Answers
Answer:
(1)
[tex]a = \frac{3\sqrt 3}{2}[/tex]
[tex]b = \frac{3}{2}[/tex]
(2)
[tex]a = \sqrt 6[/tex]
[tex]b = \sqrt 2[/tex]
Step-by-step explanation:
Solving (1):
Considering
[tex]\theta = 60^o[/tex]
We have:
[tex]\sin(\theta) = \frac{Opposite}{Hypotenuse}[/tex]
This gives:
[tex]\sin(60^o) = \frac{a}{3}[/tex]
Solve for a
[tex]a = 3 * \sin(60^o)[/tex]
[tex]\sin(60^o) = \frac{\sqrt 3}{2}[/tex]
So:
[tex]a = 3 * \frac{\sqrt 3}{2}[/tex]
[tex]a = \frac{3\sqrt 3}{2}[/tex]
To solve for b, we make use of Pythagoras theorem
[tex]3^2 = a^2 + b^2[/tex]
This gives
[tex]3^2 = (\frac{3\sqrt 3}{2})^2 + b^2[/tex]
[tex]9 = \frac{9*3}{4} + b^2[/tex]
[tex]9 = \frac{27}{4} + b^2[/tex]
Collect like terms
[tex]b^2 = 9 - \frac{27}{4}[/tex]
Take LCM and solve
[tex]b^2 = \frac{36 - 27}{4}[/tex]
[tex]b^2 = \frac{9}{4}[/tex]
Take square roots
[tex]b = \frac{3}{2}[/tex]
Solving (2):
Considering
[tex]\theta = 60^o[/tex]
We have:
[tex]\sin(\theta) = \frac{Opposite}{Hypotenuse}[/tex]
This gives:
[tex]\sin(60^o) = \frac{a}{2\sqrt 2}[/tex]
Solve for a
[tex]a = 2\sqrt 2 * \sin(60^o)[/tex]
[tex]\sin(60^o) = \frac{\sqrt 3}{2}[/tex]
So:
[tex]a = 2\sqrt 2 * \frac{\sqrt 3}{2}[/tex]
[tex]a = \sqrt 2 * \sqrt 3[/tex]
[tex]a = \sqrt 6[/tex]
To solve for b, we make use of Pythagoras theorem
[tex](2\sqrt 2)^2 = a^2 + b^2[/tex]
This gives
[tex](2\sqrt 2)^2 = (\sqrt 6)^2 + b^2[/tex]
[tex]8 = 6 + b^2[/tex]
Collect like terms
[tex]b^2 = 8 - 6[/tex]
[tex]b^2 = 2[/tex]
Take square roots
[tex]b = \sqrt 2[/tex]
Related Questions
cions: Write the decimal as a percent and as a fraction or mixed number in simplest
0.15
0.9
0.02
Answers
15%
90%
2%
Explanation
At football games, Stagg Boosters charges $2 for hot chocolate and $3 for Gatorade. The boosters sold
126 drinks totaling $306. How many hot chocolates did they sell?
Pleas help!
Answers
Answer:
72 hot chocolates
Step-by-step explanation:
2h + 3g=306 equation 1 h=hot chocolate g=Gatorade
h + g =126. equation 2
h=126-g isolate h in equation 2
2(126-g) + 3g =306 substitute h value of equation 2 (126-6) into h value eq 1
252-2g+3g=306
g=54
solve for h:
h + g = 126
h+54=126
h=72
check answer:
2h + 3g=306
2(72) +3(54)=306
144+162=306
306=306
A flagpole 15 feet tall casts a shadow 9 feet long. Find, to the nearest degree, the angle of elevation of the sun at this time of day ? trigonometry
Answers
Answer:
noon 180 degrees from 12 to 12
PLS HELP 80 POINTS AND BRAINLIEST What is the surface area of the rectangular prism below?
17 yd²
84 yd²
108 yd²
168 yd²
Answers
Answer:
168 yd²
Step-by-step explanation:
1) Dark Grey:
[tex]A_1 = 2(2 * 9) = 2* 18 = 36\ yd^2[/tex]
2) Light Grey:
[tex]A_2 = 2(2*6) = 2*12 = 24\ yd^2[/tex]
3) Whitish-Grey:
[tex]A_3 = 2(6*9) = 2 * 54 = 108\ yd^2[/tex]
4) Total Area:
[tex]A = A_1 + A_2 + A_3 = 36 + 24 + 108 = 168\ yd^2[/tex]
f(x)=x-7/x
What is the domain of f?
