Answer:
[tex]\sqrt{9x^2+36} = 6 \csc(\theta)[/tex]
Step-by-step explanation:
Given
[tex]\frac{x}{2}=\cot(\theta)[/tex]
Required
Express [tex]\sqrt{9x^2+36}[/tex] as trigonometry expression
[tex]\sqrt{9x^2+36}[/tex]
Factorize
[tex]\sqrt{9x^2+36} = \sqrt{9(x^2+4)}[/tex]
Split
[tex]\sqrt{9x^2+36} = \sqrt{9} * \sqrt{(x^2+4)}[/tex]
[tex]\sqrt{9x^2+36} = 3 * \sqrt{(x^2+4)}[/tex]
[tex]\sqrt{9x^2+36} = 3\sqrt{(x^2+4)}[/tex]
We have:
[tex]\frac{x}{2}=\cot(\theta)[/tex]
Make x the subject
[tex]x = 2 \cot(\theta)[/tex]
So:
[tex]\sqrt{9x^2+36} = 3\sqrt{(x^2+4)}[/tex]
[tex]\sqrt{9x^2+36} = 3\sqrt{((2 \cot(\theta))^2+4)}[/tex]
Evaluate all squares
[tex]\sqrt{9x^2+36} = 3\sqrt{4\cot^2(\theta)+4}[/tex]
Factorize
[tex]\sqrt{9x^2+36} = 3\sqrt{4(\cot^2(\theta)+1)}[/tex]
Split
[tex]\sqrt{9x^2+36} = 3\sqrt{4} * \sqrt{\cot^2(\theta)+1}[/tex]
[tex]\sqrt{9x^2+36} = 3*2 * \sqrt{\cot^2(\theta)+1}[/tex]
[tex]\sqrt{9x^2+36} = 6 * \sqrt{\cot^2(\theta)+1}[/tex]
In trigonometry
[tex]\cot^2(\theta)+1 = \csc^2(\theta)[/tex]
So, we have:
[tex]\sqrt{9x^2+36} = 6 * \sqrt{\csc^2(\theta)}[/tex]
Evaluate the square root
[tex]\sqrt{9x^2+36} = 6 * \csc(\theta)[/tex]
[tex]\sqrt{9x^2+36} = 6 \csc(\theta)[/tex]
Plz help me well mark brainliest if correct!!!
Answer:
C
Step-by-step explanation:
30 is to 150, like ___ is to 45 A)9 B)400 C)5 D)15
Answer:
D.
Step-by-step explanation:
divide 45 by 3
Draw the image of the rotation of quadrilateral SORT by 270° about the origin
Answer:
70
Step-by-step explanation:
24 fl.ounces = how many cups?
Answer:
3 cups
Step-by-step explanation:
Answer:
Its 3
Step-by-step explanation:
you divide the volume value by 8
24 = 3
Bart's Art Shop sells 100 colored pencils
for $5. Circle all equivalent rates.
A. 20 colored pencils per dollar
B. 10 colored pencils per 50¢
C. 1 pencil per 5¢
D. 5 pencils per dollar
Answer:
B
Step-by-step explanation:
Divided 20 by .50 and got this
The figure below shows three edge views of a square loop with sides of length ℓ = 0.420 m in a magnetic field of magnitude 2.25 T. Calculate the magnetic flux (in Wb) through the loop oriented perpendicular to the magnetic field, 60.0° from the magnetic field, and parallel to the magnetic field.
Three figures show an x y coordinate plane with the +x-axis pointing to the right and the +y-axis pointing upward. A magnetic field labeled vector B points to the right in the positive x-direction. In each figure, a bar of length ℓ is shown in different orientations.
In the first figure, the bar is oriented vertically, perpendicular to the magnetic field.
In the second figure, the bar is tilted so that the top end is further right than the bottom end, making a 60.0° angle with the magnetic field.
In the third figure, the bar is oriented horizontally, parallel to the magnetic field.
