Katarina asks Dacia how she can you derive the formula r= x2+y2. Which of Dacia's replies are correct?
Answers
Options A and B are correct. If Katarina asks Dacia how she can derive the formula r= x²+y², then the following statements should be Dacia's reply.
Because r is the hypotenuse of a right triangle, with legs x and y, you can use the Pythagorean theorem to determine 'rr is a straight line distance from the point and can be projected onto x and y axes where x = rcosθ, y = rsinθ. Writing sinθ = y/r, Cosθ = x/r and using the identity sin²θ+cos²θ = 1Given the equation by Katarina expressed as:
r = √x²+y²
One of the ways Katarina can derive the equation is to use the Pythagoras theorem which states that the sum of the square of the hypotenuse is equal to the sum of the other two sides. Let:
r be the length of the hypotenuse
x and y be the other two sides
According to the theorem:
r² = x² + y²
Take the square root of both sides
√r² = √x² + y²
r = √x² + y²
Also, Katarina can use the trigonometry identity. According to a right triangle where:
sinθ = y/r
Cosθ = x/r
According to trigonometry identity, sin²θ+cos²θ = 1
(y/r)² + (x/r)² = 1
y²/r² + x²/r² = 1
(y²+x²)/r² = 1
y²+x² = r²
Swap
r²=y²+x²
This shows that the first two options are correct.
Because r is the hypotenuse of a right triangle, with legs x and y, you can use the Pythagorean theorem to determine 'r
r is a straight line distance from the point and can be projected onto x and y axes where x = rcosθ, y = rsinθ. Writing sinθ = y/r, Cosθ = x/r and using the identity sin²θ+cos²θ = 1
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Related Questions
(-2x^2yz^-2)^4 simplify the problem
Answers
Answer:
-8x(8yz)(-8)
Step-by-step explanation:
(-2x^2yz^-2)4
-8x(8yz)(-8)
What is the value of 7−2ℎ, given g = 3 and h = 5?
Answers
Answer:
- 3
Step-by-step explanation:
Given
7 - 2h ( substitute h = 5 into the expression )
= 7 - 2(5)
= 7 - 10
= - 3
On evaluating the function at h = 5, we get -
f(5) = - 3.
We have a function -
f(h) = 7 - 2h
We have to find the value of f(h) at h = 5.
Evaluate - f(x) = Sin( [tex]\frac{\pi }{x}[/tex] ) at x = 2.f(x) = Sin( [tex]\frac{\pi }{x}[/tex] )
f(2) = Sin( [tex]\frac{\pi }{2}[/tex] )
f(2) = 1
According to the question, we have -
f(h) = 7−2ℎ
Now, evaluating the function at h = 5, we get -
f(5) = 7 - 2 x 5 = -3
Hence, on evaluating the function at h = 5, we get -
f(5) = - 3.
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In a class of 48 children there are six more girls than boys how many boys are in the class
Answers
Answer: there are 16 boys in the class which means not ever girl can have a bf
Step-by-step explanation:
please help me, if you help then thanks!
Answers
9514 1404 393
Answer:
27
Step-by-step explanation:
Evaluating this expression according to the order of operations is a straightforward calculator problem.
= (81 ÷ 27)³ = 3³ = 27
__
You can also use the rules of exponents to simplify this before evaluating.
(a^b)^c = a^(bc)
(a^b)/(a^c) = a^(b-c)
__
= ((3²)² ÷ 3³)³ = (3⁴ ÷ 3³)³ = (3¹)³ = 3³ = 27
PLS HELP ME GIVING BRAINLIEST AND POINTS
Answers
Answer:
-4(-4,2)
(16,-8)
option C is correct
Answer:
<16,-8>
Step-by-step explanation:
-4/9 ( 18/2 v)
First multiply
-4v
-4 < -4,2>
<16,-8>
how to plot 15/8 on a number line
Answers
1. Represent the fractions: 2/5, 11/5, -8/5 and -3/5 on a number line.
Since, the denominator of each given fraction is 5; divide the space between every pair of two consecutive integers (on the number line) in 5 equal parts. Each part so obtained will represent the fraction 1/5 and the number line obtained will be of the form:
Representing Fractions on Number Line
To mark 2/5; move two parts on the right-side of zero.
To mark 11/5; move eleven parts on the right-side of zero.
To mark -8/5; move eight parts on the left-side of zero.
To mark -3/5; move three parts on the left-side of zero.
