Kiran is flying a kite. He gets tired, so he stakes the kite into the ground. The kite is on a stringthat is 18 feet long and makes a 30 degree angle with the ground. How high is the kite?
Answers
ANSWER:
9 feet
STEP-BY-STEP EXPLANATION:
We can calculate the value of the height of the kite by means of the trigonometric function sine, which is the following:
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \theta=30\text{\degree} \\ \text{hypotenuse = 18} \\ \text{opposite }=x \end{gathered}[/tex]Replacing and solving for x:
[tex]\begin{gathered} \sin 30=\frac{x}{18} \\ x=\sin 30\cdot18 \\ x=9 \end{gathered}[/tex]The height of the kite is 9 feet
Related Questions
4. What is 10% of 25? Type your answer using numbers only. Your answer
Answers
10% = 10/100 = 0.10
therefore:
[tex]25\times0.10=2.5[/tex]answer: 2.5
- 10x + 100y = 30-3x + 30y = 9
Answers
The given system is
[tex]\mleft\{\begin{aligned}-10x+100y=30 \\ -3x+30y=9\end{aligned}\mright.[/tex]First, we multiply the first equation by -3/10.
[tex]\mleft\{\begin{aligned}3x-30y=-9 \\ -3x+30y=9\end{aligned}\mright.[/tex]Then, we sum the equations
[tex]\begin{gathered} 3x-3x+30y-30y=9-9 \\ 0x+0y=0 \\ 0=0 \end{gathered}[/tex]According to this result, we can deduct that the system doesn't have any solutions because the lines represented by the equations are parallel.what are the bounds of integration for the first integral ?
Answers
We are going to use the properties of definite integrals. Note that if c belongs to the interval [a,b] and is integrable in [a,c] and [c,b], then f is integrable in [a,b]. Moreover,
[tex]\int_a^cf(x)dx+\int_c^bf(x)dx=\int_a^bf(x)dx[/tex]Applying this property to the presented case, we obtain that
[tex]\begin{gathered} \int_a^bf(x)dx=\int_{-5}^9f(x)dx+\int_9^{13}f(x)dx-\int_{-5}^2f(x)dx \\ \int_a^bf(x)dx=\int_{-5}^{13}f(x)dx-\int_{-5}^2f(x)dx \\ \int_a^bf(x)dx=\int_2^{13}f(x)dx \end{gathered}[/tex]Note: Another way to interpret the exercise is to interpret the integral as the area under the curve.
Thus, the answer to the exercise is a= 2 and b = 13.
what would be the most appropriate domain for this function? Number 7
Answers
Explanation:
This function is C(n) which means it's a function of n. It is said that n is the number of observed vehicles in a specified time interval. It cannot be negative and it has to be an integer. Therefore the domain is all integers greater or equal than zero.
Answer:
4) {0, 1, 2, 3...}
how far does a person travel in ft? this word problem is a little confusing but i understood everything else before this question.
Answers
Given:
The vertical height is 30ft.
The angle of elevation is 30 degrees.
To find:
The distance travelled by the person from bottom to top of the escalator.
Explanation:
Let x be the slant distance.
Since it is a right triangle.
Using the trigonometric ratio formula,
[tex]\begin{gathered} \sin\theta=\frac{Opp}{Hyp} \\ \sin30^{\circ}=\frac{30}{x} \\ \frac{1}{2}=\frac{30}{x} \\ x=30\times2 \\ x=60ft \end{gathered}[/tex]Therefore, the distance travelled by the person from the bottom to the top of the escalator is 60ft.
Final answer:
The distance travelled by the person from bottom to top of the escalator is 60ft.
The sides of a rectangle are in a ratio of 5:7 and the perimeter is 72. Find the area of the rectangle.
Answers
Since the sides of the rectangle are in ratio 5: 7
Insert x in the 2 terms of the ratio and find its perimeter using them
[tex]\begin{gathered} L\colon W=5x\colon7x \\ P=2(L+W) \\ P=2(5x+7x) \\ P=2(12x) \\ P=24x \end{gathered}[/tex]Equate 24x by the given perimeter 72 to find the value of x
[tex]24x=72[/tex]Divide both sides by 24
[tex]\begin{gathered} \frac{24x}{24}=\frac{72}{24} \\ x=3 \end{gathered}[/tex]Then the sides of the rectangle are
[tex]\begin{gathered} L=5(3)=15 \\ W=7(3)=21 \end{gathered}[/tex]Since the rule of the area of the rectangle is A = L x W, then
[tex]\begin{gathered} A=15\times21 \\ A=315 \end{gathered}[/tex]The area of the rectangle is 315 square units
The equation and graph of a polynomial are shown below. The graph reachesits minimum when the value of xis 4. What is the y-value of this minimum?--y= 2x2-16x + 30ys
Answers
We can find the y-value of the minimum using the graph or using the equation. Let's use the equation and evaluate it when x = 4.
