chance the pilot of a boeing 727 flew e plane so it took off at an angle of elevation 21 degrees. after flying one kilometer, what is the altitude (height) of the plane that chance was flying rounded to the nearest meter? (1 km= 1000 meters)
Answers
To solve the exercise, it is convenient to first draw a picture of the situation posed by the statement:
As you can see, a right triangle is formed. So to find the height at which the plane was when the pilot had flown one kilometer, you can use the trigonometric ratio sin(θ):
[tex]\sin (\theta)=\frac{\text{Opposite side}}{\text{ Hypotenuse}}[/tex]Then, in this case, you have
[tex]\begin{gathered} \sin (21\text{\degree})=\frac{\text{ Altitude}}{1000m} \\ \text{ Multiply by 1000m on both sides of the equation} \\ \sin (21\text{\degree})\cdot1000m=\frac{\text{ Altitude}}{1000m}\cdot1000m \\ \sin (21\text{\degree})\cdot1000m=\text{ Altitude} \\ 358.37m=\text{ Altitude} \\ \text{ Rounding to the nearest meter} \\ 358m=\text{ Altitude} \end{gathered}[/tex]Therefore, the altitude or height of the plane after flying one kilometer is 358 meters.
Related Questions
POSThe expression(-4)(x) is equivalent to the expression x”. What is the value of n?n =
Answers
given expression:
[tex]\mleft(-4\mright)\mleft(x\mright)=x^n[/tex]To find the value of n.
[tex]\begin{gathered} \ln \mleft(\mleft(-4\mright)x\mright)=n\ln \mleft(x\mright) \\ n=\frac{\ln\left(-4x\right)}{\ln\left(x\right)} \end{gathered}[/tex]We start with triangle ABC and see that angle ZAB is an exterior angle created by the extension of side AC. Angles ZAB and CAB are a linear pair by definition. We know that m∠ZAB + m∠CAB = 180° by the . We also know m∠CAB + m∠ACB + m∠CBA = 180° because .
Answers
The first answer is: definition of complementary angles.
The second is: of the triangle sum theorem.
The third one is: substraction property
The following two-way table describes student'safter school activities. Find the probability that arandomly selected student is in sports.GradeMusic/DramaWorkSports20Sophomore73Junior2013255SeniorP(Sports) = [? ]%25
Answers
Solution
The Probability that a random selected students is in sports is
[tex]P(Sports)=\frac{65}{Total}=\frac{65}{20+20+25+7+13+5+3+2+5}=0.65=65\%[/tex]The answer is 65%
Can you hello me with number 2 using 3.14 and I have to round to the answer to the nearest tenth as well thanks
Answers
Given data:
Radius of the circle = 10in.
To find:
The circumference of the circle.
The formula to find the cicumference of the circle is,
[tex]C=2\pi r[/tex]subsitute the values of,
[tex]\begin{gathered} r=\text{ 10in} \\ \pi=3.14 \end{gathered}[/tex]we get,
[tex]\begin{gathered} C=2\cdot3.14\cdot10 \\ =62.8 \end{gathered}[/tex]THE CIRCUMFERENCE OF THE CIRCLE IS 62.8 IN
The sum of a number and -2 is no more than 6.
Answers
Answer: 8
Step-by-step explanation: if you add -2 and 8 you get 6. :) pls give me brainliest
What is a formula for the nth term of the given sequence?135, -225,375...
Answers
Step 1: Write out the formula for a geometric sequence
[tex]\begin{gathered} T_n=ar^{n-1} \\ \text{Where} \\ T_n=\text{ the nth term} \\ a=\text{ the first term} \\ r=\text{ the common ratio} \end{gathered}[/tex]Step 2: Write out the given values and find the formula
[tex]\begin{gathered} a=135, \\ r=-\frac{225}{135}=-\frac{5}{3} \end{gathered}[/tex]Therefore the formula is given by
[tex]T_n=135(-\frac{5}{3})^{n-1}[/tex]Hence, the correct choice is the first choice
use the equation of a parabola in standard form having a vertex at (0, 0), x^2= 8y.Solve the equation for "p" and then describe the focus (0, p), the directrix, and the 2 focal chord endpoints.
Answers
Solution
We have the following equation:
[tex]x^2=8y[/tex]the general formula for a parabola is given by:
[tex](x-h)^2=4p(y-k)[/tex]Where (h,k) =(0,0) represent the vertex, so then our equation is:
[tex]x^2=4py[/tex]By direct comparison we have this:
4p= 8
p = 2
Then the focus is given by:
(0,p) = (0,2)
the directrix is given by:
y= 0-p = 0-2= -2
y=-2
And finally the 2 focal chord endpoints are:
[tex](|2p|,p)=(4,2),(-|2p|,p)=(-4,2)[/tex]change to y=mx+b form 3x-y=6
Answers
Starting with the equation:
[tex]3x-y=6[/tex]Isolate the variable y. Substract 3x from both sides of the equation:
[tex]-y=6-3x[/tex]Multiply both sides of the equation by -1:
[tex]y=-6+3x[/tex]Use the commutative property of the sum to rewrite the right hand side of the equation:
[tex]y=3x-6[/tex]This equation is written in the form y=mx+b.
which does not name an integer a.-35 b. 0 c. 3/15d. 10/2
Answers
The integer numbers are the whole numbers or the numbers that are not written as a/b
For the given question
-35 is an integer number
0 is an integer number
10/2 = 5 is an integer number
3/15 = 1/5 is not an integer number
So, the answer will be option c. 3/15
Bruce owns a small grocery store and darges per pound et produce Ir a customer orders S pounds of prodeer, om zich das Bruxe charge the castomert function
Answers
bruce will charge the customer $23.75
Explanation:
Amount charged per pound = $4.75
Let the number of pounds of produce = x
Total cost per number of pounds = $4.75 × x
Let the total cost of produce = y
y = 4.75x
If the number of pounds of produce = x = 5
y = 4.75 (5)
y = $23.75
Therefore, bruce will charge the customer $23.75
g(x)= 6/x find (g°g). and domain in set notation.
Answers
We have to find the expression for the composition
[tex]g\circ\text{ g\lparen x\rparen}[/tex]Where
[tex]g(x)=\frac{6}{x}[/tex]And express its domain in set notation. We will start by finding the expression for the composition
[tex]g\circ\text{ }g(x)=g(g(x))=g(\frac{6}{x})[/tex]that is we firsts evaluate the inner functions that in this case is g, now taking as argument y=6/x, we evaluate the outer function that in this case also is g, as follows:
[tex]g\text{ \lparen }\frac{6}{x})=\frac{6}{\frac{6}{x}}=\frac{6}{6}=x[/tex]That is, the composition g*g is equal to x, the identity.
Now we will find the domain of g*g:
Note that the domain of a composition is an interception, as follows:
[tex]Domain\text{ }g\circ\text{ g=\textbraceleft Domain of }g\text{ \textbraceright }\cap\text{ \textbraceleft Image of }g\text{ \textbraceright}[/tex]Therefore, we have to find the domain and image of g, and intercept both sets. We start with the domain of g_
[tex]Domain\text{ of }g\text{ }=\text{ }\mathbb{R}\text{ - \textbraceleft0\textbraceright}[/tex]That is all the real numbers except the 0. Now note that the image of g is
[tex]Image\text{ g= }\mathbb{R}\text{ - \textbraceleft0\textbraceright}[/tex]Finally, the domain of the composition g*g, can be obtained by the formula above:
[tex]Domain\text{ of }g\circ\text{ g=}\mathbb{R}\text{ -\textbraceleft0\textbraceright }\cap\text{ }\mathbb{R}\text{ - \textbraceleft0\textbraceright= }\mathbb{R}\text{ - \textbraceleft0\textbraceright=}(-\infty\text{ },0)\text{ }\cup\text{ }(0,\infty)\text{ }[/tex]Therefore, the domain of the composition are all the real numbers excluding the 0.
-
Factor 3x² + 10x + 8 using earmuff method.
Answers
To factor the above quadratic equation using Earmuff Method, here are the steps:
1. Multiply the numerical coefficient of the degree 2 with the constant term.
[tex]3\times8=24[/tex]2. Find the factors of 24 that when added will result to the middle term 10.
1 and 24 = 25
2 and 12 = 14
3 and 8 = 11
6 and 4 = 10
Upon going over the factors, we will find that 6 and 4 are factors of 24 and results to 10 when added.
3. Add "x" on the factors 6 and 4. We will get 6x and 4x.
4. Replace 10x in the original equation with 6x and 4x.
[tex]3x^2+6x+4x+8[/tex]5. Separate the equation into two groups.
[tex](3x^2+6x)+(4x+8)[/tex]6. Factor each group.
