The equation y = -10 (x) (x - 5) models the height.
Option A is the correct answer.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
66x = 8 is an equation.
We have,
From the table,
We can make ordered pairs in the form of (x, y).
(0, 0), (1, 40), (2, 60), (3, 60), (4, 40), (5, 0).
So,
We will choose the equation that satisfies the ordered pairs.
y = -10 (x) (x – 5)
This can be used as the equation.
For (0, 0), (1, 40), (2, 60), (3, 60), (4, 40), (5, 0)
i.e x = 0, 1, 2, 3, 4, 5
y = -10 x 0 = 0
y = -10 x 1 x -4 = 40
y = -10 x 2 x -3 = 60
y = -10 x 3 x -2 = 60
y = -10 x 4 x -1 = 40
y = - 10 x 5 x 0 = 0
y = 10 (x) (x - 5)
This can not be used since the y value is a negative value.
y = -10 (x – 5)
This is not possible.
y = 10 (x – 5)
This is not possible.
Thus,
The equation y = -10 (x) (x - 5) satisfy the given table values.
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To find which equation models the height of a projectile \( y \) seconds after being fired based on the given data, we can substitute the given x-values (time in seconds) into each equation and check whether the result matches the corresponding y-values (height in meters).
Let's go through each of the given equations and the provided points one by one:
1. Equation \( y = -10(x)(x – 5) \)
When \( x = 0 \), the height \( y \) should be 0.
Substituting the value into the equation, \( y = -10(0)(0 – 5) = 0 \), which matches the given point (0, 0).
When \( x = 1 \), the height \( y \) should be 40.
Substituting the value into the equation, \( y = -10(1)(1 – 5) = -10(-4) = 40 \), which matches the given point (1, 40).
When \( x = 2 \), the height \( y \) should be 60.
Substituting the value into the equation, \( y = -10(2)(2 – 5) = -10(-1) = 60 \), which matches the given point (2, 60).
When \( x = 3 \), the height \( y \) should be 60.
Substituting the value into the equation, \( y = -10(3)(3 – 5) = -10(-2) = 60 \), which matches the given point (3, 60).
When \( x = 4 \), the height \( y \) should be 40.
Substituting the value into the equation, \( y = -10(4)(4 – 5) = -10(-1) = 40 \), which matches the given point (4, 40).
When \( x = 5 \), the height \( y \) should be 0.
Substituting the value into the equation, \( y = -10(5)(5 – 5) = -10(0) = 0 \), which matches the given point (5, 0).
Since all the points match perfectly with the results from Equation 1, we confirm that Equation 1 models the height of the projectile accurately. Therefore, the correct equation is:
\( y = -10(x)(x – 5) \)
This quadratic equation represents a parabolic trajectory, which is typical for the motion of a projectile under gravity, with no air resistance, and assuming that the projectile lands at the same level from which it was fired.
A group of 8 friends (5 girls and 3 boys) plans to watch a movie, but they have only 5 tickets. How many different combinations of 5 friends could
possibly receive the tickets?
A. 13
B. 40
C. 56
b. 64
[tex]_8C_5=\dfrac{8!}{5!3!}=\dfrac{6\cdot7\cdot8}{2\cdot 3}=56[/tex]
The function f(x) = -(x - 20)(x - 100) represents a company's monthly profit as a function of x, the number of purchase
orders received. Which number of purchase orders will generate the greatest profit?
20
O 60
O 80
O 100
Answer:
The correct option is B
Step-by-step explanation:
Lets put the values in the given function one by one: You will get the answer
f(x)=-(x - 20)(x - 100)
The first option is 20. Substitute the value in the function:
f(x)=-(20-20)(20-100)
f(x)=(- 0)(-80)
f(x)= 0
Second option is 60.
Substitute the value in the function
f(x)=-(x - 20)(x - 100)
f(x)=-(60 - 20)(60 - 100)
f(x)=(-40)(-40)
f(x)=160
Third option is 80:
Substitute the value in the function
f(x)=-(x - 20)(x - 100)
f(x)=-(80 - 20)(80 - 100)
f(x)=(-60)(-20)
f(x)=120
Fourth option is 100:
Substitute the value in the function
f(x)=-(x - 20)(x - 100)
f(x)=-(100 - 20)(100 - 100)
f(x)=(-80)(0)
f(x)= 0
Therefore the values we got are 0, 160, 120, 0
The greatest value is 160.
Thus the correct option is B....
Answer:
B.) 60
Step-by-step explanation:
Find the value of x using the laws of sine.