HINT
(a)
perpendicular to the magnetic field
Wb
(b)
60.0° from the magnetic field
Wb
(c)
parallel to the magnetic field
Wb
The magnetic flux of the following options are; 0.072, 0.062, 0.
How to calculate the magnetic flux?The magnetic flux can be calculated by the given formula;
Flux = magnetic field B x area A x cos(angle between B and normal of A)
Given;
Magnetic field B = 2.25 T
The length ℓ = 0.420 m
Flux = 2.25 * 0.42^2 * cos(angle)
Flux = 0.072 * cos(angle)
a) The perpendicular to the magnetic field Wb
So, angle = 0°, flux = 0.072 Wb
b) 60.0° from the magnetic field Wb
So, angle = 30°,
flux = 0.072*cos(30) = 0.062 Wb.
c) parallel to the magnetic field Wb
So, angle = 90°, flux = 0
Learn more about magnetic flux here;
https://brainly.com/question/15655691
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Which expression can be used to find the surface area of the following rectangular prism?
Choose 1 answer:
(Choice A)
30+15
B
15+15+30+30+18+18
C
15+15+30+30+6
D
15+18+30
Many freeways have service (or logo) signs that give information on attractions, camping, lodging, food, and gas services prior to off-ramps. These signs typically do not provide information on distances. The article Evaluation of Adding Distance Information to Freeway-Specific Service (Logo) Signs (J. of Transp. Engr., 2011; 78-888) reported that in one investigation, six sites along Virginia interstate high ways where service signs are posted were selected. For each site, crash data was obtained for a three-year period before distance information was added to the service signs and for a one-year period afterward. The number of crashes per year before and after the sign changes were as follows:
Before: 15 26 66 115 62 64
After: 16 24 42 80 78 73
The cited article included the statement A paired t test was performed to determine whether there was any change in the mean number of crashes before and after the addition of distance information on the signs. Carry out such a test. [Note: The relevant normal probability plot shows a substantial linear pattern.] a seventh site were to be randomly selected among bearing service signs, between what values predict the difference in number of crashes to lie?
Answer:
H0 : μd = 0
H1 : μd ≠ 0
Test statistic = 0.6687 ;
Pvalue = 0.7482 ;
Fail to reject H0.
Step-by-step explanation:
H0 : μd = 0
H1 : μd ≠ 0
Given the data:
Before: 15 26 66 115 62 64
After: 16 24 42 80 78 73
Difference = -1 2 24 35 -18 -9
Mean difference, d ; Σd / n
d = Σx / n = ((-1) + 2 + 24 + 35 + (-18) + (-9))
d = Σx / n = 33 / 6 = 5.5
Test statistic = (d / std / sqrt(n))
std = sample standard deviation = 20.146
Test statistic = 5.5 ÷ (20.146/sqrt(6))
Test statistic = 0.6687
The Pvalue :
P(Z < 0.6687) = 0.7482
At α = 0.05
Pvalue > α ; Hence we fail to reject H0
The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.
9. Which of the following fractions is equivalent to 1.68?*
25
17
25
42
A
OB.
42
7
25
4.
Given: cos θ=-4/5, sin x = -12/13, θ is in the third quadrant,
x is in the fourth quadrant; evaluate
tan2θ
A. 24/5
B. 24/7
C.12/13
By definition of tangent,
tan(2θ) = sin(2θ) / cos(2θ)
Recall the double angle identities:
sin(2θ) = 2 sin(θ) cos(θ)
cos(2θ) = cos²(θ) - sin²(θ) = 2 cos²(θ) - 1
where the latter equality follows from the Pythagorean identity, cos²(θ) + sin²(θ) = 1. From this identity we can solve for the unknown value of sin(θ):
sin(θ) = ± √(1 - cos²(θ))
and the sign of sin(θ) is determined by the quadrant in which the angle terminates.
We're given that θ belongs to the third quadrant, for which both sin(θ) and cos(θ) are negative. So if cos(θ) = -4/5, we get
sin(θ) = - √(1 - (-4/5)²) = -3/5
Then
tan(2θ) = sin(2θ) / cos(2θ)
tan(2θ) = (2 sin(θ) cos(θ)) / (2 cos²(θ) - 1)
tan(2θ) = (2 (-3/5) (-4/5)) / (2 (-4/5)² - 1)
tan(2θ) = 24/7
HELP ME !!!!!!!! a car is moving 70 miles per hour. how far does it travel in 16seconds
i’ll give 15points pls help
Answer:
0.311 mile
Step-by-step explanation:
There are 3600 seconds in 1 hour.
Thus, 70 mph, when multiplied by the appropriate conversion factors, comes out to:
70 mi 1 hr
--------- * --------------- = 0.019 mi/sec
1 hr 3600 sec
and so the desired distance is found by multipying (0.019 mi/sec) by 16 sec:
0.311 mile
Joaquin gets paid every Friday. His paychecks for the past 8 fridays were $324, $245.25, $245.25, $245.25, $324,$324,$245.25 and $402.75 find the median
Answer:
284.625
Step-by-step explanation:
Arrange the numbers highest to lowest.
Find the middle value in the arrangement.
Solve for angle X in the diagram
NO LINKS PLEASE
Answer:
it would be 145
Step-by-step explanation:
the two angles make a straight line, 180-35 is 145
Answer: 145
Step-by-step explanation:
supplementary angle rule: on a straight line, all angles add up to 180
180 = 35 + x
180 - 35 = x
145 = x
Hi, I need the area to this problem i need the answer and to show my work no hackers please
Althea needs 147 ounces of coldcuts for a party. How many pounds and ounces does she need?
Answer:
9 pounds and 3 ounces
Step-by-step explanation:
Althea needs 9 pounds and 3 ounces of cold cuts for her party.
How to convert ounces to pounds?To convert ounces to pounds, divide the number of ounces by 16 since there are 16 ounces in one pound.
147 divided by 16 is equal to 9.1875, which can be rounded to 9.
Then, to find the remaining ounces, multiply the decimal part of the result (0.1875) by 16.
This is equal to 3 ounces.
Therefore, 147 ounces is equal to 9 pounds and 3 ounces.
Learn more about Arithmetic operations here:
brainly.com/question/25834626
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The graph of y=f(x) is given below. Which of the answer choices shows the graph of y=f(1/3x)?
up one over three
Step-by-step explanation:
start at 3
Find the value of "x" in each angle
Answer:
x = 45°
Step-by-step explanation:
x = 90° - 45° = 45°
can someone help me with this question I tried all apps and it gives me the wrong answer, the due date is today plus its half of my grade if u helped ilysm u saved my life
Answer:
[tex]4\frac{1}{12}[/tex] miles.
Step-by-step explanation:
The goal of the family is to hike [tex]11 \frac{2}{3}[/tex] miles in total. Converting this to an improper fraction, we need a total of [tex]\frac{35}{3}[/tex] miles.
On Monday the family completed [tex]2 \frac{1}{12}[/tex] miles, or [tex]\frac{25}{12}[/tex] miles.
On Tuesday the family completed [tex]2 \frac{1}{3}[/tex] miles, or [tex]\frac{7}{3}[/tex] miles.
On Wednesday the family completed [tex]3 \frac{1}{6}[/tex] miles, or [tex]\frac{19}{6}[/tex] miles.
Next, we can add the total amount of hiking the family has completed from Monday-Wednesday.
[tex]distance= \frac{25}{12} + \frac{7}{3} + \frac{19}{6}[/tex]
In order to add these values, we need to convert all of the fractions so that they have the same denominator. The least common multiple (LCM) of 12, 3, and 6 is 12, so the fractions can all be converted into having a denominator of 12.
Monday's distance [tex]\frac{25}{12}[/tex] already has a denominator of 12.