Answers
Answer:
domain: {x ≠ 0}
Step-by-step explanation:
Verify: 4tan(θ)sec(θ) = (1+sin(θ)/1−sin(θ)) − (1−sin(θ)/1+sin(θ))
Answers
Working with the right side,
(1 + sin(θ))/(1 - sin(θ)) - (1 - sin(θ))/(1 + sin(θ))
multiply the first term by (1 + sin(θ))/(1 + sin(θ)) and the second one by (1 - sin(θ))/(1 - sin(θ)). This gives
(1 + sin(θ))/(1 - sin(θ)) • (1 + sin(θ))/(1 + sin(θ)) = (1 + sin(θ))^2 / (1 - sin^2(θ))
… = (1 + sin(θ))^2 / cos^2(θ)
and
(1 - sin(θ))/(1 + sin(θ)) • (1 - sin(θ))/(1 - sin(θ)) = (1 - sin(θ))^2 / (1 - sin^2(θ))
… = (1 - sin(θ))^2 / cos^2(θ)
Now combine the fractions, expand the numerator, and simplify:
(1 + sin(θ))^2 / cos^2(θ) - (1 - sin(θ))^2 / cos^2(θ) = ((1 + sin(θ))^2 - (1 - sin(θ))^2) / cos^2(θ)
… = ((1 + 2 sin(θ) + sin^2(θ)) - (1 - 2 sin(θ) + sin^2(θ))) / cos^2(θ)
… = 4 sin(θ) / cos^2(θ)
… = 4 • sin(θ)/cos(θ) • 1/cos(θ)
… = 4 tan(θ) sec(θ)
Please Help i need the answer done step by step!
Answers
Answer:
55°
Step-by-step explanation:
180-125= 55
since they are supplementary, just subtract from 180
Find the area of this triangle round to the nearest tenth
Answers
Answer:
128.08 in^2
Step-by-step explanation:
A=1/2 ab SinC
=1/2×11×24×Sin 76
The area of given triangle is 128.1 square inches.
What is area of SAS triangle?The area of a SAS triangle is the total amount of space it encloses in a 2-dimensional plane. "SAS" which means "Side, Angle, Side", is the property of a triangle whose 2 sides and the angle between these sides is given.
The formula to calculate the area of a triangle using SAS is given as,
1. When sides 'b' and 'c' and included angle A is known, the area of the triangle is: 1/2 × bc × sin(A)
2. When sides 'b' and 'a' and included angle B is known, the area of the triangle is: 1/2 × ab × sin(C)
3. When sides 'a' and 'c' and included angle C is known, the area of the triangle is: 1/2 × ac × sin(B)
Given
a = 24 inches
b = 11 inches
∠C=76°.
Area of SAS triangle = [tex]\frac{1}{2} absinc[/tex]
Area = [tex]\frac{1}{2}(24)(11)sin76^{0}[/tex]
Area = 128.079 ≅ 128.1 (nearest tenth)
Hence, the area of given triangle is 128.1 square inches.
Find out more information about area of SAS triangle here
brainly.com/question/3509451
#SPJ2
Which of the following values are in the range of the function graphed below?
Check all that apply
Answers
Answer:
6
Step-by-step explanation:
I Just answered the question on my test
don invested $ 5 000 in an account paying 5% simple interest per year for 7 years. a) how much interest will don earn at the end of 7 years?b) how much will be in Don's account at the end of 7 years?
Answers
Answer:
Results are below.
Step-by-step explanation:
Giving the following information:
Initial investment (P)= $5,000
Interest rate (r)= 5% simple interest
Number of periods (t)= 7 years
To calculate the interest earned, we need to use the following formula:
I= P*r*t
I= 5,000*0.05*7
I= $1,750
To calculate the future value of the investment, we need to use the following formula:
FV= I + P
FV= 1,750 + 5,000
FV= $6,750
This figure shows two identically sized posters that need to be hung on a
10-foot-wide wall.
How far apart, in feet, should each poster be for x to be the same distance
at all three places
Answers
Answer: 2.5 ft
Step-by-step explanation: Add 1 1/4 + 1 1/4 = 2.5
Subtract 2.5 ft from 10 ft = 7.5 ft divided by 3 places = 2.5 ft
To check answer: 2.5ft + 2.5ft + 2.5ft + 1 1/4ft + 1 1/4ft = 10 ft
The distance between the two identically sized posters should be 2,5 ft at all three places.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.
Let x be the distance between the two identically sized posters.