Answer:
Rounded to nearest hundredths is 8.75.
Rounded to nearest tenths is 8.7.
Step-by-step explanation:
Law of sines:
[tex]\frac{\sin(A)}{\text{ side opposite to }A}=\frac{\sin(B)}{ \text{ side opposite to }B}[/tex]
Measure of angle [tex]A[/tex] is 28 and the side opposite to it is [tex]x[/tex].
Measure of angle [tex]B[/tex] is 105 and the side opposite to it is 18.
Plug in to the formula giving:
[tex]\frac{\sin(28)}{x}=\frac{\sin(105)}{18}[/tex]
Cross multiply:
[tex]18 \sin(28)=x \sin(105)[/tex]
Divide both sides by sin(105):
[tex]\frac{18 \sin(28)}{\sin(105)}=x[/tex] is the exact answer.
I'm going to type it in my calculator now:
18*sin(28) / sin(105) is what is going in there.
The output is 8.748589074.
Rounded to nearest hundredths is 8.75.
Rounded to nearest tenths is 8.7.
Write an equation: After withdrawing $7 from a checking account, Carla’s balance was $89
The equation for the situation where Carla withdraws $7 and is left with an $89 balance is: B - $7 = $89. So Carla's initial balance was $96.
When writing an equation based on the statement that after withdrawing $7 from a checking account, Carla’s balance was $89, we are essentially working out what Carla's balance was before she made the withdrawal.
If we let the variable B represent Carla's initial balance, then after she withdraws $7, her new balance is B - $7.
Since it's given that her balance after the withdrawal is $89, we can write the following equation to represent the situation:
B - $7 = $89
To find the value of B, we would add $7 to both sides of the equation, which would give us:
B = $89 + $7
B = $96
So, Carla's initial balance before the withdrawal was $96.
What type of triangle can an isosceles triangle be? Secalene acute obtuse isosceles
An isosceles triangle is the following options, acute and isosceles, which is B and D. Remember that an isosceles triangle has 2 sides that are the same, so its D and every isosceles triangles are acute, not obtuse, so its B.
Hope this helped!
Nate
Answer:
Acute triangle
Step-by-step explanation:
A isosceles triangle is a triangle that has two equal sides.
It would not be a scalene triangle because in scalene triangles all the sides have different lengths.
It might be an acute triangles because all the angles in an acute triangle would be acute angles.
it wouldn't be an obtuse triangle because in an obtuse triangle there is at least one obtuse angle and the other 2 angles would be either acute, right, or obtuse.
It could be an isosceles triangle but that wouldn't make sense since its already an isosceles triangle.
Hope This Helps!!!
The length of an edge of a cube is 4 ft.
What is the volume of the cube?
Enter the answer.
[1] ft3
Answer:
V = 64 ft^3
Step-by-step explanation:
The volume of a cube is given by
V = s^3 where s is the side length of the cube
V = (4)^3
V = 64 ft^3
Answer:
64 ft
Step-by-step explanation:
Volume=Height*Length*Base
=4*4*4
=16*4
=64 ft
Factor completely.
6x4 – 9x3 – 36x2 + 54x
3x(x2 + 6)(2x + 3)
6x(x2 – 6)(2x – 3)
3x(x2 – 6)(2x – 3)
6x(x2 + 6)(2x + 3)
Answer:
3x[x² - 6][2x - 3]
Step-by-step explanation:
Group each term carefully [two-by-two], and you will arrive at your answer.
Madison represented the sentence
"The product of 3 and the difference of -4 and the quotient of a number and -2 is at most 5"
by using the inequality 3 (-4 - n/-2) < 5
What is madison's error?
Answer:
The mistake is that it can be 5. They forget to include the equals in the less than or equals
Step-by-step explanation:
Start at the inside and work out
quotient of a number and -2
n/-2
difference of -4 and the quotient of a number and -2
-4 - n/-2
product of 3 and the difference of -4 and the quotient of a number and -2
3* (-4 - n/-2)
is at most 5
3* (-4 - n/-2)≤5
The mistake is that it can be 5. They forget to include the equals in the less than or equals
Answer: C
Step-by-step explanation:
A student stands on a bathroom scale that uses the U.S. system of units. Which
of the following is most likely to be the weight shown on the scale?
A. 85 grams
B. 85 ounces
C. 85 pounds
D. 85 kilograms
Answer: 85 pounds,
Step-by-step explanation: Americans don't use the other things to measure weight.
The system of equations y=2x-1 and y=-1/4x+3 is shown on the graph below. What is a reasonable estimate for the solution?
Answer:
Something close to (1.8,2.6)
Step-by-step explanation:
y=2x-1
y=-1/4 x+3
Since y=2x-1 and y=-1/4 x +3 then 2x-1=-1/4 x +3.
I'm going to multiply both sides by 4 to get rid of the fraction:
8x-4=-x+12
Add x on both sides:
9x-4=12
Add 4 on both sides:
9x=16
Divide both sides by 9:
x=16/9 is approximately 1.8 when put into calculator.
Now if x=16/9 and y=2x-1, then y=2(16/9)-1=32/9-1=32/9-9/9=(32-9)/9=23/9.
y=23/9 is approximately 2.6 when put into calculator.
So we are looking for an ordered pair pretty close to (1.8,2.6).
The graph is shown to you so I will put one here as well:
Answer:
A. 1 3/4, 2 1/2
Step-by-step explanation:
the probability of picking rotten apple in a box is 1/100 .if there are 6 boxes containing 1200 apples each how many rotten apple may be picked
[tex]\huge{\boxed{72}}[/tex]
Explanation:First, find the total number of apples. [tex]6*1200=7200[/tex]
Now, multiply this by the probability of picking a rotten apple, which is [tex]\frac{1}{100}[/tex]. This is also the same as dividing by [tex]100[/tex], or moving the decimal point two places to the left. [tex]7200*\frac{1}{100}=72[/tex]
This means that based on the probability given, [tex]72[/tex] rotten apples will be picked.
Number of rotten apple may be picked are 72.
What is probability?Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are.
Given
Probability of picking rotten apple in a box is [tex]\frac{1}{100}[/tex].
There are 6 boxes containing 1200 apples each
Number of rotten apple may be picked to be find.
Total number of apples = [tex]6 \times 1200 = 7200[/tex]
Number of rotten apple may be picked = [tex]7200 \times \frac{1}{100}[/tex]
= 72
Number of rotten apple may be picked are 72.
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Find the x-intercept of the line whose equation is 8x+2y=4
Answer:
x = 1/2
Step-by-step explanation:
Plug in 0 for y
8x + 2(0) = 4
Simplify
8x + 0 = 4
8x = 4
Divide both sides
8x/8 = x
4/8 = 1/2
Simplify
x = 1/2
Answer
x = 1/2
Answer:
X=1/2
Step-by-step explanation:
The equation y=mx+b is the slope-intercept form of a linear equation.
Solve y=mx+b for m
Answer: [tex]m=\frac{y-b}{x}[/tex]
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
To solve for the slope "m", you can follow these steps:
- Subtract "b" from both sides of the equation:
[tex]y-b=mx+b-b\\\\y-b=mx[/tex]
- Divide both sides of the equation by "x". Then:
[tex]\frac{y-b}{x}=\frac{mx}{x}\\\\m=\frac{y-b}{x}[/tex]
It takes 36 minutes for 7 people to paint 4 walls.
How many minutes does it take 9 people to paint 7 walls?
Answer:
49 minutes
Step-by-step explanation:
It would take 49 minutes for 9 people to paint 7 walls.
4 walls need 262 people/minutes (7)(36)
9 people could do that in 49 minutes (441/9)
Answer:
49 minutes
Step-by-step explanation:
first we need to find the rate at which a person paints the walls :
it takes 36 minutes to paint 4 walls by 7 people :
so for 7 people the rate at which they paint the walls is : [tex]\frac{4}{36}[/tex] walls/minute
if we simplify we get [tex]\frac{1}{9}[/tex]
now that was for 7 people , for 1 person the rate is : [tex]\frac{1}{9} \frac{1}{7}[/tex] which is [tex]\frac{1}{63} walls / minute[/tex]
now we have the rate for one person
so for 9 people they will paint [tex]\frac{9}{63} =\frac{1}{7}[/tex] walls/minute
so it takes them 7 minute to paint 1 wall
which means it takes them 7 x7 = 49 minutes to paint 7 walls
2y3 - 27 + 5y2 + (25 / 5)
What is the value of the expression when y = 2?
a)14
B)0
c)7
d)68
Answer:
The correct option is A
Step-by-step explanation:
The expression is
2y3 - 27 + 5y2 + (25 / 5)
Substitute the value of y=2 in the expression:
=2(2)³-27+5(2)²+(25/5)
We know that 2³ means multiply 2 three times
2³= 2*2*2=8
Likewise 2²=2*2=4
=2(8)-27+5(4)+(25/5)
=16-27+20+25/5
Now take the L.C.M which is 5
=80-135+100+25/5
Solve the values in the numerator:
=70/5
=14
Thus the correct option is A....
