A soccer player is 30 feet from the goal line. He shoots the ball directly at the goal.
The goal is 8 feet high. What is the maximum angle of elevation at which the player
can shoot the ball and still score a goal?
Answers
Answer:
14.93°
Step-by-step explanation:
Using trigonometry :
From the diagram attached :
Angle of elevation = x
To obtain the value of x
Tan x = opposite / Adjacent
Tan x = 8 / 30
Tan x = 0.266666
x = tan^-1(0.26666)
x = 14.93°
Therefore, the angle of elevation is 14.93°
Related Questions
Omar is painting a 24-square-foot wall. The wall is divided into squares that each measure 14 square foot. How many squares is the wall divided into? Enter your answer in the box.
Answers
Complete question :
Omar is painting a 24-square-foot wall. The wall is divided into squares that each measure 1/4 square foot. How many squares is the wall divided into?
Answer:
96
Step-by-step explanation:
Given that:
Total area of wall = 24 ft²
Area of each division =. 1/4 ft²
Number of division = x
The number of divisions * area of each division = total area of wall
x * 1/4ft² = 24ft²
Divide both sides by 1/4 ft²
x = 24ft² ÷ 1/4 ft²
x = 24 * 4 /1
x = 96
Hence, wall is divided into 96 squares
A rectangle has side measurements of 12 units and 8 units.
What is the approximate measure of a diagonal that cuts through the rectangle?
Round to the nearest tenth.
Answers
d=√8^2+12^2
d=√64+144
d≈14.4
The approximate measure of a diagonal that cuts through the rectangle are 14.4.
What is a diagonal?A diagonal in geometry is a line segment that connects two vertices of a polygon or polyhedron that are not on the same edge. Informally, any sloping line is referred to as a diagonal.
Given that a rectangle has side measurements of 12 units and 8 units. The measure of the length of the diagonal will be,
d =√ ( w²+l² )
d =√ ( 8²+12² )
d =√ ( 64 + 144 )
d ≈14.4
Therefore, the approximate measure of a diagonal that cuts through the rectangle is 14.4.
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1
Over the weekend, Cedrick drove 45-miles. He used 2-gallons of gasoline. What is the unit rate for miles per gallon?
Answers
22,5
Step-by-step explanation:
45 :2 = 22,5 mark me plz thanks
if Susan is able to read 3 pages in 5 minutes how many pages would you expect her to read in 20 minutes
Answers
Answer:
I would expect 12 pages...lol
Step-by-step explanation:
find the inverse of y=100-x^2
Answers
Answer:
The inverse is ±sqrt(100-x)
Step-by-step explanation:
To find the inverse, exchange x and y
x = 100 -y^2
Solve for y
Subtract 100 from each side
x - 100 = -y^2
Divide by -1
-x +100 = y^2
Take the square root of each side
±sqrt(100-x) = sqrt(y^2)
±sqrt(100-x) =y
The inverse is ±sqrt(100-x)
If f (x) = x-5 and g(x) = 4x what is the value off [g(4)]?
Answers
Step-by-step explanation:
f[g(4)]
g(x) = 4x
g(4) = 4(4)
= 16
f(x) = x-5
f[g(4)] = f(16) = 16 - 5 = 11
So, f[g(4)] = 11
can u PLEASE stop ignoring me i really do need help): try#7263738 of trying to get help lol
Answers
Answer:
SSS for the top one
SSS for the second one
Step-by-step explanation:
how do I solve use elimination
x+3y=13
5x+6y=38
Answers
Answer:
(4, 3 )
Step-by-step explanation:
Given the 2 equations
x + 3y = 13 → (1)
5x + 6y = 38 → (2)
Multiplying (1) by - 2 and adding to (2) will eliminate the y- term
- 2x - 6y = - 26 → (3)
Add (2) and (3) term by term to eliminate y
3x + 0 = 12
3x = 12 ( divide both sides by 3 )
x = 4
Substitute x = 4 into either of the 2 equations and solve for y
Substituting into (1)
4 + 3y = 13 ( subtract 4 from both sides )
3y = 9 ( divide both sides by 3 )
y = 3
solution is (4, 3 )
Which of the following functions has a rate of change that stays the same? (1 point)
O y = x2 - 5x -14
O y = 19x - 10
O y = 5*
O y = 0.03x² + 11x + 1
Answers
this is the answer y=19x-10
Find the number of three digit natural numbers
which are divisible by 11
Answers
Answer:
121. three digits. 121/11=11
Step-by-step explanation:
Answer:
90.
