Given sin 0 = ā, find cos 0.
✓[?
cos e
=
ө
Step-by-step explanation:
when you look at the graphic and the right-angled triangle :
sine is the length of the vertical leg (opposite of the associated angle) divided by the length of the Hypotenuse (the baseline opposite of the 90° angle), because the sine function values are defined for the norm circle with radius 1. for any larger circle (or triangle inscribed in such a larger circle), we get the basic trigonometric function values by measuring the sides and norming to a radius of 1 (dividing them by the length of the actual radius).
cosine is the horizontal leg (at the "bottom").
the same principle applies. the cosine value is the length of that leg divided by the length of the Hypotenuse.
we know from the given ratio for sine, that the length of the Hypotenuse is 6.
so, we know 2 sides of the right-angled triangle :
the vertical leg is 5, the Hypotenuse is 6.
now, we use Pythagoras to get the horizontal leg :
6² = 5² + leg²
36 = 25 + leg²
11 = leg²
leg = sqrt(11)
and so cosine of the angle is
sqrt(11)/6
Find the area of the triangle 14 Ft 17 ft
Answer:
119
Step-by-step explanation:
14x17 = 238)/2
A plane flying horizontally at an altitude of 3 miles and a speed of 500 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 4 miles away from the station. (Round your answer to the nearest whole number.)
Answer:
The rate at which the distance from the plane to the station is increasing is 331 miles per hour.
Step-by-step explanation:
We can find the rate at which the distance from the plane to the station is increasing by imaging the formation of a right triangle with the following dimensions:
a: is one side of the triangle = altitude of the plane = 3 miles
b: is the other side of the triangle = the distance traveled by the plane when it is 4 miles away from the station and an altitude of 3 miles
h: is the hypotenuse of the triangle = distance between the plane and the station = 4 miles
First, we need to find b:
[tex] a^{2} + b^{2} = h^{2} [/tex] (1)
[tex] b = \sqrt{h^{2} - a^{2}} = \sqrt{(4 mi)^{2} - (3 mi)^{2}} = \sqrt{7} miles [/tex]
Now, to find the rate we need to find the derivative of equation (1) with respect to time:
[tex]\frac{d}{dt}(a^{2}) + \frac{d}{dt}(b^{2}) = \frac{d}{dt}(h^{2})[/tex]
[tex] 2a\frac{da}{dt} + 2b\frac{db}{dt} = 2h\frac{dh}{dt} [/tex]
Since "da/dt" is constant (the altitude of the plane does not change with time), we have:
[tex] 0 + 2b\frac{db}{dt} = 2h\frac{dh}{dt} [/tex]
And knowing that the plane is moving at a speed of 500 mi/h (db/dt):
[tex]\sqrt{7} mi*500 mi/h = 4 mi*\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt} = \frac{\sqrt{7} mi*500 mi/h}{4 mi} = 331 mi/h[/tex]
Therefore, the rate at which the distance from the plane to the station is increasing is 331 miles per hour.
I hope it helps you!
solve by completing the square! (will give brainliest for work!!!)
x ^ 2 - 2x = - 26
Answer:
Step-by-step explanation:
x²-2x=-26
add both sides (-2/2)² or 1
x²-2x+1=-26+1
x²-2x+1=-25
(x-1)²=25×-1
(x-1)²=5²×i²=(5i)²
x-1=±5i
x=1±5i
The total cost for one t the total cost for a dozen donuts includes the cost to make the donuts and the cost of the box. Create expression to model the cost for one dozen donuts where T represents the total surface area of the box
The expression that represents the total cost of the donuts is: c + d
How to determine the total expression?To determine the expression that represents the total cost, the following parameters are needed
The cost of the donut boxThe cost of the donut, itselfLet c represents the cost of the donut box, and d represents the cost of the donut, itself
Hence, the expression that represents the total cost is:
c + d
Read more about algebraic expressions at:
https://brainly.com/question/4344214
Find the area of the figure.
(20 pts)
Answer:
d. 122 units^2
Step-by-step explanation:
Can somebody help me?
Answer:
C) v≤-5
Step-by-step explanation:
[tex]4v\leq -20[/tex]
Divide each side by 4,
[tex]v\leq -5[/tex]
HELP WILL GIVE BRANLIEST!
Answer:
512
Step-by-step explanation:
To find the volume of a rectangular prism you multiply the length × width × height
= 8 × 8 ×8
= 512
Two tracking stations 525 m. apart measure angles of elevation of a weather balloon to be 73.5 degree and 54.2 degree. How high is the balloon at the time of the measurement? Round to the nearest meter.(show your work)
9514 1404 393
Answer:
516 m or 1235 m
Step-by-step explanation:
The height of the balloon depends on the geometry of the problem. Assuming the stations are in line with each other and the balloon, there are a couple of possible configurations that satisfy the problem description. They are shown in the attachment.
If the balloon is between the stations, the height is 516 m.
If the balloon is not between the stations, the height is 1235 m.
_____
A graphing program solves the problem nicely. If you want to solve it algebraically, You can write equations for the horizontal distance from each station to the balloon.
d1 = h/tan(54.2°)
d2 = h/tan(73.5°)
In one of the possible geometries, ...
d1 + d2 = 525
h(1/tan(54.2°) +1/tan(73.5°)) = 525
h = 525tan(54.2°)tan(73.5°)/(tan(54.2°) +tan(73.5°)) ≈ 516.0 . . . meters
In the other possible geometry, ...
d1 -d2 = 525
h(1/tan(54.2°) -1/tan(73.5°)) = 525
h = 525tan(54.2°)tan(73.5°)/(tan(73.5°) -tan(54.2°)) ≈ 1235.3 . . . meters
The balloon could be 516 or 1235 meters high.
Size of each of mr sirac's classes
Answer:
You didn't add any images maybe it was a mistake?
Step-by-step explanation:
3 Terrence uses pieces of wood that are 10 inches long to
make whistles. He has a piece of wood that is 122 feet
long. How many whistles can he make?
Answer:
146 whistles
Step-by-step explanation:
First, convert 122 feet to inches, by multiplying it by 12
122(12)
= 1464
Divide this by 10 to find how many whistles he can make
1464/10
= 146.4
Since we can only have a whole number of whistles, we have to round down to 146.
So, he can make 146 whistles
5. Find the surface area of the prism.
(1 point)
5 m
6 m
13 m
Not drawn to scale.
048 m2
O 346 m2
0780 m2
O 195 m2
Answer:
[tex]Area = 346m^2[/tex]
Step-by-step explanation:
Given
[tex]Length = 5m\\Width = 6m\\Height = 13m[/tex]
Required
Determine the surface area
This is calculated as:
[tex]Area = 2 * (Length * Width + Length * Height + Width * Height)[/tex]
So, we have:
[tex]Area = 2 * (5m * 6m + 5m * 13m + 6m * 13m)[/tex]
[tex]Area = 2 * (30m^2 + 65m^2 + 78m^2)[/tex]
[tex]Area = 2 * (173m^2)[/tex]
[tex]Area = 346m^2[/tex]
Please help me solve this problem
Answer:
62 + 64 + 55 + s = 242
61 students will ride Bus #4.
Step-by-step explanation:
The equation I will use here is 62 + 64 + 55 + s = 242
62 + 64 + 55 + s = 242 {Going from left to right, subtract 62, 64, & 55 from 242}
64 + 55 + s = 180 {242 - 62 = 180}
55 + s = 116 {180 - 64 = 116}
s = 61 {116 - 55 = 61}
61 students will ride Bus #4.
The grade point average of 4 randomly selected college students is recorded at the end of the fall and spring semesters of their senior year, as follows: Student 1 2 3 4 Fall 2.6 3.0 1.5 1.4 Spring 1.7 2.2 1.4 0.90 Construct a 95% confidence interval for the mean difference in GPA
Answer:
(-0.607 ; 1.757)
Step-by-step explanation:
Student: __ 1 ___ 2 ___ 3 ___ 4
Fall _____2.6__ 3.0__ 1.5 __1.4
Spring___ 1.7__ 2.2 __1.4 __0.90
Using calculator :
Fall:
Xbar1 = 2.125
Sample size, n1 = 4
Standard deviation, s1 = 0.8
Spring :
Xbar2 = 1.55
Sample size, n2 = 4
Standard deviation, s2 = 0.54
Confidence interval :
(xbar1 - xbar2) ± Tcritical * Sp* √1/n1 + 1/n2
Sp = √[(df1*s1² + df2*s2²) ÷ (n1 + n2 - 2)]
df = n - 1
(xbar1 - xbar2) = 2.125 -1.55 = 0.575
Hence,
Sp = √(((3*0.8^2) + (3*0.54^2)) / 6)
Sp= √2.7948 ÷ 6
Sp = √0.4658
Sp= 0.682
Tcritical at 95%, df = 4 = 2.45
Error margin = 2.45 * 0.682 * √1/4 + 1/4 = 1.182
Confidence Interval:
Lower boundary = 0.575 -1.182 = -0.607
Upper boundary = 0.575 + 1.182 = 1.757
(-0.607 ; 1.757)
Two angles are complementary.
If one angle measures 45
degrees, then what is the
measure of the other angle? *
Answer:
45
Step-by-step explanation:
Which of the following statements is true for the quadratic equation x2 – 16x + 64 = 0?
Answer:
Please provide the statements.
Step-by-step explanation:
Answer:
the equation has one anser
Step-by-step explanation:
Please answer this for 15 points :) <333
Answer:
A.
Elena can run 3 miles per hour.
Step-by-step explanation:
Given that:
a circular running track = 1/5 mile
On this track, Elena runs completing each of the laps in 1/15 of an hour
We are to find Elena running speed.
It implies that the distance of Elena = [tex]\dfrac{1}{5}[/tex]
Time to run each lap = [tex]\dfrac{1}{15} \ of \ an \ hour[/tex]
Speed is the amount of distance covered in a specified period of time.
Recall that the formula for calculating speed is:
[tex]Speed = \dfrac{distance}{time}[/tex]
[tex]Speed = \dfrac{\dfrac{1}{5}}{\dfrac{1}{15}}[/tex]
[tex]Speed ={\dfrac{1}{5}\times \dfrac{15}{1}[/tex]
Speed = 3miles / hour
As such, Elena can run 3 miles each hour.
Find the measure of angle x 142
Answer:
x= 142°
I hope it's helps you
Answer:
x = 142°
(x and 142° are vertically opposite angles.)
According to a health statistics center, the mean weight of a 20-to-29-year-old female is 156.5 pounds, with a standard deviation of 51.2 pounds. The mean weight of a 20-to-29-year-old male is 183.4 pounds, with a standard deviation of 40.0 pounds. Who is relatively heavier: a 20-to-29-year-old female who weighs 160 pounds or a 20-to-29-year-old male who weighs 185 pounds
mind fact sub happy wala birthday quiz frist video
Sarah uses a recipe to make 8 gallons of her favorite mixed-berry juice. The containers she plans to use to
store the juice have a capacity of 1 pint.
How many containers will Sarah need?
Sarah will need
containers
if 4200 out of 5600 person's voted in an election the percentage which did not vote was
Answer:
25%
Step-by-step explanation:
If the total number of people is 5600, then to find the number of people that did not vote you subtract 4200 from 5600.
5600-4200=1400
Then you can set up the number of people who didnt vote as equal to a percentage over 100
1400/5600=x/100
140000/5600=x
25=x
Suppose that each observation in a random sample of 100 fatal bicycle accidents in 2015 was classified according to the day of the week on which the accident occurred. Data consistent with information on the Insurance Institute for Highway Safety are given in the following table.
Day of the Week Frequency
Sunday 16
Monday 12
Tuesday 12
Wednesday 13
Thursday 14
Friday 15
Saturday 18
a. Based on these data, is it reasonable to conclude that the proportion of fatal bicycle accidents in 2015 was not the same for all days of the week? Use a significance level of 0.05.
b. Write interpretation
Answer:
The calculated χ² = 0.57 does not fall in the critical region χ² ≥ 12.59 so we fail to reject the null hypothesis and conclude the proportion of fatal bicycle accidents in 2015 was the same for all days of the week.
Step-by-step explanation:
1) We set up our null and alternative hypothesis as
H0: proportion of fatal bicycle accidents in 2015 was the same for all days of the week
against the claim
Ha: proportion of fatal bicycle accidents in 2015 was not the same for all days of the week
2) the significance level alpha is set at 0.05
3) the test statistic under H0 is
χ²= ∑ (ni - npi)²/ npi
which has an approximate chi square distribution with ( n-1)=7-1= 6 d.f
4) The critical region is χ² ≥ χ² (0.05)6 = 12.59
5) Calculations:
χ²= ∑ (16- 14.28)²/14.28 + (12- 14.28)²/14.28 + (12- 14.28)²/14.28 + (13- 14.28)²/14.28 + (14- 14.28)²/14.28 + (15- 14.28)²/14.28 + (18- 14.28)²/14.28
χ²= 1/14.28 [ 2.938+ 5.1984 +5.1984+1.6384+0.0784 +1.6384+13.84]
χ²= 1/14.28[8.1364]
χ²= 0.569= 0.57
6) Conclusion:
The calculated χ² = 0.57 does not fall in the critical region χ² ≥ 12.59 so we fail to reject the null hypothesis and conclude the proportion of fatal bicycle accidents in 2015 was the same for all days of the week.
b. It is reasonable to conclude that the proportion of fatal bicycle accidents in 2015 was the same for all days of the week
Leo is saving money to buy a snowboard. In March, he saved
$200. In April, he saved 35% more than what he saved in
March. How much did he save in April?
Answer:
$270
Step-by-step explanation:
35%= 0.35
200*0.35 =70
He saves $70 more.
Altogether saves $270
A Business Has 384 cases of water. There Are 42 bottles of water does the business have
Answer:
Step-by-step explanation:
-2 + 12/25 enter the answer as an exact decimal
Answer:
-1.52
Step-by-step explanation:
-2+0.48=-1.52
What is the volume of this rectangular prism 2/3cm 5cm 6cm?
Please help me i dont understand
Answer:
It is linear. It is linear because it is a strait line which means that it is a function. A not linear line would look like a noodle.
there are 50 pupils in a class out of this 1/10 speak french only and 4/5 of the remainder speak both french and english. if the rest speak to english only, find the number of students who speaks both english and french?
English only?
Answer:
English and French:40 and English:10
Step-by-step explanation:
English and French:4÷5×50
=40
English:1÷10×50
=10
2x - 5 < 33 what are all the values to this inequality
Answer:
x < 19
Step-by-step explanation:
Given that,
An inequality 2x - 5 < 33.
LHS of the inequality is 2x - 5
RHS of the inequality is 33
LHS < RHS
i.e.
2x - 5 < 33
Add 5 to both sides of the inequality
2x - 5 +5 < 33+5
2x < 38
Divide both sides by 2.
x < 19
So, the value of x is less than 19.
explain it how a 9th grader would
Answer:
a) The golf ball reaches a height of 64 feet.
b) The golf ball will take 2 seconds to reach maximum height.
c) The golf ball will take 4 seconds to land after being hit.
d) The golf ball will be 48 feet above ground 1 and 3 seconds after being hit.
Step-by-step explanation:
a) The parabolic motion of the golf ball is described by a second order polynomial, that is, the equation of the parabola. To determine the maximum height of the golf ball, we need to transform the equation of the parabola given into vertex form:
[tex]h = -16\cdot (t^{2}-4\cdot t)[/tex]
[tex]h - 64 = -16\cdot (t^{2}-4\cdot t + 4)[/tex]
[tex]h - 64 = -16\cdot (t-2)^{2}[/tex]
From this form we can obtain relevant information of the maximum height of the golf ball, contained in the left side of the equation. On this approach, we conclude that the golf ball reaches a height of 64 feet.
b) The time taken by the golf ball is contained in the right side of the formula. That is, the golf ball will take 2 seconds to reach maximum height.
c) In this case, we need to factor the polynomial to find right times, that is:
[tex]h = 64\cdot t - 16\cdot t^{2}[/tex]
[tex]h = 16\cdot t \cdot (4 - t)[/tex]
The time taken by the golf ball to land is contained in the second binomial. In a nutshell, the golf ball will take 4 seconds to land after being hit.
d) If we know that [tex]h = 48[/tex], the time taken by the golf ball to be 48 feet above the ground is:
[tex]64\cdot t - 16\cdot t^{2} = 48[/tex]
[tex]16\cdot t^{2}-64\cdot t +48 = 0[/tex]
By Quadratic Formula, we have the following roots:
[tex]t_{1} = 3[/tex], [tex]t_{1} = 1[/tex]
The golf ball will be 48 feet above ground 1 and 3 seconds after being hit.