Answer:
x : 15
y : 8
or
y : 15
x : 8
base of your graph
h(x) = x - 3
g(x) = -2x2 + 4x
Find h (x) · g(x)
-3x^4 + 9x^3 - x + 3
-2x^3 + 10x^2 - 12x
2x^3 + 10x^2 + 12x
x^4 + 6x^3 + 8x^2
Answers
Answer:
h(x) = x - 3
g(x) = -2x2 + 4x
Find h (x) · g(x)
-3x^4 + 9x^3 - x + 3
-2x^3 + 10x^2 - 12x
2x^3 + 10x^2 + 12x
x^4 + 6x^3 + 8x^2
least to greatest 7.0, 0.07, 0.7, 0.077
Answers
Step-by-step explanation:
1. 0.07 is the lowest like 7 cents
2. 0.077 is the second one and closer to 8 cents
3. 0.7 the 3rd and like 70 cents
4. 7.0 the greatest like 7 dollars
solve each equation for y
2x+y=5
2x-y+=5
x+2y=5
Answers
Mr. Santiago can buy light fixtures in packages of 12 and light bulbs in packages of 9. He bought the fewest number of light fixtures and light bulbs so that there is exactly one bulb per fixture with none left over.
How many packages of light fixtures and how many packages of light bulbs did Mr. Santiago buy?
I WILL GIVE BRANLIEST PLEASE HELP AND RIGHT ANSWER
Answers
Answer:
3 and 4 packagesStep-by-step explanation:
We need to find the LCM of 12 and 9.
9 = 3*312 = 2*2*3Their LCM is:
LCM(12, 9) = 2*2*3*3 = 36Number of light fixtures and light bulbs is 36.
Number of packages will be:
36/12 = 3 and36/9 = 4 respectively.Step-by-step explanation:
First finding LCM of 9 and 12
9 = 3 × 3
12 = 2 × 2 × 3
LCM = 3 × 2 × 2 × 3
LCM = 36
Now,
No. of light fixtures = 36/12 = 3
No. of light bulb = 48/12 = 4
You take random sample of 200 people from Salinas and find that their average income is $48,000 per year
with a standard deviation of $9000. Also assume that population incomes are normally distributed.
Approximately how many people make between $39,000 and $57,000?
X
Answer format: Enter a positive integer
Answers
We have that The Total Number of People is
[tex]X\approx 137[/tex]
From the question we are told that
sample of 200
income is $48,000 per year
standard deviation of $9000
Generally the equation for the Ratio of people is mathematically given as
[tex]Y=P(\frac{39000-48000}{9000}<z<\frac{57000-48000}{9000})\\\\\Y=P(z<1))-(1-p(z-1))\\\\Y=0.8413-0.1582\\\\\Y=0.6826[/tex]
Therefore
The Total Number of People is
[tex]X=0.6826*200\\\\X\approx 137[/tex]
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How many gallons are in a pool that holds 758,000 Liters
Answers
Answer:
200000 gallons
Step-by-step explanation:
which expressions have a difference of 5
a. 2-3
b. 14+ (-9)
c. -5-(-10)
d. 6- (-1)
Answers
Answer:
b and c
step by step explanation:
14+(-9)
14-9=5
c) -5-(-10)
-5+10=5
Step-by-step explanation:
Let's check them,
2-3-114+(-9)14-95-5-(-10)-5+1056-(-1)6+17Hence, the expression -5-(-10) and 14+(-9) have a difference of 5 .
Find the equation of the line that passes through the point
(4, 11) and is perpendicular to y= 4/3x + 7
Answers
Answer:
y = -3/4x + 14
Step-by-step explanation:
The slope of a perpendicular line is the opposite reciprocal of the original line.
4/3x -> -3/4x
Now we need to find the y-intercept and we can do that by using the slope intercept form expression [ y = mx + b ].
11 = -3/4(4) + b
11 = -3 + b
14 = b
Put everything we know and solved for back into the expression.
y = -3/4x + 14
Best of Luck!
Find the value of this expression if x = 4 and
y = -2.
ху/5
Answers
Answer:
-1.6
Step-by-step explanation:
4x-2/5
=-8/5
=-1.6
Is 4.06 a rational number
Answers
Answer:
Yes
Step-by-step explanation:
A rational number is a number that can be expressed as an integer or the quotient of an integer divided by a nonzero integer. This means that any terminating decimal or mixed number or integer is rational, including 4.06.
I will give extra points
Answers
Two numbers, a and b, are each greater than zero, and the square root of a is equal to the cube root of b. For what value of x is a^(2x-1) equal to b ?
Answers
Answer:
x = 1/2
Step by step explanation:
Two numbers a and b are each greater than zero.
i.e a > 0 and b > 0
And;
[tex] \sqrt{a} \: = \: \sqrt[3]{b} [/tex]
Since the square root of a is equal to cube root of b then,
a = b = 1
[tex] {a}^{2x \: - \: 1} \: = \: b[/tex]
[tex] {1}^{2x \: - \: 1} = {1}^{0} [/tex]
2x - 1 = 0
x = 1/2
Two numbers are 'a' and 'b'.