Add 1 1/4 + 1 1/4 = 2.5
The total length of the given wall is 10 ft.
here, the equation formed as
x + x +x + 2.5 = 10
3x + 2.5 = 10
3x = 10 - 2.5
3x = 7.5
x = 2.5
So, The distance between the two identically sized posters should be 2,5 ft at all three places.
Learn more about linear equations;
https://brainly.com/question/27056029
9) The present ages of Juna and Jubin are in the ratio 5:8. After 4 years the sum
of their ages will be 34. Find their present ages.
Answers
Answer:
Present age of Juna = 10 years
Present age of Jubin = 16 years
Step-by-step explanation:
Ratio of present ages = 5: 8
Let the present ages of:
Juna be 5x years and Jubin be 8x years
(where x is the common multiplier of the given ratios)
Four years after:
Juna's age = (5x + 4) years
Jubin's age = (8x + 4) years
According to the question:
(5x + 4) + (8x + 4) = 34
13x + 8 = 34
13x = 34 - 8
13x = 26
x = 26/13
x = 2
5x = 5*2 = 10 years
8x = 8*2 = 16 years
Hence,
Present age of Juna = 10 years
Present age of Jubin = 16 years
Luke is driving from his house to the store. After driving 16 miles at a constant speed of 0.8 mile/minute, he realizes that he forgot his wallet. So, he turns around and drives all the way back to his house at the same speed. The equation below models Luke's distance, in miles, from home as he drives for t minutes. Using the given equation, match the number of minutes since Luke started driving from his house to his distance from the house. 12 minutes 27 minutes 31 minutes 7 minutes 10.4 miles on his return trip arrowRight 5.6 miles on his trip to the restaurant arrowRight 9.6 miles his trip to the restaurant arrowRight 7.2 miles on his return trip arrowRight
Answers
Answer:
The number of minutes since Luke started driving from his house to his distance from the house is 40 minutes. :)
Step-by-step explanation:
Plz help me well mark brainliest if correct!....
Answers
Answer:
the answer to the question is A
Need help quick thank you in advance
Answers
Answer:
eeeerrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrm i have no idea
Step-by-step explanation:
#1
Solving for x only
[tex]\\ \sf\Rrightarrow x+90+55=180[/tex](Linear pair
[tex]\\ \sf\Rrightarrow x+145=180[/tex]
[tex]\\ \sf\Rrightarrow x=35°[/tex]
#2
[tex]\\ \sf\Rrightarrow x+32=90[/tex]
[tex]\\ \sf\Rrightarrow x=90-32=58°[/tex]
And
[tex]\\ \sf\Rrightarrow y+x=90°[/tex]
[tex]\\ \sf\Rrightarrow y=90-58=32°[/tex]
Two cyclists start at the same point and travel in opposite directions. One cyclist travels 10 kmh faster than the other. If the two cyclists are 162 kilometers apart after 3 hours, what is the rate of each cyclist?
Answers
x+9=rate of faster cyclist
distance=travel time*rate
..
3x+3(x+9)=99
3x+3x+27=99
6x=72
x=12
x+9=21
rate of slower cyclist=12 km/h
rate of faster cyclist=21 km/hr
250 grams of flour cost $ 17 .00 . how muchnwill 3 bags each holding 1.5kg of flour cost
Answers
Answer:
$51.00
Step-by-step explanation:
One bag price multiply it number of price bag wanted $17.00 × 3 =$51.00
please help i dont get it
Which team has the shortest player? Explain.
Which team has the tallest player? Explain.
Which box plot has the greater IQR? Explain.
Ms.A thinks that the 25% of the NY Knicks are at least 74 inches tall. Do you agree or disagree?
Explain using mathematical reasoning.
Ms.T rann thinks that 1the NY Knicks has a larger spread than Liverpool. Do you agree or disagree? Explain using mathematical reasoning.
Answers
Answer:
1. the team of Liverpool FC has the shortest player because the minimum is 64.
2. ny Knicks has the tallest player with a height of 84.
3. the NY Knicks box has the largest IQR because 82 - 74 = 8.
MS. A is wrong bc the 75% of players are taller than 74 inches.
Step-by-step explanation:
Fun Fact that has nothing to do with this:
The Beatles meet in Liverpool.
can anybody help me please
Answers
Answer:
[tex]the \: forth \: answer \: is \: correct \: answer[/tex]
sum 1 help pls!!!!!!!!!
Answers
Answer:
5¹⁵
Step-by-step explanation:
(5³)⁹ = 5²⁷
5²⁷ ÷ 5¹² = 5¹⁵
Solve for each unknown angle measure...
Please help! This a a test btw so please give me the right answer!
