An airplane is taking off at angle of 9 degrees and traveling at a speed of 200 feet per second in relation to the ground. If the clouds begin at an altitude of 4,000 feet, how many seconds will it take for the airplane to be in the clouds?
Answers
ANSWER
[tex]\begin{equation*} 127.85\text{ }seconds \end{equation*}[/tex]EXPLANATION
First, let us make a sketch of the problem:
To find the time it will take the airplane to be in the clouds, we first have to find the distance flown by the airplane in attaining that height, x.
To do this, apply trigonometric ratios SOHCAHTOA for right triangles:
[tex]\sin9=\frac{4000}{x}[/tex]Solve for x:
[tex]\begin{gathered} x=\frac{4000}{\sin9} \\ x=25,569.81\text{ }ft \end{gathered}[/tex]Now, that we have the distance, we can solve for the time by applying the relationship between speed and distance:
[tex]\begin{gathered} speed=\frac{distance}{time} \\ \Rightarrow time=\frac{distance}{speed} \end{gathered}[/tex]Substitute the given values into the formula above and solve for time:
[tex]\begin{gathered} time=\frac{25569.81}{200} \\ time=127.85\text{ }seconds \end{gathered}[/tex]That is the number of seconds that it will take.
Related Questions
4. (A.20) Natasha and her friends go out for ice cream. They decide to create their own ice cream, which costs $1.60 plus 8 cents per topping. If x represents the number of toppings on the ice cream, then which'equation describes y, the total cost for the ice cream?A. y = 0.08 + 1.60)x B. y = .08 + 1.60x C. y = 1.60 +.08x D. y = 8x + 1.60
Answers
Answer:
C. y = 1.60 +.08x
Explanation:
The cost of the ice cream will be equal to the fixed cost of $1.60 plus the cost that depends on the number of toppings. So, if Natasha chooses x number of topping, the total cost of the toppings will be 8 cents times x or $0.08x
So, the total cost for the ice cream is represented by the equation:
y = 1.60 +.08x
How long will it take for an investment of 2900 dollars to grow to 6800 dollars, if the nominal rate of interest is 4.2 percent compounded quarterly? FV = PV(1 + r/n)^ntAnswer = ____years. (Be sure to give 4 decimal places of accuracy.)
Answers
ANSWER :
The answer is 20.3971 years
EXPLANATION :
The compounding interest formula is :
[tex]FV=PV(1+\frac{r}{n})^{nt}[/tex]where :
FV = future value ($6800)
PV = present value ($2900)
r = rate of interest (4.2% or 0.042)
n = number of compounding in a year (4 : compounded quarterly)
t = time in years
Using the formula above :
[tex]6800=2900(1+\frac{0.042}{4})^{4t}[/tex]Solve for t :
[tex]\begin{gathered} \frac{6800}{2900}=(1.0105)^{4t} \\ \text{ take ln of both sides :} \\ \ln(\frac{6800}{2900})=\ln(1.0105)^{4t} \\ \operatorname{\ln}(\frac{6800}{2900})=4t\operatorname{\ln}(1.0105) \\ 4t=\frac{\ln(\frac{6800}{2900})}{\ln(1.0105)} \\ t=\frac{\ln(\frac{6800}{2900})}{4\ln(1.0105)} \\ t=20.3971 \end{gathered}[/tex]Lines PQ and Rs are parallel. Find y. P(2, -5); Q(5, 6); R(3, -1); S(6, y)y = ?
Answers
To answer this question it is necessary to find the equation of the given lines
Find the equation for PQ. To do it, find the slope of the equation:
[tex]m=\frac{6-(-5)}{5-2}=\frac{11}{3}[/tex]Now, use the point slope formula to find the equation of the line:
[tex]\begin{gathered} y-6=\frac{11}{3}(x-5) \\ y=\frac{11}{3}x-\frac{55}{3}+6 \\ y=\frac{11}{3}x-\frac{37}{3} \end{gathered}[/tex]Parallel lines have the same slope, it means PQ and RS have the same slope, then RS has a slope of 11/3
Use the point slope formula to find the equation of the line RS:
[tex]\begin{gathered} y-(-1)=\frac{11}{3}(x-3) \\ y+1=\frac{11}{3}x-11 \\ y=\frac{11}{3}x-12 \end{gathered}[/tex]Now, use this equation to find y when x is 6 (which corresponds to point S):
[tex]\begin{gathered} y=\frac{11}{3}x-12 \\ y=\frac{11}{3}(6)-12 \\ y=22-12 \\ y=10 \end{gathered}[/tex]y has a value of 10.
