Answer:
a = 7; b = ⁷/2
Step-by-step explanation:
Recall the acronym, SOHCAHTOA
We would apply trigonometric ratio formula in finding a and b.
Reference angle [tex] (\theta) [/tex] = 60°
Opposite side to the reference angle = [tex] \frac{7\sqrt{3}}{2} [/tex]
Adjacent side = b
Hypotenuse = a
✔️To find a, we would apply SOH, which is:
[tex] sin (\theta) = \frac{opp}{hyp} [/tex]
Plug in the values
[tex] sin (60) = \frac{\frac{7\sqrt{3}{2}}{a} [/tex]
[tex] \frac{\sqrt{3}}{2} = \frac{\frac{7\sqrt{3}{2}}{a} [/tex] (sin 60 = √3/2)
[tex] \frac{\sqrt{3}}{2} = \frac{7\sqrt{3}{2}*\frac{1}{a} [/tex]
[tex] \frac{\sqrt{3}}{2} = \frac{7\sqrt{3}{2a} [/tex]
Cross multiply
[tex] \sqrt{3}*2a = 7\sqrt{3}*2 [/tex]
[tex] 2a\sqrt{3} = 14\sqrt{3} [/tex]
Side both sides by √3
[tex] 2a = 14 [/tex]
Divide both sides by 2
a = 14/2
a = 7
✔️To find b, apply TOA, which is:
[tex] tan (\theta) = \frac{opp}{adj} [/tex]
Plug in the values
[tex] tan (60) = \frac{\frac{7\sqrt{3}{2}}{b} [/tex]
[tex] \sqrt{3} = \frac{\frac{7\sqrt{3}{2}}{b} [/tex] (tan 60 = √3)
[tex] \sqrt{3} = \frac{7\sqrt{3}{2}*\frac{1}{a} [/tex]
[tex] \sqrt{3} = \frac{7\sqrt{3}{2b} [/tex]
Cross multiply
[tex] \sqrt{3}*2b = 7\sqrt{3} [/tex]
[tex] 2b\sqrt{3} = 7\sqrt{3} [/tex]
Divide both sides by √3
[tex] 2b = 7 [/tex]
Divide both sides by 2
b = 7/2
Please help- Show ur work,, and please answer correctly
I will also give brainliest
Answer:
x = -4.
n = -2.
v = -5.
Step-by-step explanation:
18 = -4x + 2
18 - 2 = -4x
x = 16/-4
x = -4.
6 + 2n = 2
2n = 2 - 6 = -4
n = -2.
5v + 8 = -17
5v = -17 - 8
5v = -25
v = -5.
Three students ran 1/2 mile around a track. The table below list the time each student took to run around the track. Complete the table by calculating the average speed of each student in miles per hour (mph).
Give answer and explanation of how you got the answer please. Give brainlyest.
Answer:
Step-by-step explanation:
Answer:
Ava 6 mph; Damon 10 mph; Reina 7.5 mph
Step-by-step explanation:
Which could be the dimensions of a rectangular prism whose surface area is greater than 140 square feet? Select
three options.
6 feet by 2 feet by 3 feet
6 feet by 5 feet by 4 feet
17 feet by 6 feet by 4 feet
8 feet by 3 feet by 7 feet
8 feet by 4 feet by 3 feet
Answer:
6 feet by 5 feet by 3 feet
17 feet by 6 feet by 4 feet
8 feet by 3 feet by 7 feet
Can someone please help with these two questions please?
1. Assume that the radius r of a sphere is expanding at a rate of 60 cm/min. The volume of a sphere is V = 4/3r^3 and its surface area is 4r^2. Determine the rate of change in surface area at t = 2 min, assuming that r = 16 at t = 0.
2. A conical tank has height 3 m and radius 2 m at the top. Water level is rising at a rate of 2.1 m/min when it is 1.8 m from the bottom of the tank. At what rate is water flowing in? (Round your answer to three decimal places.)
Answer:
Step-by-step explanation:
S=4πr²
ds/dt=4π×2r×dr/dt=8πr dr/dt
dr/dt=60 cm/min
ds/dt=8π×60r=480πr
r=16,t=0
at t=2,r=16+32=48 cm
so ds/dt=480π×48=23040 πcm²≈72382.79 cm²
2.
[tex]V=\frac{1}{3} \pi r^2*h\\\frac{r}{h} =\frac{2}{3} \\r=\frac{2}{3} h\\V=\frac{1}{3} \pi( \frac{2}{3} *h)^2h\\V=\frac{4}{27} \pi h^3\\\frac{dV}{dt} =\frac{4}{27}\pi *3h^2\frac{dh}{dt} \\\\when ~h=1.8 ~m,\frac{dh}{dt} =2.1~m/min\\\frac{dV}{dt} =\frac{4}{9}\pi h^2\frac{dh}{dt} =\frac{4}{9} \pi*(1.8)^2*2.1=27.216 \pi \approx 85.502 m^3[/tex]
The graph of y= -x2+3x-2 is shown. The ZERO(S) of the function is/ are?
A. -2
B. -2, 2
C. -2, 1, 2
D. 1, 2
A frame is 4 inches tall and 3 inches wide if it is enlarged to a height of 24 inches then how wide will it be
100 POINTS PLZ HELP ME
This graph shows a proportional relationship.
What is the constant of proportionality?
Enter your answer as a ratio in simplified form by filling in the boxes.
$$
A graph with a line running through coordinates left parenthesis 0 comma 0 right parenthesis and coordinates left parenthesis 1 over 4 end fraction comma 3 over 8 end fraction right parenthesis.
Answer:
I dont see a graph, but the constant of proportionality the ratio between two directly proportional quantities. two quantities are directly proportional when they increase and decrease at the same rate
Step-by-step explanation:
if you add a graph, ill edit my answer
hope this helps!
- Kirk is reading a book and found that after 5 days he had read 180 pages.
rate is Kirk reading the book in (b) If the book is 765 pages long, how many
days will it take him to read the book at
the rate you found in (a)?
Answer:
21.25 days
Step-by-step explanation:
We first need to find the rate that he read the book for the first 5 days:
180 (pages)/5 (days)= 36
So he reads 36 pages a day. Now we need to find how many days it will take him to read the whole book, while reading 36 pages a day.
765 (total pages)/36 (pages he reads in a day) = 21.25
Have a wonderful day, my friend.
In a research experiment, the population of a colony of bacteria doubles every hour. The population, f() of the colony atter z hours can be modeled by the function () - 25.2" What values for the domain are reasonable in the given
context
Answer:99
4/2ndjsjhowkllsnlove u
there are 84 girls in grade 3.the boys are twice the numbers of girls. how many pupils are there in all in grade 3?
Answer:
252
Step-by-step explanation:
Girls = 84
Boys = 84 * 2 = 168
Total = 252
Answer:
Step-by-step explanation:
no of girls in grade 3 = 84
by the question no of boys are twice the number of girls so
no of boys = 2 * 84 = 168
Total no of pupil in grade 3
= 168 + 84
= 252
hope it will help :)
please answer!
Find the value of x.
115°
150°
thank you :)
Answer:
35 degrees
Step-by-step explanation:
180-150=30
115+30=145
180-145=35
35
Answer:
360 degrees - 150degrees =110 degrees
add 110 and 115 degrees to get 225 degrees
next subtract 360 - 225= 135 degrees
so x equals 135
Step-by-step explanation:
can i have brainliest
Type SSS, SAS, ASA, SAA, or HL to
justify why the two larger triangles are
congruent.
8 cm
8 cm
Solve by graphing.
x + 3y = -9
5x + 3y = 3
Answer:
Step-by-step explanation:
The solution of the system of linear equations is [tex]x = 3[/tex] and [tex]y = -4[/tex].
In this question, we notice that given system of linear equations consist of two equations and two variables, which means that solution is unique and can be found by graphic means. We proceed to graph each line with a graphing tool and label the point, in which both lines intersect each other.
The outcome from the graphing tool is presented below as attachment. In a nutshell, the solution of the system of linear equations is [tex]x = 3[/tex] and [tex]y = -4[/tex].
We kindly invite you to see this question related to systems of linear equations: https://brainly.com/question/13647755
I need help with before 9
Answer:
There is no 9 on the paper.
Step-by-step explanation:
Answer:
1) p = how much he was paid per lawn
2) 4p = how much he was paid for 4 lawns
3) 4p = 24, then p = $6
4) 45-d = 21, d = $24
You are facing South. You make an about face, then turn 90 degrees right. What direction are you facing?
If you face South, perform an about face (180-degree turn), and then turn 90 degrees to the right, you will be facing West.
