. So the one of the limit of one of the integrals in the double integral we need to evaluate must be a variable. We choose x part of the integral to have a variable limit, we could well have chosen y's limits as non constant, but it wouldn't make any difference. So the double integral we need to evaluate is given by,

$V=\int\limits^2_0 {} \, \int\limits^{x=y}_0 {z} \, dx dy\\V=\int\limits^2_0 {} \, \int\limits^{x=y}_0 {9(x^{2}+y^{2})} \, dx dy$

Please note that the order of integration is very important here.We cannot evaluate an integral with variable limit last, we have to evaluate it first.after performing the elementary x integral we get,

$V=9\int\limits^2_0 {4y^{3}/3} \, dy$

After performing the elementary y integral we obtain the desired volume as below,

$V= 48 units^{3}$

4 0

3 years ago

Li walks at a constant rate of 7 ft. in 4 seconds. The table shows the relationship of feet to seconds. What is the constant of

Kisachek [45]

Answer:

The rate is 1.75 feet/seconds or 105 feet/minute.

Step-by-step explanation:

Given that,

Li walks at a constant rate of 7 feet in 4 seconds

To find the constant of proportionality, divide 7 feet by 4 seconds.

So,

$k=\dfrac{7\ \text{feet}}{4\ \text{seconds}}\\\\k=1.75\ \text{ft/s}$

1.75 ft/s is the constant of proportionality

We know that, 1 minute = 60 seconds

k = 105 feet/minute

So, the rate is 1.75 feet/seconds or 105 feet/minute.

4 0

3 years ago