Answer:
The rock takes 4.18 seconds to hit the ground
Step-by-step explanation:
Function Model
The height of a rock h, after t seconds, can be modeled by the polynomial function:
[tex]h(t)=-4.9t^2+20t+2, t\geq 0[/tex]
When the rock hits the ground, the height is 0, thus we need to find the value of t such as:
[tex]-4.9t^2+20t+2=0[/tex]
A quadratic equation can be expressed as:
[tex]at^2+bt+c=0[/tex]
where a,b, and c are constants.
Solving with the quadratic formula:
[tex]\displaystyle t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
The values for the given equation are:
a=-4.9, b=20, c=2
Applying the formula:
[tex]\displaystyle t=\frac{-20\pm \sqrt{20^2-4(-4.9)(2)}}{2(-4.9)}[/tex]
[tex]\displaystyle t=\frac{-20\pm \sqrt{400+39.2}}{-9.8}[/tex]
[tex]\displaystyle t=\frac{-20\pm 20.957}{-9.8}[/tex]
There are two possible solutions:
[tex]\displaystyle t=\frac{-20- 20.957}{-9.8}=4.18[/tex]
[tex]\displaystyle t=\frac{-20+ 20.957}{-9.8}=-0.1[/tex]
Since t > 0, the only solution is t=4.19 seconds
The rock takes 4.18 seconds to hit the ground
$3,000 is invested in an account paying 4% interest and twice that amount is invested at 6%.
Which of the following expressions represents the amount of interest earned on the money invested at 6%?
a. 2(3,000)
b. 0.06(6,000)
c. 0.06(3,000)
Answer:
B
Step-by-step explanation:
Two uniformly charged, infinite, nonconducting planes are parallel to a yz plane and positioned at x " #50 cm and x " )50 cm. The charge densities on the planes are #50nC/m2 and )25 nC/m2 , respectively. What is the magnitude of the potential difference between the origin and the point on the x axis at x " )80 cm? (Hint: Use Gauss’ law.)
Two uniformly charged, infinite, nonconducting planes are parallel to a yz plane and positioned at x = -50 cm and x = +50 cm. The charge densities on the planes are -50 nC/m² and +25 nC/m², respectively. What is the magnitude of the potential difference between the origin and the point on the x axis at x = +80 cm? (Hint:Use Gauss’ law.)
Answer:
ΔV = 2520 V
Step-by-step explanation:
We are given;
Charge density 1; σ1 = -50 nC/m² = -50 × 10^(-9) nC/m²
Charge density 2; σ2 = +25 nC/m² = +25 × 10^(-9) nC/m²
Now, formula for electric field strength is;
E = -(½ε)(|σ1| ± |σ2|)
ε is vacuum permittivity with a constant value as 8.85 × 10^(−12) C²/N.m²
|σ1| and |σ2| means we are taking the absolute values and would therefore not use the negative sign attached to them.
Now, in between x = 0 cm(0 m) and 50 cm (0.5 m), electric field generated by both charge densities would be in the same direction and thus;
E_in = -(½ε)(|σ1| + |σ2|)
E_in = -(½ × 8.85 × 10^(−12)) × [(50 × 10^(-9)) + (25 × 10^(-9))]
E_in = -4200 V/m
In contrast, when x ≥ 50 cm (0.5 m), electric field generated by both charge densities would be in opposite directions and thus;
E_out = -(½ε)(|σ1| - |σ2|)
E_out = -(½ × 8.85 × 10^(−12)) × [(50 × 10^(-9)) - (25 × 10^(-9))]
E_out = 1400 V/m
The magnitude of the potential difference from the origin to x = 80 cm(0.8 m) is calculated as attached;
From the attachment, we see that;
ΔV = 2520 V
Lily drew 37 hearts and 36 circles. What is the ratio of hearts to circles?
Simplify your answer if possible.
Answer:
37: 36
Step-by-step explanation:
You can not simplify. Have a good day!
{(5²)} ³×5⁴}÷5⁷ simplify and express the following as exponent
Answer:
The answer is 5³.
Step-by-step explanation:
You have to apply Indices Law :
[tex] {a}^{m} \times {a}^{n} ⇒ {a}^{m + n} [/tex]
[tex] {a}^{m} \div {a}^{n}⇒ {a}^{m - n} [/tex]
[tex] { ({a}^{m} )}^{n} = {a}^{mn} [/tex]
So for this question :
[tex]( {( {5}^{2}) }^{3} \times {5}^{4} ) \div {5}^{7} [/tex]
[tex] = ( {5}^{6} \times {5}^{4} ) \div {5}^{7} [/tex]
[tex] = {5}^{10} \div {5}^{7} [/tex]
[tex] = {5}^{3} [/tex]
8. What is the result of (11x + 18i)(117 - 18i)?
Help me please.
Write a ratio expressing the slope of the line passing through (5,7) and (-3,-2).
Answer:
9/8
Step-by-step explanation:
change in y/change in x= slope
so in this case -9/-8 or 9/8 bc the negatives cancel out
what is the value of the expression 12 - k
if k = (-3)
Answer:
15
Step-by-step explanation:
12-k
12- (-3)
12+3
=15
Answer:
15
Step-by-step explanation:
Substitute the variable, "k" into "12-k" from the equation "k=(-3).
12-k
12-(-3)
12+3---> two negatives make a positive
15
Find the value of x and y given that p//q. Type answers alphabetically, and separate by a comma and a space
Answer:
39
Step-by-step explanation:
Evaluate the expression when c=5 and d=6.
7c+d.
Answer:
41
Step-by-step explanation:
Step 1:
7c + d Equation
Step 2:
7 ( 5 ) + 6 Input c and d
Step 3:
35 + 6 Multiply
Answer:
41 Add
Hope This Helps :)
I need help please, can you help me?
Answer:
x= 16 degrees
Step-by-step explanation:
the angles can be a little hard to remember but just know that the angles that are outside of the transversal are exterior angles and if they are on the opposite sides of the line that passes through the parallel lines then they're alternate exterior angles and those angles that are inside are interior angles and if they are on the opposite sides of the line passing through the parallel then they are alternate interior angles .
I do not understand this
Answer:
It would be C. The hexagon.
Answer:It would be C because you have 3 sides for the triangle than 4 sides for the rectangle, 5 sides for the pentagon, and 6 sides for the hexagon
Step-by-step explanation:
Kylie's family took a road trip to the Grand Canyon, Kylie fell asleep 42% of the way through the trip. If the total length of the trip was 600 miles, how many miles had they travelled when Kylie fell asleep?
Help Me pleasee i dont understand
any luck of help? I'll brainlist uu promise . I really need it for correction :)
Answer:
the cist of entry for x adults
Answer:
i think it would be d)
Step-by-step explanation:
cuz like, it says to write an expression. for an expression, most of the time you need more than one like number and variable
hope this helped :)
A line that passes through ( 3, 1) and 0,3 in y= mx+ b form
Answer:
y = -0.7x + 3
Step-by-step explanation:
I just used a math app called geo-gebra. Put the points in made a line and bam an answer. Hope this helps!
what percentage is equal to 32/100
Answer:
32%
Step-by-step explanation:
32/100 is 32%
Alonso plans to buy a new kayak that costs $2,100. But he needs to pay a 8.5% tax. What is the total cost of the kayak?
Answer:
$ 2,273.25
Step-by-step explanation:
Please help anyone
Linear function f is shown in the graph. Write the slope-intercept form of the equation representing this function.
The equation representing the function f(x) -
y = 4x - 8
We have a linear function f(x) as shown in the graph.
We have to determine the slope-intercept form of the equation representing this function.
What is the Slope - intercept form of the equation of a straight line ?The Slope - intercept form of the equation of a straight line is as follows -
y = mx + c
where -
m - slope of line
c - intercept of line on y - axis.
According to the question, we have -
c = - 8 = intercept of line on y - axes.
Intercepting coordinates on y - axes = (0, -8).
Intercepting coordinates on x - axes = (2, 0).
Slope = m = [tex]\frac{-8-0}{-2 -0}[/tex] = 4
Therefore, the equation representing the function f(x) -
y = 4x - 8.
To solve more questions on Straight lines, visit the link below -
brainly.com/question/28091452
#SPJ6
Which of the following sets represents a function?
O [(1, 2), (3, 2), (5, 7))
O [(3,5),(-1,7), (3,9)}
O [(1, 2), (1,4), (1, 6)
Answer:
(1, 2), (1,4), (1, 6)
Step-by-step explanation:
They're adding the Y-axis
The mapping below shows y as a function fo x?
True
False
Answer:
False
Step-by-step explanation:
x is the input and y is the output
the same input cannot have more than 1 output
-8 has 1 output
5 has 1 output
but "1" has 2 outputs
Ryan and two of his friends contribute $8.33 each, to buy a baseball bat from a sports shop. Find
the price of the baseball bat.
Answer:
24.99
Step-by-step explanation:
A quarterback dropped back 5 yards behind the lone of scrimmage. Then, he passed the ball 14 yards. How far past the line of scrimmage did the ball travel? (Write an equation to represent this problem)
Answer:
9 yards
Step-by-step explanation:
-5 + 14 = 9
What’s 19,975 divided by 25 show your work
the answer to the question is 799
Find the perimeter of the polygon with the vertices Q( – 3, 2), R(1, 2), S(1, - 2), and T (-3, -2).
, -2)
Answer:
Step-by-step explanation:
Which best represents the change in the vertices of rectangle ABCD to form rectangle A'B'C'D'?
F) (x, y ) → (2x, 2y)
G) (x, y ) → (1.5x, 1.5y)
H) (x, y ) → (3x, 3y)
J) (x, y ) → (4x, 4y)
Answer:
F
Step-by-step explanation:
can you guys please help
Answer:
I cant read all of that. Im sure others ant either.
Step-by-step explanation:
Answer:
i cant read it for some reason, can you type it?
Step-by-step explanation:
Is this graph of a function yes or no
Answer: It could be, just add two dots at the smiley face, BOOM! The function of Facial muscles in humans.
Step-by-step explanation:
Write the word sentence as an equation. Then solve.
The difference between a number pand 6 is -14
Equation
Solution p=
25
Answer:
p - 6 = -14
p = -8
Step-by-step explanation:
The difference between a number p and 6 is -14
Let the number = p;
Equation:
difference between the numbers:
p - 6
equality;
p - 6 = -14
Equation; p - 6 = -14
Solution:
p - 6 = -14
add (+6) to both sides of the expression;
p - 6 + (+6) = -14 +(+6)
p = -8
M= 1/2
M= 2
M= -1/2
M=-2
Answer:
It should be 1/2
Step-by-step explanation:
On a coordinate plane, a line is drawn between points (negative 4, negative 3) and (negative 1, 4).
Use the Pythagorean theorem to find the distance on the coordinate plane.
a2 + b2 = c2
What is the distance between the two points?
StartRoot 20 EndRoot
StartRoot 40 EndRoot
StartRoot 45 EndRoot
StartRoot 58 EndRoot
Answer:
StartRoot 58 EndRoot
Step-by-step explanation:
Given the coordinates (-4, -3) and (-1, 4)
To get the distance between the two points, we will use the formula:
D =√(y2-y1)²+(x2-x1)²
From the coordinates, x1 = -4, y1 = -3, x2 = -1 and y2 = 4
Substitute
D =√(4-(-3))²+(-1-(-4))²
D = √(4+3)²+(-1+4)²
D = √7²+3²
D = √49+9
D = √58
Hence the correct option is D
StartRoot 58 EndRoot
Answer:
D. 58
Step-by-step explanation: