Answer:
3.4 seconds
Step-by-step explanation:
Given function:
[tex]h(t)=-4.9t^2+2.45t+48.314[/tex]
where
h = height of the ball (in meters)t = time (in seconds)The ball will strike the ground when its height is zero.
Therefore, to calculate when the ball strikes the ground, substitute h(t) = 0 and solve for t using the quadratic formula.
[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}[/tex]
Therefore:
a = -4.9b = 2.45c = 48.314Substitute these values into the quadratic formula:
[tex]\implies t=\dfrac{-2.45 \pm \sqrt{(2.45)^2-4(-4.9)(48.314)}}{2(-4.9)}[/tex]
[tex]\implies t=\dfrac{-2.45 \pm \sqrt{6.0025+946.9544}}{-9.8}[/tex]
[tex]\implies t=\dfrac{-2.45 \pm \sqrt{952.9569}}{-9.8}[/tex]
[tex]\implies t=\dfrac{-2.45 \pm 30.87}{-9.8}[/tex]
[tex]\implies t=\dfrac{-2.45 + 30.87}{-9.8}=-2.9[/tex]
[tex]\implies t=\dfrac{-2.45 -30.87}{-9.8}=3.4[/tex]
As time cannot be negative, t = 3.4 s only.
Therefore, the ball strikes the ground 3.4 seconds after it is launched.
A square photograph is printed on a larger rectangular sheet of paper leaving a border around the
photograph of 2 centimeters on the top and 3 centimeters on each of the remaining sides. The sheet of paper
has an area of 72 square centimeters. If x is the length of a side of the photograph measured in centimeters,
which of the following equations could be used to find x ?
The area of a shape is the amount of space, the shape can occupy. The equation to calculate the value of x is: [tex](e)\ x^2 + 11x -42= 0[/tex]
The space on the border is given as:
[tex]Top = 2[/tex]
[tex]Others = 3[/tex]
So, the dimension of the sheet of paper is:
[tex]Length = x + 2 + 3[/tex]
[tex]Length = x + 5[/tex]
[tex]Width = x + 3 + 3[/tex]
[tex]Width = x + 6[/tex]
The area of the sheet is then calculated as follows:
[tex]Area= Length \times Width[/tex]
[tex]Area= (x + 5) \times (x + 6)[/tex]
Open brackets
[tex]Area= x^2 + 5x + 6x + 30[/tex]
[tex]Area= x^2 + 11x + 30[/tex]
From the question, we understand that the area of the sheet is [tex]72cm^2[/tex]
So, the equation becomes
[tex]x^2 + 11x + 30 = 72[/tex]
Subtract 72 from both sides
[tex]x^2 + 11x + 30 -72= 0[/tex]
[tex]x^2 + 11x -42= 0[/tex]
Hence,
[tex](e)\ x^2 + 11x -42= 0[/tex] can be used to calculate the value of x
Read more about areas at:
https://brainly.com/question/16418397
Help?
Describe how to translate the graph of y= x to obtain the graph of y = x – 15.
Answer:
Shift down 15 units
Step-by-step explanation:
the number on the right is the one that determines where the line intersects through the y axis
Multiply: (–4 + i)(2 – 3i)
a. –5 – 10i
b. –8 + 11i
c. –5 + 14i
d. –11 + 14i
The result of the product of the given complex numbers as required to be determined is; Choice C; -5 + 14i.
What is the product of the given complex numbers?It follows from the task content that the result of the product of the given complex numbers is to be determined.
On this note, since the required product to be evaluated is; (–4 + i) (2 – 3i).
We can therefore multiply as follows;
-8 + 12i + 2i - 3i².
However, it is noteworthy to know that; i² = -1.
Hence, we have that;
-8 + 14i + 3
= -5 + 14i
On this note, it follows that the result of the product of complex numbers as required is; -5 + 14i.
Read more on product of complex numbers;
https://brainly.com/question/29278325
#SPJ1
The Science Club went on a two-day field trip. On the first day, the members paid $60 for transportation plus $15 per ticket to the planetarium. On the second day, they paid $95 for transportation plus $12 per ticket to the geology museum.