[tex]3x(x+2)+4(x+2)_{}[/tex]7. Since (x + 2) is a common factor, we can rewrite the equation into:
[tex](3x+4)(x+2)[/tex]Hence, the factors of the quadratic equation are (3x + 4) and (x + 2).
Another way of factoring quadratic equation is what we call Slide and Divide Method. Here are the steps.
[tex]3x^2+10x+8[/tex]1. Slide the numerical coefficient of the degree 2 to the constant term by multiplying them. The equation becomes:
[tex]\begin{gathered} 3\times8=24 \\ x^2+10x+24 \end{gathered}[/tex]2. Find the factors of 24 that results to 10 when added. In the previous method, we already found out that 6 and 4 are factors of 24 that results to 10 upon adding. So, we can say that the factors of the new equation we got in step 1 is:
[tex](x+6)(x+4)[/tex]3. Since we slide "3" to the constant term, divide the factors 6 and 4 by 3.
[tex]\begin{gathered} =(x+\frac{6}{3})(x+\frac{4}{3}) \\ =(x+2)(x+\frac{4}{3}) \end{gathered}[/tex]4. Since we can't have a fraction as a factor, slide back the denominator 3 to the term x in the same factor.
[tex](x+2)(3x+4)_{}[/tex]Similarly, we got the same factors of the given quadratic equation and these are (x + 2) and (3x + 4).
3. Determine - f(a) for f(x) =2x/x-1 and simplify.
Answers
Substitute a for x
[tex]-f\text{ (x ) = - f (a) = - }\frac{2a}{a-1}[/tex]Determine - f(a) for f(x) =2x/x-1 and simplify.
Thus, the solution becomes:
[tex]-\frac{2a}{a-1}\text{ or }\frac{2a}{1-a}[/tex]Steve made a business trip of 200.5 miles. He averaged 51 mph for the first part of the trip and 62 mph for the second part. If the trip took 3.5 hours, how long did hetravel at each rate?
Answers
Let t = time traveled at 51 mph
The total time is given as 3.5 hours
So (3.5- t )= time traveled at 62 mph
We are going to use the distance formula:
distance = speed* time
51t + 62(3.5-t) = 200.5
51t + 62*3.5 - 62*t = 200.5
51t + 217 - 62t = 200.5
Solve the equal terms
51t - 62t = 200.5 - 217
-11t = -16.5
t = -16.5/-11
t = 1.5
Then he took 1.5 at 51mph
and (3.5- t ) = (3.5-1.5) = 2h at 62 mph
To confirm these results, find the actual speed of each speed:
speed* time = distance
51*1.5 = 76.5miles
62*2. = 124 miles
76.5miles + 124 miles = 200.5miles
Find the x and y intercept then use them to graph the line
Answers
The x-intercept = (7, 0)
The y-intercept = (0, -3.5)
Explanation:The given equation is:
-2x + 4y = -14
Find the x-intercept by setting y = 0
-2x + 4(0) = -14
-2x + 0 = -14
-2x = -14
x = -14/-2
x = 7
Therefore, the x-intercept = (7, 0)
Find the y-intercept by setting x = 0
-2(0) + 4y = -14
0 + 4y = -14
4y = -14
y = -14/4
y = -3.5
Therefore, the y-intercept = (0, -3.5)
Considering the x and y-intercepts, the graph is plotted
Solve the inequality: 4x + 8 - 5x > 13
Answers
4x+8-5x > 13
Combine like terms
4x-5x+8> 13
-x +8 > 13
Subtract 8 from both sides:
-x+8-8 > 13-8
-x > 5
Multiply both sides by -1
x < -5
What is the total area patty can reach? What is the total grazing area?
Answers
as patty can not reach the square, we have that she can reach 3/4 parts of a circle with radius equal to 12 feet. Therefore the area she can reach is :
[tex]A_p=\frac{3}{4}\pi\cdot r^2=\frac{3}{4}\pi\cdot144=108\pi\approx339.3[/tex]and the gazzing area is the area of the square so we get:
[tex]A_g=12^2=144[/tex]Data: x y 4 1 5 2 6 3 7 4 y = x - ?
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
x y
4 1
5 2
6 3
7 4
y = x - ?
Step 02:
equation of the line:
y = x - ?
y = mx + b
m = slope = 1
point ( 4 , 1)
Point-slope form of the line
(y - y1) = m (x - x1)
(y - 1) = 1 (x - 4)
y - 1 = x - 4
y = x - 4 + 1
y = x - 3
The answer is:
y = x - 3
The figure below is a net for a right rectangular prism. Its surface area is 432 m2 andthe area of some of the faces are filled in below. Find the area of the missing faces,and the missing dimension.
