The rate of change of the area of the trapezoid at that instant is 5 square kilometers per second and this can be determined by differentiating the area of the trapezoid with respect to time 't'.
Given :
One base of a trapezoid is decreasing at a rate of 8 kilometers per second and the height of the trapezoid is increasing at a rate of 5 kilometers per second. The other base of the trapezoid is fixed at 4 kilometers. At a certain instant, the decreasing base is 12 kilometers and the height is 2 kilometers.First, determine the area of a trapezoid, that is:
[tex]\rm A = \dfrac{b_1+b_2}{2}\times h[/tex]
[tex]\rm \dfrac{2A}{h}=b_1+b_2[/tex]
[tex]\rm b_2 = \dfrac{2A}{h}-b_1[/tex]
Now, differentiate the above expression with respect to 't'.
[tex]\rm \dfrac{db_2}{dt} = -\dfrac{2A}{h^2}\dfrac{dh}{dt}-\dfrac{db_1}{dt}[/tex]
Now. substitute the values of the known terms in the above formula.
[tex]\rm \dfrac{db_2}{dt} = -\dfrac{2\times (16)}{2^2}\times (5)-(-8)[/tex]
[tex]\rm \dfrac{db_2}{dt} = -32\;km/sec[/tex]
So, the area is decreasing at the rate of 5.
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Right now, Kate is 4 times as old as Tim. In four years, Katie will be 2 times as old as
Tim How old is each of them right now? How old will they be in four years?
Answer:
wth kinda question is this well how old is tim they could be 15 or 30 we don't clarify for us
Step-by-step explanation:
get smarter for asking question
Answer:
ya what the guy said above me
Step-by-step explanation:
Your current CD matures in a few days. You would like to find an investment with a higher rate of return than the CD. Stocks historically have a rate of return between 10% and 12%, but you do not like the risk involved. You have been looking at bond listings in the newspaper. A friend wants you to look at the following corporate bonds as a possible investment. A 5-column table with 2 rows. Column 1 is labeled Bond with entries A B C 7 and one-half 15, X Y Z 7 and three-fourths 15. Column 2 is labeled current yield with entries 7.5, 8.4. Column 3 is labeled volume with entries 128, 17. Column 4 is labeled Close with entries 104 and three-fourths, 100 and one-half. Column 5 is labeled net change with entries blank, + one-fourth. If you buy five of the XYZ bonds with $8 commission for each, how much will it cost? a. $5025 b. $5065 c. $1005 d. $1045
Answer:
Answer is B. 5065
Step-by-step explanation:
Edge says so
Your current CD matures in a few days. You would like to find an investment with a higher rate of return than the CD. Stocks historically have a rate of return between 10% and 12%, but you do not like the risk involved. You have been looking at bond listings in the newspaper. A friend wants you to look at the following corporate bonds as a possible investment.
What was the price of the XYZ bond on the previous day?
Edge says its C. 100 1/4
Your current CD matures in a few days. You would like to find an investment with a higher rate of return than the CD. Stocks historically have a rate of return between 10% and 12%, but you do not like the risk involved. You have been looking at bond listings in the newspaper. A friend wants you to look at the following corporate bonds as a possible investment.
What was the price of the ABC bond on the previous day?
Edge says its D. 104 3/4
Answer:B
Step-by-step explanation:
need answer ASAP pls
Which is the independent variable in the graph of the U.S. population 1800-1900?
United States
straight lines
years
population
Answer: United States
Step-by-step explanation: Because threats the only independent variable the rest are dependent on others.
what is 1261/48 so then i could get done with my brain power
Answer: It is 26.27083333
26.27 if rounded
I NEED URGENT HELP
SOMEONE PLEASE HELP
Answer:
2x + 3y = -13
Step-by-step explanation:
We can first find the equation of the line in point-slope form. The slope of the line is given by [tex](y_2-y_1)/(x_2-x_1)[/tex], which is (-5-(-3))/(1-(-2)), or -2/3. The equation for a line in point-slope form is [tex]y-y_1=m(x-x_1)[/tex] where [tex]m[/tex] is the slope and [tex](x_1,y_1)[/tex] is a point on the line -- in this case, we may use (1, -5). Therefore, the equation for the line is y + 5 = -2/3 (x-1).
The question asks for the equation of the line in standard form -- which is [tex]Ax+By=C[/tex]. We can get this by simplifying the equation above to get[tex]2x+3y=-13[/tex].
lowest common multiple of 45 and 60
Answer:
180
Step-by-step explanation:
why does it have to be 20 character long
Write 3.0035 as a fraction.
Write the fraction as a mixed number (not an improper fraction). Make sure it is in simplest form.
The 3.0035 in the mixed number fraction should be [tex]3 \frac{7}{2000}[/tex]
Given that,
The given fraction is 3.0035 Calculation:[tex]= 3.0035\\\\= 30035 \div 10000\\\\= 6007 \div 2000 \\\\= 3 \frac{7}{2000}[/tex]
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5
Twenty sixth graders are going on a field trip. They will be
divided into 4 equal groups to take a tour. How many
students will be in each group?
Answer:
5 students per group
Step-by-step explanation:
20 ÷ 4 = 5 students
Answer:
5
Step-by-step explanation:
20/4=5
The volume of a cone is 1/3 that of a cylinder when the radius and height are the same (v= 1/3(pi)(r)^2(h). What is the volume of a cone with a radius of 10 inches and a height of 12 inches.
[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the Surface Areas and Volumes.
Since, Volume of cone = 1/3 π r^2 h,
here, r = 10 Inches and h= 12 inches, also π =3.14
so, VOC = 1/3 π (10)^2 × (20)
VOC = 1/3(3.14)(100)(20)= 2093.33 inch^3
=> so the volume of the cone is 2093.33 cubic inches.