Answers
Answer:
because l1//l2 => z + 65 = 180
y + 65 = 90
x + 65 = 90
<=> z = 115
y = 25
x = 25
Answer:
x=25
y=25
z=115
Step-by-step explanation:
x congruent to y
180-90-65=25
180-65=115
picture included-11 points
Answers
Answer:
Using the Pythagoras theorem, we have:
[tex]c = \sqrt{a {}^{2} + b {}^{2} } [/tex]
with a = 5, b = 6, we have:
[tex]c = \sqrt{5 {}^{2} + 6 {}^{2} } = \sqrt{61} [/tex]
Can someone please help with this math problem
Answers
Given:
The function is:
[tex]y=(f(x))^2[/tex]
To find:
The derivative of the given function at x=1, i.e., y'(1).
Solution:
Chain rule of differentiation:
[tex][f(g(x))]'=f'(g(x))g'(x)[/tex]
We have,
[tex]y=(f(x))^2[/tex]
Differentiate with respect to x.
[tex]y'(x)=2(f(x))\dfrac{d}{dx}f(x)[/tex]
[tex]y'(x)=2f(x)f'(x)[/tex]
Putting [tex]x=1[/tex], we get
[tex]y'(1)=2f(1)f'(1)[/tex]
From the given table of values it is clear that f(1)=3 and f'(1)=3. Putting these values in the above equation, we get
[tex]y'(1)=2(3)(3)[/tex]
[tex]y'(1)=18[/tex]
Therefore, the value of y'(1) is 18.
If (x, 0) lies on the graph of y = logbx , then x =
1
B
0
Answers
Answer:
1
Step-by-step explanation:
PLEASE HELP ASAP PLEASE I'VE BEEN UP ALL NIGHT TRYING TO DO IT I DON'T UNDERSTAND PLZ HELPP!!
Answers
Answer:
Angle COD=40
Step-by-step explanation:
(2a+62)+ (54-a)+(5a-20)=180
6a+96=180
6a=84
a=14
Angle AOC=2(14)+62=90
Angle COD=54-14=40
Angle DOB=5(14)-20=50
Answer:
Angle COD, 40 degrees
Step-by-step explanation:
Alrighty, to start, Angle AOB is a 180 degree angle because it is a line.
Therefore, if we combine all of the variables and numbers together, we can set it equal to 180 degrees to find a.
2a+62+54-a+5a-20
6a+96=180
6a=84
a=14
Next, plug in this value into each of the given angles provided with variables and numbers:
Angle AOB:
2a+62
2(14)+62
28+62
90 degrees
Angle COD:
54-a
54-14
40 degrees
Angle DOB:
5a-20
5(14)-20
70-20
50 degrees
From this, it can be found that Angle COD has the smallest angle, with it being 40 degrees.
Use grid paper to find the median of the data. 16, 24, 13, 36, 22, 26, 22, 28, 25 will give Briainelst
Answers
Answer:
24
Step-by-step explanation:
put them in ascending order then cross of one each side still you reach the middle
8. If KITE is a kite, find the value of x and y.
A)x=5, y=5
B)x=3, y=5
C)x=8, y=3
D)x=3, y=8
Answers
Answer:
x = 3; y = 8
Step-by-step explanation:
Sides KI and KE are congruent.
4x = 12
x = 3
Sides IT and ET are congruent.
3y - 4 = 20
3y = 24
y = 8
Answer: x = 3; y = 8
what directed number is suggested by the statement "I gained 3 pounds "?
Answers
Answer:
The directed number suggested is +3.
Step-by-step explanation:
A directed number is one that has either a positive or negative sign, so that it could be easily located on the number line. Thus, the sign shows the direction of the number. Examples are: -2, -1, +5, +6 etc.
From the given question, let the initial weight be represented by W, then:
I gained 3 pounds implies at that; 3 pounds was added to my initial weight. Thus, my present weight is my initial weight + 3 pounds.
i.e I gained 3 pounds ⇒ W + 3
So that the directed number suggested by the statement is +3.
HELP ME PLEASEEEEEEEEEEEE
Answers
Answer:
1080 in^2
Step-by-step explanation:
Answer:
180 in^2
Step-by-step explanation:
A 12" wide by 30" flag has the area A = (1/2)(base)(height) square inches, or 180 square inches.
Lucy will spend more than $26 on gifts. So far, she has spent $17. What are the possible additional amounts she will spend?
use C for the additional amount Lucy will spend
Answers
Answer:
She can spend anything greater than $9. Such as, $10, $11, $12, $13
Step-by-step explanation:
Subtract 17 from 26 to get $9