Answer:
I believe you forgot to add a picture
Please help! Photo is attached. Will give brainliest if correct answer.
0.66 inches of material is needed to be cut off to make the volume maximum.
maximum and minimum points testWhen the second derivative of a function is negative, the function has a maximum point and if the second derivative is positive, the function has a minimum point.
Analysis:
After cut and folded, length = 8-2x
Width = 3-2x
Thickness = x.
Volume of the folded shape = (8-2x)(3-2x)(x)
After expansion, V = 4[tex]x^{3}[/tex]-[tex]22x^{2}[/tex] +24x
for turning point of the function, dv/dx = 0
dv/dx = 12[tex]x^{2}[/tex] -44x + 24
lowest term = 3[tex]x^{2}[/tex] - 11x + 6
3[tex]x^{2}[/tex] - 11x + 6 = 0
3[tex]x^{2}[/tex] - 9x -2x +6 = 0
3x(x-3) -2(x-3) = 0
(3x-2)(x-3) = 0
x = 2/3 or x = 3
To test for maximum point, we differentiate dv/dx again
we have 6x - 11
for x = 3, 6(3) - 11 = 18 - 11 = 7 which is positive x= 3 is a minimum
for x = 2/3 6(2/3) - 11 = 4 - 11 = -7, x = 2/3 is a maximum.
Therefore for maximum volume, the length to be cut out is 2/3 which is 0.66 inches.
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evaluate question 4 only
Substitute [tex]y = \sqrt x[/tex], so that [tex]y^2 = x[/tex] and [tex]2y\,dy = dx[/tex]. Then the integral becomes
[tex]\displaystyle \int \frac{dx}{\sqrt{1 + \sqrt x}} = 2 \int \frac y{\sqrt{1+y}} \, dy[/tex]
Now substitute [tex]z=1+y[/tex], so [tex]dz=dy[/tex]. The integral transforms to
[tex]\displaystyle 2 \int \frac y{\sqrt{1+y}} \, dy = 2 \int \frac{z-1}{\sqrt z} \, dz = 2 \int \left(\sqrt z - \frac1{\sqrt z}\right) \, dz[/tex]
The rest is trivial. By the power rule,
[tex]\displaystyle \int \left(\sqrt z - \frac1{\sqrt z}\right) \, dz = \frac23 z^{3/2} - 2z^{1/2} + C = \frac23 \sqrt z (z - 3) + C[/tex]
Put everything back in terms of [tex]y[/tex], then [tex]x[/tex] :
[tex]\displaystyle 2 \int \frac y{\sqrt{1+y}} \, dy = \frac43 \sqrt{1+y} (y - 2) + C[/tex]
[tex]\displaystyle \int \frac{dx}{\sqrt{1+\sqrt x}} = \boxed{\frac43 \sqrt{1+\sqrt x} (\sqrt x - 2) + C}[/tex]
Maria expanded the following square as follows: (x+3)² =x²+9, is this correct?
Answer:
x² + 6x + 9
Explanation:
[tex]\sf = \left(x+3\right)^2[/tex]
Use perfect square formula: (a + b)² = a² + 2ab + b²
[tex]= \sf x^2 + 2(x) (3) + 3^2[/tex]
simplify the following
[tex]= \sf x^2 + 6x +9[/tex]
Hence Maria is not correct. The correct answer is x² + 6x + 9.
Donna took out a loan for $17,000 and was charged simple interest at an annual rate of 6.8% .
The total interest she paid on the loan was $867 . Do not round any intermediate computations.
Total amount she paid to repay her loan was $17,687
Amount is the total sum of money paid to the bank.It is basically the sum of interest and principal amount.
Principal is the sum of money taken from the bank
Interest is the sum of money charge by the bank during the period of loan repayment.
Rate of interest is the rate at which interest is charge in the principal sum
Time is the total period of the loan repayment.