Step-by-step explanation:
1000 / 11
= 90.9.
1 +tan30÷1-tan30=1+sin60÷1-sin30
can anyone help me in proving this?
Answers
Very quickly: since tan(30°) = 1/√3,
(1 + tan(30°)) / (1 - tan(30°)) = (1 + 1/√3) / (1 - 1/√3)
… = (√3 + 1) / (√3 - 1)
… = (√3 + 1)² / ((√3)² - 1²)
… = ((√3)² + 2√3 + 1²) / (3 - 1)
… = (3 + 2√3 + 1) / 2
… = (4 + 2√3) / 2
… = 2 + √3
On the other side, we have sin(30°) = 1/2 and sin(60°) = √3/2, so
(1 + sin(60°)) / (1 - sin(30°)) = (1 + √3/2) / (1 - 1/2)
… = (1 + √3/2) / (1/2)
… = 2 (1 + √3/2)
… = 2 + √3
and we're done, both sides are equal.
We can also prove this algebraically:
Force the denominator on the left side into a difference of squares:
(1 + tan(30°)) / (1 - tan(30°)) × (1 + tan(30°)) / (1 + tan(30°))
… = (1 + tan(30°))² / (1 - tan²(30°))
Expand the numerator:
… = (1 + 2 tan(30°) + tan²(30°)) / (1 - tan²(30°))
Recall that 1 + tan²(x) = sec²(x) :
… = (sec²(30°) + 2 tan(30°)) / (1 - tan²(30°))
Since sec(x) = 1/cos(x) and tan(x) = sin(x)/cos(x), multiply through every term by cos²(30°) :
… = (sec²(30°) + 2 tan(30°)) / (1 - tan²(30°)) × cos²(30°) / cos²(30°)
… = (1 + 2 sin(30°) cos(30°)) / (cos²(30°) - sin²(30°))
Recall that sin(2x) = 2 sin(x) cos(x) and cos(2x) = cos²(x) - sin²(x) :
… = (1 + sin(2×30°)) / cos(2×30°)
… = (1 + sin(60°)) / cos(60°)
Finally, recall that cos(90° - x) = sin(x), so cos(60°) = sin(30°) = 1/2, and we can write 1/2 = 1 - 1/2, so
… = (1 + sin(60°)) / (1 - sin(30°))
as required.
Carter has 37 coins, all nickels and dimes in his piggy bank. The value of the coins is $3.10. How
many dimes does Carter have?
Answers
pls help.. only one question
Answers
Answer:
sorry in advance!
i think that it is B and E
Step-by-step explanation:
Please answer ASAP no links please and thanks u
Answers
Step-by-step explanation:
the answer is b
Answer:
C. 120 ft^2
Step-by-step explanation:
The area of the triangles= (1/2*3*4)2=12
The area of the larger parallelogram=5*9=45
The area of the bottom rectangle=4*9=36
The area of the vertical rectangle=3*9=27
Totale Surface Area=12+45+36+27=120
Please help me,
11x13 = _ x 13+5 x 13
what is the number that goes in the blank
Answers
Answer:
6
Step-by-step explanation:
11x13=143
5x13 = 65
143 - 65 = 78
78/13= 6
The radius of a circle measures 5 milometers . What is the circumference of the circle? Use 3.14 for pi , and do not round your answer. Be sure to include the correct unit in your answer.