If you are facing South and make an about-face, then turn 90 degrees right, you will be facing West. This is because an about-face means to turn around 180 degrees, so you would now be facing North.
Then, turning 90 degrees to the right from the North would put you in the direction of the West. To summarize, if you start off facing South, making an about-face means turning around 180 degrees to face North.
From there, turning 90 degrees to the right puts you in the direction of the West. Therefore, you would be facing West after making an about-face and turning 90 degrees to the right.
For more questions on degrees
https://brainly.com/question/29165823
#SPJ8
-2xSquared +4x-1 minus 6x squared+3x-9
Construct 98% confidence intervals based on the following data: 49, 38, 67, 69, 58, 70, 66, 85.
Answer:
May I have a little more context please?
Step-by-step explanation:
z + y2
for y = 6 and z = 1
Answer:
37
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
z + y²
y = 6
z = 1
Step 2: Evaluate
Substitute in variables: 1 + 6²Evaluate exponents: 1 + 36Add: 37Help&EXPLAIN
Don’t use for points or will be reported and I’ll take the points back
Answer:
i guess the answer maybe A
What is 3-8 I don’t know what it is I can not figure it out
Answer:
-5
Step-by-step explanation:
Answer:
your answer is -5
Step-by-step explanation:
when your reach 0 your keep going to the negetives
Can you Help me please!!
Step-by-step explanation:
10 and under= 3
11-15=7
16-20=8
20 and over= 2
Help&EXPLAIN
Don’t use for points or will be reported and I’ll take the points back
Answer:
B = 243°
Step-by-step explanation:
Full revolution = 360°
360 - 117 = 243
Answer:
243 degrees
Step-by-step explanation:
The angle of a full circle = 360 degrees
360 - 117 = 243
COMPLETE THE SEQUENCES.
1- 0, 16, 32, 48, 64,_,_,_,
2- 2,9, 11, 18, 20, 27,_,_,_,
SOMEONE PLEASE HELP ME
Answer:
0,16,32,48,64,80,96,112
2,9,11,18,20,27,29,36,38
Step-by-step explanation:
1.Counting by 16
2. Counting by 7 and 2
The carnival is in town for 21 days. How many weeks is the carnival in town?(There are 7 days in 1 week.) Write and equation,and solve.
Answer:
egn= 7x=y
where x= weeks no.
y= days
atq...x= 3
Pls help this is due in 10 minutes
Answer:
y = 52
Step-by-step explanation:
y/4 - 7 = 6 (get the y isolated)
y/4 = 13 (add 7 to both sides)
y = 52 (multiply 4 on both sides)
Use the grouping method to factor the polynomial below completely.
3x3 + 6x2 + 5x + 10
A. (3x2 +5)(x+2)
B. (3x2 + 5)(x + 5)
C. (3x2 + 2)(x + 5)
D. (3x2 + 2)(x + 2)
Answer:
its A
Step-by-step explanation:
i did the test
A.find the price elasticity of demand at the equilibrium points? quantity demand=72-8p and quantity supply=-24 +24p. B.substitutes the equation.
Answer:
p = 3
Step-by-step explanation:
The price elasticity of demand at the equilibrium points occurs when quantity demand equals quantity supply.
So,
72-8p= -24 +24p
Taking like terms together,
72+24 = 24p+8p
96 = 32p
p = 3
Hence, the price elasticity of demand is at p = 3.
At a height of about 212 meters, One Shell Square is the tallest building in New Orleans. Marlie is creating a scale model of this building, using the scale factor 1:250.
To the nearest tenth of a meter, what will be the height of the scale model?
Enter your answer as a decimal in the box.
given 90 points for answering, thank you!
Answer:
0.8 meters
Step-by-step explanation:
The scale factor is 1:250 (can be rewritten as 1/250 or 1 to 250).
1/250 × 212 = 0.848 Meters
Round to the nearest tenth, the scale model will be 0.8 meters.
OR: SET UP A PROPORTION:
[tex] \frac{250}{1} \times \frac{212}{x} [/tex]
cross-multiply
[tex]250x = 212[/tex]
[tex]x = 0.848[/tex]
Answer:
0.8
Step-by-step explanation:
ye
I need help the question is solve the equation n+75=155
Answer:
80
Step-by-step explanation:
155-75=80
please answer quick brain list on cludded
Answer:
(-3,-4)
Step-by-step explanation: