1) A searchlight is mounted on the front of a search and rescue helicopter. The pilot is
flying the helicopter 150 m above the ground and the centre of the searchlight is angled
down at an angle of 70 degrees from the horizontal. The beam spreads out by 2.5
degrees to either side of the centre of the beam. How wide an area does the beam
illuminate on the ground?
I
I need it today please

Answer:

36y⁴ + 60y⁶ + 25y⁸

Step-by-step explanation:

(6y² + 5y⁴)² = (6y² + 5y⁴)(6y² + 5y⁴)

we can use the FOIL method to get:

36y⁴ + 30y⁶ + 30y⁶ + 25y⁸

we can simplify the two middle terms and get:

36y⁴ + 60y⁶ + 25y⁸

Answer:

[tex]\left(6y^2+5y^4\right)^2[/tex]

[tex](6y^2+5y^4)^2=36y^4+60y^6+25y^8[/tex]

[tex]=\left(25y^8+60y^6+36y^4\right)[/tex]

[tex]=\left(36y^4+60y^6+25y^8\right)[/tex]

[tex]=36y^4+60y^6+25y^8[/tex]

---------------------------

hope it helps...

have a great day!!

Answer:

we reject H0 and conclude that management's belief about variance is untrue.

Step-by-step explanation:

H0 : σ² = 250

H1 : σ² ≠ 250

Sample size, n = 25

xbar = 50.6 ; s² = 500

α = 0.01 ;

The test statistic :

χ² = [(n - 1)s²] ÷ σ²

χ² = [(25 - 1)* 500] ÷ 250

χ² = (24 * 500) / 250

χ² = 12000 / 250

χ² = 48

The critical value:

df = n-1 ; 25 - 1 = 24

χ²(0.01/2 ; 24) = 45.559

Decison :

Reject H0 : if |χ² statistic| > critical value

Since 48 > 45.559

Hemce, we reject H0 and conclude that management's belief about variance is untrue.

Answer:

yes

Step-by-step explanation:

y=-16r^2+63r+4

maximum value of y :

y'=0

-32r +63=0

r= 63/32

y = -16(63/32)²+63(63/32)+4

= -4 + 124 + 4 = 124 ft

124 > 68

the Arrow can pass over the tree

Answer:

(a) Circle Q is 9.4 units to the center of circle P

(b) Circle Q has a smaller radius

Step-by-step explanation:

Given

[tex]P:(x - 1)^2 + (y + 6)^2 = 9[/tex]

[tex]Q:(x + 4)^2 + (y + 14)^2 = 4[/tex]

Solving (a): The distance between both

The equation of a circle is:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

Where

[tex]Center: (h,k)[/tex]

[tex]Radius:r[/tex]

P and Q can be rewritten as:

[tex]P:(x - 1)^2 + (y + 6)^2 = 3^2[/tex]

[tex]Q:(x + 4)^2 + (y + 14)^2 = 2^2[/tex]

So, for P:

[tex]Center = (1,-6)[/tex]

[tex]r = 3[/tex]

For Q:

[tex]Center = (-4,-14)[/tex]

[tex]r = 2[/tex]

The distance between them is:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2[/tex]

Where:

[tex]Center = (1,-6)[/tex] --- [tex](x_1,y_1)[/tex]

[tex]Center = (-4,-14)[/tex] --- [tex](x_2,y_2)[/tex]

So:

[tex]d = \sqrt{(1 - -4)^2 + (-6 - -14)^2[/tex]

[tex]d = \sqrt{(5)^2 + (8)^2[/tex]

[tex]d = \sqrt{25 + 64[/tex]

[tex]d = \sqrt{89[/tex]

[tex]d = 9.4[/tex]

Solving (b): The radius;

In (a), we have:

[tex]r = 3[/tex] --- circle P

[tex]r = 2[/tex] --- circle Q

By comparison

[tex]2 < 3[/tex]

Hence, circle Q has a smaller radius

Answer:

4/141

Step-by-step explanation:

simplify 20/705

Answer:

4/141

Step-by-step explanation:

Let's think of this like a point. We know the y-value, but not the x-value. Therefore, in order to find b, we should plug in our known y-value, 19, for r(x).

19 = 2b + 1 || We can leave it as x in our equation or change it to b. Either way you will get the same answer. I changed it to b in this case just to follow through with what the question is asking.

18 = 2b

b = 9

Hope this helps!! :)

Answer:

9

Step-by-step explanation:

They are asking what value of x can you input into 2x+1 so that the outpot is 19.

In other words, you need to solve 2x+1=19.

Subtracting 1 on both sides gives: 2x=18.

Dividing 2 on both sides gives: x=9.

So r(9)=19 since 2(9)+1 is 19.

Answer: The answer is 60 mi^2

Step-by-step explanation:

Answer:

(0,-7)

Step-by-step explanation:

a^2+B+c

c= y intercept.

therefore the answer is (0,-7)

Answer:

the y intersept is (0,-7)

Step-by-step explanation:

Step-by-step explanation:

15*8= 120

120/2= 60

60*13= 780

So its B.  