[tex]\begin{gathered} y=2x^2-16x+30=2(4)^2-16(4)+30 \\ y=2\cdot16-64+30=32-64+30=-2 \end{gathered}[/tex]Hence, the y-value of the minimum is -2.in the figure, pr and qs are diameters of circle u. find the measure of the indicated arc
Answers
Step 1: Problem
Step 2 : Concept
QR = 136
PQS = 42 + 136 + 42 = 220
PS = 64 + 72 = 136
Write a system of equations to describe the situation below, solve using an augmented matrix.The glee club needs to raise money for the spring trip to Europe, so the members are assembling holiday wreaths to sell. Before lunch, they assembled 20 regular wreaths and 16 deluxe wreaths, which used a total of 140 pinecones. After lunch, they assembled 20 regular wreaths and 18 deluxe wreaths, using a total of 150 pinecones. How many pinecones are they putting on each wreath?The regular wreaths each have ? pinecones on them and the large ones each have ? pinecones.
Answers
Given
First : They assembled 20 regular wreaths and 16 deluxe wreaths, which used a total of 140 pinecones
Let's represent regular wreaths with r
and
Let's represent deluxe wreaths with d
[tex]20r+16d=140[/tex]Second: They assembled 20 regular wreaths and 18 deluxe wreaths, using a total of 150 pinecones
[tex]20r+18d=150[/tex]We now have
[tex]\begin{gathered} 20r+16d=140\text{ ...Equation 1} \\ 20r+18d=150\text{ ...Equation 2} \end{gathered}[/tex]we can now solve simultaneously, by subtracting the equation 1 and 2
[tex]\begin{gathered} 20r-20r+16d-18d=140-150 \\ -2d=-10 \\ Divide\text{ both sides by -2} \\ -\frac{2d}{-2}=-\frac{10}{-2} \\ \\ d=5 \end{gathered}[/tex]We can subsitute d=5 in equation 1 or 2
[tex]\begin{gathered} 20r+16d=140\text{ ... Equation 1} \\ 20r+16(5)=140 \\ 20r+80=140 \\ 20r=140-80 \\ 20r=60 \\ divide\text{ both sides by 20} \\ \frac{20r}{20}=\frac{60}{20} \\ \\ r=3 \end{gathered}[/tex]The final answer
5 pinecones on the deluxe wreath and 3 pinecones on the regular wreath
Hello hope you are doing well. Can you help me with this please
Answers
To find Mario's current grade is to find the average of all his grades for the first quarter.
The average of his grade for the first quarter is the mean which is 70 percent.
Also, 70 percent is equivalent to a C minus
What is the ones place and the hundredths place for 48.26
Answers
The first number before the decimal point is the ones place.
48.26
ones = 8
The second number after the decimal point is the hundredths place:
48.26
hundredth: 6
Find x1) -4x=362) x+6=133) -9x=36
Answers
1) -4x=36
2) x+6=13
3) -9x=36
SolutionNumber 1[tex]\begin{gathered} -4x=36 \\ divide\text{ both sides by -4} \\ -\frac{4x}{-4}=\frac{36}{-4} \\ \\ x=-9 \end{gathered}[/tex]Number 2[tex]\begin{gathered} x+6=13 \\ collect\text{ the like terms} \\ x=13-6 \\ x=7 \end{gathered}[/tex]Number 3[tex]\begin{gathered} -9x=36 \\ divide\text{ both sides by -9} \\ -\frac{9x}{-9}=\frac{36}{-9} \\ \\ x=-4 \end{gathered}[/tex]A) This graph represents Function or non function?B) is it discrete or Continuous?Because of you count dots or measure lines?The domain is:The range is:
Answers
A) It's a function because each point of x has a point on y.
B. It's a discrete functions because you can't see a continuous line.
C. Domain (-3,6)
D. Range (0,3)
* C and D if each square is equivalent to 1 unit.
Use a unit multiplier to convert 90 meters per minute to meters per second.
Answers
Hello there. To solve this question, we'll have to remember some properties about unit conversions.
We want to convert 90 meters per minute to meters per second.