Write an expression to represent the total cost for two days for the ₙ members of the club.
Answer: Let n be the number of members in the Science Club.
On the first day, the total cost for transportation plus the cost of tickets is 60 + (15n) dollars.
On the second day, the total cost for transportation plus the cost of tickets is 95 + (12n) dollars.
So, the total cost for both days is (60 + 15n) + (95 + 12n) = 155 + 27n dollars.
The expression to represent the total cost for two days for the n members of the club is 155 + 27n dollars.
This equation represents the total cost for the transportation, planetarium and geology museum for 2 days for the n members in the club.
It should be noted that this is the monetary representation and it might vary depending on other factors, such as group discounts.
Step-by-step explanation:
Answer:
(n x 27)+155
Step-by-step explanation:
15 +12 = 27
Each member pays $27 for the tickets so we multiply it by the number of members.
95 + 60 = 155
The members pay $155 in total for transportation.
Complete the equation describing how X and Y are related, only answer if you’re sure. Need full equation, not just the box. Will give Brainly.
Answer:
? = -1/2 dark gray box = - 1
y = -1/2 x - 1 or
y = -0.5x - 1
Step-by-step explanation:
The place to start is at 0.
When x = 0 then y = - 1
That means that the second box (the dark gray one) is - 1
So far what you know about the equation is
y = ?x - 1
We need to check two more points.
x = 4
y = - 3
- 3 = ? 4 - 1 Add 1 to both sides
-3 +1 = ?4 - 1 + 1 Combine The -1 and + 1 Cancel
-2 = ?4 Divide by 4
-2/4 = ?
? = -1/2 or - 0.5
Now we need 1 more point to check the result
Let x = 2. Do we get - 2 for y
y = -1/2 * 2 - 1
y = -1 - 1
y = - 2 just as it should
In the following problems the values of sin(θ)and cos(θ)are given. Determine the value of tan(θ).
a. sin(θ)=0.1 and cos(θ)=0.995
tan(θ)=
b. sin(θ)=−0.158 and cos(θ)=−0.987
tan(θ)=
c. sin(θ)=−0.631and cos(θ)=0.776
tan(θ)=
Answer:
a) ≈ 0.1
b) ≈ 0.2
c) ≈ 0.9
Step-by-step explanation:
GIVEN :-
Values of sinθ & cosθTO FIND :-
Value of tanθFACTS TO KNOW BEFORE SOLVING :-
[tex]\tan \theta = \frac{\sin \theta}{\cos \theta}[/tex]SOLUTION :-
a) [tex]\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{0.1}{0.995}[/tex] ≈ 0.1
b) [tex]\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{-0.158}{-0.987} = 0.16 (appx)[/tex] ≈ 0.2
c) [tex]\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{0.631}{0.776} = 0.81 (appx)[/tex] ≈ 0.9
Factorise 2(x-y)-a(y-x)
Answer:
( a + 2 ) ( x - y )
Step-by-step explanation:
2 ( x - y ) - a ( y - x )
= 2 ( x - y ) + a ( x - y )
= ( 2 + a ) ( x - y )
= ( a + 2 ) ( x - y )
Hence factorised.
In this figure please see attached
Answer:
Step-by-step explanation:
Formula
t = 1.06 * p
Givens
p = 8.5
Solution
t = 1.06 * 8.5
t = 9.01
I just need help with question A
Suppose your cousin missed class and asks you, “Why do we plug in 0 for x to find y-intercepts and 0 for y to find x-intercepts? That doesn’t make sense to me.” Explain to your cousin WHY this process works. Use the line
5x+4y=14 as an example.
A) A description in words why this works
The reason why the cousin's procedure for getting the x and y intercepts work is because they represent the definition of those points on a graph.
How to find the x and y intercepts?The x-intercept of a graph or function simply refers to the point at which the graph crosses the graph crosses the x-axis or the point at which y = 0. In a similar manner, the y-intercept simply refers to the point at which the graph crosses the y-axis or simply the point at which x = 0.
