An airplane is headed due south with an airspeed of 300 kph. A wind is blowing from the west at 120 kph. What is the ground speed and direction of the plane?
323 kph with a directional bearing of S 22° E
328 kph with a directional bearing of S 68° E
420 kph with a directional bearing of S 22° E
420 kph with a directional bearing of S 68° E
The ground speed and direction of the plane is 323 kph with a directional bearing of S 22° E
To find the ground speed of the plane, we need to know what a vector is
What is a vector?A vector is a variable that has both magnitude and direction.
Since the airplane is headed due south with an airspeed of 300 kph, its vector is V = (-300 kph)j.
Also, the wind is blowing from the west at 120 kph. Its vector is v = (-120 kph)i
Now, the ground speed of the plane V' is the resultant vector of the airspeed and wind speed.
What is a resultant vector?A resultant vector is the sum of two or more vectors.
So, V' = v + V
V' = (-120 kph)i + (-300 kph)j
So, its magnitude V' = √(x² + y²) where
x = -120 kph and y = -300 kph.So, V' = √[(-120 kph)² + (-300 kph)²]
= √[14400 kph² + 90000 kph²]
= √(104400 kph²)
= 323.11 kph
≅ 323 kph
The direction of the planeIts direction, Ф = tan⁻¹(y/x)
Ф = tan⁻¹(-300 kph/-120 kph)
Ф = tan⁻¹(2.5)
Ф = 68.2°
From the South-line we have α = 90° - Ф = 90° - 68.2° = 21.8° ≅ 22°
So, the directional bearing of the plane is S22°E.
So, the ground speed and direction of the plane is 323 kph with a directional bearing of S 22° E
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Answer:
A on edge 2022
Step-by-step explanation:
323 kph and 22 E
Jada fills the bathtub before taking a bath and then allows the water to drain when she is done. The graph below models the number of gallons of water, y, in the bathtub over time, t, in minutes.
On a graph, the graph increases, remains constant, and then decreases.
Is the number of gallons of water in the bathtub a function of time?
Yes because each t value is paired with exactly one number of gallons.
Yes because the number of gallons is bounded between y = 0 and y = 36.
No because each number of gallons is paired with more than one t value.
No because from t = 5 to t = 20 the number of gallons of water is constant.
Answer:
A, Yes because each t value is paired with exactly one number of gallons.
Step-by-step explanation:
Simply perform the vertical line test. On a graph, draw a vertical line, and if the line crosses the graph exactly once, it is a function. See the diagram below. Hope it helps, have a fantastic day.
Answer:
a
Step-by-step explanation:
because i am built diffrent thats why
a. find the surface area of the rectangular prism
b. find the volume.
a. find the volume of the prism
b. find the surface area of the prism.
Answer:
For rectangulasr prism
a. [tex]72cm^3[/tex]
b. [tex]108cm^{3}[/tex]
Step-by-step explanation:
For rectangulasr prism
a. Equation: Volume = length x width x height
length: 6cm
width: 4cm
height: 3cm
Volume = 6cm x 4cm x 3cm
Volume = 24cm x 3cm
b. Equation: A = 2[(width x length) + (height x length) + (heigth x width)]
A = 2[(4cm x 6cm) + (3cm x 6cm) + (3cm x 4cm)]
A = 2[(24cm) + (18cm) + (12cm)]
A = 2[(24cm) + (30cm)]
A = 2[(54cm)]
three people P, Q and R contribute to a fund. P provides 3/5 of the total, Q provides 2/3 of the remainder and R provides £8. Determine the total fund?
Answer:
Let x be the total fund
[tex] \frac{3x}{5} + \frac{2}{3}(x - \frac{3x}{5} ) + 8 = x [/tex]
3x/5 + 2/3(2x/5) + 8 = x
3x/5 + 4x/15 + 8 = x
9x/15 + 4x/15 + 120/15 = 15x/15
9x+4x+120=15x
-2x= -120
x=60£
Please answer if you can 30 points.
What is the y-intercept of the linear function given the following table?
Answer:
The y-intercept is 4
Step-by-step explanation:
You find the y-intercept by finding where x is zero. In the table, when x=0 the y=4. The y-intercept is 4. The graph of the function crosses the x-axis at the point (0,4).
Answer:
4
Step-by-step explanation:
the y-intercept is the y-coordinate where the line intersects the facis.So if we want to figure out the intercept,we're going to set x=0 and sdue for Y.
Please help me do this mathematics question experts
[tex]\textbf{(i)}\\\\~~~~~~~y= e^{3x} \sin 2x\\\\\\\implies \dfrac{dy}{dx} = \dfrac{d}{dx} \left( e^{3x} \sin 2x \right)\\\\\\~~~~~~~~~~~~=e^{3x} \dfrac{d}{dx} \sin 2x + \sin 2x \dfrac{d}{dx} e^{3x}\\\\\\~~~~~~~~~~~~=2e^{3x} \cos 2x + 3e^{3x}\sin 2x \\\\\\[/tex]
[tex]\textbf{(ii)}\\\\~~~~~~~~y = \dfrac{e^{3x}}{\cos 2x}\\\\\\\implies \dfrac{dy}{dx} = \dfrac d{dx} \left(\dfrac{e^{3x}}{\cos 2x} \right)\\\\\\~~~~~~~~~~~=\dfrac{\cos 2x \dfrac{d}{dx}\left(e^{3x} \right) -e^{3x} \dfrac{d}{dx}( \cos 2x) }{\cos^2 (2x)}\\\\\\~~~~~~~~~~~=\dfrac{3e^{3x} \cos 2x+2e^{3x}\sin2x }{\cos^2(2x)}\\\\\\~~~~~~~~~~~=\dfrac{3e^{3x} \cos 2x}{ \cos^2(2x)} + \dfrac{2e^{3x} \sin 2x}{\cos^2(2x)}\\\\\\~~~~~~~~~~~=3e^{3x}\sec (2x) + 2e^{3x}\sec (2x) \tan (2x)[/tex]
[tex]\textbf{(iii)}\\\\~~~~~~~~~y=( 3x+2)^3\\\\\\\implies \dfrac{dy}{dx} = \dfrac{d}{dx}(3x+2)^3\\\\\\~~~~~~~~~~~=3(3x+2)^2 \dfrac{d}{dx} (3x+2)\\\\\\~~~~~~~~~~~=3(3x+2)^2 \cdot 3\\\\\\~~~~~~~~~~~=9(3x+2)^2[/tex]
[tex]\textbf{(iv)}\\\\~~~~~~~~~x^2 +y^2 = 5xy\\\\\\\implies \dfrac{d}{dx}(x^2 +y^2) = 5\dfrac{d}{dx} (xy)\\\\\\\implies 2x + 2y \dfrac{dy}{dx} = 5\left(x \dfrac{dy}{dx} +y\right)\\ \\\\\implies 2x +2y \dfrac{dy}{dx} = 5x \dfrac{dy}{dx} +5y\\\\\\\implies 2y \dfrac{dy}{dx} - 5x \dfrac{dy}{dx} = 5y-2x\\\\\\\implies (2y-5x) \dfrac{dy}{dx} = 5y-2x\\\\\\\implies \dfrac{dy}{dx} = \dfrac{5y-2x}{2y-5x}[/tex]
This rectangular prism has a length of 14 inches, a height of 8 inches, and a width of 3 inches. What is the volume
height= 8 in
length= 14 in
width= 3 in
to find:the volume of the given rectangular prism.
solution:[tex]v = whl[/tex]
[tex]v = 8 \times 14 \times 3[/tex]
[tex]v = 336 \: {in}^{3} [/tex]
hence, the volume of the given rectangular prism is 336 cubic inches.
answer= option D
[tex]\large\boxed{Formula: V= lbh}[/tex]
All the values are given so we'll simply have to solve.
Let's solve!
Substitute the values according to the formula.
We'll have to multiply the length, breadth and the height.
[tex]V= 14 \times 3 \times 8[/tex]
[tex]\large\boxed{V= 336 \: {in}^{3}}[/tex]
We get a whole number to the final answer so we won't have to round off.
Therefore, the volume of the given rectangular prism is 336 cubic inches.
Correct option: Option D
In a triangle, an exterior angle formed by producing a side is half of a right angle. One of the two opposite interior angles is twice the Other; find the sizes of each interior angle of triangle.