Answers
The surface area is the sum of all the areas in the given prims, then we have:
[tex]SA=72+72+48+48+2A[/tex]Plugging the value for the surface area and silving for A we have:
[tex]\begin{gathered} 432=72+72+48+48+2A \\ 432=240+2A \\ 2A=432-240 \\ 2A=192 \\ A=\frac{192}{2} \\ A=96 \end{gathered}[/tex]Now that we know the missing area we can know the missing dimension:
[tex]\begin{gathered} 96=8x \\ x=\frac{96}{8} \\ x=12 \end{gathered}[/tex]Therefore the missing length is 12.
the total amounts of rainfall at various points And time during a thunderstorm are shown in the table. time(hours) 0.4 | 1.1 | 2.9 | 3.2 | 3.7 | 4.4Rainfall(cm) 0.3 | 0.6 | 1.8 | 2.0 | 2.2 | 2.6According to a regression calculator, what is the equation of the line of best fit for the data?answers: a y= 0.06x+0.03 | b y= 0.06x+0.29 | c y=0.59x+0.03 | d y= 0.59x+0.29Please help!
Answers
14 Find the percent increase or decrease for each of the following values (indicate whether each is an increase or a decrease). a. 4x to x/ b. 0.25m to 0.5m 5 c. + 2p to d.y to 0.687 8 р 15 Consider the following relationships. TI. 1
Answers
The percentage increase or decrease is given by
[tex]\frac{final\: \text{amount}-original\: \text{amount}}{original\: \text{amount}}\times100\%[/tex]Let us find the percentage increase or decrease for the given cases.
a) 4x to x
[tex]\begin{gathered} \frac{x-4x}{4x}\times100\% \\ \frac{-3x}{4x}\times100\% \\ -0.75\times100\% \\ -75\% \end{gathered}[/tex]Therefore, it is a percentage decrease (-75%) since it is negative.
b) 0.25m to 0.5m
[tex]\begin{gathered} \frac{0.5m-0.25m}{0.25m}\times100\% \\ \frac{0.25m}{0.25m}\times100\% \\ 1\times100\% \\ 100\% \end{gathered}[/tex]Therefore, it is a percentage increase (100%) since it is positive.
c) 1/2p to 5/8p
[tex]\begin{gathered} \frac{\frac{5}{8}p-\frac{1}{2}p}{\frac{1}{2}p}\times100\% \\ \frac{\frac{1}{8}p}{\frac{1}{2}p}\times100\% \\ \frac{1}{8}\times\frac{2}{1}\times100\% \\ \frac{2}{8}\times100\% \\ \frac{1}{4}\times100\% \\ 25\% \end{gathered}[/tex]Therefore, it is a percentage increase (25%) since it is positive
d) y to 0.68y
[tex]\begin{gathered} \frac{0.68y-y}{0.68y}\times100\% \\ \frac{-0.32y}{0.68y}\times100\% \\ -0.47\times100\% \\ -47\% \end{gathered}[/tex]Therefore, it is a percentage decrease (-47%) since it is negative.
On his way home from school board meeting , Keith fills up his car. He like the idea of using gasoline with ethanol , but think his car only handle 40% ethanol. At the gas station , he can use regular gas with 10% ethanol or E85 fuel with 85% ethanol. How many gallons of each type of fuel should Keith use if he wants to fill up his car with 10 gallons of fuel containing 40% ethanol ?
Answers
ANSWER:
6 gallons regular gas with 10% ethanol and 4 gallons E85 fuel with 85% ethanol
STEP-BY-STEP EXPLANATION:
In this case, we must test with values for each fuel class to arrive at the correct answer.
For example, 6 gallons of 10% ethanol and 4 gallons of 85% ethanol:
[tex]\begin{gathered} 10\text{\% of 6 =}\frac{10}{100}\cdot6=0.6\text{ gallons of ethanol in it} \\ 85\text{\% of 4 =}\frac{85}{100}\cdot4=3.4\text{ gallons of ethanol in it} \\ \text{ Total ethanol in 10 gallons is 0.6 + 3.4 = 4 gallons }\rightarrow\text{ 4 gallons is 40\% of 10} \\ \text{Therefore, we have 10 gallons of fuel containing 40\% ethanol } \end{gathered}[/tex]A right triangle has legs that are 5 cm and 7 cm long what is the length of the hypotenuse 1.√122.√243.√74 4.√144
Answers
Answer:
3. √74
Explanation:
By the Pythagorean theorem, the length of the hypotenuse can be calculated as:
[tex]c=\sqrt[]{a^2+b^2}[/tex]Where c is the hypotenuse and a and b are the lengths of the legs.
