Answer:
[tex]\displaystyle \displaystyle \cos A = \frac{a^2-b^2}{a^2 + b^2}\text{ and } \sin A = \frac{2ab}{a^2 + b^2}[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaystyle \tan A = \frac{2ab}{a^2 - b^2}[/tex]
And we want to find the value of cos(A) and sin(A).
Recall that tangent is the ratio of the opposite side to the adjacent side.
Therefore, the opposite side measures 2ab, and the adjacent side measures a² - b².
Using the Pythagorean Theorem, solve for the hypotenuse:
[tex]\displaystyle \begin{aligned} c^2 &= a^2 + b^2 \\ \\ c&= \sqrt{(2ab)^2 + (a^2-b^2)} \\ \\ &= \sqrt{(4a^2b^2)+(a^4-2a^2b^2+b^4)} \\ \\ &= \sqrt{a^4 + 2a^2b^2 + b^4 } \\ \\ &= \sqrt{(a^2 +b^2)^2} \\ \\ &= a^2 + b^2\end{aligned}[/tex]
Thus, our hypotenuse is given by a² + b².
Cosine is the ratio between the adjacent side and the hypotenuse. Thus:
[tex]\displaystyle \cos A = \frac{a^2-b^2}{a^2 + b^2}[/tex]
And sine is the ratio between the opposite side and the hypotenuse. Thus:
[tex]\displaystyle \sin A = \frac{2ab}{a^2 + b^2}[/tex]
In conclusion:
[tex]\displaystyle \displaystyle \cos A = \frac{a^2-b^2}{a^2 + b^2}\text{ and } \sin A = \frac{2ab}{a^2 + b^2}[/tex]
Answer:
Step-by-step explanation:
[tex]sec^2A-tan^2A=1\\sec^2A=1+tan^2A=1+\frac{4a^2b^2}{(a^2-b^2)^2} =\frac{(a^2-b^2)^2+4a^2b^2}{(a^2-b^2)^2} =\frac{(a^2+b^2)^2}{(a^2-b^2)^2} \\cos^2A=\frac{(a^2-b^2)^2}{(a^2+b^2)^2} \\cos A=\frac{a^2-b^2}{a^2+b^2} \\sin A=\sqrt{1-cos^2A} =\sqrt{1-(\frac{a^2-b^2}{a^2+b^2} )^2} =\sqrt{\frac{(a^2+b^2)^2-(a^2-b^2)^2}{(a^2+b^2)^2} } =\sqrt{\frac{4a^2b^2}{(a^2+b^2)^2} }=\frac{2ab}{a^2+b^2}[/tex]
the length of a rectangular box is 8cm. If its diagonal is 10cm. Find its width
Answer:
Step-by-step explanation:
The diagonal of this rectangular box serves as the hypotenuse of the 2 right triangles that exist within this rectangle. The length is one leg, the hypotenuse is...well, the hypotenuse, so we need to use Pythagorean's Theorem to find the missing leg.
[tex]10^2=8^2+x^2[/tex] and
[tex]100-64=x^2[/tex] and
[tex]x^2=36[/tex] so
x = 6. The width is 6.
The volume of a prism is the product of its height and area of its base, V = Bh. A rectangular prism has a volume of 16y4 + 16y3 + 48y2 cubic units. Which could be the base area and height of the prism?
a base area of 4y square units and height of 4y2 + 4y + 12 units
a base area of 8y2 square units and height of y2 + 2y + 4 units
a base area of 12y square units and height of 4y2 + 4y + 36 units
a base area of 16y2 square units and height of y2 + y + 3 units
Answer: 4. A base area of 16y^2 square units and height of y^2 + y + 3 units
Step-by-step explanation:
Using the distributive property; you can see that 16y^2(y^2+y+3)=
16y^4+16y^3+48y^2
Answer:
D. a base area of 16y2 square units and height of y^2 + y + 3 units
Step-by-step explanation:
Ed22
Which number line represents the solutions to Ix - 5= 1?
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
+
-7 -6 -5 -4 -3 -2 -1 0
1
2
3 4 5 6 7
-7 -6 -5 -4 -3 -2 -1 0 1 2
3 4 5 6 7
o
-7 -6 -5 -4 -3 -2 -1 0 1
3
4 5 6 7
N
The number line that represents the solutions to Ix - 5| = 1 is the number line in the second option.
To solve absolute value equations like |x-5| = 1
We will write that
x - 5 = 1 and x -5 = -1
For the first equation
x - 5 = 1
Add 5 to both sides
x - 5 +5 = 1+5
∴ x = 6
For the second equation
x -5 = -1
Add 5 to both sides as well
x -5 +5 = -1 +5
∴ x = 4
Hence, x = 6 and x = 4
From the image, the second option is dotted (blue) at 4 and 6 on the number line.
Hence, the number line that represents the solutions to Ix - 5| = 1 is the number line in the second option
Learn more here: https://brainly.com/question/17269252
The output of a relation is the difference of three times the input and five. Select the correct answer from each drop-down menu. The equation that represents this relation is . The relation a function. If the domain of the relation is x > 2, the range of the relation is y > .
Answer:
The equation that represents this relation is [tex]y = 3x - 5[/tex].
The relation is a function.
If the domain of the relation is x > 2, the range of the relation is [tex]y >1[/tex]
Step-by-step explanation:
Given
Output = 3 * Input - 5
Required
Complete the gap
Solving (a):The equation for the relation.
Let
[tex]x \to[/tex] input
[tex]y \to[/tex] output
The relation is:
[tex]y = 3 * x - 5[/tex]
[tex]y = 3x - 5[/tex]
Solving (b): Is the relation, a function?
Yes; Because every value of x has a distinct value in 7
Solving (c): The range:
Domain: [tex]x > 2[/tex]
Substitute 2 for x in [tex]y = 3x - 5[/tex]
[tex]y =3 * 2 - 5[/tex]
[tex]y =6 - 5[/tex]
[tex]y =1[/tex]
The range is:
[tex]y >1[/tex]
Answer:
The equation that represents this relation is [ y= 3x - 5 ]
The relation [ is ] a function.
If the domain of the relation is x > 2, the range of the relation is y > [ 1 ].
Step-by-step explanation:
The output, y, of a relation, is the difference of three times the input, or 3x, and 5. So, y = 3x − 5.
Substituting any x-value from the domain into the equation will result in exactly one value of y, so the relation is a function.
To find the range of the relation, given the domain, substitute the boundary point of the domain into the function equation:
When x = 2, y = 3(2) − 5 = 6 − 5 = 1.
Because substituting values of x that are greater than 2 will result in values of y that are greater than 1, the range of the relation is y > 1.
Hope this helps !!
I need help on this question pls
56/64 = 7/8
7/8 x 120
105.
Find the value of
x for which ABCD
must be a
parallelogram.
6
54
3
27
Answer:
3
Step-by-step explanation:
As it's a parallelogram the cross splits each diagonal exactly in half, so each half is the same:
-9-6x = x-30
7x=21
x=3
When a shape is dilated, the _________ of the lengths in the image to the corresponding lengths in the pre-image are equal to the scale factor.
A. ratios
B. lengths
C. scale factors
D. proportions
PLEASE HURRY
A. 70.8 ft^2
B. 69.1 ft^2
C. 65.8 ft^2
D. 73.6 ft^2
Answer:
D. 73.6 ft^2
Step-by-step explanation:
Using trigonometry to get our answer: (we can use SAS to find the area)
A = 0.5 * side a (10ft) * side b (16ft) * sin(67)
A = 80 ft * sin(67)
A = 73.64 ft
can i please get an answer for this and a vivid explanation of how to solve it please. WILL MARK AS BRAINLIEST!
Answer:
[tex]9a^3b^3[/tex]
Step-by-step explanation:
please help me T-T.......
Hi
1) f(x)= 0.9 x
2) g(x) = x-100
3) f °g. is first apply g then f. so :
f°g = 0.9 ( x-100) = 0.9x-90
4) g°f. is first apply f then g
so g°f = (0.9x) -100 = 0.9x-100
I let you conclude which is the best deal :)
help me with it please with steps
class 9 trigonometry
secA=√2
secA=sec45
A=45°
3cos²45+5tan²45/ 4tan²A-sin²45
= 3(1/√3)²+5(1)² / 4(1)²-(1/√2)²
=3/2+5/4-1/2
=13/7
Answer:
[tex]\frac{13}{7}[/tex]
Step-by-step explanation:
Using the identities
cos x =[tex]\frac{1}{secx}[/tex] , sin²x = 1 - cos²x
tan²x = sec²x - 1
Given
[tex]\frac{3cos^2A+5tan^2A}{4tan^2A-sin^2A}[/tex]
= [tex]\frac{3(\frac{1}{sec^2A}+5(sec^2A-1) }{4(sec^2A -(1-cos^2A)}[/tex]
= [tex]\frac{3.(\frac{1}{\sqrt{2})^2 } +5((\sqrt{2})^2-1) }{4((\sqrt{2})^2-1)-(1-(\frac{1}{\sqrt{2} })^2 }[/tex]
= [tex]\frac{\frac{3}{2}+5(2-1) }{4(2-1)-(1-\frac{1}{2} )}[/tex]
= [tex]\frac{\frac{3}{2} +5}{4-\frac{1}{2} }[/tex]
= [tex]\frac{\frac{13}{2} }{\frac{7}{2} }[/tex]
= [tex]\frac{13}{2}[/tex] × [tex]\frac{2}{7}[/tex]
= [tex]\frac{13}{7}[/tex]
Algebra!! In the triangle to the below, the measure of ∠A equals the measure of ∠B. Find the value of x.
Answer:
x=21
Step-by-step explanation:
45=2x+3
Subtract 3 from both sides of the equation.
42=2x
Divide 2 from both sides of the equation.
21=x
Hope this helps!
Answer:
x=21°
Step-by-step explanation:
Angle A = Angle B
Angle A = 45°
2x+3 =45°
To work out what x is, you would have to do inverse operations.
45-3=42°
2x=42°
42÷2=21° (We divide by 2 because, in algebra, whenever a number is next to a letter, it means times, so then we have to do the opposite and divide).
So, x=21°
Hope this helps :)
adhiambo buys t litres of milk everyday.A litre of milk is she 25.She spends sh 3000 on milk on November.How many litres does she buy every day?
Determine the slope for the equation.
[tex]y = \frac{6}{5} x - 4[/tex]
Steps would help tremendously because I wanna remember how to do these :)
Answer:
slope = [tex]\frac{6}{5}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{6}{5}[/tex] x - 4 ← is in slope- intercept form
with slope m = [tex]\frac{6}{5}[/tex]
Answer:
6/5
Step-by-step explanation:
this equation is already in the slope intercept form, meaning the slope (gradient)is the coefficient of x( the number before x). in this case it's 6/5.
I hope this helps
Tameeka tells Marcus, "When you add 16 to my mystery number then subtract 20, you get the same result as when you add my mystery number to itself, then add 20 and subtract 16.” What is Tameeka’s mystery number?
Write and solve an equation to represent this situation.
Answer:
-8.
Step-by-step explanation:
x + 16 - 20 = 2x + 20 - 16
x - 4 = 2x + 4
x - 2x = 4 + 4
-x = 8
x = -8.
The mystery number 'm' that satisfies the stated conditions is - 8.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let, The mystery number be 'm'.
So, When you add 16 to my mystery number then subtract 20,
m + 16 - 20,
you get the same result as when you add my mystery number to itself, then add 20 and subtract 16,
m + m + 20 - 16.
Therefore,
m + 16 - 20 = m + m + 20 - 16
m - 4 = 2m + 4.
- m = 8.
m = - 8.
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Use ratios to convert each measurement.