Tuesday's distance is [tex]\frac{7 * 4}{3 * 4} = \frac{28}{12}[/tex].
Wednesday's distance is [tex]\frac{19 * 2}{6 * 2} = \frac{38}{12}[/tex].
Convert the total distance goal to have a denominator of 12 as well. [tex]\frac{35 * 4}{3 * 4} = \frac{140}{12}[/tex].
Sum the total distance the family has walked on Monday-Wednesday. [tex]\frac{25}{12} + \frac{28}{12} + \frac{38}{12} = \frac{91}{12}[/tex].
Subtract this value from the total hiking distance. [tex]\frac{140}{12} - \frac{91}{12} = \frac{49}{12}[/tex]. The family needs to walk [tex]\frac{49}{12}[/tex] miles, or [tex]4 \frac{1}{12}[/tex] miles on Thursday to complete their goal.
As the question told , the goal of they hiking is reaching to the 11 2/3 hours of hiking which means :
The sum of the hours they hiking during those four days must equal 11 2/3 hours .
Suppose they hiking for x hours on Thursday so we have the following equation :
2 1/12 + 2 1/3 + 3 1/6 + x = 11 2/3
To simplify the addition and subtraction of fractions, we must find a common denominator between them ;
The smallest common multiple between the numbers 3, 6, and 12 is the denominator we want, which is 12. But because day 24 is easier to understand, I consider the common denominator of fractions to be 24.
2 + 2 + 3 + 1/12 + 1/3 + 1/6 + x = 11 + 2/3
7 + 2/24 + 8/24 + 4/24 + x = 11 + 16/24
7 + ( 2 + 8 + 4 )/ 24 + x = 11 + 16/24
7 + 14/24 + x = 11 + 16/24
Subtract sides minus 14/24
7 + 14/24 - 14/24 + x = 11 + 16/24 - 14/24
7 + 0 + x = 11 + 2/24
7 + x = 11 + 2/24
subtract sides minus 7
7 - 7 + x = 11 - 7 + 2/24
0 + x = 4 + 2/24
x = 4 + 1/12
x = 4 1/12
solve 2x^2+3x-2 when x=5
Answer:
63
Step-by-step explanation:
2(5)²+3(5)-2
50+15-2
using bodmas
65-2
63
Answer:
63
Step-by-step explanation:
Can you solve for x and type the correct code? Please remember to type in ALL CAPS with no spaces.
Answer:
Hypotenuse = 85 cm
Hypotenuse = 89 cm
Hypotenuse = 103.08 cm (Approx.)
Hypotenuse = 54.71 cm (Approx.)
Step-by-step explanation:
Shape 1
Hypotenuse = √Perpendicular² + Base²
Hypotenuse = √36² + 77²
Hypotenuse = √1,296 + 5,929
Hypotenuse = √7,225
Hypotenuse = 85 cm
Shape 2
Hypotenuse = √Perpendicular² + Base²
Hypotenuse = √39² + 80²
Hypotenuse = √1,521 + 6,400
Hypotenuse = √7,921
Hypotenuse = 89 cm
Shape 3
Hypotenuse = √Perpendicular² + Base²
Hypotenuse = √25² + 100²
Hypotenuse = √625 + 10,000
Hypotenuse = √10,625
Hypotenuse = 103.08 cm (Approx.)
Shape 4
Hypotenuse = √Perpendicular² + Base²
Hypotenuse = √17² + 52²
Hypotenuse = √289 + 2,704
Hypotenuse = √2,993
Hypotenuse = 54.71 cm (Approx.)
If 8 minus some number divided by 3 = 6 what is the number?
Answer:
n = 6
Step-by-step explanation:
Represent the unknown number by n. Then 8 - n/3 = 6.
Consolidate the constants on the left side: 2 - n/3 = 0, or n/3 = 2.
Multiplying both sides by 3 results in: n = 6
(3b^3)^2 without exponents
Answer:
When (3b³)² is simplified, it equals 3b⁶
Step-by-step explanation:
3 × 2 = 6
The exponent is 6
Help. I need the homework done.
Area (ABC)=82
Area (MNK)=78
Area (MQLK)= 53
Calculate the area of the whole shaded shape (AMBQNLCK)
https://homework.russianschool.com/resource?key=13066ibamxerc
Answer:
the area of the triangle ABC is ,then value of a is 27cm.
Solution:
Given Data:
Area of the triangle ABC is
To Find:
Value of a?
Step 1:
Step 2:
By Law of Sines
Simplify the above expression
--- eqn 1
Step 3:
Step 4:
Substitute the A, B and C value from the given Data.
Apply the Sin theta respective value.
From the above we finally got the value of "a" which is 27 cm.
Step-by-step explanation:
What are the slope and y-intercept of the graph of the equation?
Answer:
Slope= -1/2
y-intercept= 2/3
ZA and B are vertical angles. If m A = (5x + 6) and m B = (6.2 – 25)°, then find the value of x.
Answer:
The value of x is 25.83.
Step-by-step explanation:
Vertical angles:
If two angles are vertical, they have the same measure.
In this question:
Angle A has measure 5x + 6
Angle B has measure 6.2x - 25
Since they are vertical:
[tex]A = B[/tex]
[tex]5x + 6 = 6.2x - 25[/tex]
[tex]1.2x = 31[/tex]
[tex]x = \frac{31}{1.2}[/tex]
[tex]x = 25.83[/tex]
The value of x is 25.83.
What is the median of the following set?
28, 45, 12, 34, 36, 45, 19, 20
28
34
31
35
Answer:
31 IS YOUR ANSWER!!
Step-by-step explanation:
I would not mind the brainliest please!!
The Pacheco family has a monthly income of $ 7,300 . They have monthly fixed expenses of $ 3,280 . In July, they had monthly variable expenses of $ 2,620 . They have annual expenses totaling $ 14,000 . Assuming annual expenses are paid off at an equal rate monthly, what was the Pacheco’s cash flow for July?
Answer:
Positive 233
Step-by-step explanation:
7300-3280-2620-1167(14000/12)=233.
Find the surface area of the cylinder represented by the trunk of the tree.
Answer:
43.98
Step-by-step explanation:
PLEASE ANSWER ILL GIVE YOU BRAINLIEST
Answer:
V=3052.1 square units.
Step-by-step explanation:
Using the formulas
V=4
3πr^3
d=2r
Solving for V
V=1
1/6πd^3=1
1/6·3.14·18^3=3052.08
round to the nearest tenth place so your volume would be 3052.1 :)
Answer:
3052.1
Step-by-step explanation:
The formula for volume of a sphere: 4/3 x pi x r^3 (4/3 x pi x radius x radius x radius).
Here, only the diameter is shown. To find the radius, we must divide the diameter (18) by 2.
18 / 2 = 9
9 is the radius.
Now, we have our final equation:
4/3 x pi x radius x radius x radius
4/3 x 3.14 x 9 x 9 x 9 = 3052.08
(3.14 is commonly used for pi)
3052.08 rounded to the nearest tenth is 3052.1
Therefore, 3052.1 is the volume of the sphere.
pls help figure out any triangle. It would be nice if the formula and steps are included, thank u!
Answer:/Step-by-step explanation:
We would apply pythagorean theorem to find the variable in each triangle.
Pythagorean theorem is given as: c² = a² + b², where c is the hypotenuse length or longest leg while a and b are the two other legs.
Thus:
a. h² = (√20)² + 4²
h² = 20 + 16
h² = 36
h = √36
h = 6 units
b. t² = 9² - (√17)²
t² = 81 - 17
t² = 64
t = √64
t = 8 units
c. h² = (√8)² + (√8)²
h² = 8 + 8
h² = 64
h = √64
h = 8