So, replacing a by 5 and b by 7, we get:
[tex]\begin{gathered} c=\sqrt[]{5^2+7^2} \\ c=\sqrt[]{25+49} \\ c=\sqrt[]{74} \end{gathered}[/tex]Therefore, the answer is 3. √74
Hello I need help with this please , I was studying it I don’t get this
Answers
Given that
The Pythagoras theorem is true for all right triangles or not.
Explanation -
For each and every right-angled triangle the Pythagoras theorem can be used.
So the final answer is True.A couple plans to save for their child's college education. What principal must be deposited by the parents when their child is born in order to have $37,000 when the child reaches the age of 18? Assume the money earns 9% interest, compounded quarterly. (Round your answer to two decimal places.)
Answers
We can use the compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where:
A = Amount = $37000
P = Principal
r = Interest rate = 9% = 0.09
n = Number of times interest is compounded per unit of time = 4 (Since it is compounded quarterly)
t = time = 18
Therefore:
[tex]37000=P(1+\frac{0.09}{4})^{18*4}[/tex]Solve for P:
[tex]\begin{gathered} P=\frac{37000}{4.963165999} \\ P=7454.918 \end{gathered}[/tex]What should your brain immediatelythink when it sees5(11 + 4y)
Answers
Distributive Property , I need to multiply!
Explanation
[tex]5(11+4y)[/tex]
Step 1
to find the value of y, you need isolate it
to do that, you will have to eliminate the parenthesis, you can remove it using
THE DISTRIBUTIVE PROPERTY
[tex]\begin{gathered} a(b+c)=ab+ac \\ \end{gathered}[/tex]Step 2
then
[tex]5(11+4y)=5\cdot11+5\cdot4y=55+20y[/tex]I hope this helps you.
Solve the following inequality for kk. Write your answer in the simplest form.8k - 3 > 9k + 10
Answers
Given:
[tex]8k-3>9k+10[/tex]To solve for k:
Solving we get,
[tex]\begin{gathered} 8k-3>9k+10 \\ 8k-9k>10+3 \\ -k>13 \\ k<-13 \end{gathered}[/tex]Hence, the answer is,
[tex]k<-13[/tex]Tank (#1) Capacitybarrels per Ft: 62.50Barrels per inch: 5.21.Convert Barrels to Feet, and inches with the information given.If you deposited 190 barrels of water into tank #1. What would be the total amount deposited (feet) and (inches).*remember there are only 12 inches in a foot*
Answers
To answer this question, we have to convert the given amount of barrels to feet and to inches using the conversion factors shown.
Barrels to feet:
[tex]190barrels\cdot\frac{1ft}{62.50barrel}=3.04ft[/tex]Barrels to inches:
[tex]190barrels\cdot\frac{1in}{5.21barrel}=36.47in[/tex]It means that the total amount deposited would be 3.04 ft or 36.47 in.
10.Find the approximated circumference of a circle whose area is 136.46
Answers
The area of a circle is given by the following formula:
[tex]A=\pi r^2[/tex]Where r is the radius.
We know the area of the circle, then we can replace it in the formula and find r:
[tex]\begin{gathered} 136.46=\pi\cdot r^2 \\ r^2=\frac{136.46}{\pi} \\ r^2=43.44 \\ r=\sqrt[]{43.44} \\ r=6.59 \end{gathered}[/tex]The circumference of a circle is given by the formula:
[tex]C=2\pi r[/tex]By replacing the r-value that we found, we can solve for C:
[tex]\begin{gathered} C=2\cdot\pi\cdot6.59 \\ C=41.41 \end{gathered}[/tex]The approximated circumference of the circle is 41.41
my work is saying solve for the value of a
Answers
Using the definition of suplementary angles we know that the angle that contains a and the 75° added together are 180°
[tex]75+(9a+6)=180[/tex]solve the equation for a
[tex]\begin{gathered} 81+9a=180 \\ 9a=180-81 \\ 9a=99 \\ a=\frac{99}{9} \\ a=11 \end{gathered}[/tex]