Answer:
[tex]zw=76 * (cos(\frac{3\pi}{16}) +isin(\frac{3\pi}{16}) )[/tex]
Step-by-step explanation:
Given
[tex]z =38 (cos(\frac{\pi}{8})+ i sin(\frac{\pi}{8})[/tex] and
[tex]w = 2 (cos(\frac{\pi}{16} ) + i sin(\frac{\pi}{16})[/tex]
Required
Determine zw
Given that:
[tex]x = v_1(cos(a) + isin(a))[/tex] and [tex]y = v_2(cos(b) + isin(b))[/tex]
[tex]x * y = (v_1 * v_2)*((cos(a+b) + isin(a+b))[/tex]
So, we have:
[tex]zw=(38 * 2) * (cos(\frac{\pi}{8} + \frac{\pi}{16}) + isin(\frac{\pi}{8} + \frac{\pi}{16}))[/tex]
[tex]zw=76 * (cos(\frac{2\pi + \pi}{16})+isin(\frac{2\pi + \pi}{16}))[/tex]
[tex]zw=76 * (cos(\frac{3\pi}{16}) +isin(\frac{3\pi}{16}) )[/tex]
The value of ZW is [tex]\begin{aligned} (76) [Cos(\frac{3\pi}{16})+ \i\ Sin(\frac{3\pi}{16})]\end{aligned}[/tex].
Given to us,
[tex]\begin{aligned} Z &= 38 [cos(\frac{\pi}{8}) + i\ sin(\frac{\pi}{8}) ]\end{aligned}[/tex],
[tex]\begin{aligned}W &= 2 [cos(\frac{\pi}{16}) + i\ sin(\frac{\pi}{16}) ]\end{aligned}[/tex],
We know that,
[tex]{x = v_1 [ cos\ (a) +i\ sin\ (a)]}[/tex] and [tex]{y = v_2 [ cos(b) +i\ sin(b)]}[/tex]
So,
[tex]xy = (v_1 \times v_2) [ cos(a+b) + i\ sin(a+b)][/tex]
Therefore, we can write it as,
[tex]\begin{aligned}ZW &= [38cos(\frac{\pi}{8}) + 38\ i\ sin(\frac{\pi}{8}) ]\times [2cos(\frac{\pi}{16}) + 2\ i\ sin(\frac{\pi}{16}) ]\\&= (38 \times 2) \{Cos[\frac{\pi}{8} + \frac{\pi}{16}]\}+ \{i\ Sin[\frac{\pi}{8} + \frac{\pi}{16}]\} \end{aligned}[/tex]
[tex]\begin{aligned}&= (76) [Cos(\frac{3\pi}{16})+ \i\ Sin(\frac{3\pi}{16})]\end{aligned}[/tex]
Hence, the value of ZW is [tex]\begin{aligned} (76) [Cos(\frac{3\pi}{16})+ \i\ Sin(\frac{3\pi}{16})]\end{aligned}[/tex].
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Darnell rented a moving truck, the weight of the truck was 7,860 pounds but the truck is empty, nothing is in there. When he puts the items of his own in the truck, it weighs 6 tons. What was the weight in pounds of the item that Darnell placed in the truck?
Answer:
The item weighed 4140 pounds.
Step-by-step explanation:
1 ton = 2000pounds, 6 tons=12000pounds.
12000-7860=4140pounds.
The length of time the Sun is above the horizon is called the
Angle of insolation
Intensity of insolation
Duration of insolation
Longitude of insolation
Write 5 x 10^6 in standard notation.
Thank you for taking the time to read this!
And I hope you have a good day, Loves!
Also if I'm right can you let me know, please?
Also Also if I am right can I please have Brainliest??
You don't need to, I'm just glad I could help. ^^
(If I did help-)
And don't forget to eat a full meal, and have at least one cup of water today!
The standard notation of the number 5 × 10⁶ would be 50,00,000.
Used the concept of scientific notation that states,
Scientific notation is a way of writing very large or very small numbers.
For example; 230,000,000 can be written in scientific notation as
2.3 x 10⁸.
Given that the number is,
5 × 10⁶
Now it can be written in standard notation,
5 × 10⁶
5 × 10 × 10 × 10 × 10 × 10 × 10
5 × 1000000
50,00,000
Therefore, The standard notation of the number is 50,00,000.
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3. A ladder is standing on horizontal ground and rests against a vertical
wall. The ladder is 4.5 m long and its foot is 1.6 m from the wall.
Calculate how far up the wall the ladder will reach. Round your
answer to three decimal places.
(Show your working)
Answer:
4.206 m
Step-by-step explanation:
[tex]a^{2} +b^{2} =c^{2} \\a^{2} +1.6^{2}=4.5^{2}\\a^{2}+2.56=20.25\\20.25-2.56=17.69\\\sqrt{a^{2}}=\sqrt{17.69}\\a=4.205948169\\rounded: a=4.206[/tex]
help pls all the questions i dont get it :(
Answer:
A. The graph is not proportional, although it has a consistent slope, it does now go through the point of origin or (0,0). The equation of a proportional line is y=kx, so the y-intercept must be at (0,0).
B. Slope is found by [tex]\frac{rise}{run}[/tex], from 1 point to the next, the y-value (rise) increases by 2 and the x-value (run) increases by 1, [tex]\frac{4}{1} = 4[/tex] giving us a slope of 4.
C. The y-intercept is the lines point of intersection with the y-axis. In the graph, this point is (0,10).
D. y = mx + b is the slope-intercept form where m is the slope and b is the y-intercept, the slope (m) is 4 and the y-intercept (b) is 10. y = 4x + 10
E. The equation is not proportional because the b value is 10 rather than 0.
Answer:
A. The graph is not proportional. I know this because the line doesn't go through the origin (0, 0). B. The slope (m) of the graph is 4. C. The y-intercept is 10. D. The equation in slope-intercept form is y=4x+10. E. The equation is not proportional. I know this because the line began from 10.
Step-by-step explanation:
The graph will be proportional when the line goes through the origin, (0, 0). The equation [tex]m=\frac{y2-x2}{y1-x1}[/tex] is used to solve for the slope (m). Pick any given points from the graph that's on the line to solve for slope (m). (0, 10) and (1, 14) makes it easier to solve for "m".
[tex]m=\frac{14-10}{1-0} =\frac{4}{1} =4[/tex] (4 is the slope)
Substitute x and y with any point given to find the y-intercept:
[tex]14=4(1)+b[/tex]
[tex]14=4+b[/tex]
[tex]-4[/tex] [tex]-4[/tex]
----------------
[tex]10=b[/tex]
*Note that the y-intercept is always (0, any number)
Example: (0, -24)
Once you know what the slope and the y-intercept are, you'll have the equation set as y=4x+10.
can someone help me please ;-;
9514 1404 393
Answer:
coffee shopfire departmentlibraryparkpolice stationStep-by-step explanation:
Fractions with the same numerator are smaller if their denominator is larger.
1/4 < 1/3 < 1/2
If you know your decimal equivalents, you know that ...
1/2 = 0.5
3/5 = 0.6
7/8 = 0.875
so, the order of the fractions is ...
1/4 < 1/3 < 1/2 < 3/5 < 7/8
Listing the places in the same order, we have ...
coffee shopfire departmentlibraryparkpolice stationif y/8=4,then y/8x 8=4x
Answer:
y = 32
Step-by-step explanation:
y/8 = 4
multiply both sides by 8:
y = 4 x 8 = 32
You pick one tile without looking from a bag that has 2 blue, 3 red, and 5 yellow tiles. Find each probability. Write your answer in simplest form.
Answer:
Blue: 1/5
Red: 3/10
Yellow: 1/2
Help me pls help I don’t get it
i think maybe your supposed to find an answer choice that is basically equal to the equation given already
Answer:
2) 1 3/4 = 4/4 + 3/4
Step-by-step explanation:
hope it helps
easy 5th grade math please help!! look at photo. Giving brainliest!!
Helppp pls
Another one
Answer:
25 percent
Step-by-step explanation:
There is 12 spots on the chart
3 of these spots are green or 3/12
3/12 is equivalent to 1/4
1/4 of 100 in 25 percent
-14x > - 3
Please respond fast
Answer:
x<3/14 is the answer
Step-by-step explanation:
Impossible question for me plz help
Answer:
The line x = 3 is simply a vertical line that passes through every single point where x is equal to 3.
One that is is parallel and passes through (-4, 7) will be in the same format, just with another number. The given point has an x-coordinate of -4, so the line is:
x = -4
kalya walks 3 7/10 miles each day what is the total of miles she walks 31 days
Answer:
114.7
Step-by-step explanation:
im smart fam
A cone shaped ice cream cone is 6.0 inches tall the base of ice cream cone has a circumference of 9.5 inches what is the approximate volume of the ice cream cone
Answer:
14.32
Step-by-step explanation:
I rounded the answer slightly btw
What is the next number in the sequence -16, -6, 4, 14
Answer
24
Step-by-step explanation:
you are adding by 10
-16+10=-6
-6+10=4
4+10=14
14+10=24
dude, I just got almost all of my points taken away from somebody that has 0 answers, 0 questions, and almost 2 million points..
Answer:
:O
Step-by-step explanation:
Solve by elimination:
-20x-20y=0
-8x-8y=0
Answer:
Step-by-step explanation:
-20x-20y=0 -8x-8y=0
Substitute
-8(-y)-8y=0
simplify
0=0
x=-y
what is the median out of: 81, 82, 84, 75, 73, 75, 83
Answer:
81
Step-by-step explanation:
For more questions like this:
order numbers from smallest to largest:
73, 75, 75, 81, 82, 83, 84
Next, find the central number:
73, 75, 75, 81, 82, 83, 84 (remove one number from either side at the same time, so remove 73 and 84, and then 75, and 83)
If the list consist an even number, take the two central numbers, and find the number that is in the exact middle of it.
ex: 1,2,3,4,5,6
central numbers: 3, 4
median : 3.5
Evaluate b(x)=5x-5/3x-16 for b(7)
Step-by-step explanation:
5(7) - 5/3(7) - 16
35 - 35/3 -16
19 - 35/3 = 22/3 or 7 1/3
Mr. Tuyen uses
7/8
of a tank of gas each week to drive to and from his job.
How many tanks of gas does Mr. Tuyen use in 7 weeks? Enter your answer as a fraction and as a mixed number.
Answer:
Mr.Tuyen uses 3 1/8 tanks of gas in 5 weeks. The improper fraction version would be 25/8 if that is what you're looking for
THIS IS AN ESSAY NOT JUST AN ANSWER
Prompt:
What does it mean to multiply polynomials?
Explain how to multiply (x + 2) (X - 4) as if you're teaching a student a year
younger than you.
Answer:
We assume before this you have learned how to multiply two monomials and monomial with binomial.Use the following formula to multiply binomials:
(a + b)(c + d) = ab + ad + bc + bdApplied to the given expression, we have:
(x + 2)(x - 4), where a = x, b = 2, c = x , d = -4Expand as indicated above:
(x + 2)(x - 4) =x(x) + x(-4) + 2(x) + 2(-4)Now simplify
x² - 4x + 2x - 8Collect like terms, (-4x) and (2x):
x² + (-4x + 2x) - 8 = x² - 2x - 8This is how you can do same order operations with any binomials.
We can simply use distributive law of grade 1
(a+b)(c+d)=ac+ad+bc+bdI assume you know multiplication of monomials
So
(x+2)(x-4)x(x-4)+2(x-4)x²-4x+2x-8x²-2x-8Some researchers have conjectured that stem-pitting disease in peach-tree seedlings might be controlled with weed and soil treatment. An experiment is conducted to compare peach-tree seedling growth when the soil and weeds are treated with one of two herbicides. In a field containing 20 seedlings, 10 are randomly selected throughout the field and assigned to receive herbicide A. The remainder of the seedlings is assigned to receive herbicide B. Soil and weeds for each seedling are treated with the appropriate herbicide, and at the end of the study period, the height in centimeters is recorded for each seedling. The following results are obtained: Herbicide A = 94.5 cm s1 = 10 cm Herbicide B = 109.1 cm s2 = 9 cmWhat is a 90% confidence interval (use the conservative value for the degrees of freedom) for μ2 – μ1?
a. 14.6 ± 7.00
b. 14.6 ± 7.38
c. 14.6 ± 7.80
d. 14.6 ± 9.62
Answer:
A. 14.6 ± 7.00
Step-by-step explanation:
Formula for the confidence interval between the two mean is;
CI = (μ2 - μ1) ± z√[((s1)²/n1) + ((s2)²/n2)]
We are given;
μ1 = 94.5
μ2 = 109.1
s1 = 10
s2 = 9
n1 = 10
n2 = 10
The z-value at confidence interval of 90% is 1.645
Thus;
CI = (109.1 - 94.5) ± 1.645√[(10²/10) + (9²/10)]
CI = 14.6 ± 7.00
what is the x in x/2=7
Answer:
14
Step-by-step explanation:
7x2=14
Answer:
14
Step-by-step explanation:
x/2=7 multiply 2 on both sides x=14
I’m having trouble on number 4
Help me find m angle k
Answer:
angle k is equal to 58 and angle is equal to 60
Find the Volume of the figure. Write the answer in terms of pi.
Answer:
Step-by-step explanation:
[tex]\text{The volume of a cone is}\\ \\ V=\frac{h\pi r^2}{3},\ h=7mi,\ r=2mi\\ \\ V=\frac{7\pi 2^2}{3}\\ \\ V=\frac{28\pi }{3}mi^3[/tex]
Answer:
answer 29.32
Step-by-step explanation:
3.14x2^2 is 12.56 then 12.56x7/3=29.32 because the formula for cone is V=πr2h 3
pls answer asap I'll mark u brainliest
Answer:
a)29
b)70
Step-by-step explanation:
The sum of the interior angles in a triangle is 180.
a)95+56+a=180 b)40+2b=180
151+a=180 2b=180-40
a=180-151 2b=140 /2
a=29 b=70
What is the remainder when 20152015 is divided by 2014?
Answer:
.9657
Step-by-step explanation:
What is -456 divided by -18
Answer:
25.3333333
Step-by-step explanation:
Answer: 25.33
Step-by-step explanation:
First yo divide -456 / -18
Last is the result (what you get): 25.33
