Step-by-step explanation:
A you see here, we have 3 different shapes. a Triangle, a big and small rectangle. Lets start with the triangle.
between the 8 in's, theres a gap. 5+4=9,
9+8+8=25. we have the length of the triangle.
9*25 divided by 2= 112.5. thats are area of the triangle.
for the bigger rectangle, 20*9=180, the area of the rectangle, and the smaller rectangle at the bottom is 16.
Now we add:
112.5+180+16=308.5
hope this helps!
Rationalise the denominator
Answer:
sqrt(3) /3
Step-by-step explanation:
1 / sqrt(3)
Multiply the top and bottom by sqrt(3)
1/ sqrt(3) * sqrt(3)/ sqrt(3)
sqrt(3) / sqrt(3)*sqrt(3)
sqrt(3) /3
Answer:
[tex] = { \sf{ \frac{1}{ \sqrt{3} } }} \\ \\ { \sf{ = \frac{1}{ \sqrt{3} } . \frac{ \sqrt{3} }{ \sqrt{3} } }} \\ \\ = { \sf{ \frac{ \sqrt{3} }{ {( \sqrt{3}) }^{2} } = \frac{ \sqrt{3} }{3} }} [/tex]
Factorize this and solve no p, q, s, t, w
explanation:
all the questions are solved
in question no. s and t u need to divide the number in two different parts to slove
for no. w we can get two type of solution.
p and q u need to give the power of whole .
s the function represented by the table non-linear?
x
y
6
4
7
2
8
0
9
–2
Select the correct answer from each drop-down menu.
A company makes cylindrical vases. The capacity, in cubic centimeters, of a cylindrical vase the company produces is given by the
function C() = 6.2873 + 28.26x2, where x is the radius, in centimeters. The area of the circular base of a vase, in square
centimeters, is given by the function A () = 3.14.2
To find the height of the vase, divide
represents the height of the vase.
the expressions modeling functions C(x) and A(z). The expression
Answer:
divide, 2x+9
Step-by-step explanation:
got it right
Pls help it’s due in the morning ;(
[tex]\\ \sf\longmapsto m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{1-3}{-4-3}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{-2}{-7}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{2}{7}[/tex]
10:-Points are (-7,6),(11,-4)
[tex]\boxed{\sf slope(m)=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{-4-6}{11+7}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{-10}{18}[/tex]
[tex]\\ \sf\longmapsto m=-\dfrac{5}{9}[/tex]
Answer:
Step-by-step explanation:
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
9) Mark any two point on the line
(x₁ , y₁) = (3 , 3) ; (x₂, y₂) = (-4 ,1)
[tex]Slope =\frac{1-3}{-4-3}\\\\=\frac{-2}{-7}\\\\=\frac{2}{7}[/tex]
10) (x₁ , y₁) = ( -7 , 6) ; (x₂, y₂) = (11 ,-4)
[tex]Slope =\frac{-4-6}{11-[-7]}\\\\ =\frac{-4-6}{11+7}\\\\=\frac{-10}{18}\\\\=\frac{-5}{9}[/tex]
Please help me solve this problem guys
Answer:
17%
Step-by-step explanation:
Again, as the amount of years increase, the population of bees gets multiplied by 0.83. We can rewrite this to 83%, and then again rewrite this to 100%-17%. We can see now that the population of bees decreases by 17% each year.
On a map, 1 in represents 420 miles. How much does 3/4 in represent?
Answer:
315
Step-by-step explanation:
420 x 3/4 = 315
Answer:
315 miles
Step-by-step explanation:
We can write a ratio to solve
1 inch 3/4 inches
------------ = ---------------
420 miles x miles
Using cross products
1 * x = 420 * 3/4
x=315
Write the equation of the sinusoidal function shown?
A) y = cos x + 2
B) y = cos(3x) + 2
C) y = sin x + 2
D) y = sin(3x) + 2
Answer:
günah(3x) + 2
Step-by-step explanation:
Gösterilen sinüzoidal fonksiyonun denklemini yazınız? A) y = cos x + 2 B) y = cos(3x) + 2 C) y = günah x + 2 D) y =
Answer:
y = sin(3x) + 2
help help help help
Answer:
abc is a triangle so ,
a is ( 9,6 )
b is ( 9,3 )
and c is ( 3,3 )
Find the value of the sum 219+226+233+⋯+2018.
Assume that the terms of the sum form an arithmetic series.
Give the exact value as your answer, do not round.
Answer:
228573
Step-by-step explanation:
a = 219 (first term)
an = 2018 (last term)
Sn->Sum of n terms
Sn=n/2(a + an) [Where n is no. of terms] -> eq 1
To find number of terms,
an = a + (n-1)d [d->Common Difference] -> eq 2
d= 226-219 = 7
=> d=7
Substituting in eq 2,
2018 = 219 + (n-1)(7)
1799 = (n-1)(7)
1799 = 7n-7
1799 = 7(n-1)
1799/7 = n-1
257 = n-1
n=258
Substituting values in eq 1,
Sn = 258/2(219+2018)
= 129(2237)
= 228573
Please help I’ll mark as brainlist
Answer:
Ekta and Preyal
Step-by-step explanation:
Where did term “infinity” come from
help me pls??????? :)
Answer:4 in each bad 2 left over
Step-by-step explanation:
Answer:
4 in each bag and 2 left over
Step-by-step explanation:
divide 14 by 3
3 goes into 14, 4 times
14 - 12 = 2
4 in each bag and then 2 left over
plzzzz heeeeeeellllllllppppppppp again...
ANS=40
hope this help you
bye have a great day :)
what does this equal 2^3 + 6^5=
[tex]\\ \sf\longmapsto 2^3+6^5[/tex]
[tex]\\ \sf\longmapsto 2^3+(2\times 3)^5[/tex]
[tex]\\ \sf\longmapsto 8+2^5\times 3^5[/tex]
[tex]\\ \sf\longmapsto 8+32\times 243[/tex]
[tex]\\ \sf\longmapsto 40+7776[/tex]
[tex]\\ \sf\longmapsto 7784[/tex]
Answer:
2*2*2= 8
6*6*6*6*6= 7,776
7,776+8=
7,784
−30=5(x+1)
what is x?
[tex]\\ \rm\Rrightarrow -30=5(x+1)[/tex]
[tex]\\ \rm\Rrightarrow -30=5x+5[/tex]
[tex]\\ \rm\Rrightarrow 5x=-30-5[/tex]
[tex]\\ \rm\Rrightarrow 5x=-35[/tex]
[tex]\\ \rm\Rrightarrow x=\dfrac{-35}{-5}[/tex]
[tex]\\ \rm\Rrightarrow x=7[/tex]
Answer:
x = -7
Step-by-step explanation:
-30 = 5 (x -1 )
5 ( x + 1 ) =-30
5 (x + 1 ) = - 30
5 5
x + 1 = -6
x + 1 -1 = -6 -1
x = - 7
Translate this phrase into an algebraic expression.
the sum of 4 and twice a number is 12
Answer:
4+2x = 12
Step-by-step explanation:
sum means add an is means equal
4+2x = 12
Step-by-step explanation:
the sum of 4 and twice a number is 12:
Have a great day! I hope this helps!! :)Determine the sum of the first 33 terms of the following series:
−52+(−46)+(−40)+...
Answer:
1320
Step-by-step explanation:
Use the formula for sum of series, s(a) = n/2(2a + (n-1)d)
The terms increase by 6, so d is 6
a is the first term, -56
n is the terms you want to find, 33
Plug in the numbers, 33/2 (2(-56)+(32)6)
Simplify into 33(80)/2 and you get 1320
Classify the triangle as acute, right, or obtuse and as equilateral, isosceles, or scalene.
9514 1404 393
Answer:
(d) Right, scalene
Step-by-step explanation:
The little square in the upper left corner tells you that is a right angle. Any triangle with a right angle is a right triangle. This one is scalene, because the sides are all different lengths.
__
Additional comment
An obtuse triangle cannot be equilateral, and vice versa.
An equilateral triangle has all sides the same length, and all angles the same measure: 60°. It is an acute triangle.
PLSSS HELPPPP AYUDA PLSSS URGENT AS WELL PLSS PSL PSL evaluate this expression “(-7x^3 + 9x^2 - 3) x (-2x^2 - 5x + 6)???
Answer: 14x^5 + 17x^4 - 87x^3 + 60x^2 + 15x - 18
Step-by-step explanation: You would need to simplify the expression by using distributive property.
result of 5 and 75 with dividid by 3
Answer:
your answer is 30
Step-by-step explanation:
I hope this help
Write and solve a word problem that can be modeled by addition of two negative integers.
Answer:
Step-by-step explanation:
Question:
Max needs to purchase a car and withdraws $100 from his bank. In a few days he withdraws another $50 to make same repairs. In total what is the change in his bank balance from theese two costs?
Solution:
(-100) + (-50) =
-150
Answered by G a u t h m a t h
How do we derive the sum rule in differentiation? (ie. (u+v)' = u' + v')
It follows from the definition of the derivative and basic properties of arithmetic. Let f(x) and g(x) be functions. Their derivatives, if the following limits exist, are
[tex]\displaystyle f'(x) = \lim_{h\to0}\frac{f(x+h)-f(x)}h\text{ and }g'(x)\lim_{h\to0}\frac{g(x+h)-g(x)}h[/tex]
The derivative of f(x) + g(x) is then
[tex]\displaystyle \big(f(x)+g(x)\big)' = \lim_{h\to0}\big(f(x)+g(x)\big) \\\\ \big(f(x)+g(x)\big)' = \lim_{h\to0}\frac{\big(f(x+h)+g(x+h)\big)-\big(f(x)+g(x)\big)}h \\\\ \big(f(x)+g(x)\big)' = \lim_{h\to0}\frac{\big(f(x+h)-f(x)\big)+\big(g(x+h)-g(x)\big)}h \\\\ \big(f(x)+g(x)\big)' = \lim_{h\to0}\frac{f(x+h)-f(x)}h+\lim_{h\to0}\frac{g(x+h)-g(x)}h \\\\ \big(f(x)+g(x)\big)' = f'(x) + g'(x)[/tex]
100 POINTS AND BRAINLIEST FOR THIS WHOLE SEGMENT
a) Find zw, Write your answer in both polar form with ∈ [0, 2pi] and in complex form.
b) Find z^10. Write your answer in both polar form with ∈ [0, 2pi] and in complex form.
c) Find z/w. Write your answer in both polar form with ∈ [0, 2pi] and in complex form.
d) Find the three cube roots of z in complex form. Give answers correct to 4 decimal
places.
Answer:
See Below (Boxed Solutions).
Step-by-step explanation:
We are given the two complex numbers:
[tex]\displaystyle z = \sqrt{3} - i\text{ and } w = 6\left(\cos \frac{5\pi}{12} + i\sin \frac{5\pi}{12}\right)[/tex]
First, convert z to polar form. Recall that polar form of a complex number is:
[tex]z=r\left(\cos \theta + i\sin\theta\right)[/tex]
We will first find its modulus r, which is given by:
[tex]\displaystyle r = |z| = \sqrt{a^2+b^2}[/tex]
In this case, a = √3 and b = -1. Thus, the modulus is:
[tex]r = \sqrt{(\sqrt{3})^2 + (-1)^2} = 2[/tex]
Next, find the argument θ in [0, 2π). Recall that:
[tex]\displaystyle \tan \theta = \frac{b}{a}[/tex]
Therefore:
[tex]\displaystyle \theta = \arctan\frac{(-1)}{\sqrt{3}}[/tex]
Evaluate:
[tex]\displaystyle \theta = -\frac{\pi}{6}[/tex]
Since z must be in QIV, using reference angles, the argument will be:
[tex]\displaystyle \theta = \frac{11\pi}{6}[/tex]
Therefore, z in polar form is:
[tex]\displaystyle z=2\left(\cos \frac{11\pi}{6} + i \sin \frac{11\pi}{6}\right)[/tex]
Part A)
Recall that when multiplying two complex numbers z and w:
[tex]zw=r_1\cdot r_2 \left(\cos (\theta _1 + \theta _2) + i\sin(\theta_1 + \theta_2)\right)[/tex]
Therefore:
[tex]\displaystyle zw = (2)(6)\left(\cos\left(\frac{11\pi}{6} + \frac{5\pi}{12}\right) + i\sin\left(\frac{11\pi}{6} + \frac{5\pi}{12}\right)\right)[/tex]
Simplify. Hence, our polar form is:
[tex]\displaystyle\boxed{zw = 12\left(\cos\frac{9\pi}{4} + i\sin \frac{9\pi}{4}\right)}[/tex]
To find the complex form, evaluate:
[tex]\displaystyle zw = 12\cos \frac{9\pi}{4} + i\left(12\sin \frac{9\pi}{4}\right) =\boxed{ 6\sqrt{2} + 6i\sqrt{2}}[/tex]
Part B)
Recall that when raising a complex number to an exponent n:
[tex]\displaystyle z^n = r^n\left(\cos (n\cdot \theta) + i\sin (n\cdot \theta)\right)[/tex]
Therefore:
[tex]\displaystyle z^{10} = r^{10} \left(\cos (10\theta) + i\sin (10\theta)\right)[/tex]
Substitute:
[tex]\displaystyle z^{10} = (2)^{10} \left(\cos \left(10\left(\frac{11\pi}{6}\right)\right) + i\sin \left(10\left(\frac{11\pi}{6}\right)\right)\right)[/tex]
Simplify:
[tex]\displaystyle z^{10} = 1024\left(\cos\frac{55\pi}{3}+i\sin \frac{55\pi}{3}\right)[/tex]Simplify using coterminal angles. Thus, the polar form is:
[tex]\displaystyle \boxed{z^{10} = 1024\left(\cos \frac{\pi}{3} + i\sin \frac{\pi}{3}\right)}[/tex]
And the complex form is:
[tex]\displaystyle z^{10} = 1024\cos \frac{\pi}{3} + i\left(1024\sin \frac{\pi}{3}\right) = \boxed{512+512i\sqrt{3}}[/tex]
Part C)
Recall that:
[tex]\displaystyle \frac{z}{w} = \frac{r_1}{r_2} \left(\cos (\theta_1-\theta_2)+i\sin(\theta_1-\theta_2)\right)[/tex]
Therefore:
[tex]\displaystyle \frac{z}{w} = \frac{(2)}{(6)}\left(\cos \left(\frac{11\pi}{6} - \frac{5\pi}{12}\right) + i \sin \left(\frac{11\pi}{6} - \frac{5\pi}{12}\right)\right)[/tex]
Simplify. Hence, our polar form is:
[tex]\displaystyle\boxed{ \frac{z}{w} = \frac{1}{3} \left(\cos \frac{17\pi}{12} + i \sin \frac{17\pi}{12}\right)}[/tex]
And the complex form is:
[tex]\displaystyle \begin{aligned} \frac{z}{w} &= \frac{1}{3} \cos\frac{5\pi}{12} + i \left(\frac{1}{3} \sin \frac{5\pi}{12}\right)\right)\\ \\ &=\frac{1}{3}\left(\frac{\sqrt{2}-\sqrt{6}}{4}\right) + i\left(\frac{1}{3}\left(- \frac{\sqrt{6} + \sqrt{2}}{4}\right)\right) \\ \\ &= \boxed{\frac{\sqrt{2} - \sqrt{6}}{12} -\frac{\sqrt{6}+\sqrt{2}}{12}i}\end{aligned}[/tex]
Part D)
Let a be a cube root of z. Then by definition:
[tex]\displaystyle a^3 = z = 2\left(\cos \frac{11\pi}{6} + i\sin \frac{11\pi}{6}\right)[/tex]
From the property in Part B, we know that:
[tex]\displaystyle a^3 = r^3\left(\cos (3\theta) + i\sin(3\theta)\right)[/tex]
Therefore:
[tex]\displaystyle r^3\left(\cos (3\theta) + i\sin (3\theta)\right) = 2\left(\cos \frac{11\pi}{6} + i\sin \frac{11\pi}{6}\right)[/tex]
If two complex numbers are equal, their modulus and arguments must be equivalent. Thus:
[tex]\displaystyle r^3 = 2\text{ and } 3\theta = \frac{11\pi}{6}[/tex]
The first equation can be easily solved:
[tex]r=\sqrt[3]{2}[/tex]
For the second equation, 3θ must equal 11π/6 and any other rotation. In other words:
[tex]\displaystyle 3\theta = \frac{11\pi}{6} + 2\pi n\text{ where } n\in \mathbb{Z}[/tex]
Solve for the argument:
[tex]\displaystyle \theta = \frac{11\pi}{18} + \frac{2n\pi}{3} \text{ where } n \in \mathbb{Z}[/tex]
There are three distinct solutions within [0, 2π):
[tex]\displaystyle \theta = \frac{11\pi}{18} , \frac{23\pi}{18}\text{ and } \frac{35\pi}{18}[/tex]
Hence, the three roots are:
[tex]\displaystyle a_1 = \sqrt[3]{2} \left(\cos\frac{11\pi}{18}+ \sin \frac{11\pi}{18}\right) \\ \\ \\ a_2 = \sqrt[3]{2} \left(\cos \frac{23\pi}{18} + i\sin\frac{23\pi}{18}\right) \\ \\ \\ a_3 = \sqrt[3]{2} \left(\cos \frac{35\pi}{18} + i\sin \frac{35\pi}{18}\right)[/tex]
Or, approximately:
[tex]\displaystyle\boxed{ a _ 1\approx -0.4309 + 1.1839i,} \\ \\ \boxed{a_2 \approx -0.8099-0.9652i,} \\ \\ \boxed{a_3\approx 1.2408-0.2188i}[/tex]
PLEASE HELP I WILL GIVE BRAINLIEST
Step-by-step explanation:
A natural number is a positive whole number.
A whole number is a positive number with no fractions or decimals.
A interger is a whole number negative or positive.
A rational number is a number that terminates or continue with repeating digits.
A irrational number is a number that doesn't terminate or continue with repeating digits.
1. Rational Number
2. Natural,Whole,Interger,Rational
3. Whole,Rational,Interger
4. Rational
5.Irrational
6.Rational
7.Natural,Whole,Interger,Rational
8.Interger,Rational
9.Irrational
The ratio of Mitchell's age to Connor's age is 8:5. In thirty years, the ratio of their ages will be 6:5. How much older is Mitchell than Connor now?
Answer:
9 years older
Step-by-step explanation:
The ratio of their ages is 8 : 5 = 8x : 5x ( x is a multiplier )
In 30 years their ages will be 8x + 30 and 5x + 30 and the ratio 6 : 5 , so
[tex]\frac{8x+30}{5x+30}[/tex] = [tex]\frac{6}{5}[/tex] ( cross- multiply )
5(8x + 30) = 6(5x + 30) ← distribute parenthesis on both sides
40x + 150 = 30x + 180 ( subtract 30x from both sides )
10x + 150 = 180 ( subtract 150 from both sides )
10x = 30 ( divide both sides by 10 )
x = 3
Then
Michell is 8x = 8 × 3 = 24 years old
Connor is 5x = 5 × 3 = 15 years old
Mitchell is 24 - 15 = 9 years older than Connor
solue for &
X(3 + X) = 3x + x²
3x+x^2=3x+x^2
3x-3x=x^2-x^2
which means x=0
help pleasseeeeeeeee
Answer:
-1
Step-by-step explanation:
I know that i^4 = 1
i^10 = i^4 * i^4 * i^2
= 1 * 1 * i^2
We know that i^2 = -1
=1 *1 *-1
= -1
convert 10.09% to a decimal
Answer:
0.1009
Step-by-step explanation:
To convert percentage into decimal, you need to divide the percentage by 100
10.09/100
= 0.1009
Determine three consecutive odd integers whose sum is 2097.
Answer:
first odd integer=x
second odd integer=x+2
third odd integer=x+4
x+x+2+x+4=2097
x+x+x+2+4=2097
3x+6=2097
3x=2097-6
3x=2091
3x/3=2091/3
x=697
therefore, x=697
x+2=697+2=699
x+4=697+4=701