Answers
Answer:
We know that the height equation is given by:
H(t) = -16*t^2 + 108*t + 28
in ft.
First, we want to find the maximum height of the ball.
The first thing we can see is that the leading coefficient of the quadratic equation is negative, this means that the arms of the graph will open downwards, so the vertex of the quadratic equation is the maximum.
We also know that the ball will reach its maximum height when its velocity is zero (this means that the object stops going upwards at this point).
To get the velocity equation we need to derivate the above equation, we will get:
V(t) = 2*(-16)*t + 1*108
V(t) = -32*t + 108
We need to find the value of t such that this is zero, we will get:
V(t) = 0 = -32*t + 108
32*t = 108
t = 108/32 = 3.375
So the ball reaches its maximum height after 3.375 seconds.
Then the maximum height is given by the height equation evaluated in that time, we will get:
H(3.375) = -16*(3.375)^2 + 108*3.375 + 28 = 210.25
Then the maximum height of the ball is 210.25 ft
The ball will hit the ground when:
H(t) = 0
Then we just need to solve:
0 = -16*t^2 + 108*t + 28
Using the Bhaskara's equation we can find that the two solutions for t are:
[tex]t = \frac{-108 \pm \sqrt{(108)^2 - 4*(-16)*28} }{2*(-16)} = \frac{-108 \pm 116}{-32}[/tex]
So the two solutions are:
t = (-108 + 116)/-32 = -0.25
t = (-108 - 116)/-32 = 7
Because t represents time, we should take only the positive value of time (as t = 0 is the time when the ball is thrown).
Then we can conclude that the ball hits the ground after 7 seconds.
Related Questions
What is the value of 21 - 4 × ❒ = 5 ? in the equation below? (Show your work)
Answers
Answer:
4
Step-by-step explanation:
21 - 4 × ❒ = 5
-4x = 5 - 21
-4x = 16 (divide both sides)
x = 4
What is the total distance that two people travel in 2 h if one of them is riding a bike at 20 mi/h and the other is walking at 3 mi/h?
Answers
Answer:
46 miles
Step-by-step explanation:
First, find the distance traveled by the person riding at 20 mph.
Multiply 20 by 2:
20(2)
= 40 miles
Find the distance traveled by the person riding at 3 mph.
Multiply 3 by 2:
3(2)
= 6 miles
Add these distances together:
40 + 6
= 46
So, the total distance is 46 miles
Answer:
46 miles
Step-by-step explanation:
Assuming both travel at a constant rate of miles per hour.
Time allowed: 2 hours.
Biker: 20 miles/hr, or (20 x 2) miles/ (2 x 1) hrs. = 40 miles/ 2 hours
Walker: 3 miles/hr or (3 x 2) miles/(2 x 1) hrs. = 6 miles/2 hours.
You are finding the total distance traveled together, and so add the two miles together:
40 + 6 = 46
46 miles in 2 hours is your answer.
~
Solve 8 = 2x + 4.
Helppppppp
Answers
Answer:
x = -1
Step-by-step explanation:
8 = 2^(x + 4)
Rewriting 8 as 2^3
2^3 = 2^(x + 4)
Since the bases are the same, the exponents must be the same
3 = x+4
Subtract 4 from each side
3-4 =x+4-4
-1 =x
Answer:
This is the answer :
x=–1
Choose (B)
What is the coefficient for the variable d
Answers
Solve x^2 -6x=-5 by completing the square. Show all work for the steps below. (a) For x^2 -6x+c+-5+c, what value of c is used to complete the square? (b) Substitute the value for c in Part 2(a). Then complete the square to rewrite the equation as the square of a binomial. (c) Solve for x
Answers
To complete the square we are going to rewrite the equation to a quadratic equation in the form:
ax² + bx + c
To do this we are going to transpose.
x² - 6x = -5
x² - 6x + 5 = 0
Now we are going to rewrite the new equation in the form
a(x + h)² + k
Where a = 1
h = 6x
k = 5
1(x² - 6x) + 5 = 0
1(x² - 6x/2 + 3²) + 5 = 0, to find h, divide it by 2 then square the quotient and add it to the equation.