1. 3 yards = _____ feet
2. _____ cups= 5 gallons
3. 72 inches =_____ yards
4. ______ ounces = 5 pounds
5. ______ inches =7 feet
6. 24 feet = _____ yards
7. 40 pints = ______ gallons
8. 16 cups = ______ quarts and
9. ________ inches = 4 yards
10. 48 ounces = ________ Pounds
Answer:
1. 3 yards= 9 feet
2. 78 cups=5 gallons
3. 72 inches = 2 yards
4. 80 ounces = 5 pounds
5. 84 inches = 7 feet
6. 24 feet = 8 yards
7. 40 pints = 5 gallons
8. 16 cups = 5 quarts
9. 144 inches = 4 yard
10. 48 ounces = 3 pounds
Find the length of the third side. If necessary, round to the nearest tenth. 16 12
Answer:
20
Step-by-step explanation:
Use the Pythagorean theorem. a^2+b^2=c^2
12^2+16^2=c^2
144+256=c^2
400=c^2
20=c
Find an equation of the line through the given points right the answer and slope intercept form
Answer:
equation is y = 2-x
Step-by-step explanation:
x1 = -3
y1 = 5
x2 = 4
y2 = -2
now
m(slope) = rise/run =(y2-y1)/(x2-x1) =(-2-5)/(4+3) = -7/7 = -1
so m = -1
now
y =mx + b
-2 = -1×4 + b
or, -2 = -4 +b
so, b = 2
now
y = mx+b
y = -1x + 2
or, y = 2-x
A car of 1000 kg starts to move from rest and travels a distance of 150 m in 10 second. How much force is needed?
Using second equation of kinematics
[tex]\\ \sf\longmapsto s=ut+\dfrac{1}{2}at^2[/tex]
[tex]\\ \sf\longmapsto 150=0(10)+\dfrac{1}{2}a(10)^2[/tex]
[tex]\\ \sf\longmapsto 150=\dfrac{1}{2}\times 100a[/tex]
[tex]\\ \sf\longmapsto 50a=150[/tex]
[tex]\\ \sf\longmapsto a=\dfrac{150}{50}[/tex]
[tex]\\ \sf\longmapsto a=3m/s^2[/tex]
Mass=m=1000kgForce=FUsing newtons second law
[tex]\\ \sf\longmapsto F=ma[/tex]
[tex]\\ \sf\longmapsto F=1000(3)[/tex]
[tex]\\ \sf\longmapsto F=3000N[/tex]
First get the gcf of 16x³ + 250 which is 2 then divide it which has the result of 8x³ + 125 then get the square root of 8x³ and 125
What is the value of the expression 3y−z
y+5z
when y = 6 and z = 2?
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{Question \#1}[/tex]
[tex]\huge\textsf{3y - z}[/tex]
[tex]\huge\textsf{= 3(6) - 2}[/tex]
[tex]\huge\textsf{= 18 - 2}[/tex]
[tex]\huge\textsf{= 16}[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: 16}}}\huge\checkmark[/tex]
[tex]\huge\text{Question \#2}[/tex]
[tex]\huge\textsf{y + 5z}[/tex]
[tex]\huge\textsf{= 6 + 5(2)}[/tex]
[tex]\huge\textsf{= 6 + 10}[/tex]
[tex]\huge\textsf{= 16}[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: 16}}}\huge\checkmark[/tex]
[tex]\huge\textsf{\boxed{\star\underline{\underline{16 = 16}}\star}\star}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
I need help ASAP!!! Please explain your answer
Answer:
804.2 km³
Step-by-step explanation:
Volume of a cylinder: πr²h
r = radius, h = height
[tex]\pi r^2h\\\pi(8)^2(4)\\\pi(64)(4)\\\pi(256)\\804.2[/tex]
Consider the function ƒ(x) = x2. Which of the following functions shifts ƒ(x) downward 5 units and to the right 3 units?
