Mathematics High School

An airplane takes off from the ground and reaches a height of 500 feet after flying 2 miles. given the formula h = d tan θ, where h is the height of the plane and d is the distance (along the ground) the plane has flown, find the angle of ascent θ at which the plane took off.

Answers

Answer 1
First we convert everything to the same unit taking into account the following conversion:
 1 mile = 5280 feet
 So, we have:
 h = 500 feet
 d = 2 (5280) = 10560 feet
 Substituting in the given formula we have:
 h = d tan θ
 500 = 10560tan θ
 tan θ = 500/10560
 θ = Atan (500/10560)
 θ = 2.71 degrees.
 Answer:
 the angle of ascent θ at which the plane took off is: 
 θ = 2.71 degrees.

Related Questions

Find all solutions in the interval [0, 2π).

sec2x - 2 = tan2x

a) No solution

b) x = pi/3

c) x = pi/4

d) x = pi/6

Answers

we have that
sec²x - 2 = tan²x--------> equation 1

and we know
identity-----------> tan²x=sec²x-1------------> equation 2

I substitute 2 in 1
sec²x - 2 = sec²x-1----------> -2=-1---------> no solution

the answer is the option a) No solution
The answer is no solution.
Explanation:
sec²x - 2 = tan²x
tan²x=sec²x-1
sec²x - 2 = sec²x-1
 -2=-1

there is no solution

A rectangular box contains 336 cubic inches. If it is 12 inches long and 7 inches wide, how deep is it?

Answers

Hello

Your answer is 4 inches deep :))

Hope this helps
4.36in deep rounded to the nearest hundredth

Two buildings are 200 feet apart. the height of the taller building is 50 ft. the angle of depression from the top of the taller building to the top of the shorter building is 8°. what equation below will correctly determine the height (h) of the shorter building?

Answers

The height of the taller building is 50ft, the height of the shorter building is h. The difference in heights will be:
(50-h) ft
tan x=opposite/adjacent
thus
tan 8=(50-h)/200
200*tan 8=50-h
28.11=50-h
h=50-28.11
h=21.89
the height of the shorter building is h=21.89 ft

Bailey writes 5 + 8 on the left-hand side of a paper and then writes 4 + 9 to the right of it. Which symbol should Bailey write between the two sets of numbers to show they have the same sum
a. +
b. –
c. ≠
d. =

Answers

5 + 8 = 4 + 9
13 = 13

ANSWER: D) =

The equals sign should be in between because the numbers on each side add up to the same number.

Hope this helps! :)

Someone help with math?

Answers

The answer is the second one (the one on the top right)

HELPPPPPPPPPPPPPPPPPPPPPPPP

Answers

The discriminant is
.. d = b^2 -4*a*c
When the roots are imaginary, it is less than zero. You have a=4, so that means
.. b^2 -16c < 0
.. b^2 < 16c . . . . . . . . . . . . . . . . . coresponds to the 7th choice
This does not say it is part of a timed test. I will trust you to tell me if it is.
The discriminate is sqrt(b^2 - 4ac)
a is given as 4.
That makes the discriminate = sqrt(b^2 - 16c)
To get imaginary roots, you have to be taking the square root of something < 0

The answer is 
b^2 < 16c <<<< answer

Twice the sum of two consecutive integers equals 42

Answers

Hello,

Let's assume n the first integer
n+1 the greater
n+(n+1)=2n+1 is odd but 42 (universel answer in Robots IE) is even!!!!
Not answer!



Which expressions are polynomials?

Select each correct answer.

A.20x² + y
B.20x2+y12
C.20x2y
D.20x²

Answers

Hi!

All the given answers are polynomials
A.20x² + y
B.20x*2+y*12
C.20x*2*y
D.20x²

Answer:


Step-by-step explanation:

Polynomial :  

An expression that can have constants (like 4), variables (like x or y) and exponents (like the 2 in [tex]y^{2}[/tex]), that can be combined using addition, subtraction, multiplication and division, but:

no division by a variable.

a variable's exponents can only be 0,1,2,3,... etc.

it can't have an infinite number of terms.

Thus according to definition all are polynomials

A.20x² + y


B.20x2+y12


C.20x2y


D.20x²



Printer paper is sold in packages of 500 sheets. of a printing job uses 1 3/4 packages of paper how may sheets is that

Answers

[tex]\text {1 package of papers = 500 sheets}[/tex]

[tex]1 \dfrac{3}{4} \text { package of papers = } 500 \times 1 \dfrac{3}{4} [/tex]

[tex]1 \dfrac{3}{4} \text { package of papers = } 500 \times \dfrac{7}{4} [/tex]

[tex]1 \dfrac{3}{4} \text { package of papers = } 875 \text { sheets}[/tex]

The printing job that uses 1 3/4 packages of printer paper requires 875 sheets.

To determine how many sheets of paper are used in a printing job that uses 1 3/4 packages of paper, follow these steps:

First, understand that 1 package contains 500 sheets of printer paper.Next, convert the mixed number 1 3/4 to an improper fraction. This is done by multiplying the whole number (1) by the denominator (4) and adding the numerator (3), giving us 7/4.Now, multiply the number of packages (7/4) by the number of sheets per package (500):

7/4 * 500 sheets = (7 * 500) / 4 = 3500 / 4 = 875 sheets.

Therefore, the printing job uses 875 sheets of paper.

Place the indicated product in the proper location on the grid.

(3a + 2c )(9a 2 - 6ac + 4c 2 )

Answers

Answer
27a^3+8c^3

Explanation.
In this question you are expected to expand (3a+2c)(9a^2-6ac+4c^2
(3a+2c)(9a^2-6ac+4c^2
=(3a×9a^2 )-(3a×6ac)+(3a×4c^2 )+(2c×9a^2 )-(2c×6ac)+(2c×4c^2 )
27a^3-18a^2 c+12ac^2+18a^2 c-12ac^2+8c^3
27a^3+8c^3
The expansion of the expression, (3a+2c)(9a^2-6ac+4c^2) is 27a^3+8. This is what the question requires.  

Answer:

The product of [tex]\left(3a+2c\right)\left(9a^2-6ac+4c^2\right)=8c^3+27a^3[/tex]

Step-by-step explanation:

Given: Polynomial [tex]\left(3a+2c\right)\left(9a^2-6ac+4c^2\right)[/tex]

We have to place the indicated product in the proper location o the grid.

Consider the given product [tex]\left(3a+2c\right)\left(9a^2-6ac+4c^2\right)[/tex]

Using distributive property, Multiply each term of first bracket with each term of last bracket, we have,

[tex]=3a\cdot \:9a^2+3a\left(-6ac\right)+3a\cdot \:4c^2+2c\cdot \:9a^2+2c\left(-6ac\right)+2c\cdot \:4c^2[/tex]

Apply plus-minus rule [tex]+\left(-a\right)=-a[/tex] , we have,

[tex]=3\cdot \:9a^2a-3\cdot \:6aac+3\cdot \:4ac^2+2\cdot \:9a^2c-2\cdot \:6acc+2\cdot \:4c^2c[/tex]

Simplify, we have,

[tex]=27a^3-18a^2c+12ac^2+18a^2c-12ac^2+8c^3[/tex]

Adding similar terms, we have,

[tex]=8c^3+27a^3[/tex]

Thus, The product of [tex]\left(3a+2c\right)\left(9a^2-6ac+4c^2\right)=8c^3+27a^3[/tex]

Location on grid is as shown below

Question 2(Multiple Choice Worth 2 points)
(10.06 MC)

Compare the functions shown below:

f(x) = 4 sin (2x − π) − 1

g(x)
x y
−1 6
0 1
1 −2
2 −3
3 −2
4 1
5 6

h(x) = (x − 2)2 + 4


Which function has the smallest minimum y-value?
f(x)
g(x)
h(x)
Both f(x) and g(x) have the same minimum y-value.

Answers

Answer:

1. f(x)=4 sin (2 x-π)-1

 =4 sin [-(π-2 x)] -1

 = -4 sin 2 x -1

-1 ≤ sin 2 x ≤1

f(x) is minimum, when, sin 2 x=1

= -4 × 1 -1

= -5→Minimum value of f(x).

2. Minimum y value of g(x) by looking at the table is ,

g(x)=-3→Minimum

3. h(x)=(x-2)²+4

As, (x-2)², will yield always a positive value.

So, minimum of h(x), will be at , x=2

h(2)=(2-2)²+4=4→Minimum

Among the three function given, f(x) has minimum y -value,equal to -5.

Option A: f(x)

How do I solve this?

Answers

In the first step, you match the pattern of
.. (-3/2)x^2 +0x +3
to the pattern of
.. ax^2 +bx +c

and you can see that
.. a = -3/2 . . . b = 0 . . . c = 3
____
Because a is negative, the parabola opens down. Because it opens down, the vertex is the high point, the maximum.

____
The y-intercept is always c. Here c=3, so the y-intercept is (0, 3).

____
The axis of symmetry is given by
.. x = -b/(2a)
.. x = -0/(2*(-3/2)) = 0

____
Because the y-intercept is on the axis of symmetry, it is the vertex.
.. vertex = (0, 3)

____
Put x=±2 in the equation and evaluate.
.. y = (-3/2)*(±2)^2 +3
.. = (-3/2)*4 +3
.. = -6 +3 = -3
The two points are (-2, -3) and (2, -3).

How many feet are in 100 meters if 1 meter is 1.09 yards? Will mark brainliest if you include clear steps. Thank you!

Answers

well, there are 3 feet in 1 yard, and 1.09 yards in 1 meter, so then

[tex]\bf 100~\underline{m}\cdot \cfrac{1.09~\underline{yd}}{\underline{m}}\cdot \cfrac{3~ft}{\underline{yd}}\implies \cfrac{100\cdot 1.09\cdot 3~ft}{1}\implies 327~ft[/tex]

notice, we use the ratio, and whichever unit you want cancelled, you simply flip the ratio to have it cancelled, if the "m" is atop and you need that cancel, use the ratio with the "m" at the bottom, m/m = 1, and so they cancel out, and so on.

what is the factored form of the expression? w^2 + 12w + 36

Answers

THE ANSWER IS(w+6)2(w+6)2

Answer:

[tex](w+6)^2[/tex] is the factored form of the given expression.

Step-by-step explanation:

The given expression is:

[tex]w^2+12w+36[/tex]

Simplifying the above given expression, we get

[tex]w^2+6w+6w+36[/tex]

[tex]w(w+6)+6(w+6)[/tex]

[tex](w+6)(w+6)[/tex]

[tex](w+6)^2[/tex]

Which is the required factored form of the given expression.

If someone can answer this, you are BEYOND SMARTT!!! But tell me how to do it too!!!!

Answers

look at all the choices

we know that at t = 0, the height of the rock is 16

choices H and I do not have a value of 16 at t = 0.

H: h(0) = -5.2(0)² + 24(0) - 12 = -12
I: h(0) = -4.2(0)² + 26(0) - 20 = -20

so we are left with F and G

if we take choice F and plug in t = 1
h(1) = -4.7(1)² - 25(1) + 16 = -13.7
if we take choice G and plug in t = 1
h(1) = -4.7(1)² + 25(1) + 16 = 36.3

only choice G works for us since it has 36.3 at t = 1

you could have also put these points in a graphing calculator and then use the quadratic regression feature to get an equation that will model this data

Which description best describes the graph?

A graph is shown. A straight line begins at the upper left side of the coordinate plane and moves down towards the right side. The line crosses the y-axis at y equals 3 and the x-axis at x equals 1.5

Linear increasing
Linear decreasing
Nonlinear increasing
Nonlinear decreasing

Answers

This is a linear decreasing graph.

As the x-values increase, the y-values decrease; this means it is a decreasing graph.

The graph shows a straight line with a constant rate of change, so it is linear.

Answer:

B. Linear decreasing

Step-by-step explanation:

We are given that,

The graph of the function is passing through the points (0,3) and (1.5,0).

Then, the rate of change is [tex]m=\frac{0-3}{1.5-0}=\frac{-3}{1.5}=-2[/tex]

So, the function is represented by a straight line with constant rate of change -2.

Thus, the function is a linear function.

Moreover, as the value of x is increasing, we see that the value of y is decreasing.

So, the function is a decreasing function.

Hence, option B is correct.

A charged particle is projected in the air such that its horizontal (x) and vertical (y) shifts are given by x(t) = 10t − t2 and y(t) = 6t, where x and y are in meters and time t is in seconds. What is the ratio of y to x at t = 4 seconds?

Answers

[tex]\bf \stackrel{ratio}{y:x}\implies \cfrac{y}{x}\implies \left. \cfrac{6t}{10t-t^2} \right|_{t=4}\implies \cfrac{6(4)}{10(4)-(4)^2} \\\\\\ \cfrac{24}{24}\implies \cfrac{1}{1}\implies \stackrel{ratio}{1:1}[/tex]

Find the area of the shaded polygons:

Answers

check the picture below.

now, notice, is really just a large triangle in red, with a base of 4 and a height of 3 units, and two smaller triangles below it, one has a base 1 and a height of 1, and the other has a base of 3 and a height of 1.

so just get the area of each, sum them up, and that's the shaded area.

The total area of the figure is 8 square units.

How to find the area?

Remember that the area of a triangle is equal to its height times its base over 2.

In the image we can see 3 triangles, the larger one has a height of 3 units and a base of 4 units, so its area is:

A = 3*4/2 = 6 square units.

The bottom left triangle has a base of 1 unit and a height of 1 unit, so its area is:

A' = 1*1/2 = 0.5 square units.

The bottom right triangle has a base of 3 units, and a height of 1 unit, so its area is:

A'' = 1*3/2 = 1.5 square units.

The total area is:

A + A' + A'' = (6 + 0.5 + 1.5) square units = 8 square units.

If you want to learn more about area, you can read:

https://brainly.com/question/24487155

Find the length of the hypotenuse of a right triangle with legs of lengths 9 and 12 If necessary round your answer to two decimal places

Answers

you can get help from Pythagoras theorem :
[tex] {x}^{2} = {9}^{2} + {12}^{2} \\ {x}^{2} = 81 + 144 = 225 \\ x = \sqrt{225} = 15[/tex]
hope this helps

Two numbers are in the ratio of 5:6 if the sum of the numbers is 66 find the largest number

Answers

5k + 6k = 66 



k = 6

30 : 36 



Solution 2:

so 5x+6x=66
or 11x=66
or x=6
so the value of the larger number is 6*6=36


3x - 5y = 17 y = -7 Solve by substitution.

Answers

Substitute the value of y given by the second equation into the first.
.. 3x -5(-7) = 17
.. 3x +35 = 17
.. 3x = -18
.. x = -6

The solution is (x, y) = (-6, -7).

Determine if x + 3 is a factor of -3x^3+6x^2+6x+9, and how do you know?

Answers

Begin by taking out -3 as a common factor.
-3(x^3 - 2x^2 - 2x - 3)
If x + 3 is a factor, what is inside the brackets should be 0 when x = - 3 It is not. There is only one real root and that is when (x - 3) is equated to 0. Just to show the root is +3, the graph is included.  

Which of the following is the graph of


btw A is wrong (the 2nd pic)

Answers

I say the 3rd one it is

Asymptotes: Values of x that makes the denominator equal to zero:
x+2=0→x+2-2=0-2→x=-2
Asymptote x=-2

Lim x→Infinite y =
Lim x→Infinite 1/(x+2)+1
1/(Infinite+2)+1
1/Infinite+1
0+1
1
Horizontal asymptote y=1

Answer: Third graph (left to right)

A plane begins to descend from a height of 202 meters. The plane decreases in altitude at an average rate of 1.8 meters per second. Which function can be used to find the altitude of the plane in meters x seconds since it started. Show work please!

Multiple choice :
F. t(x) = 202- 1.8x
G. t(x) -1.8 (x + 202)
H. t(x) = 202 + 1.8x
I. t(x) = 1.8 ( x + 202)u

Answers

The plane starts at 202 m.
All altitudes are in meters.
After 1 second, it is at 202 - 1.8
After 2 seconds, it is at 202 - 1.8 * 2
After 3 seconds, it is at 202 - 1.8 * 3
etc.
After x seconds, it is at 202 - 1.8 * x

202 - 1.8 * x is the same as 202 - 1.8x

Answer: F. t(x) = 202 - 1.8x

Given sinx=0.9 , what is cosx ? Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.

