The resulting speed and direction of the airplane are approximately 377.492 miles per hour and 93.413°, respectively.
How to apply vectors to find absolute velocity of the airplane
In this question we must apply vectors in rectangular form to determine the absolute velocity of an airplane. which is the sum of velocity at still air ([tex]\vec v_{A/W}[/tex]) and wind velocity ([tex]\vec v_{W}[/tex]), both in miles per hour. If we know that [tex]v_{W} = 50\,\frac{mi}{h}[/tex], [tex]\theta_{W} = 40^{\circ}[/tex], [tex]v_{A/W} = 350\,\frac{mi}{h}[/tex] and [tex]\theta_{A/W} = 100^{\circ}[/tex], then resulting velocity is:
[tex]\vec v_{A} = 50\cdot (\cos 40^{\circ}, \sin 40^{\circ}) + 350\cdot (\cos 100^{\circ}, \sin 100^{\circ})[/tex]
[tex]\vec v_{A} = (-22.474, 376.822)[/tex]
Whose magnitude ([tex]v_{A}[/tex]), in miles per hour, and direction ([tex]\theta[/tex]), in degrees, are, respectively:
[tex]v_{A} = \sqrt{(-22.474)^{2}+376.822^{2}}[/tex]
[tex]v_{A} \approx 377.492\,\frac{mi}{h}[/tex]
[tex]\theta_{A} = \tan^{-1} \left(\frac{376.822}{-22.474} \right)[/tex]
[tex]\theta_{A} \approx 93.413^{\circ}[/tex]
The resulting speed and direction of the airplane are approximately 377.492 miles per hour and 93.413°, respectively. [tex]\blacksquare[/tex]
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-4/5 + 33/10 Write your answer as a mixed number in simplest form.
Answer:
2 1/2
Step-by-step explanation:
−45+3310=?
The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD(-4/5, 33/10) = 10
Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.
(−45×22)+(33/10×11)=?
Complete the multiplication and the equation becomes
−8/10+33/10=?
The two fractions now have like denominators so you can add the numerators.
Then:
−8+33/10=25/10
This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 25 and 10 using
GCF(25,10) = 5
25÷5/10÷5=5/2
The fraction
52
is the same as
5÷2
Convert to a mixed number using
long division for 5 ÷ 2 = 2R1, so
52=212
Therefore:
−4/5+33/10= 2 1/2
find the gradient of the line segment between the points (0,3) and (1,8)
The gradient of the line segment between the points (0,3) and (1,8) is : 5
What is gradient?Gradient is the ratio of the increase or decrease in the y-coordinates to the increase ore decrease in the x-coordinates of points that form a line segment.
Analysis:
x1 = 0, x2 = 1, y1 = 3, y2 = 8,
Gradient(M) = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
= [tex]\frac{8 - 3}{1 - 0}[/tex] = 5/1 = 5
In conclusion, the gradient of the given points (0,3) and (1,8) is : 5
Learn more about gradients : brainly.com/question/21727173
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Answer:
Step-by-step explanation:
difference in x = 1
difference in y= 5
5 divided by 1 = 5
gradient= 5
The 150 Grade 7 students participated in school's Math Olympics. 64 students registered in Math Trail , 78 students registered in Amazing Race and 28 students registered in both Math Trail and Amazing Race. How many students registered in Math Trail only and in Amazing Race only? Are there students who did not registered in both events, how many?
Answer:
Number of students registered in Math trail only and in Amazing Race only is 86.
Number of students who did not registered in both events = 36
Step-by-step explanation:
There are 150 students totally.
64 students registered in Math trail.
78 registered in Amazing race.
28 registered in both Math trail and Amazing Race.
We can make Venn diagram for this and answer the question.
I've attached the Venn diagram.
Using the diagram,
Number of students registered in Math trial only and in Amazing race only is 36+50= 86.
Number of students who did not registered in both events = (150-(36+28+50))=36
Suppose a group of dancers performed the Round Dance at an Indigenous Peoples' Day
celebration. If the circumference of the circle was 44 feet, what was the diameter of the circle?
Answer:
4.27 meters
Step-by-step explanation:
Please help!! ASAP!! Math Help!k
[tex]f(x) = 4x^3 + Ax^2 + 2x - 5[/tex]
[tex]f(2) = 5[/tex]
[tex]5 = 4 \cdot 2^3 + A \cdot 2^2 + 2 \cdot 2 - 5\\5 = 4 \cdot 8 + 4A + 4 - 5\\5 = 32 + 4A + 4 - 5\\5 - 32 - 4 + 5 = 4A\\-26 = 4A\\A = \frac{-26}{4} = -\frac{13}{2} = -6.5[/tex]
Two points are plotted on the number line.
Answer:
-2/3+1/3= - 1/3
Step-by-step explanation:
if you look at the number line you just go once to the right
PLEASE HELP AND EXPLAIN!! I will mark brainliest <3
Answer: AB is 40
Step-by-step explanation: CD=CE+ED ED is 5 and it is also the midpoint meaning it is 1/2 of the value of the line. Therefore CD is 10, BC=BD+CD CD as we know is 10 and D is the mid point meaning it is also 1/2 of the value of BC. 10+10=20, AB=AC+BC, BC is 20 so AC must also be 20;therefore AB is 40
FIRST ANSWER GETS BRAINLIEST! PLEASE HURRY!
