what is the minimum value of "f(x)=7(x-8)^2+5" ?
Answers
minimum is: (8,5)
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if you ever need help you can use a source that has a caculator.
Related Questions
A circular helipad has a circumference of 78.5 meters. Find the approximate diameter of the helipad. Use 3.14 for π
. Round to the nearest hundredth if necessary.
Answers
Answer:
Step-by-step explanation:
2\(\pi\)r = 78.5
r = 78.5/2π
d = 2r = 78.5/π
d = 78.5/3.14
d = 25
father wants to gift his daughter a present for her marriage, he offers her three options: Option A: $55,000 today Option B: $8,000 every year for 10 years Option C: $90,000 in 10 years Assuming a discount rate of 7%, calculate the present value of each option (give an answer for each) and decide what option is best for the daughte
Answers
The best option for the daughter would be receiving $8,000 every year for 10 years.
To determine the present value of each option, we need to calculate the present value of the cash flows associated with each option using the discount rate of 7%.
Option A: $55,000 today (present value of a lump sum)
The present value of Option A can be calculated as the initial amount itself since it is received today:
Present Value (Option A) = $55,000
Option B: $8,000 every year for 10 years (present value of an annuity)
The present value of Option B can be calculated using the formula for the present value of an ordinary annuity:
PV (Option B) = C [(1 - (1 + r)⁻ⁿ / r]
Where:
C = Cash flow per period = $8,000
r = Discount rate = 7% = 0.07
n = Number of periods = 10
Plugging in the values, we get:
PV (Option B) = $8,000 [(1 - (1 + 0.07)⁻¹⁰ / 0.07] ≈ $57,999.49
Option C: $90,000 in 10 years (present value of a future sum)
The present value of Option C can be calculated using the formula for the present value of a future sum:
PV (Option C) = F / (1 + r)^n
Where:
F = $90,000
r = 7% = 0.07
n = 10
Plugging in the values, we get:
PV (Option C) = $90,000 / (1 + 0.07)¹⁰ ≈ $48,667.38
Now, let's compare the present values of the options:
PV (Option A) = $55,000
PV (Option B) = $57,999.49
PV (Option C) = $48,667.38
Based on the present values, the best option for the daughter would be receiving $8,000 every year for 10 years.
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f(x) = x · 2x on [0, 4] with 4 subintervals of equal width and midpoints for sample points
Answers
To provide the final numerical answer, the exact values of f(x1), f(x2), f(x3), and f(x4) need to be calculated using a calculator or numerical approximation techniques.
To approximate the integral of the function f(x) = x · 2^x over the interval [0, 4], we can use the midpoint rule with four equal-width subintervals. The midpoint rule estimates the integral by evaluating the function at the midpoint of each subinterval and multiplying it by the width of the subinterval.
To apply the midpoint rule, we divide the interval [0, 4] into four equal-width subintervals. The width of each subinterval is (4-0)/4 = 1.
The midpoints of the subintervals are located at x = 0.5, 1.5, 2.5, and 3.5. Let's denote these midpoints as x1, x2, x3, and x4, respectively.
For each subinterval, we evaluate the function f(x) = x · 2^x at the corresponding midpoint and multiply it by the width of the subinterval:
I ≈ Δx [f(x1) + f(x2) + f(x3) + f(x4)]
Now, let's calculate the values of f(x) at each midpoint:
f(x1) = 0.5 · 2^(0.5) = 0.5 · sqrt(2)
f(x2) = 1.5 · 2^(1.5)
f(x3) = 2.5 · 2^(2.5)
f(x4) = 3.5 · 2^(3.5)
Finally, we substitute these values into the midpoint rule formula:
I ≈ 1 [f(x1) + f(x2) + f(x3) + f(x4)]
Replace the values of f(x) at each midpoint and simplify to find the approximate value of the integral.
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find endpoint T, given an endpoint S (-2, 9) and Midpoint M (8, 0)
Answers
original price of 80$ precent of discount of 20%
Answers
Answer:
$74
Step-by-step explanation:
$80 * 20%
20/100 = 0.2
80 * 0.20 = 16
80 - 16 = $74
You will now be paying a total of $74.
Hope this helps!
(06.04 mc)
jake tossed a paper cup 50 times and recorded how it landed. the table shows the results
position
open side up closed side up landing on side
number of times landed in position
1
5
44
based on the table, determine the experimental probability of each outcome (landing open side up, landing closed side up, and landing on its side). show your work.
