Answer:
sqrt21/5
Step-by-step explanation:
You can solve this by taking advantage of the trigonometric identity of sin^2(x) + cos^2(x) = 1
So square sinθ to get, 4/25
Subtract that from one to get:
cos^2(θ) = 21/25
Take the square root to get:
cosθ = sqrt21/5
The value of cosθ = (√21)/ 5.
What is a sine function?The sine function in trigonometry is the ratio of the hypotenuse's length to the opposite side's length in a right-angled triangle. To determine a right triangle's unknown angle or sides, utilize the sine function.
Given that the angle θ lies in Quadrant I.
That means all the value of in θ the first quadrant are positive from 0° to 90°.
Here sinθ = 2/5.
And we know cosθ = √(1-sin²θ )
So cosθ = √{1- (2/5)²}
⇒ cosθ = √{1- (4/25)}
⇒ cosθ = √{21/25)}
⇒ cosθ = (√21)/ 5
Therefore, cosθ = (√21)/ 5
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Stunt Double A movie stunt double jumps from the top of a
building 50 feet above the ground onto a pad on the ground
below. The stunt double jumps with an initial vertical velocity
of 10 feet per second.
a. Write and graph a function that models the height h (in feet)
of the stunt double t seconds after she jumps.
b. How long does it take the stunt double to reach the ground?
Answer:
2.1 s
Step-by-step explanation:
1. Write the equation
The formula for vertical displacement is
y = h + v₀t - ½gt²
h = 50 ft
v₀ = 10 ft/s
g = 32.2 ft/s²
Insert the values
y = 50 + 10t - ½ × 32.2t²
y = 50 + 10t - 16.1t²
The graph below shows the height as a function of time.
2. Solve the equation
a = -16.1; b = 10; c = 50
[tex]\begin{array}{rcl}x & = & \dfrac{-b\pm\sqrt{b^2 - 4ac}}{2a}\\\\& = & \dfrac{-10\pm\sqrt{10^2-4(-16.1) \times 50}}{2(-16.1)}\\\\& = & \dfrac{-10\pm\sqrt{100 - (-3220)}}{-32.2}\\\\& = & \dfrac{-10\pm\sqrt{100 + 3220}}{-32.2}\\\\& = & \dfrac{-10\pm\sqrt{3300}}{-32.2}\\\\& = & \dfrac{-10\pm 57.62}{-32.2}\\\\\end{array}[/tex]
[tex]\begin{array}{rcl}x = \dfrac{-10 + 57.62}{-32.2}& \qquad & x = \dfrac{-10 -57.62}{-32.2}\\\\x = \dfrac{47.62}{-32.2}& \qquad & x = \dfrac{-67.62}{-32.2}\\\\x = -1.479& \qquad & x =\textbf{ 2.1 s}\\\\\end{array}\\\text{It takes the stunt double $\large \boxed{\textbf{2.1 s}}$ to reach the ground.}[/tex]
An airplane travels 150 miles horizontally during a decrease of 35,000 feet vertically.
1. What is the angle of descent?
2. How long is the plane's path?
*teacher hint* remember to convert feet to miles or miles to feet or your answer will not make sense
The airplane's path is an illustration of right-triangles
The angle of descent is 2.5 degreesThe plane's path is 150.15 milesThe angle of descentRepresent the angle of descent with [tex]\theta[/tex]
The angle of descent, [tex]\theta[/tex] is then calculated using the following tangent identity
[tex]\tan(\theta) = \frac{35000\ feet}{150 \ miles}[/tex]
Convert feet to miles
[tex]\tan(\theta) = \frac{6.6287879\ miles }{150 \ miles}[/tex]
Divide
[tex]\tan(\theta) = 0.0442[/tex]
Take the arc tan of both sides
[tex]\theta = \tan^{-1}(0.0442)[/tex]
Evaluate the arc tan
[tex]\theta = 2.5[/tex]
Hence, the angle of descent is 2.5 degrees
The plane's pathRepresent the plane's path with p
The plane's path is calculated using the following Pythagoras theorem
[tex]p^2 = (150\ miles)^2 + (35000\ feet)^2[/tex]
Convert feet to miles
[tex]p^2 = (150\ miles)^2 + (6.6287879\ miles)^2[/tex]
Evaluate
[tex]p^2 = 22543.940829[/tex]
Take the square roots
[tex]p = 150.15[/tex]
Hence, the plane's path is 150.15 miles
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If one of the short sides of a 45-45-90 triangle equals 5, how long is the hypotenuse?
Possible Answers:
√10
5
π
√15
5√2
Answer:
hypotenuse= 2[tex]\sqrt{5}[/tex]
Step-by-step explanation:
the triangle is equal tow side so it is two side =5 cm
then the hypotenuse by Phitagors theory the triangle hypotenuse =
[tex]\sqrt{5^{2} +5^{2} }[/tex] = 2[tex]\sqrt{5}[/tex]
Parallel lines e and f are cut by transversal b. Horizontal and parallel lines e and f are cut by transversal b. At the intersection of lines b and e, the uppercase right angle is (2 x + 18) degrees. At the intersection of lines b and f, the top right angle is (4 x minus 14) degrees and the bottom right angle is y degrees. What is the value of y? 16 50 130 164
Answer:
Angle y measures 130 degrees
Step-by-step explanation:
Notice that the angles marked as "2x+18", and "4x-14" must be equal angles since they are generated on the same sector (top right) of the parallel lines by the transverse line "b".
Then by finding the value of "x" we can deduce the value of the actual angle these two angles measure:
[tex]2x+18=4x-14\\18+14=4x-2x\\32=2x\\x=16^o[/tex]
Now, we can find the actual value of these two angles, we use for example the first expression:
Top-right angle = [tex]2\,(16^o)+18^o=50^o[/tex]
Now, if these two angles measure [tex]50^o[/tex], then angle "y" (which is the supplementary angle (angle which added renders [tex]180^o[/tex] ) for them, must equal [tex]180^o-50^o=130^o[/tex]
Answer:
It's C. 130
Step-by-step explanation:
O just did the math and got it right on the test.
how can you add 8 to get the number 1000
Answer:
8+92=100
Step-by-step explanation:
You can get that by subtracting 8 from 100 :)
Answer:
if the number ur adding it to is 991 and u add 8 you will get 1,000
Step-by-step explanation:
Use the distance formula to find the distance between A(-3,4) and B(7, -6). Round your answer to the nearest tenth.
The answer is 10√2
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
please please please help
Answer:
S: 1st quadrant
K:2nd quadrant
W:3rd quadrant
C: y-axis
Step-by-step explanation:
Please answer correctly !!!!!! Will mark brainliest !!!!!!!!!!
Answer:
[tex]2a^2\sqrt{35a}[/tex]
Step-by-step explanation:
[tex]\sqrt{2a} .\sqrt{14a^3} .\sqrt{5a} \\=\sqrt{2a\times 14a^3\times 5a}\\=\sqrt{140a^5}\\=2a^2\sqrt{35a}\\[/tex]
Calculate the rate of change for the quadratic function over the given interval: f\left( x \right) = {x^2} + 4x + 5;\; - 1 \le x \le 2f(x)=x 2 +4x+5;−1≤x≤2 1 5 2 -4
Answer: The rate of change is 5.
Step-by-step explanation:
Our equation is:
f(x) = x^2 + 4x + 5
And we want to find the rate of change in the range −1≤ x ≤2
when we want to find the rate between x1 ≤ x ≤ x2
we have:
Rate = (f(x2) - f(x1))/(x2 - x1)
So we have:
Rate = ( f(2) - f(-1))/(2 - 1)
Rate = (2^2 + 4*2 + 5 - (-1)^2 - 4*(-1) - 5)/3 = 15/3 = 5
The rate of change is 5.
What is the percent change from 90 to 63
Answer:
-42.86%
Step-by-step explanation:
Mathematically, the percentage change is;
(new value -old value)/old value * 100%
According to this question
new value = 63
old value = 90
Inputing these values we have ;
(63-90)/63 * 100
-27/63 * 100%
= -3/7 * 100% = -42.86 #
Aitanacompreparaaitana compra para su fiesta de cumpleaños 5 litros de refresco y vasos de plastico de una capacidad de 250 metros cubicos ¿cuantos vasos podria servir en total?
Answer:
None
Step-by-step explanation:
In this case we must pass everything to the same unit of measure, we know that the total is 5 liters of soft drink and that each plastic cup has a capacity of 250 cubic meters.
We know that 1 liter is equivalent to 0.001 cubic meters, therefore we will pass the cubic meters of the plastic cup to liters, like this:
250 m ^ 3 * 1 L / 0.001 m ^ 3 = 250,000 L
Therefore we realize that the glass has a very large capacity, which suggests that there is an error in the statement, maybe it is not a cubic meter but a cubic centimeter, but as it is, it cannot serve any plastic cup because the capacity of this cup is very large with respect to the total amount of soft drink.
Please Solve Now!!! Will Give Brainliest!!!
1. secθ×sinθ 2. cscθ×cosθ
3. tanθ×cscθ 4. cotθ×secθ
5. 1-cos²θ 6. sec²θ-1
7. csc²θ-cot²θ 8. 1-sin²θ
Answer:
Step-by-step explanation:
1, sec theta * sin theta = 1/cos * sin = sin/cos =tan theta
2. cosec theta * cos theta = 1/ sin * cos = cos/sin = cot theta
3, tan theta * cosec theta =sin/cos * 1/sin = 1/cos
4, cot theta * sec theta = cos /sin * 1/cos= 1/sin
5, 1 - cos^2 theta = sin ^2 theta
6, sec^2 theta - 1 =tan ^2 theta
7 , cosec^2 theta - cot^2 theta = 1
8, 1 - sin^2 theta = cos^2
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Find an equation that meets the conditions p varies inversely as d, and p= 7 when d = 2.
Answer: 3.5
Step-by-step explanation:
What is the mission factor of
18y^3=(G)(2y^2)
g = 9y
this is true because khan academy
The missing factor of the given equation is 9y.
What is factor of the expression?The factors of the expressions are the simplified expression which when multiplied results in the original expression.
Divide 18y³ by 2y² to determine the missing factor.
G=18y³/2y²
Express the numerator and denominator in the factored form and simplify.
G=(2·3·3·y·y·y)/(2·y·y)
G=3·3·y
G=9y
So, the missing factor of the given equation is 9y.
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A rectangle has a length of 9.00 inches and a width of 4.25 inches. What is the area in square inches? Round to the correct significant digits
Answer:
38.25 square inches
Step-by-step explanation:
Length = 9 inches
width = 4.5 inches
Area of Rectangle = Length × width
Area of Rectangle = 9 × 4.5 = 38.25
fifteen percent means fifteen out of
Answer:
15 out of 100
Step-by-step explanation:
15 %= 15/100 it means 15 out of 100
If 3m+2n=16 and m−2n=0, then what is the value of m?
Answer:
m= 4
Step-by-step explanation:
3m +2n= 16 -----(1)
m -2n= 0 -----(2)
From (2):
m= 2n -----(3) (+2n on both sides)
subst. (3) into (1):
3(2n) +2n= 16
6n +2n= 16
8n= 16 (simplify)
n= 16 ÷8
n= 2
subst. n=2 into (3):
m= 2(2)
m= 4
What is the measure of angle Y, in degrees?
Answer:
The answer would be 116
Step-by-step explanation:
The angles X and Z would be equal at 32 so multiply them by 2 and you would get 64 subtract 64 from 180 and you would get 116
Answer:
Y =116
Step-by-step explanation:
We know that angle Z = angle X since they are base angles and the sides are the same length
The sum of the angles of a triangle are 180
X+Y+Z = 180
32+ Y + 32 = 180
64+Y=180
Y = 180-64
Y =116
Solve -3+7y=5x+2y when x=-5
Answer:
y = -22/5
Step-by-step explanation:
-3+7y=5x+2y
Subtract 2y from each side
-3+7y-2y=5x+2y-2y
-3 +5y = 5x
Add 5 to each side
5y = 5x+3
Divide each side by 5
y = 5x/5 +3/5
y = x +3/5
Let x = -5
y = -5 + 3/5
y = -25/5 +3/5
y = -22/5
Answer:
[tex]y=-\frac{22}{5}[/tex]
Step-by-step explanation:
[tex]-3+7y=5x+2y\\x=-5[/tex]
Replace:
[tex]-3+7y=5(-5)+2y\\-3+7y=-25+2y[/tex]
Subtract -2y
[tex]-3+7y-2y=-25[/tex]
Add 3
[tex]7y-2y=-25+3[/tex]
Combine like terms;
[tex]5y=-22[/tex]
Divide by 5.
[tex]y=-\frac{22}{5}[/tex]
Proof
[tex]For x=-5, y=-\frac{22}{5}[/tex]
[tex]-3+7y=5x+2y[/tex]
[tex]-3+7(-\frac{22}{5} )=5(-5)+2(-\frac{22}{5} )[/tex]
[tex]-3-\frac{154}{5}=-25-\frac{44}{5}[/tex]
To make it easier to solve, add 154/5
[tex]-3=-25-\frac{44}{5}+\frac{154}{5}[/tex]
Now add 25
[tex]-3+25=-\frac{44}{5}+\frac{154}{5}[/tex]
Combine like terms;
[tex]22=\frac{110}{5} \\22=22[/tex]
Please help thank you
Answer:
6.5%
Step-by-step explanation:
15.40 * 5 = 77
77 is in the 6.5% range.
What is the slope?
Write it as an integer ,improper fraction or proper fraction
Answer:
-3/2
Step-by-step explanation:
pick any 2 points on the graph. I chose (80,10) and (60, 40) because they are easy to identify.
40- 10 = 30
60-80 = -20
slope = -30/20 or -3.2
1. Line A's equation is y = -1/3x - 5. Line B is perpendicular to Line A and and goes
through the point (2, 3). Write the equation for Line B in slope-intercept form.
2. Line A's equation is y = 2/5x - 5. Line B is perpendicular to Line A and and goes
through the point (10.3). Write the equation for Line B in slope-intercept form.
Answer:
y = -1/3x - 11/3
Step-by-step explanation:
line a: y = -1/3x - 5
3 = -1/3(2) - b
3 = -2/3 - b
3 + 2/3 = b
3/1 + 2/3 = b
9/3 + 2/3 = b
11/3 = b
An angle measures 50.2° less than the measure of its supplementary angle. What is the measure of each angle?
Answer:
10
Step-by-step explanation:
On a coordinate plane, 2 triangles are shown. The first triangle has points F (3, 2), H (4, 5), G (1, 2). The second triangle has points F prime (negative 2, 3), H prime (negative 5, 4), G prime (negative 2, 1). Quinton tried to transform triangle FGH according to the rule (x, y) → (–y, x). Which best describes his attempt? Correct. He transformed the triangle according to the rule (x, y) → (–y, x). Incorrect. He transformed the triangle according to the rule (x, y) → (y, –x) Incorrect. He transformed the triangle according to the rule (x, y) → (–y, –x) Incorrect. He transformed the triangle according to the rule (x, y) → (–x, –y)
Answer:
Correct. He transformed the triangle according to the rule (x, y) → (–y, x)
Step-by-step explanation:
Given
F(3, 2), H(4, 5), G 1, 2)
F'(-2, 3), H'(-5, 4), G'(-2, 1)
Find
Whether the triangle was correctly transformed using the rule ...
(x, y) → (–y, x).
Solution
For point F, we have ...
x = 3
y = 2
Then the rule tells us the point F' should be ...
F' = (-y, x) = (-2, 3)
This is the point Quinton found for F', so his transformation was correct. (We can similarly verify that H' and G' are also correct.)
Answer:
The answer is A. Correct. He transformed the triangle according to the rule (x, y) → (–y, x).
Step-by-step explanation:
Which point would map onto untalented after reflection across the line Y = -X
Answer:
(4, -4)
Step-by-step explanation:
Since the point (4, -4) rests on the line y=-x, it does not change positions and stays in the same spot.
Name the set(s) of numbers to which -2/5 belongs.
Answer:
1. integers
2. rational no.
Short Answer Questions:
1. The perimeter of a square is 18.4 m. What is its area?
Answer:
A ≈ 21.16m²
Step-by-step explanation:
Answer:
21.16 m^2
Step-by-step explanation:
If the perimeter is 18.4 m, then the length of a side is 18.4 m / 4, or 4.6 m.
Then the area of the square is (4.6 m)^2, or 21.16 m^2
Find the surface area of the following cylinders. Round to the nearest hundredth.
Answer:
surface area of cylinder= 2πrh + 2πr²
2×22/7×1×8+2×22/7×1×1
352. + 44
7. 7
= 50.3 + 6.25
= 56.55cm²
What is the value of the 4 in the number 17.884?
Write your answer as a fraction.
Answer:
4/1000
Step-by-step explanation:
the value of 4 is 0.004 which in fraction form is 4/1000
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