Step-by-step explanation:
let's explain this a bit.
when the exterior angle is a certain size, then the interior angle is 180 - that exterior angle.
in our case the exterior angle is half of a right angle, so it is 90/2 = 45°.
the corresponding interior angle is 180-45 = 135°.
the sum of all angles inside a triangle is always 180°.
so,
x + 2x + 135 = 180
3x = 45
x = 15°
2x = 30°
so, the 3 interior angles are
135°, 15°, 30°
A store buys a bike for $140. They mark up the bike 25%. What is the selling price?
Answer:
$175
Step-by-step explanation:
Original Price = $140
Mark up (% increase) = 25%
Selling Price = Original Price (1 + Mark up)
SP = 140 (1 + 25%)SP = 140 (1 + 0.25)SP = 140 (1.25)SP = $175Can someone please help me.
Answer:
The answer can be seen in the image attached to this message (containing the full steps).
short: 27cm
long: 36cm
hypotenuse: 45cm
Step-by-step explanation:
The image attached to this message contains explained steps.
rewrite! Write an new and equivalent equation that is easier to solve
[tex]{\huge{\fcolorbox{yellow}{red}{\orange{\boxed{\boxed{\boxed{\boxed{\underbrace{\overbrace{\mathfrak{\pink{\fcolorbox{green}{blue}{Answer}}}}}}}}}}}}}[/tex]
[tex] \sf 7( \sqrt{m + 1} - 3) = 21[/tex]
we will multiply 7 with bracket
[tex] \sf 7 \sqrt{m + 1} - 21 = 21[/tex]
Now we will take (-21) on LHS to RHS
[tex] \sf 7 \sqrt{m + 1} = 21 + 21 \\ \\ \sf7 \sqrt{m + 1 } = 42 \\ \\ \sf \sqrt{m + 1} = \frac{42}{7} \\ \\ \sf \sqrt{m + 1} = 6[/tex]
Now we will do squaring both sides
[tex] \sf {( \sqrt{m + 1}) }^{2} = {(6)}^{2} \\ \\ \sf \red {m + 1 = 36}[/tex]
[tex]\sf{ 7( \sqrt{m+1} - 3)=21}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\sf{\sqrt{m+1} - 3)=\frac{21}{7}}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\sf{ 7( \sqrt{m+1} - 3)=3}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\sf{\sqrt{m+1} =6}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
Get the power of 2 in both sides.
[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\sf{( \sqrt{m + 1})^2 = 6^2}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\sf{m+1=36}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\sf{m=35}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
So the answer is m = 35
if x-y=5 and xy=4,find the value of x3-y3
[tex]\text{Given that,} ~ x-y = 5~ \text{amd}~ xy = 4\\\\\text{Now,}\\\\x^3 -y^3\\\\=(x-y)(x^2 +xy+y^2)\\\\=(x-y)[(x-y)^2 +2xy +xy]\\\\=(x-y)[(x-y)^2 +3xy]\\\\=5(5^2+3\cdot 4)\\\\=5(25+12)\\\\=5(37)\\\\=185[/tex]
You invested money in two funds. Last year, the first fund paid a dividend of 9% and the second a dividend of 3%, and you received a total of $858. This year, the first fund paid a 10% dividend and the second only 1%, and you received a total of $867. How much money did you invest in each fund?
The amount that was invested in the first fund is $8300.
The amount that was invested in the second fund is 3700.
What are the linear equations that represent the question?0.09a + 0.03b = $858 equation 1
0.1a + 0.01b = $867 equation 2
Where:
a = amount invested in the first fund b = amount invested in the second fund How much was invested in the second fund?Multiply equation 2 by 0.9:
0.09a + 0.009b = 780.30 equation 3
Subtract equation 1 from equation 3
0.021b = 77.70
Divide both sides by 0.021
b = $3700
How much was invested in the first fund?
Substitute for b in equation 1: 0.09a + 0.03(3700) = $858
0.09a + 111 = 858
a = (858 - 111) / 0.09
a = $8300
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The temperature outside changed from 82°F to 46°F over a period of six days. If the temperature changed by the same amount
each day, what was the daily temperature change?
A. 36°F
B. -6°F
C. 6°F
D. -36°F
Answer:
B. -6
Step-by-step explanation:
You know immediately that it will be negative, because the temp is going down.
To find the exact answer, start by finding the difference between the two temps
82-46 = 36
since its a six day period, divide 36 by 6
36/6 = 6
so, the answer is -6
ANSWER THIS CORRECTLY FOR BRAINLIEST!!!!
Answer:
v=2143.57
Step-by-step explanation:
4/3 x 3.14 x 8³
3.14 x 512 x 4/3
3.14 x 512=1607.68
1607.68 x 4/3=2143.57333333
round to nearest hundreth
v=2143.57
Answer:
V ≈ 2143.57= 2144
Step-by-step explanation:
[tex]v=\frac{4}{3} *3.14*8^3[/tex]
=2143.57333333
you dont need to round, so!
=2144 (if you want)
sorry for the confusion
Help find the probability
Answer:
18. 0.25
19. 0.33
Step-by-step explanation:
Problem 18
Number of oranges = 2Number of fruits = 2 + 6 = 8P (orange) = 2/8 = 1/4P (orange) = 0.25Problem 19
Number of 1 or 6 faces = 2Total faces = 6P (1 or 6) = 2/6 = 1/3P (1 or 6) = 0.33 (2 DP)The present shown below is a cube. Find the surface area.
Answer:
SA = 2,400 cm²
Step-by-step explanation:
Surface Area (SA) of a cuboid: 2(lw) + 2(wh) + 2(hl)
SA = 2(lw) + 2(wh) + 2(hl)
l = 20 cmw = 20 cmh = 20 cmSubstitute the values above and multiply:
SA = 2(lw) + 2(wh) + 2(hl)
SA = 2(20)(20) + 2(20)(20) + 2(20)(20)
SA = 2(400) + 2(400) + 2(400)
SA = 800 + 800 + 800
SA = 2,400 cm²
Final answer: 2,400 cm²
Hope this helps!
================================
[tex] \large \sf \underline{Direction:}[/tex]
The present shown below is a cube. Find the surface area.================================
[tex] \large \sf \underline{Answer:}[/tex]
[tex] \qquad \qquad \huge \bold{2,400cm^{2} }[/tex]
================================
[tex] \large \sf \underline{Solution:}[/tex]
[tex] :\sf{SA=2(lw)+2(wh)+2(hl)}[/tex]
[tex]:\sf{SA=2(20)(20)+2(20)(20)+2(20)(20)}[/tex]
[tex]:\sf{SA=2(400)+2(400)+2(400)}[/tex]
[tex]:\sf{SA=800+800+800}[/tex]
[tex]\therefore\sf\underline{SA = \pmb{2,400cm^{2} }}[/tex]
Hence, the surface area that you are looking for is 2, 400cm².
================================
find the length of a diagonal of a square whose side is 2 cm
Answer:
2√2 cm
Step-by-step explanation:
Formula to be understood :
Diagonal of a square = Side length√2Deriving the formula :
Apply Pythagorean Theorem by taking the side lengths as altitudes and the diagonal as a hypotenuseside length² + side length² = hypotenuse²2(side length)² = hypotenuse²hypotenuse = side length√2Solving for the length of the diagonal :
diagonal = 2√2 cmLength of diagonal
side√2a√22√2cm4.1 A bag contains 6 red, 4 green, 2 yellow and 3 blue balls. In each case, give the ratio (in simplest form) of the asked number of balls in the bag.( 4 ) 4.1.1 The number of red balls to the number of green balls.
The number of red balls to the number of green balls is 3 : 2
How to determine the ratio?The distribution of the balls is given as:
6 red, 4 green, 2 yellow and 3 blue balls
The number of red balls to the number of green balls is represented as:
Ratio = Red : Green
So, we have:
Ratio = 6 : 4
Simplify
Ratio = 3 : 2
Hence, the number of red balls to the number of green balls is 3 : 2
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QUICKKK!! PLEASE
The probability of picking the winning 4-digit number in a Pick 4 lottery is 1/10000.
(a) Explain what this probability means.
(b) If 10000 people play the Pick 4 lottery, will exactly 1 person win the lottery? Explain.
(c) The winning number in a Pick 4 lottery was 1234 two days in a row. What is the likelihood o
this number occurring on the next drawing? Explain
A probability of 1/10000 means that only one person can get the Pick 4 lottery among 10000 pickers.
What is probability?The term probability has to do with the chance that an event will occur or not. Usually probability is expressed as a fraction.
The meaning of the saying that the probability of picking the winning 4-digit number in a Pick 4 lottery is 1/10000 is that only one person can get the Pick 4 lottery among 10000 pickers.
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ANSWER THIS CORRECTLY FOR BRAINLIEST!!!!
This is 8th grade
algebra btw
Answer:
V = 2143.57
Step-by-step explanation:
To find the volume of a sphere you need to use this formula:
[tex]V = \frac{4}{3}\pi r^{3}[/tex]
r = radius
Solve:
You need the radius from the diameter. Divide 16/2 which is
8.
[tex]V = \frac{4}{3}(3.14) 8^{3}[/tex]
V = 2143.57
Can someone pls help me
The complete statement is 67000 pounds is equivalent to 33.5 tons
How to convert the units?The unit is given as:
Weight = 67000 pounds
As a general rule;
1 pound = 0.0005 tons
Multiply both sides by 67000
67000 * 1 pound = 67000 * 0.0005 tons
Evaluate
67000 pounds = 33.5 tons
Hence, 67000 pounds is equivalent to 33.5 tons
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va rog, dau coroana + 20 de puncte (doar exercitiul 2)
Step-by-step explanation:
a) 1*7=7 (Litres);
b) 1*2*5=10 (Litres);
c) 10*0.5*1/0.5=10 (bottles)
−8 ≤ −3; Add 11 to both sides
The resulting inequality is:
Answer:
True, (-∞, ∞) 3 ≤ 8
Step-by-step explanation:
−8 + 11 ≤ −3 + 11
3 ≤ 8
*2.) Which trinomial is equivalent to 4(x - 5)^2– 3(x - 2)?
Answer:
4x² - 43x - 106
Step-by-step explanation:
4(x - 5)²– 3(x - 2)
4(x - 5)(x - 5) - 3 (x - 2)
distribute
4(x(x - 5) - 5(x - 5)) - 3 (x - 2)
4(x² - 5x - 5x - 25) - 3 (x - 2)
↓
combine like terms ↓
4(x² - 10x - 25) ((( ↓
distribute again ↓
4x² - 40x - 100 ↓
↓
distribute ↔ ↓
4x² - 40x - 100 - 3 (x - 2)
4x² - 40x - 100 - 3x + 6
add
4x² - 40x - 106 - 3x
combine
4x² - 43x - 106
x^2 +8 x+ y^2-12 y =14 what is the center and radius
Answer:
Step-by-step explanation:
Find the probability giving brainlest
Answer:
[tex]0.33[/tex]
Step-by-step explanation:
There are 6 sides on dice, therefore the sample space would be 6 (the sample space is the denominator). We were asked to find the probability of getting a 1 or a 6. Since we were given 2 options 1 or 6, it therefore means that we are trying to find the probability of the dice rolling on 2 out of the 6 sides it has. Therefore the probability would be:
[tex] \frac{2}{6} \: or \: \frac{1}{3} [/tex]
A third as a decimal is
[tex]0.33[/tex]
Please help me with this problem
Answer:
1516
Step-by-step explanation:
hope can help you
2000x 2%=40
9000x 5%= 450
(30000-9000-2000) x 5.4% = 1026
total tas 40+450+1026=
You wish to test the following claim (
H
a
) at a significance level of
α
=
0.002
.
H
o
:
μ
=
63.5
H
a
:
μ
<
63.5
You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size
n
=
62
with mean
M
=
56.3
and a standard deviation of
S
D
=
13.2
.
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =
What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =
Using the t-distribution, it is found that the desired measures are given as follows:
The test statistic is t = -4.29.The p-value is of 0.What are the hypotheses tested?At the null hypotheses, it is tested if the mean is of 63.5, that is:
[tex]H_0: \mu = 63.5[/tex]
At the alternative hypotheses, it is tested if the mean is less than 63.5, that is:
[tex]H_1: \mu < 63.5[/tex]
What is the test statistic?The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The values of the parameters are given as follows:
[tex]\overline{x} = 56.3, \mu = 63.5, s = 13.2, n = 62[/tex]
Hence, the test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{56.3 - 63.5}{\frac{13.2}{\sqrt{62}}}[/tex]
t = -4.29.
What is the p-value?We have a left-tailed test, as we are testing if the mean is less than a value, with 62 - 1 = 61 df and t = -4.29. Hence, using a t-distribution calculator, the p-value is of 0.
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Please help me slove this i really need the answer