Answers
Based on the given data, the experimental probability of landing open side up is 0.1, landing closed side up is 0.88, and landing on its side is 0.02.
To determine the experimental probability of each outcome (landing open side up, landing closed side up, and landing on its side), we need to calculate the ratio of the number of times the cup landed in each position to the total number of tosses.
Let's calculate the experimental probability for each outcome based on the given table:
1. Landing open side up:
The cup landed open side up 5 times out of 50 tosses.
Experimental Probability = Number of times landed open side up / Total number of tosses
Experimental Probability = 5 / 50
Experimental Probability = 0.1
2. Landing closed side up:
The cup landed closed side up 44 times out of 50 tosses.
Experimental Probability = Number of times landed closed side up / Total number of tosses
Experimental Probability = 44 / 50
Experimental Probability = 0.88
3. Landing on its side:
The cup landed on its side 1 time out of 50 tosses.
Experimental Probability = Number of times landed on its side / Total number of tosses
Experimental Probability = 1 / 50
Experimental Probability = 0.02
Based on the given data, the experimental probability of landing open side up is 0.1, landing closed side up is 0.88, and landing on its side is 0.02. These probabilities indicate the likelihood of each outcome occurring in a toss.
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There are two numbers between 30 and 40 that have just two factors.
What are they?
Answers
Answer:
31 and 37
Step-by-step explanation:
Those are the only two numbers
Answer:
The two numbers between 30 and 40 which have only 2 factors are -
31 and 37
Hope it helps you.
Determine the surface area of the portion of z = 3 + 2y + 3x4 that is above the region in the xy-plane bounded by y = x5, x = 1 and the x-axis.
Answers
The surface area of the portion of the surface \(z = 3 + 2y + 3x^4\) that is above the region bounded by\(y = x^5\), x = 1, and the x-axis is given by the double integral ∫∫√\((1 + 144x^6 + 4) dy dx\), with the limits of integration from 0 to 1 for x and from 0 to \(x^5\) for y.
To determine the surface area of the portion of the surface \(z = 3 + 2y + 3x^4\) that is above the region in the xy-plane bounded by \(y = x^5\), x = 1, and the x-axis, we can set up a double integral.
The surface area can be calculated using the formula for surface area:
S = ∬√(1 +\((dz/dx)^2 + (dz/dy)^2\)) dA
First, let's find the partial derivatives dz/dx and dz/dy:
\(dz/dx = d(3 + 2y + 3x^4)/dx \\= 12x^3\\dz/dy = d(3 + 2y + 3x^4)/dy \\= 2\\\)
Now, we can set up the double integral:
S = ∬√(1 + \((12x^3)^2 + (2)^2\)) dA
The limits of integration are determined by the region in the xy-plane bounded by\(y = x^5\), x = 1, and the x-axis.
The region is bounded by \(y = x^5\) and the x-axis, so the limits of integration for y are from y = 0 to \(y = x^5.\)
The region is bounded by x = 1 and the x-axis, so the limits of integration for x are from x = 0 to x = 1.