Remember 1 minute is equal to 60 seconds, therefore we can write
90 meters per 60 seconds
Simplify it by a factor of 30
3 meters per 2 seconds
Which is the same as
1.5 meters per second
The unit multiplier was divide the number by 60, in order to get minutes to seconds and, therefore, find the value in m/s.
Neals family spends $7,104 annually for food. Approximately what percent of their $34,910 annual net income is this amount?
Answers
Total income= $34910
Amount spent on food = $7104
[tex]\begin{gathered} \text{ \% of income spent on food =}\frac{\text{ Amount spent on food}}{\text{ Total income }}\text{ x 100} \\ =\frac{7104}{33910}\text{ x 100} \\ =20.95\text{ \%} \end{gathered}[/tex]use a unit rate to find the unknown value.2/4=?/16the unknown value is?
Answers
Let x be the unknown value.
Therefore we have
[tex]\frac{2}{4}=\frac{x}{16}[/tex]So we can inform from the first term that the denominator is double the numerator, since this term is equal to second term with the unknown x, same applies there also.
So,
[tex]\begin{gathered} 2x=16 \\ x=\frac{16}{2}=8 \end{gathered}[/tex]This can be further confirmed by applying cross multiplication,
[tex]\begin{gathered} \frac{2}{4}=\frac{x}{16} \\ 16\times2=4x \\ x=\frac{16\times2}{4}=8 \end{gathered}[/tex]Find the equation of a line perpendicular to y + 1 =-1/2xthat passesthrough the point (-8, 7).
Answers
step 1
Find out the slope of the given line
we have
y+1=-(1/2)x
The slope is m=-1/2
Remember that
If two lines are perpendicular
then
their slopes are negative reciprocal
so
The slope of the perpendicular line is
m=2
step 2
Find out the equation of the line in slope-intercept form
y=mx+b
we have
m=2
point (-8,7)
substitute and solve for b
7=2(-8)+b
7=-16+b
b=23
therefore
the equation of the line is
y=2x+23Given v=7i - 5j and w=-i+j,a. Find project wv .b. Decompose v into two vectors V, and v2, where vy is parallel to w and v2 is orthogonal to w.
Answers
For the given vector v=7i - 5j and w=-i+j,
projwv = 6i - 6j
v1 = 6i -6j
v2 = i +j
Vector:
A quantity that has both magnitude and direction are called vector. It is typically represented by an arrow whose direction is the same as that of the quantity and whose length is proportional to the quantity's magnitude.
a) projwv is the projection of v onto w. Use the following equation:
projwv = [(v•w)/((magnitude(w))2)] w
v•w = (7*-1) + (-5*1) = -12
(magnitude w)^2 = ([tex]\sqrt{1^{2} + 1^{2}}[/tex])^2 = 2
projwv = ((-12)/2)(-i + j)
= 6i - 6j
b) The two components of the decomposed v will add to create the original vector v. v1 that is parallel to w will be the same as the projection of v onto w.
v = v1 + v2
v2 = v - v1 = (7i - 5j) - (6i -6j) = i +j
You can check that v2 is orthogonal by taking the dot product (v2•w). This equals 0.
To learn more about vector visit: https://brainly.com/question/13322477
#SPJ9
A is the set of even numbers greater than or equal to 4 and less than or equal to 8B=1-29, -25,-24, -22, -21, 22, 27(a) Find the cardinalities of A and B.n(A)=3(b) Select true or false.12 € A22 € B67 A-24 € BTruen(B) = 1FalseX%S3
Answers
Set A is composed of all the even numbers equal or greater than 4 and equal or less than 8 so set A is:
[tex]A=\lbrace4,6,8\rbrace[/tex]The cardinalities of A and B are equal to their number of elements so we have n(A)=3 and n(B)=7.
With both sets explicitly written we can complete the true or false table. The only thing to take into account is that the symbol ∈ means "belongs to" and that ∉ means "does not belong to".
The first statement of the table is:
[tex]12\in A[/tex]This is false because 12 does not belong to set A since it is not included in it.
The second statement is:
[tex]22\in B[/tex]As you can see 22 is in deed one of the elements of set B which means that this statement is true.
The third one is:
[tex]6\notin A[/tex]This statement is false because as we saw before 6 is an element of set A.
The last statement is:
[tex]-24\in B[/tex]As you can see -24 is one of the elements of set B so this statement is true.