Answer:

The answer is D. 1 cubic foot.

Step-by-step explanation:

To solve for the volume of a cube, use the formula V= [tex]a^{3}[/tex]. This is the formula because the volume of a cube formula equals length times width times height. Since the length, width, and height are all the same values, the simplest volume of a cube formula is [tex]a^{3}[/tex].

Next, plug in the information from the question into the formula, which will look like V= [tex]1^{3}[/tex]. Then, solve the equation, and the final answer will be 1 cubic foot.

Answer: The actual area of the base of the building is 4900 square feet.

Step-by-step explanation:

We have given, the scale on the model: 1 inch = 35 feet

In model,

Length= 4 feet , Width = 1 inch

As per scale ,

Actual length =  4 x 35 feet

= 140 feet

Actual width = 35 feet

Area of base of the building = Length x width

= 140 x 35

= 4900 square feet

Hence, the actual area of the base of the building is 4900 square feet.

Answer:

2 °F

Step-by-step explanation:

Overnight temperature = -7 °F

Total Noon temperature = 9 °F

What was the temperature in Chicago that afternoon?

Temperature in Chicago that afternoon = Total Noon temperature + Overnight temperature

= 9 °F + (-7 °F)

= 9 °F - 7 °F

= 2 °F

Temperature in Chicago that afternoon = 2 °F

Answer:

25.5 = c

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

17^2 + 19 ^2 = c^2

289+361 = c^2

650 = c^2

Take the square root of each side

sqrt(650) = sqrt(c^2)

25.49509757=c

To the nearest tenth

25.5 = c

Answer:

C = 25.5

Step-by-step explanation:

17² + 19² = x²

289 + 361 = x

289 + 361 = 650

√650 = 25.495097567963924150141120545114

25.495097567963924150141120545114 ≅ 25.5

Answer:

I only know this much.....

A) Deepthi has won the election.

B) Rashmi got minimum number of votes.

Answer:

11 1/5 minutes

Step-by-step explanation:

All you have to do is add up all the songs together.

3 1/2 = 3 30/60

2 57/60= 2 57/60

4 3/4 = 4 45/60

Add this all up

9 132/60

11 12/60

11 1/5

11 1/5 minutes

If this helps please mark as brainliest

Answer: 24

Step-by-step explanation: First, you fill in the values for each letter; replace any a with 12, replace any b with 6, and replace any c with 3. Then, enter the equation into the calculator like so, and it should be equal to 24.

I hope this helps. Have a nice day.

Answer:

g(x) = 12*x^2 + 8

Step-by-step explanation:

For a function f(x), a vertical stretch of scale factor k is defined as:

g(x) = k*f(x)

In this case, we know that f(x) = 3*x^2 + 2

And the function g(x) is the function f(x) vertically stretched by a factor of 4, then we have k = 4

and:

g(x) = 4*f(x)

Replacing by the actual function, we get

g(x) = 4*(3*x^2 + 2)

g(x) = 4*3*x^2 + 4*2

g(x) = 12*x^2 + 8

Answer:

a

Step-by-step explanation:

To obtain f(b) substitute x = b into f(x) , that is

f(b) = 6(b) - 1 = 6b - 1

f(x) and f(b) are very similar. The only difference is that in every place where x is in the function, we now will plug in b. This is just like plugging in a number. For example, if our function was f(x) and we had to plug in 4, it might look something like this: f(4). Very similar, and we know how to plug that number in.

Let's do the same thing with b.

f(x) = 6x - 1

f(b) = 6b - 1

Hope this helps!! :)

Answer: Down

Step-by-step explanation:

down nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn

Answer:

C, 11/12.

Step-by-step explanation:

There is only one February in one year, and there are eleven other months (January, March, April, May, June, July, August, September, October, November, December) so therefore 11/12 is the correct answer.

Answer:

0.51

Step-by-step explanation:

#1.

For this problem, we can use Pythagorean Theorem (a^2 + b^2 = c^2, where a and b are the legs, and c is the hypotenuse). We are given C, the hypotenuse, and A, a leg of the triangle in this problem.

9^2 + b^2 = 41^2

81 + b^2 = 1681

b^2 = 1600

b = 40 feet

#2.

We will again use Pythagorean Theorem. We are given the height and the length of a leg in this problem.

33^2 + b^2 = 65^2

1089 + b^2 = 4225

b^2 = 3136

b = 56 inches

Hope this helps!! :)

Given = V= 4p²

and P= 3

V= 4×3²

V= 36.

yh

so

there is another answer, it is above me

9514 1404 393

Answer:

  2/3

Step-by-step explanation:

The value of the function at x=-1 can be found by substituting that value for x and doing the arithmetic.

  f(-1) = 1/3(-1)³ -(-1)

  f(-1) = -1/3 +1 = 2/3

The relative maximum value is 2/3.