Answers

The answer is 0.44. I don't know how it got there but that was the answer that the quiz said was correct lol

It is given sinx=0.9 .We need to find cosx.

We use the identity :

[tex] sin^{2} x + cos^{2} x =1 [/tex]

Substituting sinx=0.9

[tex] (0.9)^{2} +cos^{2} x =1 [/tex]

[tex] 0.81+cos^{2} x=1 [/tex]

Substracting 0.81 both sides:

[tex] cos^{2} x =1-0.81 [/tex]

[tex] cos^{2} x=0.19 [/tex]

Taking root of both sides cosx=0.435

Rounding to nearest hundredth

cosx=0.44.


The table shows the height of an object, h(t), in meters after t seconds. Use your calculator to find the quadratic function. Find the approximate time, to the nearest hundredth of a second, after which the object will reach its maximum height.

Answers

My calculator models the function as
.. h(t) = -4.9t^2 +23.4t +120

The maximum height is reached at t=-23.4/(2(-4.9)) ≈ 2.39 seconds.

Round each number to the nearest hundred and estimate the sum.

1,841 + 964

2,900
2,800
2,700
2,600

Answers

1841 ≈ 1800 (nearest hundred)
964 ≈ 1000 (nearest hundred}

1,841 + 964 ≈ 1800 + 1000 = 2800 (Answer B)

Answer:

The answer is 2,800 (B)

Good Luck :)

How many 12 inch sections can you get out of 9 foot calculator?

Answers

To solve this problem, the first thing you should keep in mind is the following conversion:
 1 foot = 12 inches.
 Therefore doing the conversion:
 (12 inch) * (1 foot / 12 inch) = 1 foot.
 The number of sections is:
 N = (9 feet) / (1 foot) = 9
 Answer:
 you can get out 9, 12 inch sections of 9 foot calculator

Choose the graph that matches the following system of equations: 2x + y = −1 3x + 2y = −6
Select one:
a. picture of coordinate plane with line y equals negative 2x plus 1 and line y equals 3 halves x minus 6. They intersect at 2, negative 3
b. picture of coordinate plane with line y equals negative 2x minus 1 and line y equals negative 3 halves x minus 3. They intersect at 4, negative 9
c. picture of coordinate plane with line y equals 2x minus 1 and line y equals negative 3x minus 3. They intersect at negative 0.4, negative 1.8
d. picture of coordinate plane with line y equals negative 2x minus 1 and line y equals 3 halves x plus 6. They intersect at negative 2, 3

Answers

Hi! You don't actually need to graph this nor find the intersection in order to know the answer. Through the process of elimination we can rule out incorrect answers.

Firstly, we express both equations with y on the left hand side since all choices are in that form:

[tex]y=-2x-1[/tex]
[tex]y=- \frac{3}{2}x-3 [/tex]

Knowing these, we can immediately rule out options a, c, and d since they have the wrong equations. This will leave us with option b.

You can verify if the point of intersection provided in option b is true by plugging in the values of x and y to both equations (you will find that it is indeed true).

ANSWER: b. picture of coordinate plane with line y equals negative 2x minus 1 and line y equals negative 3 halves x minus 3. They intersect at 4, negative 9.

Answer:

B

Step-by-step explanation:

Got it right on the test

Hope this helps :)

Given ​ f(x)=x2+14x+40 ​.
Enter the quadratic function in vertex form in the box.
f(x)=

Answers

we know that
the quadratic function in vertex form is--------------> y=a*(x-h)²+k

we have
f(x)=x²+14x+40
y=x²+14x+40

We can convert to vertex form by completing the square on the right hand side
y-40=x²+14x
y-40-49=x²+14x-49------> subtract 49 on BOTH sides to preserve the equality
y-40=(x²+14x+49)-49
y=(x²+14x+49)-49+40---------> y=(x+7)²-9

the answer is
the quadratic function in vertex form-----------> y=(x+7)²-9
the vertex is the point (-7,-9)

Answer: f(x) = (x+7)^2 -9

Step-by-step explanation:

I know that this is late but hopefully it will help someone else.

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