Matrices X and Y both measure 2x2 and are inverses of each other. Which matrix represents their product?
Answer:
When a matrix is multiplied by its inverse the result will be the identity matrix. If we multiply two matrix with the same size, the resulting matrix will have the same dimension.
Therefore, if we multiply the matrices X and Y we will get a 2x2 identity matrix, as follows:
[tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]
Answer:
[tex]\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]
Step-by-step explanation:
We are asked find the matrix that represent the product of matrices X and Y both measures [tex]2\times 2[/tex] and inverse of each other.
For a matrix multiplication to be defined, the number of columns in the first matrix must be equal to number of rows in the second matrix.
Since the both matrices are [tex]2\times 2[/tex] (same number of column and row), then the product of both matrices would result in [tex]2\times 2[/tex] matrices.
We also know that the multiplication of a matrix with its inverse results in identity matrix.
Therefore, our matrix would be a [tex]2\times 2[/tex] identity matrix as:
[tex]\left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex].
For each geometric sequence, write a recusive rule by finding the commom ratio by calculating the ration of consecutive terms. Write an exlicit rule for the sequence by writing each term as the product of the first tern and a power of the common ratio.
n- 1, 2, 3, 4, 5
An- 2, 6, 18, 54, 162
Answer:
[tex]a_n=2.(3)^{n-1}[/tex]
Step-by-step explanation:
Given sequence is:
2,6,18,54,162
So the common ratio can be found by dividing the second term by first term:
r = 6/2 = 3
The standard formula for geometric sequence is:
[tex]a_n=a_1r^{n-1}[/tex]
Putting the value of r
[tex]a_n=2.(3)^{n-1}[/tex]
So,
[tex]a_1=2.(3)^{1-1} => 2.3^0 = 2*1 = 2\\a_2=2.(3)^{2-1} => 2.3^1 = 2*3 = 6\\a_3=2.(3)^{3-1} => 2.3^2 = 2*9 = 18\\a_4=2.(3)^{4-1} => 2.3^3 = 2*27 = 54\\a_5=2.(3)^{5-1} => 2.3^4 = 2*81 = 162[/tex]
The perimeter of a square is equal to four times the length of its side write the direct variation equation that represents this situation let y be the dependent variable and let x be the independent variable
Answer:
y = 4x
Step-by-step explanation:
Let x = length of the side = independent variable
Let y = perimeter of the square = dependent variable
y = 4x
Let f(x) = 9x3+ 21x2^ - 14 and g(x) = 3x + 1. Find "
f (x) over g (x)
Answer:
[tex]\frac{f(x)}{g(x)}=3x^2+6x-2-\frac{12}{3x+1}[/tex]
Step-by-step explanation:
The first function is [tex]f(x)=9x^3+21x^2-14[/tex]
The second function is [tex]g(x)=3x+1[/tex].
[tex]\frac{f(x)}{g(x)}=\frac{9x^3+21x^2-14}{3x+1}[/tex]
We perform the long division as shown in the attachment to obtain the quotient as: [tex]Q(x)=3x^2+6x-2[/tex] and remainder [tex]R=-12[/tex].
Therefore:
[tex]\frac{f(x)}{g(x)}=3x^2+6x-2-\frac{12}{3x+1}[/tex]
where [tex]x\ne -\frac{1}{3}[/tex]
Answer:
on the flvs test it is option A
Step-by-step explanation:
identify an equation in point-slope form for the line perpendicular to y=-1/2x+11 that passes through (4,-8).
A. y+8=2(x-4)
B. y+8+1/2(x-4)
C.y-8=1/2(x+4)
D.y-4=2(x+8)
Answer:
A. y+8=2(x-4)
Step-by-step explanation:
A line perpendicular to y=-1/2x+11 would have slope +2, which is the negative reciprocal of -1/2.
Starting with the slope-intercept form of the equation of a straight line, find the y-intercept based upon this new line's passing through (4, -8):
y = mx + b becomes -8 = 2(4) + b. Then b = -16, and the desired new line is
y = 2x - 16.
Eliminate answer choices B and C, because 1/2 is not the correct slope.