Now, we are given the equation of the line as;
5x + 4y = 14
The general form of equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Rewriting the equation of the line in slope intercept form is;
y = -⁵/₄x + ⁷/₂
Now, the reason why we plug in 0 for x to get the y-intercept is because when x = 0, that is only where we can get the y-intercept as the corresponding value of x will be traced to 0.
Similarly, the reason why we plug in 0 for y to get the x-intercept is because when y = 0, that is only where we can get the x-intercept as the corresponding value of y will be traced to 0.
Read more about x and y intercepts at; https://brainly.com/question/24363347
#SPJ1
Peter works in the Spring Roll restaurant. He earns $15.50 per hour plus tips of 15% of food sales. If Peter works 35 hours this week and has $4000 of food sales, how much does he earn in total?
Base salary =
Tips =
Total earnings =
If you cannot see my apologies, but you can zoom in!
DO NOT ANSWER IF YOU DO NOT KNOW THE ANSWER!! Whoever answers correctly will get Brainliest! :)
Answer:
C
Step-by-step explanation:
The sum of the angles is 90
2x + x = 90
3x = 90
x = 30
the angle ABC is 2x, so it means that is the double of x, so it is 60 degrees
Mary can make a quilt in 3 days and Eva can make
a quilt in 5 days. In how many days can they make
quilt working together?
Answer: in explanation
Step-by-step explanation
Sandi can perform 1/9 of the task in a day
Eva can perform 1/5 of the task in a day
Working together, they can perform
1/9 + 1/5 of the task per day
= 5/45 + 9/45 = 14/45 of the task in a day
or 45/14 days in the task = 3.2 days
So
It would take about 3.2 days to complete the task working togethe
16^x^2
= 8⁰
I’ll put a picture of it so you can better understand it. Also I’ll give you 30 points, so one of you better answer by 10:00 tomorrow.
Answer:
x=0
Step-by-step explanation:
[tex]16^{x^2}=8^0\\\\16^{x^2}=1\\\\x^2\ln(16)=0\\\\x^2=0\\\\x=0[/tex]
If the dimensions of the following cylinder are doubled, what factor will the surface area change by? 8 in 0.5 ft answers 2 8 4 6
Question: If the dimensions of the following cylinder are doubled, what factor will the surface area change by?
8
6
4
2
Answer: i think it is 8 but i will update it if not i am on the test
If the dimensions of the cylinder are doubled, then by 4 factor the surface area changed
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface.
The radius of cylinder is r=8 inches
Height is 0.5 feet.
Surface area of cylinder=2πr(r+h)
We know that 0.5feet=6 inches
Suface area of original cylinder=2πr(r+h)
=2×π×8(8+6)
=224π
Now the dimensions are doubled ,so r=16 inches , h=12 inches
Suface area of changed cylinder=2πr(r+h)
=2π×16(16+12)
=32π×(28)
=896π
=4(224π)
Hence by 4 factor the surface area is changed.
To learn more on Three dimensional figure click:
https://brainly.com/question/2400003
#SPJ2
Help answer this pls if really appreciate it!! Also if you could explain a little I’d appreciate it extra since I’m a little lost. Thank you!!!
According to the question the angle between right angle triangle hence the M∠1 = [tex]90^{0}[/tex] .
What does a triangle's right angle look like?90 degrees or a straight angle is always one angle. The hypotenuse is the side that has an angle of 90° on it. Always, the hypotenuse is the longest side. The remaining two inner angles add up to a total of 90°.
Which three angles make up a right triangle?Right triangles are triangles with one of the internal angles at a right angle of 90 degrees. Since a triangle's three interior angles sum up to 180 degrees, a right triangle's three interior angles must always add up to 90 degrees since one of them is always 90 degrees (they are complementary).
To know more about right triangle visit:-
https://brainly.com/question/29285631
#SPJ1
How do you write 0.0912 in scientific notation?
Therefore , the solution of the problem of expression comes out to be
9.12 x 10 ^-2.
How does one select expression?An algebraic expression must be checked via replacing each variable with a number and performing arithmetic operations. In the example above, the answer variable is comparable to 6, since 6 + 6 equal 12. If we know the values of the variables, we can replace them with those values and evaluate the expression.
Here,
Given : 0.0912 in scientific notation
=> 9.12 /100
By using scientific notation
=> 9.12 × 10^-2
=> 9.12 x 10 ^-2
So, we get 9.12 x 10 ^-2 as the scientific notation for the given expression
Therefore , the solution of the problem of expression comes out to be
9.12 x 10 ^-2.
To know more about expressions visit :-
brainly.com/question/14083225
#SPJ1
The value of
Arc sin(1/2) + Arc tan(1) is
Answer:
75°Step-by-step explanation:
We know that:
sin 30° = 1/2, therefore arcsin (1/2) = 30°tan 45° = 1, therefore arctan (1) = 45°So the value of the expression is:
arcsin (1/2) + arctan (1) = 30° + 45° = 75°Answer:
75°
Step-by-step explanation:
Recall the common trigonometric angles:
[tex]\sin 30^{\circ}=\dfrac{1}{2}[/tex]
[tex]\tan 45^{\circ}=1[/tex]
Arcsin is the inverse of sin.
Arctan is the inverse of tan.
[tex]\implies \arcsin \left(\dfrac{1}{2}\right)=30^{\circ}[/tex]
[tex]\implies \arctan (1) = 45^{\circ}[/tex]
Therefore:
[tex]\implies \arcsin \left(\dfrac{1}{2}\right)+\arctan (1) = 30^{\circ}+ 45^{\circ}=75^{\circ}[/tex]
Please help me, I need help asap !! I can’t figure it out
What angle would it be?
Answer:
A cute
Step-by-step explanation:
Given that the polynomial x² - 10x + 14 leaves the same remainder when divided by x + 2b orx + 2c where 3b - 2c = 0 and b # c . Find the values of b and c.
Step-by-step explanation:
please refer to the 3 pages of sketch for details
Read the scenarios and decide which type of interaction (absorption or transmission) took place between the wave
and the object.
People are able to hear footsteps because the sound made by a foot hitting the floor travels through the air to reach
their ears.
When light from the sun hits the sidewalk, the sidewalk becomes warmer.
Answer:
transmission absorption
Step-by-step explanation:
This is because the sound of the foot striking the floor is being transmitted through the air. The sun's light is absorbed when it strikes the sidewalk.
What is absorption and transmission?
Absorption is the process or action by which one thing absorbs or is absorbed by another.
The act of sending something, such as a cold or a message, or the component of a machine that transfers power from the engine to the moving parts is known as transmission.
Which process is represented by the given statements?Because of the air pressure, people can hear when their foot strikes the ground. In a similar manner, when sunlight strikes a sidewalk, it warms up as a result of absorbing the heat.
Therefore, the first statement is transmission and second statement is absorption.
Learn more: https://brainly.com/question/13901349
#SPJ2
Find the inverse of the function.
y = x + 2
Write your answer in the form ax + b. Simplify any fractions.
y =
Given:
The function is:
[tex]y=x+2[/tex]
To find:
The inverse of the given function.
[tex]y=x+2[/tex]
Solution:
We have,
[tex]y=x+2[/tex]
Step 1: Interchange x and y.
[tex]x=y+2[/tex]
Step 2: Solve to y.
[tex]x-2=y[/tex]
[tex]y=x-2[/tex]
Therefore, the inverse of the given function is [tex]y=x-2[/tex].
Marlowe earned $5,000 over the summer.
• He spent $800 of his earnings.
He invested the remainder into an account that pays 3.5% interest compounded annually.
.
Which equation represents the value of the account, V, after x years?
A. V = 4,200(1.35)*
OB V = 4,200(1.035)*
OC V = 5,000(1.35)
.