Simple interest = (P x Rx T)/100
where, P=principal
R=rate of interest
T= time
Amount= Principal +Interest
As per question,
P=$17000
R=6.8%
I=$687
Amount=P+I
=$17000+687
=$17687
Therefore,Total amount she paid to repay her loan was $17,687
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An entrance examination for a job consists of 25% English, 50% Mathematics, 5% Typing and 20% Accounting, and the passing mark is 50. If an applicant sat for the examination and scored 48% in English, 35% in Mathematics, 80% in Typing and 50% in Accounting, do you think she will be accepted? Why?
Answer:
No, the total is 43.5 which is below 50.
Step-by-step explanation:
English: 25% × 48 = 12
Mathematics: 50% × 35 = 17.5
Typing: 5% × 80 = 4
Accounting 20% × 50 = 10
12 + 17.5 + 4 + 10 = 43.5
Total: 43.5
Passing: 50
Answer: No. The total is too low.
what is the %rf for .04?
6/64 reduce to lowest terms
Answer:
[tex]\frac{3}{32}[/tex]
Step-by-step explanation:
-> Simplify
[tex]\frac{6}{64} =\frac{6/2}{64/2} =\frac{3}{32}[/tex]
6/64 simplified.
Another day, another math problem
Answer:
4x+2h+5
Step-by-step explanation:
[tex]\frac{(2(x+h)^{2}+5(x+h)) - (2x^{2} +5x) }{h} \\[/tex]
For now I'm just going to ignore the denominator for simplicity
[tex](2(x^{2}+2xh+h^{2})+5x+5h) - (2x^{2} +5x)\\(2x^{2}+4xh+2h^{2}+5x+5h) - (2x^{2} +5x)\\(4xh+2h^{2}+5h)\\\\\frac{(4xh+2h^{2}+5h)}{h}\\ 4x+2h+5[/tex]
Final step just distributes the division
Use linear equation to calculate intercepts.
x minus one-half y = negative 4
Complete the table with values for a and b.
A 2-column table with 3 rows. Column 1 is labeled x with entries 0, negative 2, b. Column 2 is labeled y with entries a, 4, 0.
a =
b =
The x intercept of the linear equation is -4 and y intercept is 8.
Intercept of the linear equation
The intercept of the linear equation is calculated as follows;
x - y/2 = -4
make y the subject of the formula;
y/2 = x + 4
y = 2x + 8
y intercept is obtained at point, x = 0y = 0 + 8
y = 8
x intercept is obtained at point, y = 00 = 2x + 8
2x = -8
x = -4
Thus, the x intercept of the linear equation is -4 and y intercept is 8.
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Answer:
The x intercept of the linear equation is -4 and y intercept is 8
Step-by-step explanation:
Chef Fabio does beginning inventory on Thursday night and finds that he has $1456 in food products in the restaurant. Throughout the week he purchases:
$457 produce,
$632 protein,
$356 dry goods, and
$147 dairy.
The following Thursday he does ending inventory and finds that he has $1643 in food. He looks at his sales and finds that he made $5546 over the same 7 day period. What is his food cost as a percentage of sales (food cost percentage)?
Using it's concept, it is found that the percentage of his sales that area food costs is of 29.62%.
What is a percentage?The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
[tex]P = \frac{a}{b} \times 100\%[/tex]
In this problem, he has $1643 out of $5546 in food, hence the percentage is given by:
[tex]P = \frac{1643}{5546} \times 100\% = 29.62%[/tex]
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Which graph shows the greatest integer function?
By critically observing the given graphs, we can logically deduce that "graph C" returns greatest integer that is less than or equal (≤) to x.
What is a greatest integer function?A greatest integer function can be defined as a type of function which returns the greatest integer that is less than or equal (≤) to the number.
Mathematically, the greatest integer that is less than or equal (≤) to a number (x) is represented as follows:
y = [x].
By critically observing the given graphs, we can logically deduce that y in "graph C" returns greatest integer that is less than or equal (≤) to x.
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Find the zeros of the quadratic polynomial f(x) = 6x²-3, and verify the relationship between the zeros and its coefficients.
Step-by-step explanation:
1) zeros of the given function:
6x²-3=0; ⇔ 6(x²-0.5)=0; ⇔ x²=0.5; ⇔
[tex]\left[\begin{array}{ccc}x=-\sqrt{0.5} \\x=\sqrt{0.5} \end{array}[/tex]
2) relationship:
if to see the equation x²-0.5=0 (ax²+bx+c=0 is standart form!), then the sum of the zeros is '0' (it is 'b' of the standart form), the product of equation roots is '-0.5' (it is 'c' of the standart form).
[tex]{\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}[/tex]
★ The polynomial
f(x) = 6x² - 3
[tex]{\large{\textsf{\textbf{\underline{\underline{To \: find :}}}}}}[/tex]
★ Zeroes of the polynomial f(x) = 6x² - 3
[tex]{\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}[/tex]
We have,
[tex]f(x) = \tt 6 {x}^{2} - 3[/tex]
Which can also be written as
[tex] \implies f(x) = \tt {(\sqrt{6} x)}^{2} - { (\sqrt{3}) }^{2} [/tex]
Using a² - b² = (a - b) (a + b)
[tex] \implies f(x) = \tt ( \sqrt{6} x - \sqrt{3} )( \sqrt{6} x + \sqrt{3} )[/tex]
To find the zeroes, solve f(x) = 0
[tex] \longrightarrow \tt ( \sqrt{6} x - \sqrt{3} )( \sqrt{6} x + \sqrt{3} ) = 0[/tex]
either [tex] \tt \sqrt{6} x - \sqrt{3} = 0 \: or \: \sqrt{6} x + \sqrt{3} = 0[/tex]
[tex] \implies \tt \sqrt{6} x = \sqrt{3 \: } \: or \: \: \sqrt{6} x = - \sqrt{3}[/tex]
[tex] \implies \tt x = \dfrac{ \sqrt{3} }{ \sqrt{6} } \: or \: x = - \dfrac{ \sqrt{3} }{ \sqrt{6} }[/tex]
[tex] \implies \tt x = \dfrac{ \sqrt{3} }{ \sqrt{2 \times 3} } \: or \: x = - \dfrac{ \sqrt{3} }{ \sqrt{2 \times 3} }[/tex]
[tex]\implies \tt x = \dfrac{ \cancel{ \sqrt{3} }}{ \sqrt{2} \: \cancel{\sqrt{3}} } \: or \: x = - \dfrac{ \cancel{ \sqrt{3} }}{ \sqrt{2} \: \cancel{\sqrt{3}} }[/tex]
[tex]\implies \tt x = \dfrac{1}{ \sqrt{2} } \: \: or \: \: - \dfrac{1}{ \sqrt{2} }[/tex]
Hence, the zeroes of f(x) = 6x² - 3 are:
[tex] \tt \alpha =\sf \boxed {{ \red{ \dfrac{1}{ \sqrt{2} } } }}\: \: and \: \: \beta =\sf \boxed {{ \red{ - \dfrac{1}{ \sqrt{2} } } }}[/tex]
• Verification
Sum of zeroes = [tex] ( \alpha + \beta )[/tex]
[tex] = \tt \dfrac{1}{ \sqrt{2} } + \bigg(- \dfrac{1}{ \sqrt{2} } \bigg)[/tex]
[tex] = \tt \dfrac{1}{ \sqrt{2} } + - \dfrac{1}{ \sqrt{2} } [/tex]
[tex]= \tt 0[/tex]
and, [tex]\tt - \dfrac{Coefficient \: of \: x}{Coefficient \: of \: {x}^{2} }[/tex]
[tex] \tt = - \dfrac{0}{6} [/tex]
[tex] \tt = 0[/tex]
[tex] \therefore \tt \: Sum \: of \: zeroes = {\boxed{ \red{\dfrac{ \tt Coefficient \: of \: x}{ \tt Coefficient \: of \: {x}^{2}}}}}[/tex]
Also,
Product of zeroes = [tex] \alpha \beta [/tex]
[tex] = \dfrac{1}{ \sqrt{2} } \times - \dfrac{1}{ \sqrt{2} } [/tex]
[tex] = - \dfrac{1}{ 2 } [/tex]
and, [tex]\tt - \dfrac{Constant \: term}{Coefficient \: of \: {x}^{2} }[/tex]
[tex] \tt = \dfrac{ - 3}{6} [/tex]
[tex] \tt = \dfrac{ - 1}{2} [/tex]
[tex] \therefore \tt \: Product \: of \: zeroes = {\boxed{ \red{\dfrac{ \tt Constant \: term}{ \tt Coefficient \: of \: {x}^{2}}}}}[/tex]
[tex]\rule{280pt}{2pt}[/tex]
A car travels 18 mile in 213 minutes. What is its speed in terms of miles per minute?
Answer:
[tex]\textsf {0.08 miles per minute}[/tex]
Step-by-step explanation:
[tex]\textsf {Speed = Distance (Miles) / Time (Minute) }[/tex]
[tex]\textsf {Speed = 18 miles / 213 minutes }[/tex]
[tex]\textsf {Speed = 0.08 miles per minute }[/tex]
Answer:
The speed in miles per minute is 0.0845 mpm.
Step-by-step explanation:
The explanation above clearly states that a car travel a distance of 18 miles in a time of 213 minutes . And it is asking for speed in miles per minute. Keep this in mind that the symbol for miles per minute is mpm. Speed formula is distance ÷ time.
Speed = Distance ÷ Time
Speed = 18 m / 213 min
18 divided by 213 = 0.0845
speed = 0.0845 mpm
Therefore the speed in miles per minute is 0.0845 mpm.
answer a-d please!!!!!!!!!!!!!!!!
a) Intercepts are the points on the x and y axis
In the graph:
x-int: (-2,0), (2,0)
y-int: (0,1)
b) Domain is the list of x-values and Range is the list of y-values that make this graph true
Interval notations of domain and range
(Square brackets because the circles are closed)
Domain: [3,3]
Range: [0,3]
c) Intervals of increase and decrease: where the graph is increasing and decreasing
Increasing: -2 to 0 & 2 to 3
Decreasing: -3 to -2 & 0 to 2
d)Even, odd or neither
It is an even degree as both of its hands are facing upwards
Hope it helps!
Grace is looking at a report of her monthly cell-phone usage for the last year to determine if she needs to upgrade her plan. The list represents the approximate number of megabytes of data Grace used each month.
700, 735, 680, 890, 755, 740, 670, 785, 805, 1050, 820, 750
If the value of mean is 781.67, then the standard deviation will be 100. Then the correct option is C.
The complete question is given below.
Grace is looking at a report of her monthly cell-phone usage for the last year to determine if she needs to upgrade her plan. The list represents the approximate number of megabytes of data Grace used each month.
700, 735, 680, 890, 755, 740, 670, 785, 805, 1050, 820, 750
What is the standard deviation of the data? Round to the nearest whole number.
65
75
100
130
What is a standard deviation?It is a metric for statistical information dispersion. The degree of spread indicates how much the result varies.
Grace is looking at a report of her monthly cell-phone usage for the last year to determine if she needs to upgrade her plan.
The list represents the approximate number of megabytes of data Grace used each month.
700, 735, 680, 890, 755, 740, 670, 785, 805, 1050, 820, 750
The mean of the data will be
Mean = (700 + 735 + 680 + ...... + 820 + 750) / 12
Mean = 781.67
Then the standard deviation will be
SD² = [(700 – 781.67)² + (735 – 781.67)² + ..... + (750 – 781.67)²] / 12
SD² = 10072.2222
SD = 100.36 ≈ 100
Then the correct option is C.
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Renate launched an object vertically from a point that is 58.9 meters above ground level with an initial velocity of 21.6 meters per second. This situation can be represented by the equation h=−4.9t2+21.6t+58.9, where h is the height of the object in meters and t
is the time in seconds after the object is launched.
What is the maximum height of the object?
The maximum height of the object is 82.7034 from the ground
What is Velocity ?Velocity is the measure of movement of an object with respect to time.
It is measured in m/sec
h = -4.9t²+21.6t +58.9
dh/dt = -9.8t +21.6
At maximum height , velocity = 0
therefore
-9.8t +21.6 = 0
9.8t = 21.6
t = 2.204 sec
h = -4.9 (2.204)²+ 21.6 * 2.204 +58.9
h = -23.803 +47.606 +58.9
h = 82.7034 from the ground
h = 23.80 from the point it is launched.
The maximum height of the object is 82.7034 from the ground
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Which number comes next in this series 1/64 1/32 1/16 1/8 1/4 1/2
Answer:
1/1
Step-by-step explanation:
As the question is halfing by 2
So
2 divide 2 equals 1
Answer:
1
Step-by-step explanation:
it's fractions of divided half. next one will be number 1
-2/9u=12
Solve for u
u=-54
you have -54 because
-54(-2)=108/9=12
Answer:
u =-54
Step-by-step explanation:
-2/9u=12
To solve for u multiply each side by -9/2 to isolate u
-9/2 * -2/9 u= 12 * -9/2
u =-54
Suppose that
f
(
x
,
y
)
=
x
+
5
y
f
(
x
,
y
)
=
x
+
5
y
at which
−
1
≤
x
≤
1
,
−
1
≤
y
≤
1
-
1
≤
x
≤
1
,
-
1
≤
y
≤
1
.
Absolute minimum of
f
(
x
,
y
)
f
(
x
,
y
)
is
Absolute maximum of
f
(
x
,
y
)
f
(
x
,
y
)
is
========================================================
Explanation:
The range of x values is [tex]-1 \le x \le 1[/tex] which means x = -1 is the smallest and x = 1 is the largest possible.
Similarly the smallest y value is y = -1 and the largest is y = 1.
----------
Plug in the smallest x and y value to get
f(x,y) = x+5y
f(-1,-1) = -1+5(-1)
f(-1,-1) = -6
Therefore, the absolute min is -6
----------
Now plug in the largest x and y values
f(x,y) = x+5y
f(1,1) = 1+5(1)
f(1,1) = 6
The absolute max is 6
The following table shows how far a bus has gone in t hours. Which of the following equations represents this information?
Step-by-step explanation:
You need to attach the table in order to get an answer.
Given f of x is equal to the quantity x plus 6 end quantity divided by the quantity x squared minus 9x plus 18 end quantity, which of the following is true?
A- f(x) is decreasing for all x < 6
B- f(x) is increasing for all x > 6
C- f(x) is decreasing for all x < 3
D- f(x) is increasing for all x < 3
Answer:
Step-by-step explanation:
The graph of the given f(x) shows you what you need to know. Nothing cancels. Two answers are going to be true: one for x<3 and one for x>6.
From the graph, you can see that for x>6 the graph is decreasing. That makes B incorrect.
You can also see that for x < 6 The bottom parabola shape is decreasing which makes A true.
Finally at least one of C or D has to be true. As you can see, they both are depending on which shape you look at.
The correct answer is B: f(x) is increasing for all x > 6.
To determine the intervals of increase and decrease for the function f(x), we can analyze the critical points and the behavior of the derivative. The derivative of f(x) is given by:
f'(x) = [(x² - 9x + 18)'(x + 6) - (x + 6)'(x² - 9x + 18)] / (x² - 9x + 18)²
Simplifying the derivative and finding the critical points, we get:
f'(x) = (x² - 3x - 18) / (x² - 9x + 18)²
Setting the numerator equal to zero and solving for x, we find the critical points:
x² - 3x - 18 = 0
(x - 6)(x + 3) = 0
x = 6 or x = -3
Analyzing the intervals created by the critical points and using test points, we find that f(x) is increasing for all x > 6. Therefore, the correct answer is B: f(x) is increasing for all x > 6.
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Need help!!!!!!!!!!!!!!!!!
One number is 6 more than twice another. If their sum is 51, find the numbers.
Which of the following systems of equations represents the word problem?
y = 2x + 6 and y = x + 51
y = 2x + 6 and x + y = 51
y = 2(x + 6) and x + y = 51
Answer:
y = 2x + 6 and y + x = 51
Step-by-step explanation:
the first number is y
the second number is X
" 6 is more than" implying +
"6 is more than twice another" implying y = 6 + 2 multiples by the second number "X"
their sum is equal to 51
add first and the second number
that is
y+x = 51
so we have
y = 6+2x and y +x = 51
Perform the operation and
simplify.
x² + 10x + 24
3x² + 3x
÷ (x + 6)
244x3+1474x2+63x/
x+6
6. The diagram on the right shows the cross-section of a cylindrical pipe with water lying in the bottom. a) If the maximum depth of the water is 2 cm and the radius of the pipe is 7 cm, find the area shaded. b) What is the volume of water in a length of 30 cm?
Answer:
404 cm³ Anyway... Look down here for my explanation.
Step-by-step explanation:
Let's Draw a line from the center of the circle to one of the ends of the chord (water surface) and another to the point at greatest depth on your paper. A right-angled triangle is formed too. The Length of side to the water-surface is 5 cm, the hospot is 7 cm.
We Calculate the angle θ in the corner of the right-angled triangle by: cos θ = 5/7 ⇒ θ = cos ˉ¹ (5/7)
44.4°, so the angle subtended at the center of the circle by the water surface is roughly 88.8°
The area shaded will then be the area of the sector minus the area of the triangle above the water in your diagram.
Shaded area 88.8/360*area of circle - ½*7*788.8°
= 88.8/360*π*7² - 24.5*sin 88.8°
13.5 cm²
(using area of ∆ = ½.a.b.sin C for the triangle)
Volume of water = cross-sectional area * length
13.5 * 30 cm³
404 cm³
Use slopes and y-intercepts to determine if the lines 10x+3y=−3 and 5x−4y=−3 are parallel.
Answer:
They are not parallel
Step-by-step explanation:
original equation
10x + 3y = -3
subtract 10x
3y = -10x - 3
divide by 3
y = -10/3x - 1
original equation
5x - 4y = -3
subtract 5x
-4y = -5x-3
divide by -4
y = 5/4x + 3/4
the slopes are not equal to each other (5/4x and -10/3x) so they are not parallel
What is the area of a circle with 20cm diameter
Answer:
area of the circle
area=7.54
Let f(x)=(3)^x−3. What is f(0) in fraction form?
Answer:
1/27
Step-by-step explanation:
We can substitute x=0 into the function to get:
f(0) = 3^(0-3)f(0) = 3^(-3)f(0) = 1/27Suppose that land in downtown Savannah is valued at $20 per square foot. What is
the value of a triangular lot with side lengths of 112, 148, and 190 feet?
Answer:
$165554
Step-by-step explanation: I use the Law of Cosines to find one of the angles of the triangle. Then use the formula for the area of the triangle: A = (1/2)absinC.
C= 92.856 degree
Area = (1/2)(112)(148)sin(92.856°) = 8277.7 ft^2
To find the price just need to take 8277.7 time 20 = 165554
So the answer is $165554
What is the surface area of a sphere with radius 3?
Answer:
A≈113.1
Step-by-step explanation:
A=4πr2=4·π·32≈113.09734