1(x² - 3x + 9) + 5 - 9 = 0, to find k, subtract the square rooted quotient after multiplying it by a.
1(x - 3)²- 4 = 0
Now we solve.
1(x - 3)² - 4 = 0
1(x - 3)² = 4
±√1(x - 3)² = ±√4
(x - 3) = √4 or (x - 3) = -√4
x = 5 or x = 1
If the triangles are similar which are true
Answers
Answer:
b
Step-by-step explanation:
Answer the questions about the following polynomial.
-10x +1
Answers
Answer:
Step-by-step explanation:
Given polynomial is (-10x + 1).
This polynomial has two terms.
Therefore, it's a binomial with two separate terms.
The expression represents a binomial polynomial with two terms. The constant term is 1, the leading term is -10x, and the leading coefficient is (-10).
I’ll give brainliest
Answers
OPTION A
y= 3x+6
This equation satisfies for all the value given in the table.
For (0,6)
y = 3(0)+6 = 6
For (2,12)
y=3(2) +6 = 6+6= 12
And so on.
I need help with this question
Answers
Answer:
56 degrees
Step-by-step explanation:
We know, the sum of the three angles of any triangle is equal to 180 degrees.
63 + 61 = 124
Now, 180 - 124 = 56 degrees
Hope this will help. Please give me brainliest.
What number must you add to complete the square? x^2+26x=23
Answers
Answer:
169
Step-by-step explanation:
x²+26x=23
=> to complete the square, the equation should be : x²+26x + (26/2)² = 23 + (26/2)²
<=> x² +26x + 13² = 23 + 13²
<=> x² +26x +169 = 23 + 169
<=> (x+13)² = 192
so, (x+13)² is the square form , and 169 must be added to complete the square
For 2ab to complete in (a+b)² formula
2ab=26a=1
2b=26b=13b²=169So 169 must be added
Write an equation of the line with a slope of 2/3
and -8
Answers
I assume the -8 was the y intercept?
Keith is looking at a cliff. He determines that the angle of elevation to the top is 70° from where he is at. 70m away from Keith, Alan estimates the angle between the base of the cliff, himself, and Keith to be 29° while Keith estimates the angle between the base of the cliff, himself, and Alan to be 48°. What is the height, h, of the cliff to the nearest tenth of a metre?
1) 78.8m
2) 83.9m
3) 89.0m
4) 95.7m
This question completely baffled me on my homework, I still haven't done it because I don't even know how to approach it (Since it's a 3D problem)
Please help me out
Also, this homework is due in an hour so I'm starting to sweat
Answers
9514 1404 393
Answer:
4) 95.7 m
Step-by-step explanation:
The angle at the cliff base between Alan and Keith is ...
B = 180° -29° -48° = 103°
The law of sines will tell you the distance KB from Keith to the cliff base is
KB/sin(A) = KA/sin(B)
KB = KA×sin(A)/sin(B) = (70 m)sin(29°)/sin(103°) ≈ 34.82935 m
The height of the cliff is found from the tangent relation ...
Tan = Opposite/Adjacent
tan(70°) = height/(34.83 m)
height = (34.83 m)tan(70°) = 95.693 m
The height of the cliff is about 95.7 m.
_____
Additional comment
These problems can usually be resolved into two 2-D problems. Here, we can work out the distance we need from Keith to the cliff by considering only the ground plan of the site. Then we can work out the height of the cliff only considering the vertical plane containing Keith and the base of the cliff.
The attachment shows the ground plan triangle KAB.
Which expression could be used to find the volume of the prism shown below? A rectangular prism with length of 11, height of 5, and width of 8. (11 times 8) times 5 (11 + 8) times 5 (11 times 8) + 5 (11 + 5) times 8 Mark this and retu
Answers
Answer:
(11 x 8) x 5
Step-by-step explanation:
We find volumes of rectangular prims by multiplying the length by the width to get the area of a said prism, and multiplying the area by the height in order to get the volume.
Answer:
A
Step-by-step explanation:
Can y’all help me on question 22?!
Answers
Answer:
245 cubic inches
Step-by-step explanation:
The volume of a rectangular prism is length times width times height.