And a > 0, b > 0
[tex]\sqrt{a}=\sqrt[3]{b}[/tex]
[tex]a^{\frac{1}{2} }=b^{\frac{1}{3}}[/tex]
[tex]a=(b)^{\frac{2}{3} }[/tex]
We have to find the value of [tex]x[/tex] if [tex]a^{2x-1}=b[/tex],
By substituting the value of [tex]a[/tex] in the given expression,
[tex](b^{\frac{2}{3}})^{2x-1}=b[/tex]
Now use the laws of exponents,
[tex]b^{\frac{2}{3}(2x-1)}=b[/tex] [Since, [tex](a^m)^n= a^{mn}[/tex]]
By comparing the exponents on both the sides,
[tex]\frac{2}{3}(2x-1)=1[/tex]
[tex]2(2x-1)=3[/tex]
[tex]4x-2=3[/tex]
[tex]4x=5[/tex]
[tex]x=\frac{5}{4}[/tex]
[tex]x=1.25[/tex]
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2. Jessica's dining room in her new townhouse is 11 feet wide by 12 feet deep. How many square feet is it?
Answers
Answer:
132 sq ft
Step-by-step explanation:
Determine the value of x
A. 13.95
B. 15
C. 4.375
D. 4.59
Answers
Answer:
A. 13.95
Step-by-step explanation:
By using the sine rule:
ne
The lowest temperature ever recorded in a certain town was -22°F. The highest temperature ever recorded there was 139°F more than the lowest. What was the
highest temperature?
ents
The town's highest temperature was ?
Answers
Answer:
highest temperature would be
-22 + 139 = 117°F
multiplying monomials. please
Answers
Answer:
[tex] {4a}^{4} \times {7a}^{5} \\ \\ = (4 \times 7)( {a}^{4} \times {a}^{5} ) \\ \\ = 28( {a}^{4} \times {a}^{5} )[/tex]
from law of indices:
[tex] {n}^{x} \times {n}^{y} = {n}^{(x + y)} [/tex]
therefore:
[tex] = 28 \{ {a}^{(4 + 5)} \} \\ \\ = 28 {a}^{9} [/tex]
Answer:
28a^9
Step-by-step explanation:
Benny spent half of his allowance going to the movies. He washed the family
car and earned 8 dollars. What is his weekly allowance if he ended with
13 dollars ?
Answers
Let it be x
He spent x/2 dollars then
[tex]\\ \sf\longmapsto \dfrac{x}{2}+8=13[/tex]
[tex]\\ \sf\longmapsto \dfrac{x+16}{2}=13[/tex]
[tex]\\ \sf\longmapsto x+16=13(2)=26[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{26}{16}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{13}{8}[/tex]
[tex]\\ \sf\longmapsto x=1.6\$[/tex]
[tex]\\ \sf\longmapsto Weekly allowance=13+7(1.6)[/tex]
[tex]\\ \sf\longmapsto 13+112=125[/tex]
The temperature is dropping 3 degrees every 4 hours.
It started at 62 degrees. What will the temperature be
in 16 hours? Please and Thank you !!
Answers
Answer: It will be 50º :)
Step-by-step explanation: 4 hours * 4 = 16, 3*4 = 12, 62- 12 = 50
Answer:
50 degrees
Step-by-step explanation:
16/4 = 4
4 * - 3 = - 12
62 - 12 = 50 degrees
Evaluate -7x + y5x
When x = -3, y = -9
Answers
Answer:
156
Step-by-step explanation:
-7(-3)+(-9)(5)(-3)
21+135
156
Answer:
156
Step-by-step explanation:
Substitute x and y values in the equation-7x+y5x
(-7)(-3)+(-9)*5*(-3)
21+135
156
Hope you got it
If you have any question just ask me
If you think this is the best answer please mark me as brainliest
Question 6
1 pts
Write the equation of a line through (-5,-5), parallel to y=
Oy=
- 1
O y=-x+4
O y=4x-1
O y=-x-1
Question 7
1 pts
Answers
Answer:
2nd, y=x-2
ignore this, just for 20char limit
which value is equivalent to -5/6?
Answers
Answer:
-5/6 or -0.833333333333
Step-by-step explanation:
step-by-step-ecuation
PLEASE HURRY IM IN A RUSH!!!<3
Answers
Answer:
64 and 100 are the squares
Answer:
[tex]8^{2} = 8*8=64\\10^{2} = 10*10=100[/tex]
Step-by-step explanation:
Hope it helps,... Chow,...!
(-7) (2) (-2) as multiplication
Answers
Answer:
28
Step-by-step explanation:
-7*2=-14*-2=28
Anybody else think the coronavirus vaccine is absolutely bologna? I dont even know why the FDA approved it.... like....?????
Answers
Answer: The vaccine help prevent cases with the virus, but if you have the virus and the vaccine, you do not fare as well as you would without the vaccine.