Choice A is correct. Note that the result of subbing 4 for x and -8 for y into A: y + 8 = 2(x - 4) is a true equation: -8 + 8 = 2(4 - 4)
Also note that y + 8 = 2(x - 4) can be written in slope-intercept form:
y = -8 + 2x - 8, or y = 2x - 16 (same as obtained earlier)
Answer:Y+8=2(x-4)
Step-by-step explanation:
it’s correct I promise
cos x cos (-x) -sin x sin (-x) = 1. Verify the Identity. Please Show All Steps.
Answer:
cos x cos (-x) -sin x sin (-x) = 1 ⇒ proved down
Step-by-step explanation:
* Lets revise the angles in the four quadrants
- If angle x is in the first quadrant, then the equivalent angles to it are
# 180 - x ⇒ second quadrant (sin (180 - x) = sin x , cos (180 - x) = -cos x
tan (180 - x) = -tan x)
# 180 + x ⇒ third quadrant (sin (180 - x) = -sin x , cos (180 - x) = -cos x
tan (180 - x) = tan x)
# 360 - x ⇒ fourth quadrant (sin (180 - x) = -sin x , cos (180 - x) = cos x
tan (180 - x) = -tan x)
# -x ⇒fourth quadrant (sin (- x) = -sin x , cos (- x) = cos x
tan (- x) = -tan x)
* Lets solve the problem
∵ L. H .S is ⇒ cos x cos (-x) - sin (x) sin (-x)
- From the rules above cos x = cos(-x)
∴ cos x cos (-x) = cos x cos x
∴ cos x cos (-x) = cos² x
- From the rule above sin (-x) = - sin x
∴ sin x sin (-x) = sin x [- sin x]
∴ sin x sin (-x) = - sin² x
∴ cos x cos (-x) - sin (x) sin (-x) = cos² x - (- sin² x)
∴ cos x cos (-x) - sin (x) sin (-x) = cos² x + sin² x
∵ cos² x + sin² x = 1
∴ R.H.S = 1
∴ L.H.S = R.H.S
∴ cos x cos (-x) -sin x sin (-x) = 1
Three consecutive integers have a sum of –21. Which equation can be used to find the value of the three numbers?
x+x+x=-21
x+2x+3x=-21
x+(x+1)+(x+2)=-21
x+(x+2)+(x+4)=-21
Answer:
The third one, x+(x+1)+(x+2)=-21 because x, x+1 and x+2 are three consecutive numbers.
60 POINTSZZZ HELLPP!!
Question 1(Multiple Choice Worth 5 points)
(06.07A MC)
What is the length of the third side of the window frame below?
(Figure is not drawn to scale.)
15 inches
27 inches
25 inches
32 inches
Question 2(Multiple Choice Worth 5 points)
(06.07A LC)
Ross calculated the missing side length of one of these triangles using the Pythagorean Theorem. Which triangle was it?
E
F
G
H
Question 3(Multiple Choice Worth 5 points)
(06.07A MC)
The figure shows the location of 3 points around a lake. The length of the lake, BC, is also shown.
(Figure is not drawn to scale.)
Which of the following options is closest to the distance (in miles) between points A and B?
3.46 miles
4.24 miles
4.90 miles
5.92 miles
Question 4(Multiple Choice Worth 5 points)
(06.07A LC)
The legs of a right triangle are 3 units and 8 units. What is the length of the hypotenuse? Round your answer to the nearest hundredth.
8.54 units
9.54 units
11.00 units
24.00 units
1st picture is for question 1 2nd picture 2nd question n 3ed for the 3ed question
What is the scale factor of LMN to OPQ?
Answer:
The scale factor is 1 because it has not increased or decreased and therefore are congruent
Which is the correct calculation for the volume of the pyramid?
Answer:
h×a²×1/3
Step-by-step explanation:
where h is the vertical height of pyramid a is the length of base ..this formula is applicable for square based pyramid only.
Answer:
1/3 A h.
Step-by-step explanation:
The volume of a pyramid is 1/3 * area of the base * height = 1/3 A h.
So for example the area of a square-based pyramid = 1/3 s^2 h where s is the length of a side of the square.
2(5x+3)=4x+18 how would i solve this problem
Answer:
x=2
Step-by-step explanation:
2(5x+3)=4x+18 Remove the brackets
10x + 6 = 4x + 18 Subtract 4x from both sides.
10x - 4x + 6 = 4x-4x + 18 Combine
6x + 6 = 18 Subtract 6 from both sides
6x + 6 - 6 = 18 - 6 Combine
6x = 12 Divide by 6
6x/6 = 12/6 Do the division
x = 2
If sin0=-1/2 and 0 is in quadrant III then tan0=
Answer:
tan O = √3/ 3.