Therefore, the double integral becomes:
S = ∫∫√\((1 + 144x^6 + 4)\) dy dx
0 to 1 0 to \(x^5\)
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HELP ASAPPPPPPPPPP 25 POINTSSSSSS
Answers
Answer:
(1). \(h(t)=-4(t-1)^2+36\)
(2). 1 minute
Step-by-step explanation:
They want you to factorize the equation in such a way that the vertex appears as a number in the equation; and you do that by using a method called completing the squareHere is our equation: \(h(t)=-4t^2+8t+32\)We factor it by completing the square: But first remember this:A quadratic equation has the general form \(f(x)=ax^2+bx+c\) Where a and b are the numbers before x squared and x respectively, and c is the number without an x, and f(x) is the value dependent on xIn this case x is tSo the steps are as followsEquate the equation to zero: \(-4t^2+8t+32=0\) Divide each term by the (a) of the equation in this case is it -4, and we get: \(t^2-2t-8=0\) Then take the new (c) to the other side of the equation, in the case we add 8 to both sides to get: \(t^2-2t=8\) Now the tricky part, you have to add to both sides of the equation the square of half of the coefficient of t or number before t, not t squared just t and you get: \(t^2-2t+(-1)^2=8+(1)^2\) Now the left side is in the square form, or it just means when you factor the left side, you get it as the square of a certain single term, in this case we get: \((t-1)^2=8+1\) When we simplify we get: \((t-1)^2=9\) Now any equation in this form, will give you the vertex when you equate the term in parenthesis to zero, and simplify: \(t-1=0,t=1\) \(t=1\) is the value of the t or time at the vertex To write the equation again, multiply every term with the (a) you used to get: \(h(t)=-4(t-1)^2+36\) , and this is the equation for #(1)Now here is why we needed to get the vertex; the vertex tells us at what point the height either reaches its maximum/highest level, or where it reaches its minimum/lowest level So since the time (t) at the vertex is 1, in order to find the height at this time, just plug it into the equation:\(h(1)=-4((1)-1)^2+36\\h(1)=-4(0)+36\\h(1)=36\) So that's the height at the vertexNow it can either be the maximum/highest height or the minimum/lowest height, in order to know this we check as followsRemember the (a) we used to factor the equation? -4, if the (a) value of a quadratic function is less than 0, then it is a maximum equation, mean whatever vertex you get will be the point where the equation reaches its biggest value.So at a height of 36 meters, and a time of 1 minute, the craft reaches its highest point.HELPPPP DUE SOON!!! WILL MARK BRAINLYIST AND 10 POINTS
Answers
Answer:
688.7
Step-by-step explanation:
Top and Bottom
Area = 3/4 * pi * r^2
r = 6
Area = 3/4 * 3.14 * 6^2
Area = 84.78
Don't round yet.
Vertical surface
Vertical surface = 3/4 * pi * d * h
d = 12 inches (the diameter)
Vertical surface = 3/4 * 3.14 * 12 * 15
Vertical surface = 423.9
Two inner faces
They are both rectangles
Area = 2 * L * W
L = 15
w=6
Area = 2 * 15 * 6 180
Total 688.68
Total = 688.7
Please answer please please
Answers
Answer: T
Step-by-step explanation: The vertex is where the two lines meet at the endpoint, meaning that the vertex is always where the lines begin to spread out.
In 1970, the population of a small town was 4,200. The population is decreasing at the rate of 2. 4% per year. Find the quarterly decay rate. Write the exponential function that models the decaying population
Answers
To find the quarterly decay rate, we first need to convert the annual decay rate of 2.4% into a quarterly rate. Since there are 4 quarters in a year, we divide the annual rate by 4.
Quarterly decay rate = (2.4% / 4) = 0.6%
Now, let's write the exponential function that models the decaying population. We can use the formula:
P(t) = P₀ * (1 - r/100)^t
Where:
P(t) is the population at time t
P₀ is the initial population
r is the decay rate
t is the time in quarters
Given that the initial population P₀ is 4,200 and the quarterly decay rate r is 0.6%, the exponential function becomes:
P(t) = 4200 * (1 - 0.6/100)^t
This function can be used to calculate the population at any given time t in quarters, taking into account the decay rate of 0.6% per quarter.
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This equation shows how the length of Pamela's essay depends on the number of hours she spends writing this week.
p = h + 5
The variable h represents the number of hours she spends writing this week, and the variable p represents the total number of pages that have been written. After spending 10 hours writing this week, how many pages will Pamela have written in total?
Answers
Answer:
15
Step-by-step explanation:
Given:
p=h+5
with h being hours
If Pamela spends 10 hours writing, substitute in 10 for h:
p=10+5
p=15
So, 15 pages will be written.
Hope this helps! :)
please help me out and answer this i need it ASAP <3
Answers
Answer:
\(y-1=\frac{5}{6}\left(x+8\right)\)
I hope this is good enough:
What is sin 30°?
60
90
√3
2
30
OA. 1
O B.2
O C. √3
OD.
1|2
OE 3
OF √3
2
Answers
Step-by-step explanation:
Sin(30 degrees) = 1/2
The value of sin 30° is 1/2 and it lies in 1 st quadrant.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
sin 30° can be calculated using the unit circle or a calculator that has a sin function.
In the unit circle, 30° is in the first quadrant, and the sine of an angle in the unit circle is defined as the y-coordinate of the point on the circle that corresponds to that angle.
For a 30° angle, the point on the unit circle is (cos 30°, sin 30°)
= (√3/2, 1/2).
Therefore, the value of sin 30° is 1/2.
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Help out
Aaaaaaaaaaaa
Answers
Answer:
\(y=\frac{6}{5}x-8\)
Step-by-step explanation:
we know the slope (or m in y=mx+b) is 6/5 we just need to solve for b
we will do this by plugging in the required coordinates
-2=(6/5)*5+b
-2=6+b
-8=b
put it all together
Answer:
y = \(\frac{6}{5}\) x - 8
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = \(\frac{6}{5}\) , then
y = \(\frac{6}{5}\) x + c ← is the partial equation
To find c substitute (5, - 2) into the partial equation
- 2 = 6 + c ⇒ c = - 2 - 6 = - 8
y = \(\frac{6}{5}\) x - 8 ← equation of line
Answer this please I need help
Answers
Answer:
£700000
Step-by-step explanation:
an increase of 7% represents 100% + 7% = 107% = \(\frac{107}{100}\) = 1.07
then
original price = \(\frac{749000}{1.07}\) = £700000
HELPPP! Cari knows that it is a 45 mile drive from her house to the airport. She also knows that it is a 45 mile drive from her house to her grandparents house in the woods. How many miles is it directly from the airport to her grandparents house in the woods? Show your work.
Answers
Answer:
We can use the Pythagorean theorem to solve this problem. Let's assume that Cari's house is at point A, the airport is at point B, and her grandparents' house is at point C. We know that the distance from A to B is 45 miles and the distance from A to C is 45 miles. We want to find the distance from B to C, which we can call x.
We can form a right triangle with sides AB, AC, and BC. The distance we want to find, x, is the length of the hypotenuse of this triangle (side BC).
Using the Pythagorean theorem, we know that:
AB^2 + AC^2 = BC^2
Substituting in the values we know:
45^2 + 45^2 = x^2
Simplifying:
2025 + 2025 = x^2
4050 = x^2
Taking the square root of both sides:
x = sqrt(4050)
x is approximately equal to 63.64 miles (rounded to two decimal places).
Therefore, the direct distance from the airport to Cari's grandparents' house is approximately 63.64 miles.
can someone please help me find the answer to the following
Answers
ANSWER
\(14.4\pi ft^2\)EXPLANATION
The surface area of a cone is given as:
\(SA=\pi\cdot r(r+l)\)where r = radius; l = slant height
From the question:
\(\begin{gathered} r=2.4ft \\ l=3.6ft \end{gathered}\)Therefore, the surface area of the cone, in terms of pi, is:
\(\begin{gathered} SA=\pi\cdot2.4(2.4+3.6) \\ SA=\pi\cdot2.4\cdot6 \\ SA=14.4\pi ft^2 \end{gathered}\)Mariel and Sam Trent's savings account had a balance of $9,544 on May 1. The account earns interest at a rate of 5.25% compounded monthly until the end of August.
Answers
The amount in the savings account at the end of August is $11711.4424.
What is the compound interest?
Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest =
Given that, principal =$9544, rate of a interest =5.25% and time period between May 1 to the end of August is 4 months.
Here, Amount =9544(1+5.25/100)⁴
= 9544(1+0.0525)⁴
= 9544(1.0525)⁴
= 9544×1.2271
= $11711.4424
Therefore, the amount in the account is $11711.4424.
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Step 1, when solving a two dimensional, multi-charge problem, is to define the vectors. please identify the next five steps, in order. step 2: step 3: step 4: step 5: step 6:
Answers
Step 1, when solving a two dimensional, multi-charge problem, is to define the vectors.
Step 2: calculate A and B magnitudes
Step 3: calculate x, y components
Step 4: sum vector components
Step 5: calculate magnitude of R
Step 6: calculate direction of R
What is a vectorA vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geometrical representation of such a quantity.
Examples of vectors in nature are velocity, momentum, force, electromagnetic fields and weight. A quantity or phenomenon that exhibits magnitude only, with no specific direction, is called a scalar. Examples of scalars include speed, mass, electrical resistance and hard drive storage capacity.
What are vector attributesVectors are typically represented by an arrow with a beginning, or tail, and an end, or head, that is usually represented by an arrowhead. Vectors delineate the movement from point A to point B and can be defined as an entity with a designation, such as vector a.
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Find the area of triangle XYZ if length XY equals 7 and length XZ equals 4.3. You also
know that angle Y equals 79°.