Answers
Answer:
circumference = 31.4 milometers
Step-by-step explanation:
circumference = 5(2)(π)
circumference = 31.4 milometers
Someone please help me
Answers
Answer:
Step-by-step explanation:
cone: attached picture below
composite shape: To calculate the area of a composite shape you must divide the shape into rectangles, triangles or other shapes you can find the area of and then add the areas back together. You may have to calculate missing lengths before finding the area of some of the shapes.
ratio: not sure about that question sorry
last question: i have no idea what it is about because my device won't open the picture sorry
though i have answered 2 question of yours
have a great evening
Answer:
ConeSurface area:
A = πr(r + l) r = √(10² - 8²) = √36 = 6A = 3.14(6)(6 + 10) = 301.44#1A = 25π, C = ?A = πr² ⇒ 25π = πr² ⇒ r² = 25 ⇒ r = 5C = 2πr = 2*3.14*5 = 31.4#2A = 5*7 + (5 - 2)*4 + 1/2*4*(6 - (5 - 2)) = 35 + 12 + 6 = 53#10Scale factor
k = 3/4Area is a function of two dimensions, each has k applied
The ratio of areas is the k² = (3/4)² = 9/16Option C
#6Volume of prism:
V = Bh = 1/2(8*5)*6 = 120Volume of pyramid:
V = 1/3Bh = 1/3(8*5)*9 = 120Option A, same volume
#7Ratio of areas:
20/45 = 4/9Scale factor is:
k² = 4/9k = √4/9k = 2/3In the opening credits of each episode of
the TV show Fawlty Towers, the sign on the
front of the hotel rearranged the letters in
the hotel's name.
a) How many arrangements are there of all
the letters in FAWLTY TOWERS?
b) How many arrangements of these letters
are possible if the A, Y, O, and E must
remain in their original order?
Answers
the vertices of a triangle are formed by the intersections of the following three lines:
y=x
x=8
y=1/4x + 3
graph the triangle and its image after the composition
Answers
help pls lol what is the range of the function
Answers
Answer:
all real number greater than or equal to -3.
Hunter is going to invest in an account paying an interest rate of 1.7% compounded continuously. How much would Hunter need to invest, to the nearest cent, for the value of the account to reach $4,500 in 18 years?
Answers
Answer:
$3333.33 approx
Step-by-step explanation:
Given data
Rate r= 1.7%
Final Amount A=$4500
Time = 18years
Principal P= ????
The expression for the compound interest is given bellow as
A=P(1+r)^t
4500= P(1+0.017)^18
4500= P(1.017)^18
4500= P*1.35
P= 4500/1.35
P= $3333.33
Hence the principal is $3333.33 approx
Answer:3313.74
Step-by-step explanation:
The line plot shows the distances, in miles, run by joggers in a park.
How many runners ran at least 3 miles?
Enter your answer in the box.
runners
Answers
Explanation: You count the number of x’s above the number of miles. So in this case it is 3 so you would count all of the x’s above the 3
I’ll give points but please help me on this and if you don’t know the answer please don’t answer the question thank you
Answers
The volume of the hemisphere is equal to V = 56.5486678 ft3 or 18pi
And the cone volume is
V = 47.1238898 ft3 or 15pi
The total volume will be 103.6725576ft3
Or 33pi ft3
Factorise by grouping: x² - 5x + 2x - 10
Answers
Answer:
[tex]\boxed {\boxed {\sf (x+2)(x-5)}}[/tex]
Step-by-step explanation:
To factor by grouping, first divide the polynomial into 2 groups with parentheses.
[tex]x^2-5x+2x-10[/tex]
[tex](x^2-5x)+ (2x-10)[/tex]
Factor the greatest common factor (GCF) out of both binomials.
For the first binomial, the GCF is x.
[tex]x(x-5) +(2x-10)[/tex]
For the second binomial, the GCF is 2.
[tex]x(x-5)+2(x-5)[/tex]
Factor out the common binomial which is (x-5).