A)
ƒ(x) = (x – 5)2 – 3
B)
ƒ(x) = (x – 3)2 – 5
C)
ƒ(x) = (x + 3)2 – 5
D)
ƒ(x) = (x – 5)2 + 3
Answer:
B
Step-by-step explanation:
f(x)=(x+3)2 3 units to the left
f(x)=(x-3)2 3 units to the right
f(x)=(x)2+5 upward 5 units
f(x)=(x)2-5 downward 5 units
Triangles ABC and XYZ are similar. Find side x.
Answer:
x=6
Step-by-step explanation:
side AB is proportional to side XY
side AC is proportional to side XZ
Since we know side AB and side XY are proportional to each other, if we divide side AB by side XY, we can find the size difference...
12 / 4 = 3
The smaller triangle is 3 times smaller than the bigger triangle so we can find side XZ by dividing side AC by 3...
18 / 3 = 6
x = 6
The measure of the length of x is 9 units.
What are similar triangles?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is indicated here by the symbol "≈".
Given triangles ABC ≈ XYZ
for similar triangles, corresponding sides are proportionately equal and corresponding angles are congruent,
so AB/XY = AC/XZ = BC/YZ
substitute the values
12/4 = 18/x = 9/YZ
12/4 = 18/x
x= 9 units
Hence the value of x is 9 units.
Learn more about similar triangles;
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16. Choose the wrong statement: a) Every natural number is a whole number. b) Every integer is a rational number. c) Every rational number is an integer. d) Every rational number is a real number.
Answer:
C
Step-by-step explanation:
YES
Use the table and the graph to answer the questions.
Function 1
x
2
3
y
3
5
7
Function 2
Graph
A graph shows numbers negative 5 to 5 on both the x-axis and the y-axis, in equal intervals of 1. A straight line goes through the points negative 1 comma 0 and 0 comma 4.
What is the rate of change for each function? Show your work.
Which function has the greater rate of change?
Answer:
55774210778899900000
super easy question, will mark brainliest if the answer is correct
a water container is 1/8 full. 35 litres if water are now poured into the container. The container is now 3/4 full.
When the container is full, how much water does it hold?
Answer:
56 litres
Step-by-step explanation:
let x be the amount when the container is full.
1/8x + 35 = 3/4x
-5/8x = -35
x = 56
Can i please get this answered
Answer:
0 is the answer . The explanation is in the attachment .
Valeria purchases a can of chicken noodle soup and a can of tomato soup. The can of chicken noodle soup has a height of 4 inches and a radius of 2 inches. What is the volume of the can of chicken noodle soup?
Use ≈3.14 and round your answer to the nearest whole number.
The can of tomato soup has the same volume, but a radius of 2.5 inches. What is the height of the can of tomato soup?
Use ≈3.14 and round your answer to the nearest tenth.
Questions
Answer:
The height of the tomato soup can is 2.6 in.
Step-by-step explanation:
"The can of chicken noodle soup has a height of 4 inches and a radius of 2 inches."
We can find the volume of this can.
V = pi r² h
V = 3.14 * (2 in.)² * (4 in.)
V = 50.24 in.³
"The can of tomato soup has the same volume, but a radius of 2.5 inches."
Now we know the volume of the can, so we can find the height, h.
V = pi r² h
50.24 in.³ = 3.14 * (2.5 in.)² * h
50.24 in.³ = 19.625 in.² * h
h = (50.24 in.³)/(19.625 in.²)
h = 2.56 in.
Answer: The height of the tomato soup can is 2.6 in.
Answer:
:Volume of can of chicken noodle soup=50.24inch^3
:Height of can of tomato soup=2.56inches
Step-by-step explanation:
CHICKEN NOODLE SOUP :height=4inches
:radius=2inches
[ V=πr2h]
V=(3.14×2×2×4)=50.14
Now, Volume is same of both the can.
Volume of can of tomato soup=50.24;radius=2.5inches;
Height of can of tomato soup,
50.24=(3.14×2.5×2.5×h)
50.24=19.625h
h=50.24/19.625
=2.56inches
Evaluate: ab for a = 2 and b = 5
please mark this answer as brainlist