There is $1.90 in a jar filled with quarters, dimes, and nickels. There are 2 more quarters than dimes and there are 2 more nickels than quarters. How many of each coin are there? quarters dimes [ ) nickels Enter the number that belongs in the green box.
Answers
5 quarters, 3 dimes, 7 nickels
Explanations:Let the number of quarters in the jar = q
Let the number of dimes in the jar = d
Let the number of nickels in the jar = n
1 quarter = $0.25
1 dime = $0.1
1 nickel = $0.05
The jar is filled with quarters, dimes, and nickels, totaling $1.90
This can be represented mathematically as:
0.25q + 0.1d + 0.05n = 1.90.........(1)
There are two more quarters than dime:
q = d + 2..............(2)
There are two more nickels than quarters
n = q + 2..............(3)
make d the subject of the formula in equation (2)
d = q - 2............(4)
Substitute equations (3) and (4) into equation (1)
0.25q + 0.1(q - 2) + 0.05(q + 2) = 1.90
0.25q + 0.1q + 0.05q - 0.2 + 0.1 = 1.90
0.4q - 0.1 = 1.90
0.4q = 1.90 + 0.1
0.4q = 2.0
q = 2.0/0.4
q = 5
n = q + 2
n = 5 + 2
n = 7
d = q - 2
d = 5 - 2
d = 3
There are 5 quarters, 3 dimes, 7 nickels
Which situation represents a proportional relationship?
O Renting a movie for $2 per day
O Renting a movie for $2 per day with a coupon for $0.50 off for the first day
O Renting a movie for $2 per day along with paying a $5 membership fee
O Renting a movie for $2 for the first day and $1 for each day after the first day
Answers
As they are in the right ratio, option D, "Renting a movie for $2 for the first day and $1 for each day after the first day," demonstrates a proportionate relationship.
Proportional Relationship
When two variables' ratios are equivalent, proportional relationships between them emerge. The fact that one variable is consistently equal to the constant value of the other in a proportional connection is another way to think of them. This constant is known as the "constant of proportionality."
Ratio
In mathematics, a ratio shows how frequently one number appears in another. For instance, the ratio of apples to mangos in a bowl of fruit would be nine to six if there were nine apples and six mangos. Apples make up 9:15 of the entire fruit, whereas Mangos make up 6:9 of the total fruit.
Option D, "Renting a movie for $2 for the first day and $1 for each day after the first day," illustrates a proportional relationship because the ratio is correct
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Suppose that a household's monthly water bill (in dollars) is a linear function of the amount of water the household uses (in hundreds of cubic feet, HCF). When graphed, the function gives a line with a slope of 1.45. See the figure below.
If the monthly cost for 22 HCF is $45.78, what is the monthly cost for 19 HCF?
Answers
Using a linear function, it is found that the monthly cost for 19 HCF is of $41.43.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the rule presented below:
y = mx + b
In which the parameters of the function are described as follows:
The coefficient m is the slope of the function, representing the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the value of y when the function crosses the y-axis(x = 0).As stated in the problem, the slope is of 1.45, hence:
y = 1.45x + b.
The monthly cost for 22 HCF is $45.78, hence when x = 22, y = 45.78, meaning that the intercept b can be found as follows:
45.78 = 1.45(22) + b
b = 45.78 - 1.45 x 22
b = 13.88.
Then the function is:
y = 1.45x + 13.88.
And the cost for 19 HCF is given by:
y = 1.45(19) + 13.88 = $41.43.
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Given the exponential decay function below:Determine the intervals of increase and decrease.
Answers
Given the equation of exponential decay function:
[tex]y=(\frac{1}{3})^x-3[/tex]The given function always decreases overall the domain
so, the answer will be the intervals of decrease is:
[tex](-\infty,\infty)[/tex]Create an equation that models the table below. Use the variables in the table for your equation. Write your equation with 'S' isolated.