[tex](x+2)(x-5)[/tex]
The factorized form of x²-5x+2x-10 is (x+2)(x-5)
The sum of the angles of any triangle is
Find all the missing angles in the triangles. Write each answer on the line
provided beside the corresponding letter.
Answers
Answer:
A: 40
B: 90
C: 53.5
D: 34
E: 90
F: 52.9
G: 90
H: 59.6
I: 119.1
J: 30.4
K: 90
L: 72
M: 107.3
N: 47.7
O: 36
P:90
Step-by-step explanation: In every triangle the angles will add up to 180. The little square means 90. You can just subtract all the number you already know in the triangle from 180 to find the one you don’t know.
The values of the angle is given along with angle name.
What is Angle Sum Property ?The sum of all angles of a triangle is equal to the angle of a straight line i.e. 180°.
If we have a triangle ABC , then
Sum of angle A , B and angle C will be 180 °.
and the value of the exterior angle is equal to the sum of two interior opposite angle
In the given figure we will apply the angle sum property and the exterior angle property to determine the values .
The values will be
A: 40
B: 90
C: 53.5
D: 34
E: 90
F: 52.9
G: 90
H: 59.6
I: 119.1
J: 30.4
K: 90
L: 72
M: 107.3
N: 47.7
O: 36
P:90 in degree
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A mechanical device makes a clicking sound every 3 seconds. If the device was plugged on for 15 hours, calculate the number of times the device made the clicking sound.
Answers
Why?
15•60=900
(The 60 is because there are 60 mins in an hour).
Hope this helps!!
Alaska's tundra is a wet marsh in the summer—it's hard to walk through and slowed them down. It took 1 week to hike the 45.5 miles over the Brooks Range. What was the average number of miles per day that they traveled?
Answers
Answer: 6.5 miles per day
Step-by-step explanation:
First and foremost, we should note that 7 days = 1 week. Therefore, from the question, we are given the information that it took took 1 week to hike the 45.5 miles over the Brooks Range.
The average number of miles per day that they traveled will then be:
= 45.5 miles / 1 week
= 45.5 miles / 7 days
= 45.5/7
= 6.5 miles per day
multiply on the number line 4x(-3)
Answers
Answer:
-12x
Step-by-step explanation:
4x* -3 = -3* 4 *x= -12x
Mr. and Mrs. Doran have a genetic history such that the probability that a child being born to them with a certain trait is 37%. If they have six children, what is the probability that at most one of their six children will have that trait? Round your answer to the nearest thousandth.
Answers
Answer:
Yes
Step-by-step explanation:
Answer:
Sum: 0.78619≈0.786
Step-by-step explanation:
n=4
r=1, 2, 3, 4
r=1,2,3,4
"At least" counts up.
p=32\%=0.32
p=32%=0.32
q=1-0.32=0.68
q=1−0.32=0.68
The chance a success does NOT occur.
_{n}C_{r}p^rq^{n-r}
The probability that at most one of their six children will have that trait is 0.68
How to determine the probability?From the question, the given parameters are
Number of children, n = 6
Probability of a child with the trait, p = 37%
The required probability that at most one will have that trait is represented as P(x ≤ 1)
This probability is calculated ;
P(x ≤ 1) = P(0) + P(1)
Where
P(x) = ⁿCₓ * pˣ (1 - p)ⁿ⁻ˣ
So, we have
P(x ≤ 1) = ⁷C₀ (37%)⁰ (1 - 37%)⁷⁻⁰ + ⁷C₁ (37%)¹ (1 - 37%)⁷⁻¹
Evaluate;
P(x ≤ 1) = ⁷C₀ * 1 * (63%)⁷ + ⁷C₁ * (37%) * (63%)⁶
So, we have;
P(x ≤ 1) = 1-0.32= 0.68
Hence, the probability is 0.68
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9x - 7i < 3 (3x - 7u)
Answers
Answer:
Step-by-step explanation:
9x - 7i < 3(3x - 7i)
9x - 7i < 9x - 21i
-7i < -21i
14i < 0i < 0