So in this case we would do, 8 * 2.5 * 12.25 to get 245. So your answer would be 245 cubic inches.
*side note*: 2 1/2 is the same thing as 2.5 and 12 1/4 is the same thing as 12.25
The price of a product is increased by 30% and then again by 10%. How many per cent did the price increase altogether?
Answers
Answer:
40%
Step-by-step explanation:
Because you want to know the total percent the price increased so you add the amounts. 30% plus 10% makes 40%
Evaluate the work below
Answers
Answer:
[tex]3 \sqrt{2} [/tex]
Step-by-step explanation:
Given
[tex] \frac{ \sin(60) \sec(60) \cot(30) }{ \cos( 45) ) } [/tex]
Using the unit circle, we know that
[tex] \sin(60) = \frac{ \sqrt{3} }{2} [/tex]
[tex] \cos(45) = \frac{ \sqrt{2} }{2} [/tex]
We can find sec and cot by using reciprocal identies.
[tex] \sec(x) = \frac{1}{ \cos(x) } [/tex]
[tex] \cos(60) = \frac{1}{2} [/tex]
So
[tex] \sec(60) = 2[/tex]
[tex] cot(x) = \frac{1}{ \tan(x) } [/tex]
[tex] \tan(30) = \frac{1}{ \sqrt{3} } [/tex]
so
[tex] \cot(30) = \sqrt{3} [/tex]
Plug in the values.
[tex] \frac{ \frac{ \sqrt{3} }{2} \times 2 \times \sqrt{3} }{ \frac{ \sqrt{2} }{2} } [/tex]
[tex] \frac{ \frac{ \sqrt{3} }{2} \times \frac{ \sqrt{12} }{1} }{ \frac{ \sqrt{2} }{2} } [/tex]
[tex] \frac{3}{ \frac{ \sqrt{2} }{2} } [/tex]
[tex]3 \sqrt{2} [/tex]
What is the distance of -55 from zero?
Answers
Answer:
55
Step-by-step explanation:
The answer is 55 as distance is a scalar quantity that means quantities that depend on magnitude and not on direction. Therefore we cannot write - 55 as answer.
Whoever answers correct first I will give BRAINLIEST!!
How many fives
are in 100?
Answers
Answer:
20
Step-by-step explanation:
100/5=20
Below are two parallel lines with a third line intersecting them
Answers
Answer:
hey, there is no attached photo. so I don't know how to help
Janet hiked 3/8 mile in 1/4 hour. How fast did she hike, in miles per hour
Answers
Answer: answer is A
A:3/32
B:2/3
C: 1 1/2
D:4
What is the perimeter of the quadrilateral ABCD?
Answers
Given:
The figure of a quadrilateral ABCD.
To find:
The perimeter of the quadrilateral ABCD.
Solution:
In an isosceles triangle, the two sides and base angles are congruent.
In triangle ABD,
[tex]\angle DAB\cong \angle ABD[/tex] [Given]
[tex]\Delta ABD[/tex] is an isosceles triangle [Base angle property]
[tex]AD=BD[/tex] [By definition of isosceles triangles]
[tex]8=BD[/tex] ...(i)
In triangle BCD,
[tex]\angle BCD\cong \angle CDB\cong \angle CBD[/tex] [Given]
All interior angles of the triangle BCD are congruent, so the triangle BCD is an equilateral triangle and all sides of the triangle area equal.
[tex]BC=CD=BD[/tex]
[tex]BC=CD=8[/tex] [Using (i)] ...(ii)
Now, the perimeter of quadrilateral ABCD is:
[tex]Perimeter=AB+BC+CD+AD[/tex]
[tex]Perimeter=11+8+8+8[/tex]
[tex]Perimeter=35[/tex]
Therefore, the perimeter of the quadrilateral ABCD is 35 units.
Help Please!
Please answer the question and please don't type a random thing just to get points.
Answers
Step-by-step explanation:
We need to find a midpoint. A midpoint splits the two end coordinates to meet at a point.
Use midpoint formula
[tex] \frac{ - 2 + 10}{2} = 4[/tex]
[tex] \frac{ - 11 + 1}{2} = - 5[/tex]
So the coordinates will be at
(4,-5)
PLEASE ANSWER FAST
A-1 Equipment Rental Company charges $195 per day to rent a backhoe. The rental cost at A-1 can be represented by the function a(x) 195x, where x is the number of days the backhoe is rented. A competitor charges $150 per day plus an extra $90 fee. The cost at the competitor can be represented by the function c(x) 150x 90, where x is the number of days the backhoe is rented. Describe the transformation from the graph of a to the graph of c.
a. vertical shrink by 10/13 and then a vertical translation 90 units down
b. vertical stretch by 10/13and then a vertical translation 90 units up
c. horizontal stretch by 13/10and then a vertical translation 90 units up
d. vertical shrink by 10/13and then a vertical translation 90 units up
Answers
Answer:
cccccccccccccccccccc
Drag each value to the correct location on the equation. Each value can be used more than once, but not all values will be used.
A yacht is traveling 35° west of south at 15 miles/hour in still water. Find the component form of vector r, which represents the yacht's motion.
Answers
Answer:
(xou)2
Step-by-step explanation:
A yacht is traveling 35° west of south at 15 miles/hour in still water. Find the component form of vector r, which represents the yacht's motion.
5a. A salad bar has five kinds of salad. In how many different ways can you choose two different salads from five?
5b. Which has more different ways :
Choosing two out of five OR
choosing three our of five?
Answers
Answer:
a) 10 salads
b) 5 Choose 2 and 5 Choose 3 result in the same amount
Step-by-step explanation:
a) ₅C₂ = 5! / (5-2)! 2!
= 5! / 3! 2!
= (5 × 4) / 2
= 10 salads
b) ₅C₃ = 5! / (5-3)! 3!
= 5! / 2! 3!
= (5 × 4) / 2
= 10
How can I describe an angle's measure?
Answers
Find the angle of depression
from point A to point C.
?
66°
5 mi
B
Angle of depression = [ ? ]
Answers
Given:
In triangle ABC, [tex]m\angle A=66^\circ, AB=5\text{ mi}[/tex].
To find:
The angle of depression from point A to point C.
Solution:
According to angle sum property, the sum of all interior angles of a triangle is 180 degrees.
In triangle ABC,
[tex]m\angle A+m\angle B+m\angle C=180^\circ[/tex]
[tex]66^\circ+90^\circ+m\angle C=180^\circ[/tex]
[tex]156^\circ+m\angle C=180^\circ[/tex]
[tex]m\angle C=180^\circ-156^\circ[/tex]
[tex]m\angle C=24^\circ[/tex]
We know that if a transversal line intersect the two parallel lines, then alternate interior angles are equal. So, the angle of depression from point A to point C is equal to the measure of angle C in triangle ABC.
Therefore, the angle of depression is 24 degrees.
Thankssssssss smmmmmmm
Answers
9514 1404 393
Answer:
46
Step-by-step explanation:
The length of base CD is twice the length of midsegment FG, so you can write the equation ...
CD = 2×FG
-3x +52 = 2(13 +5x)
52 = 26 +13x . . . . . . . . add 3x, simplify
26 = 13x . . . . . . . . . subtract 26
2 = x . . . . . . . . . . divide by 13
Then the measure of CD is ...
CD = -3x +52 = -3(2) +52 = -6 +52
CD = 46
help please! no links :)
Answers
Answer:
The answer is D-27.00 because you are rounding off to the nearest 100 I hope this helps you
Answer:
C. 26.75
Step-by-step explanation:
26.745 is rounded to 26.75
PLSSSSSSS HELP !!!!! ASAP PLSSSS !!
Answers
Answer:
Step-by-step explanation:
same side interior angles also mean co interior angle
heree,
1.angle 4 and 6 are same side interior angle
2.angle 3 and 5 are also same side interior angle.
Co-interior angles or same side interior angles lie between two lines and on the same side of a transversal. In each diagram the two marked angles are called co-interior angles. If the two lines are parallel, then co-interior angles add to give 180o and so are supplementary.
Step-by-step explanation:
i) Angle 4 and 6
ii) Angle 3 and 5