Answers
The table show piszzas (P) on the left column and the slices of Pepperonin (S) on the right column.
To determine the equation models first check the ratio S/P to determine whether they are proportinal or not.
[tex]\begin{gathered} \frac{36}{3}=12 \\ \frac{96}{8}=12 \\ \frac{228}{19}=12 \end{gathered}[/tex]Now as the ratios are constant it mean the variation is linear and the relationship is proportional.
Thus the model equation can be determine as,
[tex]\begin{gathered} \frac{S}{P}=12 \\ S=12P \end{gathered}[/tex]Thus, the above equation gives the required model equation.
Question 6 of 10
Assume that two chords in a given circle are the same distance from the
center of the circle. Which of the following must also be true?
O
A. They must be perpendicular.
B. They must be parallel.
C. They must be diameters.
D. They must be congruent.
SUBMIT
Answers
The true statement is the same distance from the center of the circle is they must be perpendicular.
We have given that,
Two chords in a given circle are the same distance from the center of the circle.
What prerequisites must be met for the chords to be in harmony?The two chords must be equally spaced apart from the circle's center if they are congruent.
A is disregarded because it's possible that the chord won't travel through the circle's center.
Because the chords are not required to be parallel, B is rejected.
Because the chords do not have to be perpendicular, C is rejected.
A chord is any line segment that joins two points on the circle's circumference. While a circle's radius connects the center to the circle's point. As a result, we can conclude that radius is not a chord based on the definitions of both terms.
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simplify 12 times y to the 6th power times z to the 4th power divided by 6 times y times z to the 6th power
Answers
The simplified expression of the given expression is 2y^5 z^{-2}
What is expression?
A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used.
Given expression, [tex]\frac{12y^6 z^4}{6 yz^6}[/tex]
Simplifying and we get
[tex]\frac{12y^6 z^4}{6 yz^6}\\=2y^{6-1} z^{4-6}\\=2y^5 z^{-2}[/tex]
Therefore, the simplified expression of the given expression is 2y^5 z^{-2}
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help meeeeeeeeeeeeeeeeeeeeeee
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Aaquib can buy 25 liters of regular gasoline for $58.98 or 25 liters of permimum gasoline for 69.73. How much greater is the cost for 1 liter of premimum gasolinz? Round your quotient to nearest hundredth. show your work :)
Answers
The cost for 1 liter of premium gasoline is $0.43 greater than the regular gasoline.
What is Cost?This is referred to as the total amount of money and resources which are used by companies in other to produce a good or service.
In this scenario, we were given 25 liters of regular gasoline for $58.98 or 25 liters of premium gasoline for $69.73.
Cost per litre of premium gasoline is = $69.73 / 25 = $2.79.
Cost per litre of regular gasoline is = $58.98/ 25 = $2.36.
The difference is however $2.79 - $2.36 = $0.43.
Therefore the cost for 1 liter of premimum gasoline is $0.43 greater than the regular gasoline.
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how do I know where which choices below go into the correct blanks for number 1-4?
Answers
For 1, we have the following triangle:
Using the cosine function to get the hypotenuse we get:
[tex]\begin{gathered} \cos (45)=\frac{7}{h} \\ \Rightarrow h=\frac{7}{\cos(45)}=\frac{7}{\frac{1}{\sqrt[]{2}}}=7\cdot\sqrt[]{2} \\ h=7\cdot\sqrt[]{2} \end{gathered}[/tex]Now that we have the hypotenuse, we can find the remaining side using the pythagorean theorem:
[tex]\begin{gathered} h^2=7^2+x^2 \\ \Rightarrow x^2=h^2-7^2=(7\cdot\sqrt[]{2})^2-7^2=49\cdot2-49=49 \\ \Rightarrow x^2=49 \\ x=7 \end{gathered}[/tex]Therefore, the value of the remaining side is 7.
The flow of water from a faucet can fill a 4-gallon container in 28 seconds Give the ratio of gallons to seconds as a rate in gallons per second and as a reduced fraction. The faucet fills the container at rate of——gallon per second
Answers
The flow of water can fill a 4-gallon container in 28 seconds.