The area of a rectangle is 45 square units. The length is 15 units and the width is z units.
Area = length x width
What is the value of z?
Answer:
z = 3 units
Step-by-step explanation:
45 ÷ 15 = 3
Step-by-step explanation:
A is wl
45 = 15 x z
45 = 15z
3 = z
A package of 6 insulated gloves cost $50.94. what is the unit price of the pair of gloves.
Answer:
i think your answer would be $8.49 for a pair of gloves.
Step-by-step explanation:
50.94 / 6 = 8.49
To transmit information on the internet, large files are broken into packets of smaller sizes. Each packet has 1,500 bytes of information. An equation relating packets to bytes of information is given by b = 1,500p where p represents the number of packets and b represents the number of bytes of information. Each byte contains 8 bits of information. Write an equation to represent the relationship between the number of packets and the number of bits. (X = form)
Answer: [tex]x= 187.5p[/tex]
Step-by-step explanation:
Given : An equation relating packets to bytes of information : [tex]b = 1,500p[/tex] where p represents the number of packets and b represents the number of bytes of information.
1 byte = 8 bits
Let x= Number of bits such that 1 b = 8x
Put b = 8x in given equation , we get
[tex]8x=1500p[/tex]
Divide both sides by 8 , we get
[tex]x= 187.5p[/tex]
Hence, the equation represent the relationship between the number of packets and the number of bits : [tex]x= 187.5p[/tex]
Answer:
x=12000p
Step-by-step explanation:
It is Right
I Fink
Solve for a:
35= -7a+14
Ok help me?? Uhhhhhhhhhhhh
Answer:with?
Step-by-step explanation:
eh what is 2(h + 1) =5h - 7
Answer:
h=3
Step-by-step explanation:
A slope of 2/3 and a y-intercept of -9/7?
Answer:
Slope intercept form:
[tex]y = \frac{2}{3}x - \frac{9}{7}[/tex]
Answer:
y = 2/3x - 9/7
Step-by-step explanation:
If you want the slope intercept form:
y = 2/3x - 9/7
^ ^
slope y-intercept
Solve for s:
14=-2s-8
Answer: 11
Step-by-step explanation:
2 times 11 is 22. 22-8=14
Answer:
14= -2s - 8
22= -2s
-11=s
Step-by-step explanation:
Add 8 to both sides, on one sided the number will be undo but on the other it won't
Then divide both sides by -, wich leaves the unknown variable alone
Finally you have your answer!
44% of ten is what number
Answer:
4.4
Step-by-step explanation:
You have to turn 44% into a decimal which will be 0.44
Then multiply 0.44 by 10
0.44*10
4.4
which expression has a value of 4
Answer:
7x=28
Step-by-step explanation:
The table of values below represents a linear function and shows the amount of money in Juanita’s savings account since she began her part-time job. What is her monthly rate of savings?
Amount in Juanita’s Savings Account
Number of Months Working at Part-Time Job
0
2
4
6
8
Amount in Savings Account (in dollars)
$36
$60
$84
$108
$132
a.$12 per month
b.$18 per month
c.$24 per month
d.$36 per month
Answer:
The answer is C., $24 per month.
Answer:
A $12
Step-by-step explanation:
she has saved $36 before she gets a part time job, after 2 months, her savings have increased from 36 to 60. 2 months = 60 - 36, 2 months = 24. now we divide 24 by 2, and the answer is 12. option A is correct.
What are the 4 major types of special Angle Pairs formed by Parallel Lines and Transversals? 20 points Vertical Angles, Angle Bisectors, Linear Pairs, Perpendicular Bisectors Alternate Interior, Corresponding, Consecutive Interior, Alternate Exterior Straight, Acute, Obtuse, Right Adjacent Angles, Supplementary Angles, Complementary Angles, Opposite Angles
Answer:
Alternate Interior, Corresponding, Consecutive Interior, Alternate Exterior
Step-by-step explanation:
When a transversal cuts across two parallel lines, there are 4 major types of special angles that are formed as shown in the attachment below. They are:
1. Alternate interior angle pairs are angles that are positioned inside the two parallel lines but lie on opposite sides of the transversal that cuts across the two parallel lines.
In the figure attached below, the alternate exterior angle pairs are labelled:
<3 and <6;
<4 and 5
2. Corresponding angles: these are angle pairs that are lie in the same position of the transversal, one interior, and the other exterior to a parallel lines respectively.
In the figure attached below: the following are corresponding angles pairs:
<1 and <5;
<2 and 6;
<3 and <7;
<4 and <8
3. Consecutive Interior angle pairs: these are angles that lie in the same side of the transversal and also found opposite each other within the parallel lines.
They are labelled:
<3 and <5;
<4 and <6
4. Alternate exterior angle pairs are angles that are positioned outside of the two parallel lines but lie on opposite sides of the transversal that cuts across the two parallel lines.
They are labelled:
<1 and <8;
<2 and <7;
Onya selected a pair of shoes for the regular price of $80. How much money will she save by using the 20% off coupon? Justify your answer using equations, models, and/or words to explain your mathematical reasoning. Part B: Katie selected a pair of shoes for the regular price of $120. After the 20% off discount is applied, what will be the discounted cost of the shoes (before tax)? Justify your answer using equations, models, and/or words to explain your mathematical reasoning.
Answer:
a. [tex]Savings = \$16[/tex]
b. [tex]Price = \$96[/tex]
Step-by-step explanation:
Solving (a):
[tex]Price = \$80[/tex]
[tex]Coupon = 20\%[/tex]
Required
Determine her savings.
[tex]Savings = Coupon * Price[/tex]
[tex]Savings = 20\% * \$80[/tex]
[tex]Savings = \$16[/tex]
Solving (a):
[tex]Price = \$120[/tex]
[tex]Coupon = 20\%[/tex]
Required
Determine the price before tax
First, we need to determine her savings
[tex]Savings = Coupon * Price[/tex]
[tex]Savings = 20\% * \$120[/tex]
[tex]Savings = \$24[/tex]
The price before tax is calculated as follows:
[tex]Price = \$120 - \$24[/tex]
[tex]Price = \$96[/tex]
How many 3/6 are there in 1 whole
Don’t give me glibberish answers or I will report u
Answer:2
Step-by-step explanation:because
x=1x6/3
X=2
Its not gibberish so gimme brainliest
Answer:
It would be 2.
Step-by-step explanation:
3/6 is half of a whole. Which means, there is a half missing. So multiply 3/6 by 2, to make it a whole.
whats the answer to this?
Answer:
5
Step-by-step explanation:
Add the two coordinates and divide by 2.
-2 + 12 = 10
10/2 = 5
Answer: 5
2^n-5×5^n-4=5
Please help me
I will mark as brainist
please do the sum in a paper and post...
[tex]\huge{\fbox{\sf{n=5 }}}[/tex]
Step 1:
[tex]⇒ {2}^{n - 5} \times {5}^{n - 4} = 5[/tex]
Step 2:
[tex] ⇒{2}^{n - 5} \times {5}^{n - 4} = {5}^{1} \times {2}^{0} [/tex]
On comparing values we get:
Taking:
[tex] {2}^{n - 5} = {2}^{0} [/tex]
n-5=0
n=5✓
or
Taking:
[tex] {5}^{n - 4} = {5}^{1} [/tex]
n-4=1
n=5✓
Which of these values could be the slope of the line? Select 2 options.
-2
-8/5
0
7/4
3
Answer:
7/4 and 3
Step-by-step explanation:
correct on edge 2020
Answer: 7/4 & 3
Step-by-step explanation:
The price of gas rose from $2.40 per gallon in January to
$3.00 per gallon in April. What was the percent increase
based on the original price?
A. 20%
B. 25%
C. 60%
D. 80%
Answer:
Step-by-step explanation:
The answer is 25%
25% of 2.40= 0.6 3.00-0.6= 2.4 just ad a 0 so 2.40
Answer is 25%
These are statements about factors and prime and composite numbers. Which statements are true? Check all that apply. The numbers 4, 9, 25, and 49 are composite numbers. The number 1 is a prime number. The first prime number is 2. A composite number can be written as the product of prime numbers.
Answer:
The numbers 4, 9, 25, and 49 are composite numbers.
The number 1 is a prime number.
Step-by-step explanation:
A prime number can be defined as a number that is divisible by 1 and itself only. Examples are: 1, 3, 5, 7, 11 e.t.c
A composite number can be defined as a positive number that can be formed by multiplying two smaller positive numbers together. These two positive integers may or may not be prime number.
It is a positive integer that has at least one divisor other than 1 and itself.
Examples are: 4, 6, 8, 9, 12, 25, 49, e.t.c
Therefore, the true statements in the questions above =
The numbers 4, 9, 25, and 49 are composite numbers.
The number 1 is a prime number.
On a coordinate plane, Broadway is 4 units to the right and 4 units up. Empire State Building is 1.50 units to the right and 1 unit up. Brooklyn Bridge is 5 units to the left and 4.5 units down. Statue of Liberty is 4 units to the left and 3.5 units up. Which ordered pairs show the location of the Empire State Building? Check all that apply. (1 and one-half, 1) (1, 1 and one-half) (–1.5, –1.0) (1.5, 1.0) (1.0, 1.0)
Answer:
upove is correct
Step-by-step explanation:
hehe
-5 2/3 - 1/6 please help
Answer:
-5 5/6
Step-by-step explanation:
I just used my calculator.
If $7,300 is invested in an account that offers 7% interest compounded semi-annually, how much money is in the account after 3 years?
Answer:
The answer to your question is $8973.56
Step-by-step explanation:
PLEASE HELP! I WILL MAKE YOU BRAINLIST!
Answer:
micro organism
Step-by-step explanation: