Answer:
[tex](a)[/tex] [tex]V = -H^3+ 5H^2 + 36H[/tex]
[tex](b)[/tex] [tex]Length = 5in; Width = 9in; Height = 5in[/tex] or [tex]Length = 3in; Width = 10in; Height = 6in[/tex]
Step-by-step explanation:
Let:
[tex]W=Width; L = Length; H = Height[/tex]
Given
[tex]W = 4 + H[/tex]
[tex]L = 9 - H[/tex]
Solving (a): The polynomial for the volume in terms of height
Volume (V) is calculated using:
[tex]V = L * W * H[/tex]
[tex]V = (9 - H) * (4 + H) * H[/tex]
Expand
[tex]V = (9 - H) * (4H + H^2)[/tex]
Open brackets
[tex]V = 36H + 9H^2 - 4H^2 - H^3[/tex]
[tex]V = 36H + 5H^2 - H^3[/tex]
Rewrite as:
[tex]V = -H^3+ 5H^2 + 36H[/tex]
Solving (b): The dimensions when Volume = 180
Substitute 180 for V in: [tex]V = -H^3+ 5H^2 + 36H[/tex]
[tex]180 = -H^3+ 5H^2 + 36H[/tex]
Rewrite as:
[tex]H^3 - 5H^2 - 36H + 180 = 0[/tex]
Factorize:
[tex]H^2(H - 5) - 36(H - 5) = 0[/tex]
[tex](H^2 - 36)(H - 5) = 0[/tex]
Express [tex]H^2 - 36[/tex] as difference of two squares
[tex](H - 6)(H + 6)(H - 5) =0[/tex]
This gives:
[tex]H - 6 =0==> H = 6[/tex]
[tex]H + 6 =0==> H = -6[/tex]
[tex]H - 5 =0==> H = 5[/tex]
Since the height can not be negative, then H = 5 or H = 6
Recall that:
[tex]W = 4 + H[/tex]
[tex]L = 9 - H[/tex]
When H = 5
[tex]W = 4 + 5 = 9[/tex]
[tex]L = 9 - 5 = 4[/tex]
When H = 6
[tex]W = 4 + 6 = 10[/tex]
[tex]L = 9 - 6 = 3[/tex]
Hence, the dimensions of the box are:
[tex]Length = 5in; Width = 9in; Height = 5in[/tex]
or
[tex]Length = 3in; Width = 10in; Height = 6in[/tex]
The volume of the box is given by -h³ + 5h² + 36h
Volume
Volume is the amount of space occupied by a three dimensional object. The volume (V) of a box is given by:
V = length * width * height
Let h represent the the height, hence width = h + 4, length = (9 - h)
V = h(h + 4)(9 - h) = h(5h -h² + 36) = -h³ + 5h² + 36h
For a volume of 180 in³:
180 = -h³ + 5h² + 36h
h = 5 or 6.
The volume of the box is given by -h³ + 5h² + 36h
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PLEASE HELP ASAP PLEASE
PLEASE HELP ME I DONT UNDERSTAND!!
EVERYTHING YOU NEED TO KNOW IS ON THE IMAGE BELOW!!!
Show your work so I can mark you brainliest!!!
Step-by-step explanation:
no.1 first write the equation
the write the sum and the product
so the sum will be 8x and the product
will be 15.In the product part look for a no
that when you multiply it by another no
it will give you 15 by when you add it will
become 8.The no.is 5 and 3.you now rewrite the equation x^2+3x+5x+15=0
you now simply the equation x(x+3)+5(x+3)
you take (x+3)and (x+5)=0.
your answer will either be -3or-5 respectively
Keith needs to build a bridge to go across a pond. He has been able to collect the following measurements. About how long does this bridge need to be
Answer:
[tex]\Huge\boxed{11.9}[/tex]
Step-by-step explanation:
Hello There!
Basic Concepts
Geometry
Once again we are going to need to use trigonometric ratios to solve for a missing side length (the length of the bridge)
Here are the trigonometric ratios
Sine - Opposite over Hypotenuse
Cosine - Adjacent over Hypotenuse
Tangent - Opposite over Adjacent
For the angle that has a measure of 50 degrees
we are given its adjacent side length and we need to find its opposite
When working with the opposite side length and adjacent side length we use the trigonometric ratio tangent
Knowing which trigonometric ratio we are going to use we have to create an equation
Remember tan = opposite over adjacent
So we plug in the given information and solve for the missing information ( In this case the opposite side length)
[tex]tan(50)=\frac{x}{10}[/tex]
Basic Algebra
Now we solve for x
Like always we want to isolate the variable
First we want to get rid of the 10
x is being divided by 10 and the inverse of division is multiplication
So we multiply each side by 10
[tex]tan50*10=10tan50\\\frac{x}{10} *10=x\\[/tex]
now we have
[tex]10tan50=x\\[/tex]
finally we plug in 10tan50 into a calculator to get the value of x
we get that x = 11.91753594
Our last step is to round to the nearest tenth
We can conclude that the answer is 11.9
The bridge needs to be 11.92 feet long by calculating the tangent of the given angle.
What is tangent of an angle?Tangent of an angle in a right-angled triangle is the ratio of the height to the base of the triangle.
Let, the bridge is x ft. long.
Therefore, tan 50° = [tex]\frac{x}{10}[/tex].
⇒ x = 10 × tan 50°
⇒ x = 10 × 1.192
⇒ x = 11.92
Therefore, the bridge is 11.92 ft. long.
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To mail a letter to Vienna, Austria the post office charges a flat rate of $9.75 and an additional $0.50 for every ounce the letter weighs. The cost of mailing a letter is determined by the equation y=0.50x+9.75, where y is the cost of the postage and x is the weight of the letter in ounces.
Missing details
Which type of function model would be appropriate for this situation?
Answer:
Linear function
Step-by-step explanation:
Given
[tex]y = 0.50x +9.75[/tex]
Required
The function model
A function of the form:
[tex]y = mx + b[/tex]
is referred to as a linear function where
[tex]m = slope/rate[/tex]
[tex]b=y\ intercept[/tex]
By comparison:
[tex]m = 0.50\ b = 9.75[/tex]
So, it is a linear function (linear model)
How would you describe slope 0/-5? Brainliest for best answer!!!
A. positive
B. negative
C. 0
D. does not exist.
i need help with this question
Answer:
(C). [tex]\frac{22\pi }{3}[/tex] yd.
Step-by-step explanation:
Suppose you want to put trim around the floor of a rectangular room.
The room is 7 by 11 feet. If a foot of trim costs $6, how much will the
trim cost altogether?
What is the value of x in the figure? Enter your answer in the box.
Answer:
x = 65°
Step-by-step explanation:
these are vertical angles, which are congruent
145 = 2x + 15
130 = 2x
65 = x
In the early 2016 there were about 80 devils living on Maria island.Of that total, 75% are offspring from the previous two breeding seasons. How many are offspring
Answer: 60 devils
Step-by-step explanation:
Question wants to know the number of offspring from the two previous breeding seasons.
There are 80 devils on the island. 75% of this 80 are from previous breeding seasons.
We need to find this 75% in whole numbers:
= Percentage of devils from previous seasons * Total number of devils
= 75% * 80 devils
= 60 devils
can someone help me! The person who gets it right gets brainliest
Answer:
The answer is 17.6
Step-by-step explanation:
Multiply 8 x 2.2, and act as if you are cutting off the left "triangle" and simply moving it to the other side, making it act like a rectangle.
The Cougars basketball team sold tins of flavored popcorn as a fundraiser. The players competed for prizes to see who could sell the most tins. This box plot shows the results.
Popcorn tins sold
What fraction of the players sold between 8 and 16 popcorn tins?
Answer:
1/2 percent
Step-by-step explanation:
If you look at the box, the middle number is 12 or since its the middle "1/2"
so the fraction would be 1/2, hope this helped.
The fraction of the players sold between 8 and 16 popcorn tins 1/2 percent.
We have given that,
The players sold between 8 and 16 popcorn tins,
If you look at the box, the middle number is 12, or since it's the middle 1/2.
What is the fraction?
Fractions represent equal parts of a whole or a collection. Fraction of a whole When we divide a whole into equal parts, each part is a fraction of the whole.
So the fraction would be 1/2, hope this helped.
The fraction of the players sold between 8 and 16 popcorn tins 1/2 percent.
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There are 68 marbles in a bin and 50% of the marbles are red.
How many red marbles are the bin?
There are
red marbles in the bin. .
Answer:
34 because 50 percent of 68 is 34
Answer:
There are 34 red marbles in the bin
Step-by-step explanation:
50% is basically 1/2. So half of 68 is 34.
what is equvalint to 1/2a-4
Total surface area??
Answer:
total area = 207 cm²
Step-by-step explanation:
base area = 9 x 9 = 81
side area = 1/2(9)(7) = 31.5 x 4 (for 4 sides) = 126
81 + 126 = 207 cm²
WILL MRAK BRAINLIESTTTT IF GOTTEN RIGHT DONT ANSWER IF U DONT KNOW!
Answer:
BC=4
Step-by-step explanation:
didn't i do this already lol
Every year, a car loses 15% of the value it had the year before. If the car's initial value is $ 24,000, then how long will it take for the car to be worth half of its value?
Answer:
4.62 years
Step-by-step explanation:
Half the car's value =>$24,000/2 = $12,000
The formula for exponential decrease =
y = a(1 - r)^t
y = Initial value = $24,000
a = Value after time t = $12,000
r = Decrease rate = 15% = 0.15
t = time in years =??
Hence,
24,000 = 12000 ( 1 - 0.15)^t
Divide both sides by 12000
24000/12000 = 12000 ( 0.85)^t/ 12000
2 = 0.85^t
We take the logarithm of both sides
log 2 = log (0.85)^t
log 2 = t log 0.85
Divide both sides by log 0.85
t = log 2/log 0.85
t = 4.62098120373 years
Approximately = 4.62 years
It would take 4.62 years to be worth half the initial price
Paul had 3.8 pounds of bananas and 2.1 pounds of apples. About how much fruit does he have in all?
Answer:
5.9 pounds
Step-by-step explanation:
3.8 + 2.1 = 5.9
Which values for A and B will create infinitely many solutions for this system of equations? A x minus y = 8. 2 x + y = B.
Answer:
A = -2
B = -8
Step-by-step explanation:
A system of equations has infinitely many solutions when both equations are exactly the same equation, then both graphs intersect in infinitely many points, meaning that the system has infinitely many solutions.
Then if we have the equations:
A*x- y = 8
2*x + y = B
We want to find A and B such that both equations are exactly the same thing.
Notice that in the first one we have negative y, while in the second we have positive y.
Then A needs to be minus the coefficient that multiplies x in the other equation, this means that:
A = -2
And B needs to be minus the corresponding therm in the other equation, then B = -8.
Then the system becomes:
-2*x - y = 8
2*x + y = -8
We can see that one equation is -1 times the other, so if we write both of them as linear equations in the slope-intercept form, we get:
y = -8 - 2*x
y = -8 - 2*x
So both equations are exactly the same thing, meaning that we have infinitely many solutions.
HELPP PLS it’s literally almost due
A pizza parlor is creating a questionnaire to survey customers about their satisfaction with the taste of their pizzas. Which questions would be considered good questions to include on the survey?
Answer:
On a scale of 1 to 10, how satisfied are you with the taste of our pizzas?
Would you recommend our pizzas to your friends and neighbors? Please answer either yes or no.
Step-by-step explanation:
what is the measure of the complement of a 67 degree angle?
Answer:
23°
Step-by-step explanation:
Complement angles are two angles that add up to 90°.
Since we’re given that one of them is 67°, the other one must add up to 90°
90 - 67 = 23
The other angle is 23°
Answer:
the complement of 67° is the angle that when added to 67° forms when a right angle (90°)
Someone pls help im new tysm if you do!
Answer:
-24 is your answer<3.....
the parenthess are just multiplication, so 6*-4 is -24
2. 3. Edward bikes the same route to and from school each day. After 28 school days, he bikes a total distance of 389.2 miles. a. Estimate how many miles he bikes in one day.
Answer:
Step-by-step explanation:
Estimate usually means "Don't use a calculator." An estimate would be 30 days and 390 miles. That makes 13 miles / day. I get the feeling that is not what is wanted.
miles / day = total distance / number of days
miles / day = 389.2 / 28
miles / day = 13.9 miles per day. I don't know which answer to use. I'd try this one first and then use the top one.
1÷1+cosa+1÷1_cos a please solve question
ok so THIS IS UR ANSWER I THINK PLEASE MAKE ME BRAINLIEST
What is 9 x 2/3 as a fraction.
The expression 9x2/3 can be written in fraction form as, 18/3
What is a fraction?Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.
Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.
9 times 2/3 can be calculated by first converting 9 to a fraction and then multiplying that fraction by 2/3. To convert 9 to a fraction, we write it over 9/1 x 2/3
Next, we multiply the two fractions by multiplying the numerators (the top numbers) together and the denominators (the bottom numbers) together:
⇒ (9/1) x (2/3)
⇒ (9 x 2) / (1 x 3)
⇒ 18/3
So, 9 times 2/3 as a fraction is 18/3.
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if PQ and PR are tangent to circle S,find PQ
Answer:
From one point, you can draw two tangents to a circle. These two tangents will be equal.
Step-by-step explanation:
7x - 24 = 57 - 2x.
Rearrange the numbers (by adding 2x and 24 on both sides), we get:
7x+2x = 57 + 24
9x = 81.
x = 9.
Length of PQ = 57-2x = 57 - 18 = 39
If PQ and PR are tangent to circle S, then the value of PQ is 39.
What is tangent?"A line that touches the circle at a single point is known as a tangent to a circle."
What is circle?"A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre."
P is the exterior point of a circle.
PQ and PR are the tangents to circle S.
According to theorem,
The lengths of the tangents drawn from a same external point to a circle are always equal.
7x - 24 = 57 - 2x
7x + 2x = 57 + 24
9x = 81
x = 9
PQ = 7x - 24
PQ = 7(9) - 24
PQ = 63 - 24
PQ = 39
Hence, the value of PQ is 39.
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Plz Help I will give Brainliest
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer: 8.6 Ft^2
Explanation:
First find the area of the WHOLE square in FEET
2.5 x 4.5 = 11.25 ft
Then we need to find the area of the circle
r = radius
The formula is A = 3.14r^2
The radius is .9166, we can tell because the total distance from top to bottom is 22in meaning 1.83333 ft, meaning the diameter is 1.8333, then to get the radius we cut that in half.
A = 3.14(.9166^2
A = 2.64 Ft
Now we need to find the new total area
11.25 - 2.64 = 8.61 in ^2
Now we need to convert it to the nearest tenth of a square foot
8.6 Ft^2
I hope this helped !
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- Zack Slocum
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What is the percent increase when 7,200 increases by 1,800?
20 percent
25 percent
O 54 percent
O 80 percent
Answer:
25%
Step-by-step explanation:
To find the percent increase, take the increase amount over the original amount
1800/7200
.25
Multiply by 100 to get a percent
25%
25 percent
7200 divided by 1800 is 25
HOPE THIS HELPS
36 is 18% of what number?
Answer: 200
Step-by-step explanation: 36 by 100 and then divide the total by 18 as follows: (36 x 100) / 18 For 200
Answer:
200
Step-by-step explanation:
:/
I hope
Factor completely
16x^2y^4z^3+33xy^8z^5
Answer:
xy^4 z^3 ( 16x + 33y^4 z^2)
Step-by-step explanation:
step 1 : see what variable you can take out , start with x see if there is x in the left and right side. and how many time you can take it out
next y same thing and then last z
with x = left side you x^2 and right side you have x = so u can take x out once left you with x
with y = left side y^4 and right side y^8 so you can take out y ^4 out left you with y^4
with z = left side z^3 and right side z ^5 you can take out z^3 left you with z^2