Answers
Answer:
A ≈ 14.8 units²
Step-by-step explanation:
the area (A) of the triangle is calculated as
A = \(\frac{1}{2}\) yz sin Y ( that is 2 sides and the angle between them )
where x is the side opposite ∠ X and z the side opposite ∠ Z
here y = XZ = 4.3 and z = XY = 7 , then
A = \(\frac{1}{2}\) × 4.3 × 7 × sin79°
= 15.05 × sin79°
≈ 14.8 units² ( to 1 decimal place )
What is the equation of the line?
Answers
Step by step
y = mx + b is our formula
We can see on the graph the y intercept is -2 so b= -2
We can see the slope is +2 rise over +3 run, so m = 2/3
Your answer is y = 2/3x -2
Problem solved!
pleasee help!! im confused
Answers
Answer:
28k + 68
Step-by-step explanation:
7(8 + 4k) + 12
first, you use the distributive property on the parentheses
56 + 28k + 12
then you add like term, 56 + 12 = 68
68 + 28k
numbers with variables go first
28k + 68
can you please help me.
Answers
Answer:
Answer is D.
6 x 3 =1 8
9 x 3 = 27
11 x 3 = 33
14 x 3 = 42
18 x 3 = 54
c = 3 x w
Step-by-step explanation:
In her last four basketball games, Alexi has scored 12, 14, 26, and 40 points. If the pattern continues, how many points will Alexi score in her next game?
Answers
Answer:
its 26. Just take my word for it
Step-by-step explanation:
14-12=2
26-14=12
40-26=14
You see the pattern. Alexi will score 26 pts. btw, this goes against the laws of probability, but whatever.
PLEASE HELP 50 POINTS
What is the inverse of y= 1/3 * 7^x-1
Answers
Answer:
I think its C
Step-by-step explanation:
Two small buckets and 1 large bucket can hold 8 cups of gasoline. One large bucket minus 1 small bucket constitutes 2 cups of gasoline. How many cups of gasoline can each bucket hold?
Answers
Let's represent the capacity of the small bucket as "x" and the capacity of the large bucket as "y".
From the first statement, we can set up the equation:
2x + y = 8
From the second statement, we can set up another equation:
y - x = 2
Now we can solve for "x" and "y".
Rearranging the second equation, we get:
y = x + 2
Substituting this value of "y" into the first equation, we get:
2x + (x + 2) = 8
Simplifying, we get:
3x + 2 = 8
Subtracting 2 from both sides, we get:
3x = 6
Dividing by 3, we get:
x = 2
Substituting this value of "x" into the second equation, we get:
y - 2 = 2
Simplifying, we get:
y = 4
Therefore, each small bucket can hold 2 cups of gasoline, and the large bucket can hold 4 cups of gasoline.
Find x if AB = x-6, BC = 7,
and AC= -8 + 2x.
Answers
Answer:
9
Step-by-step explanation:
set up the equation: ab+bc=ac
(x-6) + 7 = (-8+2x)
Step 1: Simplify both sides of the equation.
x−6+7=−8+2x
x+−6+7=−8+2x
(x)+(−6+7)=2x−8(Combine Like Terms)
x+1=2x−8
x+1=2x−8
Step 2: Subtract 2x from both sides.
x+1−2x=2x−8−2x
−x+1=−8
Step 3: Subtract 1 from both sides.
−x+1−1=−8−1
−x=−9
Step 4: Divide both sides by -1.
−x/−1 = −9 /−1
x=9
If f(x) = -4x + 15 and g(x) = 7.x^3 find the following.
1) g(-3) + f(-3)
2) (f-g)(2)
Answers
Answer:
g(-3) + f(-3) = -162
(f - g)(2) = -49
Step-by-step explanation:
f(x) = -4x + 15
g(x) = 7x³
1)
g(-3) + f(-3)
Evaluate g(-3) and f(-3).
g(-3) = 7(-3)³, f(-3) = -4(-3) + 15
7(-3)³ + -4(-3) + 15
Evaluate (-3) to the third power.
7(-27) + -4(-3) + 15
Multiply.
-189 + 12 + 15
Add.
-177 + 15
-162.
2)
(f - g)(2) = f(2) - g(2)
Evaluate f(2) and g(2)
f(2) = -4(2) + 15
f(2) = -8 + 15
f(2) = 7
g(2) = 7(2)³
g(2) = 7(8)
g(2) = 56
Now subtract the result of g(2) from the result of f(2)
(f - g)(2) = 7 - 56
(f - g)(2) = -49.