AnswersFalse
True
False
True
Using the figure, determine the length, in units, of LM
Answers
Given the coordinates of L and M
To get the length between the two coordinates, we will follow the steps below
Step 1: List out the coordinates of L and M
[tex]L(-4,-3)[/tex][tex]M(-4,4)[/tex]step 2: calculate the distance
Since they both have the same x coordinates, we can simply subtract the y-coordinate of L from M
[tex]M-L=4-(-3)=4+3=7[/tex]Therefore, the distance LM is 7 units
I need help with this please thank you very much
Answers
So,
We can notice that the graph of g, is translated 2 units to the left and 4 units up. We can express these changes with the following equation:
[tex]g(x)=(x+2)^2+4[/tex]The locations of student desks are mapped using a coordinate plane where the origin represents the center of the classroom. Maria's desk is located at (2, −1), and Monique's desk is located at (−2, 5). If each unit represents 1 foot, what is the distance from Maria's desk to Monique's desk?
square root of 10 feet
square root of 20 feet
square root of 52 feet
square root of 104 feet
Answers
Answer:
√52 feet
Step-by-step explanation:
5 - -1 = 6
-2 - 2 = -4
6 = change in y
-4 = change in x
a² + b² = c² (pythagoras theorem)
6² = 36
-4² = 16
36 + 16 = 52
c² = 52
c = √52
Answer: square root of 52 feet
Find the volume.The measures are 4 yd, 3 yd, and 5 yd.
Answers
178.98 yd³
Explanation:The shape consists of a cone and a cylinder. So we would find the volume of each and sum them together.
Volume of a cone = 1/3 πr²h
r = radius = 3 yd
h = height = 4 yd
let π = 3.14
Volume of the cone = 1/3 × 3.14 × 3 × 3 × 4
Volume of the cone = 37.68 yd³
Volume of a cylinder = πr²h
r = radius = 3 yd
h = height = 5 yd
Volume of a cylinder = 3.14 × 3 × 3 × 5
Volume of a cylinder = 141.3 yd³
Volume of the shape = Volume of the cone + Volume of a cylinder
Volume of the shape = 37.68 + 141.3
Volume of the shape = 178.98 yd³
5. Given the degree and zeros of a polynomial function, find the standard form of the polynomial.
Degree: 5; zero: 1, i, 1+i
The expanded polynomial is:
x5 +
x4+
x3 +
x2 +
x +
Answers
The equation of the polynomial equation in standard form is P(x) = x⁵ -3x⁴ + 5x³ -5x² + 4x - 2
How to determine the polynomial expression in standard form?The given parameters are
Degree = 5
Zero = 1, i, 1 + i
There are complex numbers in the above zeros
This means that, the other zeros are
Zeros = 1 - i and -i
The equation of the polynomial is then calculated as
P(x) = Leading coefficient * (x - zero)^multiplicity
So, we have
P(x) = (x - 1) * (x - (1 + i)) * (x - (1 - i) * (x - (-i)) * (x - i)
This gives
P(x) = (x - 1) * (x - 1 - i) * (x - 1 + i) * (x² + 1)
Solving further, we have
P(x) = (x - 1) * (x² - x + ix - x + 1 - i - ix + i + 1) * (x² + 1)
P(x) = (x - 1) * (x² - 2x + 2) * (x² + 1)
Evaluate the products)
P(x) = (x³ - x² + x - 1) * (x² - 2x + 2)
This gives
P(x) = x⁵ - 2x⁴ + 2x³ - x⁴ + 2x³ - 2x² + x³ - 2x² + 2x - x² + 2x - 2
Express in standard form
P(x) = x⁵ - 2x⁴ - x⁴ + 2x³ + 2x³ + x³ - 2x² - 2x² - x² + 2x + 2x - 2
Evaluate the like terms
P(x) = x⁵ -3x⁴ + 5x³ -5x² + 4x - 2
Hence, the equation is P(x) = x⁵ -3x⁴ + 5x³ -5x² + 4x - 2
Read more about polynomial at
brainly.com/question/17517586
#SPJ1
4.
8 ft
8 ff
P = (4 X 8)
P=__ ft
A = (8 X 8)
A =
sq. ft
Answers
After multiplying the value of P is 32 ft and the value of A is 64 sq. ft.
In the given question we have to find the value of P and A.