D. V = 5,000(1.035)*
Answer:
The answer is D
Step-by-step explanation:
V= 5,000(1.035)*
let there be 800 people at school. prove that 3 of them do share a birthday. how can we prove it according to the pigeonhole principle?
Can someone pls tell me how to do this?
Simplify (5y)³
Answer: 125y³
To rise a product to a power, rise each factor to that power:
(5y)³ = 5³y³ = 125y³
A biologist tags ducks living at a pond for her research. She uses 14 blue tags, 19 red tags, 27 white tags, and 6 yellow tags on individual ducks before releasing them back into the wild. When the biologist returns to the pond to continue the study, she is more likely to find a duck with a blue tag than a duck with a ...
A red tag
B white tag
C yellow tag
D yellow or red tag
NEED HELP ASAP DUE TMR
1. The length of the altitude is 15 units.
2. The perimeter of trapezoid ABCD is 132 units.
Perimeter of a trapezoid.An altitude is the vertical height of a given object from the sea level. This is majorly a height reached by an object to the sea level as a reference.
The perimeter of a trapezoid is the sum of all its sides.
From the question;
1. To determine AE,
DE = (DG - EF)/ 2
= (22 - 6)/ 2 (since AB = EF = 6)
= 8
DE = 8 units
The altitude AE can be determined by applying the Pythagorean theorem to triangle ADE. So that;
/hyp/^2 = /opp/^2 + /adj/^2
AD^2 = DE^" + AE^2
17^2 = 8^2 + AE^2
289 = 64 + AE^2
AE^2 = 225
AE = 15
Thus the length of the altitude is 15 units.
2. To determine the perimeter of the trapezoid, we have;
AE = (AD - EF)/ 2
= (58 - 16)/ 2 (since BC = EF = 16)
= 21
AE = 21 units
So that from triangle ABE, applying the Pythagorean theorem to determine the value of AB, we have;
/hyp/^2 = /opp/^2 + /adj/^2
AB^2 = BE^2 + AE^2
= 20^2 + 21^2
AB = 841^1/2
AB = 29
Perimeter of the trapezoid = 29 + 16 + 29 + 58
= 132 units
Thus, the perimeter of the trapezoid is 132 units.
Learn more about the perimeter of a trapezoid at https://brainly.com/question/25967620
#SPJ1
Which integer in the set has the greatest value (7, -7, -3, 3)?
A. -7
B. -3
C. 3
D. 7
Answer:
-3
Step-by-step explanation:
i hope this helps
is 9.307 greater than 9.37
Answer:
No because 9.307 is less than due the facts that the seven in 9.307 is in the thousandth while the seven in 9.37 is in the hundredths
The perimeter of a rectangular field is 74 yards. The length of the field is 27 yards. What is the width in yard of the field
Answer:
width = 10 yds
Step-by-step explanation:
perimeter = 2L + 2W
74 = 2(27) + 2W
74 = 54 + 2W
subtract 54 from both sides of the equation:
2W = 20
divide both sides by 2:
W = 10
The width of the yard whose length is 27 yards and perimeter is 74 yards is evaluated to be 10 yards
How to find the perimeter of a rectangle?For a rectangle with length and width L and W units, we get:
Perimeter of the rectangle = [tex]2(L + W) \: \rm units[/tex]
For this case, let we assume that:
The width of the considered rectangular field = W yards
Then, as we're provided that:
Perimeter of the rectangular field = 74 yardsLength of the rectangular field = 27 yards.Putting these in the formula for perimeter of a rectangle, we get;
[tex]Perimeter = 2( L + W)\\74 = 2(27 + W)\\\\\text{Dividing both the sides by 2}\\\\\dfrac{74}{2} = \dfrac{2(27+W)}{2}\\\\37 = 27 + W\\\\\text{Subtracting 27 from both the sides}\\\\37 - 27 = W\\W = 10 \: \rm yards[/tex]
Thus, the width of the yard whose length is 27 yards and perimeter is 74 yards is evaluated to be 10 yards
Learn more about perimeter of a rectangle here:
https://brainly.com/question/14073514