Step-by-step explanation:
The tangent is positive in quadrant 3.
The adjacent side has length √((2^2 - (-1)^2)
= -√3.
So tan O = -1 / -√3
= 1 / √3
= √3/ 3.
To determine tan(θ) for an angle θ where sin(θ) = -1/2 and θ is in quadrant III, we perform the following steps:
1. **Understand the given information:** When sin(θ) = -1/2, it means the opposite side to angle θ in a right triangle is -1 and the hypotenuse is 2. Since θ lies in the third quadrant, both sine and cosine values are negative, implying that the adjacent side length must also be negative.
2. **Use the Pythagorean theorem:** For a right triangle:
\[ \text{hypotenuse}^2 = \text{opposite}^2 + \text{adjacent}^2 \]
Substituting hypotenuse and opposite side values:
\[ 2^2 = (-1)^2 + \text{adjacent}^2 \]
Simplify and solve for the adjacent side:
\[ 4 = 1 + \text{adjacent}^2 \]
\[ 3 = \text{adjacent}^2 \]
\[ \text{adjacent} = \sqrt{3} \] or \[ \text{adjacent} = -\sqrt{3} \]
Since the angle is in the third quadrant where cosine is also negative, we must take the negative square root:
\[ \text{adjacent} = -\sqrt{3} \]
3. **Calculate tan(θ):** By definition,
\[ \tan(θ) = \frac{\text{opposite}}{\text{adjacent}} \]
Substitute the known side lengths:
\[ \tan(θ) = \frac{-1}{-\sqrt{3}} \]
4. **Simplify the expression:**
\[ \tan(θ) = \frac{1}{\sqrt{3}} \]
To rationalize the denominator:
\[ \tan(θ) = \frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} \]
\[ \tan(θ) = \frac{\sqrt{3}}{3} \]
Thus, if sin(θ) = -1/2 and θ is in quadrant III, then tan(θ) = √3/3. Note that in the context of trigonometry, it is often assumed that the angle and the ratios are dimensionless, so a negative 'opposite' simply reflects the direction along the coordinate axis rather than a literal negative length.
Money in a savings account is compounded continuously over time, t, and is modeled by the function
f(t) = 1000e0.017. What is the rate at which the balance grows?
Answer:
1.7% compounded continuously
Step-by-step explanation:
The model used for continuous compounding is ...
f(t) = Pe^(rt)
where P is the principal amount, and r is the interest rate being compounded. Assuming a typo in your given equation, you have ...
f(t) = 1000·e^(0.017t)
Matching the various parts of the equation, we see that P = 1000 and r = 0.017 = 1.7%.
The balance grows at a continuous rate of 1.7%.
To find the growth rate of the account balance in the given function, we differentiate it to obtain [tex]f'(t) = 1000 × 0.017e^(0.017t)[/tex], which shows that the balance grows at a continuous compound rate of 1.7% per year.
The student's question refers to a savings account where the money is compounded continuously. We are given the function [tex]f(t) = 1000e^{0.017t,[/tex]that models the account balance over time t. To find the rate at which the balance grows, we can differentiate this function concerning time.
The derivative of the function[tex]f(t) = 1000e^{0.017t[/tex] concerning t gives us [tex]f'(t) = 1000 × 0.017e^{0.017t[/tex]. This represents the rate of change of the account balance at any time t, which is also the growth rate. Therefore, the rate at which the balance grows is 0.017 or 1.7% per year.
Veronica works each day and earns more money per hour the longer she works. Write a function to represent a starting pay of $20 with an increase each hour by 5%. Determine the range of the amount Veronica makes each hour if she can only work a total of 8 hours.
Answer:
20 ≤ f(x) ≤ 28.14
Step-by-step explanation:
Find the measure of stv in the figure
Answer:
STV = 153 degrees
Step-by-step explanation:
180 - 18 = 162 (angles on a straight line equal 180 degrees)
3q + 15q = 162
18q = 162
q = 162 / 18
q = 9
STV = 15q + 18
= 135 + 18
= 153
Hope this helps!
UTV is a straight line, which equals 180 degrees.
This means both angles UTS and STV when added together must equal 180.
3q + 15q +18 = 180
Simplify:
18q +18 = 180
Subtract 18 from both sides:
18q = 162
Divide both sides by 18:
q = 162 / 18
q = 9
Now you have a value for q to solve the angle.
STV = 15q +18
Replace q with 9:
STV = 15(9) +18
Simplify:
STV = 135 + 18 = 153 degrees.