The given expression for P is
P = (4 X 8)
The given expression for A is
A = (8 X 8)
In the given P representing the perimeter of square because the formula of perimeter is
P = 4* side
A representing the area of square because the area of square is
A = side*side
So the value of P
P = (4 X 8)
P = 32 ft
The value of A
A = (8 X 8)
A = 64 sq. ft
To learn more about area or perimeter of square link is here
brainly.com/question/23920809
#SPJ1
What is the x-value of the solution to the system of equations shown below? 2x + y = 20 6x - 5y = 12
Answers
Given the equation system:
[tex]\begin{gathered} 1)2x+y=20 \\ 2)6x-5y=12 \end{gathered}[/tex]To solve the system and determine the value of x, first step is to write one of the equations in terms of y:
[tex]\begin{gathered} 2x+y=20 \\ y=20-2x \end{gathered}[/tex]Then replace this expression in the second equation
[tex]\begin{gathered} 6x-5y=12 \\ 6x-5(20-2x)=12 \end{gathered}[/tex]Now that you have an expression with only one unknown, x, you can calculate its value.
Solve the parenthesis using the distributive property of multiplication
[tex]\begin{gathered} 6x-5\cdot20-5\cdot(-2x)=12 \\ 6x-100+10x=12 \\ 6x+10x-100=12 \\ 16x=12+100 \\ 16x=112 \\ \frac{16x}{16}=\frac{112}{16} \\ x=7 \end{gathered}[/tex]The value of China's exports of automobiles and parts (in billions of dollars) is approximately f ( x ) = 1.8208 e .3387 x , where x = 0 corresponds to 1998. In what year did/will the exports reach $7.4 billion?
Answers
We have the following equation:
[tex]f(x)=108208e^{0.3387x}[/tex]where x denotes the number of years after 1998.
By substituting the given information, we have that
[tex]7.4=1.8208e^{0.3387x}[/tex]and we need to find x. Then, by dividing both sides by 1.8208, we get
[tex]e^{0.3387x=}4.0641475[/tex]then by taking natural logarithm to both sides, we obtain
[tex]0.3387x=ln(4.0641476)[/tex]which gives
[tex]0.3387x=1.4022040[/tex]then, the number of years after 1998 is:
[tex]\begin{gathered} x=\frac{1.4022040}{0.3387} \\ x=4.13996 \end{gathered}[/tex]which means 4 years after 1998. Then, by rounding to the nearest year, the answer is 2002.
PLEASE HELP!!!
As part of a major renovation at the beginning of the year, Atiase Pharmaceuticals, Incorporated, sold shelving units (recorded as Equipment) that were 10 years old for $800 cash. The shelves originally cost $6,400 and had been depreciated on a straight-line basis over an estimated useful life of 10 years with an estimated residual value of $400.
2. Prepare the journal entry to record the sale of the shelving units. (If no entry is required for a transaction/event, select "No Journal Entry Required" in the first account field. Do not round intermediate calculations.)
(4 accounts)
Answers
Therefore, the total asset account balance is $400 and total liabilities and stockholders’ equity balance is $400.
Given,
The selling cost of shelving units that are 10 years old = $800
Original cost of shelving units = $6400
Estimated residual value for 10 years = $400
Assets = Liabilities +Stockholders equity
Calculate the accumulated depreciation for 10 years;-Accumulated depreciation for 10 years=[(Original cost of the equipment-Residual value) / Useful life] ×10 years
=[($6400-$400)/10 years]×10 years
=$600×10 years
=$6000
Calculate book value of equipment.Book value equipment=Original cost of the equipment-Accumulated depreciation for 10 years
=$6400-$6000
=$400
Calculate gain on sale of equipment.
Gain on equipment sale equals selling price minus book value of equipment
=$800-$400
=$400
Therefore, the total asset account balance is $400 and total liabilities and stockholders’ equity balance is $400.
Learn more about accumulated depreciation here;
https://brainly.com/question/29268369
#SPJ1
5x + 3y = 9
can you put it the following equation in slope-intercept form?
Answers
[tex]\framebox{Slope intercept: -$\dfrac{5}{3}$x+3}[/tex]
The slope intercept form of [tex]5x+3y=9[/tex] would be written as:
[tex]-\frac{5}{3} x+3[/tex]
how do you find the sum of 3+15+75+.....+46875 using the Sn formula
Answers
3+15+75+.....+46875
a1 = first term = 3
If we multiply the first term by 5, we obtain the second term.
3 x 5 = 15
15x 5 = 75
75x 5= 375
375x5= 1875
1875x5=9375
9375x5= 46875 (7th term) n=7
So,
r= 5
Apply the formula:
an= a1 * r^(n-1)
an= 3 * 5 (n-1)
Sum
Sn = a1 (1 -r^n) / 1- r
S(7) = [3 (1 - 5^7)] / 1-5
S(7) = [3 (1-78,125)] /-4
S(7) = 58,893