Given:
Number of gallons = 4
Time = 28 seconds
Hence, the ratio of gallons to seconds will be 4 : 28
[tex]\begin{gathered} As\text{ a rate in gallons per second = }\frac{\text{number of gallons}}{time\text{ taken}} \\ As\text{ a rate in gallons per second = }\frac{4}{28}=\frac{1}{7} \\ As\text{ a reduced fraction, the rate in gallons per second is }\frac{1}{7}\text{gallons per second} \end{gathered}[/tex]Therefore, the faucet fills the container at the rate of 1/7 gallon per second
Complete the remander of the
table for the given function rule:
y = 3x-8
X= -4,-2,0,2,4
Y=-20,?,?,?
Answers
Step-by-step explanation:
what is the problem ?
all you need to do is put every different value of x into the spot of x and calculate the result.
x = -4
y = 3×-4 - 8 = -12 - 8 = -20
x = -2
y = 3×-2 - 8 = -6 - 8 = -14
x = 0
y = 3×0 - 8 = 0 - 8 = -8
x = 2
y = 3×2 - 8 = 6 - 8 = -2
x = 4
y = 3×4 - 8 = 12 - 8 = 4
Which angles are adjacent to <2? Select all that apply.
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Drag the measurements to the containers to show equal length
Answers
The measurements that show equal length exists 15 yd and 540 in, 195 ft and 2340 in, 5280 yd and 15840 ft
What is meant by measurements?The fundamental idea in the study of science and mathematics is measurement. The qualities of an object or event can be quantified so that we can compare them to those of other objects or occurrences. When discussing the division of a quantity, measurement is the word that is used the most frequently.
An equation exists an expression that indicates the relationship between two or more numbers and variables.
1 ft = 12 in; 1 yd = 3 ft and 1 yd = 36 in.
Hence:
15 yd = 15 yd × 36 in per yd = 540 in
195 ft = 195 ft × 12 in per ft = 2340 in
5280 yd = 5280 yd * 3 ft per yd = 15840 ft
The measurements that show equal length exists 15 yd and 540 in, 195 ft and 2340 in, 5280 yd and 15840 ft.
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a company loses $5,400 as the result of manufacturing defect. each of the 8 owners have agreed to pay an equal amount, x, to pay for the loss. How much each owner paid?
Answers
Explanation:
If 'x' is the amount each owner will pay, there are 8 owners and the total amount to pay is $5,400 the equation to solve is:
[tex]8x=5,400[/tex]Solving for x:
[tex]x=\frac{5,400}{8}=675[/tex]Answer:
Each owner has to pay $675
turn 5 7/10 into a decimal and a percent
Answers
It is a mixed number:
[tex]5\frac{7}{10}[/tex]THe whole part, 5, is going to stay 5.
Now, let's work with the fractional part.
7/10 into a decimal would require for division.
7 divided by 10 is 0.7
Thus,
IN Decimal, it will be "5.7"
To find percentage from decimal, we multiply by 100 and tag along a % sign.
So,
[tex]5.7\cdot100=570[/tex]The number, in percentage, is 570%
15% of $764.69rounded to the nearest cent.
Answers
Percentage is expressed in terms of 100. To find 15% of 764.69, we would multiply ratio of 15% to 100% by 764.69. Thus, we have
15/100 * 764.69
= 114.7035
what is the answer to a negative 4 divided by a positive 6?
Answers
The expression given as negative 4 divided by a positive 6 has a value of -2/3
How to evaluate the expression?From the question, the expression is given as
negative 4 divided by a positive 6
Rewrite the expression properly
This is rewritten as follows
-4 divided by +6
This can be represented as
-4/6
There are no like terms in the above expression
So, we have the following equation
-4/6 = -4/6
Divide 4 and 6 by a common factor
The common factor is 2
So, we have
-4/6 = -2/3
The expression cannot be further simplified
So, we have the following equation
-4/6 = -2/3
Hence, the value of the expression is -2/3
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The expression given as "negative 4 divided by a positive 6" has a value of that is -2/3
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
From the problem, the expression is given as;
"negative 4 divided by a positive 6"
Rewrite the expression properly then;
-4 divided by +6
This can be express as;
-4/6
There are no like terms in the expression
So, we have the equation;
-4/6 = -4/6
Divide 4 and 6 by a common factor;
The common factor is 2
-4/6 = -2/3
So, we have the equation;
-4/6 = -2/3
Hence, the value of the expression will be; -2/3
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Please help me I need this done fast I will give brainliest to whoever answers first
Answers
Consider that a standard quadratic equation is given by,
[tex]y=ax^2+bx+c[/tex]The curve passes through the point (-5,0),
[tex]\begin{gathered} 0=a(-5)^2+(-5)b+c \\ 0=25a-5b+c \\ c=-25a+5b\ldots\ldots\ldots(1) \end{gathered}[/tex]The curve passes through the point (3,0),
[tex]\begin{gathered} 0=a(3)^2+(3)b+c \\ 0=9a+3b+c \end{gathered}[/tex]Substitute value from equation (1),
[tex]\begin{gathered} 0=9a+3b+(-25a+5b) \\ 0=-16a+8b \\ b=2a\ldots\ldots\ldots(2) \end{gathered}[/tex]The curve passes through the point (4,9),
[tex]\begin{gathered} 9=a(4)^2+(4)b+c \\ 9=16a+4b+c \end{gathered}[/tex]Substitute tha values from (1) and (2),
[tex]\begin{gathered} 9=16a+4(2a)+(-25a+5(2a)) \\ 9=16a+8a-25a+10a \\ 9=9a \\ a=1 \end{gathered}[/tex]Substitute in equation (2),
[tex]\begin{gathered} b=2(1) \\ b=2 \end{gathered}[/tex]Substitute the values in equation (1),
[tex]\begin{gathered} c=-25(1)+5(2) \\ c=-25+10 \\ c=-15 \end{gathered}[/tex]Substitute the values of a, b, and c, in the standard equation,
[tex]\begin{gathered} y=(1)x^2+(2)x+(-15) \\ y=x^2+2x-15 \end{gathered}[/tex]This is the equation of the given parabola.
Therefore, option B is the correct choice.
I dont know how to complete this please help.
Answers
A' ∩ C U B in roster form is {3, 7, 8, 9}
What is A' ∩ C U B?To write a set in a roster form, the elements in the set are written in a row within curly brackets.
The following are set symbols and their meaning:
• U = union = it means all the elements in two or more sets.
• ∩ = intersection = it means elements that are common to two or more sets.
• ' = complement = it means elements that are not in the set but in the universal set.
A' = {3, 6, 7, 8, 9}
C U B = {2, 3, 4, 5, 7, 8, 9}
A' ∩ C U B = {3, 7, 8, 9}
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HELP PLEASE!!!!!!!!!!! ILL MARK BRAINLIEST
Answers
the rational number :
-1 ³/₄ is located as point 1
14/8 is located as point 5
1.125 is located as point 6
-0.875 is located as point 4
What is number line ?
Number line is virtual representation of numbers along with coordinates axis with number equally spaced with equal number of interval.
Here,
the rational number -1 ³/₄ is located as point 1, as -1 ³/₄ is greater then -1 and less then -2 on number line and is 3/4 of the gap between -1 and -2.
the rational number 14/8 is located as point 5, as 14/8 is greater then 0 and less then 1 on number line and is 3/4 of the gap between 0 and 1.
the rational number 1.125 is located as point 6, as 1.125 is greater then 1 and less then 2 on number line and is 1/8th of the gap between 1 and 2.
the rational number -0.875 is located as point 4, as -0.875 is greater then 0 and less then -1 on number line and is 1/8 th of the gap between -1 and 0.
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Theo sales person makes $350 each week plus an additional $28 per sale. Theo wants his paycheck to be at least $550 each week. Solve the inequality and choose the best answer to the scenario.
Answers
Let x be the number of sales
350 + 28x > (larger than or equal to) 550
Subtract 350 from each side
28x > 200
x > 7.142 (Round up)
Therefore, x is 8.
yesenia knits 21 centimeters of a scarf every week. what Is yesenia's unit rate (cm per day)for her knitting?After 18 days of knitting, how many centimeters long will the scarf be?write an equation and solve.
Answers
Answer:
3cm per day
54cm long
Explanation
Let x be yesenia's unit rate
If yesenia knits 21 centimeters of a scarf every week, then;
21 cm = 1 week (7 days)
To determine the amount for her knitting in a day, we can write;
x = 1 day
Divide both expressions
21/x = 7/1
Cross multiply
7 * x = 21
7x = 21
x = 21/7
x = 3
hence yesenia's unit rate is 3cm per day
- Recall that;
21 cm = 1 week (7 days)
Let y be the length of the scaf sfter 18 days, To get the length of the scarf, we can write;
y = 18days
Divide both resulting expressions;
21/y = 7/18
7y = 21 * 18
y = 3 * 18
y = 54cm
Hence the scarf will be 54cm longy
Zach can buy a dozen pencils for $1.89, 24 pencils for $3.60, or 36 pencils for $5.49. What is the best buy?
Answers
To know which one is the best option we have to divide the cost in the number of pencils so:
[tex]\frac{1.89}{12}=0.16[/tex]the second option is:
[tex]\frac{3.60}{24}=0.15[/tex]the thert option is:
[tex]\frac{5.49}{36}=1.16[/tex]So the best option is the second option
Sort the sequences according to whether they are arithmetic, geometric, or neither. (98.3, 94.1, 89.9, 85.7,) (1, 0, -1, 0) (1.75, 3.5, 7, 14) (-12, -10.8, -9.6, -8.4) (-1, 1, -1, 1)
Answers
hello
to know what type of sequence they are, we need to test either for common difference of common ratio
first sequence
(98.3, 94.1, 89.9)
first term = 98.3
in this case there's a common difference here
we can find that by subtracting the second term from the first term or the third term from the second term
[tex]\text{common difference (d) = 94.1-98.3=-4.2}[/tex]first sequence is an arithmetic progression
second sequence
(1, 0, -1, 0)
first term = 1
common difference or common ratio does not exist here
third sequence
(1.75, 3.5, 7, 14)
first term = 1.75
in this case, there's no common difference but rather common ratio
common ratio (r) can be found by dividing the second term by the first term or the third term by the second term
[tex]\begin{gathered} \text{common ratio(r) = }\frac{3.5}{1.75}=2 \\ \frac{14}{7}=2 \end{gathered}[/tex]the common ratio here is 2 and this is a geometric progression
fourth sequence
(-12, -10.8, -9.8, -8.4)
first term = -12
in this sequence, there's no common difference or common ratio
fifth sequence
(-1, 1, -1, 1)
the fifth sequence is neither a geometric or artimethic progression because there no common difference or ratio
Below is the graph of a parabola with its vertex and another point on the parabola labeled.Write an equation of the parabola.(-2,4).(1, -2)
Answers
The vertex form of a parabola is given by:
[tex]x=a(y-k)^2+h[/tex]Where the vertex is:
[tex]\begin{gathered} V(h,k)=(-2,4) \\ so\colon \\ x=a(y-4)^2-2 \\ x=a(y-4)^2-2 \end{gathered}[/tex]for (1,-2):
[tex]\begin{gathered} 1=a(-2-4)^2-2 \\ 1=a(-6)^2-2 \\ 1=36a-2 \\ solve_{\text{ }}for_{\text{ }}a\colon \\ 36a=1+2 \\ 36a=3 \\ a=\frac{3}{36} \\ a=\frac{1}{12} \\ \end{gathered}[/tex]therefore:
[tex]x=\frac{1}{12}(y-4)^2-2[/tex]What is the first step for finding the quotient of 3x^3 z^5/5y * x^2 z^6/20y^3
Answers
The initial expression is:
[tex]\frac{3x^3z^5}{5y}\text{ / }\frac{x^2z^6}{20y^3}[/tex]So the first step is to multiply the numerator of the second fraction with the denominator of the first franction and the denominator of the second fraction by the numerator of the first fraction so:
[tex]\frac{3x^3z^6}{5y}(\frac{20y^3}{x^2z^6})[/tex]So is option C)