7,574 divided 5 if u get it right ur my best friend i will give v go to https://brainly.com/app/ask?entry=similar&q=7%2C574+divided+5+if+u+get+it+right+ur+my+best+friend&skip=19641526 https://brainly.com/app/ask?entry=similar&q=7%2C574+divided+5+if+u+get+it+right+ur+my+best+friend&skip=19641526https://brainly.com/app/ask?entry=similar&q=7%2C574+divided+5+if+u+get+it+right+ur+my+best+friend&skip=19641526https://brainly.com/app/ask?entry=similar&q=7%2C574+divided+5+if+u+get+it+right+ur+my+best+friend&skip=19641526https://brainly.com/app/ask?entry=similar&q=7%2C574+divided+5+if+u+get+it+right+ur+my+best+friend&skip=19641526https://brainly.com/app/ask?entry=similar&q=7%2C574+divided+5+if+u+get+it+right+ur+my+best+friend&skip=19641526https://brainly.com/app/ask?entry=similar&q=7%2C574+divided+5+if+u+get+it+right+ur+my+best+friend&skip=19641526https://brainly.com/app/ask?entry=similar&q=7%2C574+divided+5+if+u+get+it+right+ur+my+best+friend&skip=19641526https://brainly.com/app/ask?entry=similar&q=7%2C574+divided+5+if+u+get+it+right+ur+my+best+friend&skip=19641526
Answer:
1514.8
Step-by-step explanation:
Answer:
1,514.8
Step-by-step explanation:
When using inverse operations, what should you do to solve y - 7 = 10?
Answer:
17
Step-by-step explanation:
There is a SUBTRACTION symbol in the problem. So, you will do the opposite, & ADD the 2 available numbers in the equation. 10+7=17
When you replace that y with 17, the equation is correct.
Car Sales A manufacturer of economy cars has determined that 50,000 cars per month can be sold at a price of $18,000 per car. At a price of $17,500, the number of cars sold per month would increase to 55,000. Determine a linear function that predicts the number of cars that will be sold at a price of x dollars. Use this model to predict the number of cars that will be sold at a price of $17,000.
Answer: 60,000 cars would be sold at $17000.
Step-by-step explanation:
• first we find the slope of the function between two points
(50,000, 18000) and ( 55,000, 17500)
• Let the number of cars sold be the x axis coordinate.
and the price is the y axis coordinate.
• next we plot this points.
m= Change in y / Change in x = rise / run
The slope m = (18000 - 17500/ 50,000 - 55,000)
= -0.1
• The equation of the line in point slope form is m(x-x1)=(y-y1)
• substituting for the first point
-0.1 (X-50,000) = y-18000
-0.1x - 5000 = y - 18000
-0.1x = 18000 + 5000
y = -0.1x + 23000
our slope -0.1 is negative.
In order to find the number of cars to be sold at a price of $17000, substitute this value y in the equation such that:
17000 =-0.1x+23000
solve for x
-0.1x = 23000-17000
0.1x = 6000
divide both sides by 0.1
x = 60000
60,000 cars would be sold at $17,000
what's the answer plz
Answer:
x ≥ 33
Step-by-step explanation:
Answer: the answer is 33
An estate of $485,000 is left to three siblings. The eldest receives 3 times as much as the youngest. The middle sibling receives $13,000 more than the youngest. How much did each receive?
Answer:
Step-by-step explanation:
the youngest received 94,200
the middle received 107,200
the eldest received 283,600
Step-by-step explanation:
Given parameters:
Worth of the estate = $485000
Unknown:
Amount received by each sibling = ?
Solution:
Let the amount received the eldest = e
middle = m
youngest = y
e = 3y
m = y + 13000
so;
e + m + y = 485000
3y + y + 13000 + y = 485000
5y = 485000 - 13000
5y = 472000
y = $94400
Eldest = 3y = 3 x 94400 = $283200
Middle = $94400 + $13000 = $107400
Youngest = $94400
If ABCD is a parallelogram. BC=13 and AB=5, what is the perimeter of the parallelogram?
Answer:
36
Step-by-step explanation:
In a Parallelogram , it is important to note that opposite sides are equal to each other.
We are given parallelogram ABCD.
We have sides: AB, BC, CD, AD.
Since opposite sides are equal then:
AB = CD
BC = AD
The perimeter of a parallelogram is the sum of all its sides.
In the question: BC=13 and AB=5
Hence,
AB = CD = 5
BC = AD = 13
Perimeter of Parallelogram ABCD = 5 + 5 + 13 + 13
= 36.
Alyssa had to read 110 pages over the weekend. By Saturday, she had completed 60 pages. What percent did she complete? Which proportion can be used to solve? *
60/110 = x/100
x/110 = 60/100
110/60 = x/100
Answer:
i believe the answer is c or 110/60=x/100
Step-by-step explanation:
A recipe calls for “18 ounces of cream cheese with 15 ounces of sugar” How many ounces of sugar are there per ounce of cream cheese?
Answer:
1.2
Step-by-step explanation:
18 divided by 15 equals 1.2
Please please help me
Answer:
the answer is c. it’s commutative property
Step-by-step explanation:
12-(y•2) is the same as 12-(2•y) 2 and y are just flipped around. hope this helps!
The graph of y = sin(x + 4) compared to the graph of
y = sin x has moved:
Yessss The answer is:
The graph of y = sin(x + 4) compared to the graph of
y = sin x has moved: It will be more voilentary and smaller but more larger with the aixs (x,y)
Connor and Maria are doing yard work for a neighbor. They make a total of $596.58. Since Maria works more hours than Connor, Maria gets 59% of the money. About how much (in whole dollars) does Maria make?
Maria makes about:
$300
$310
$240
$360
$410
$420
Answer:
360
Step-by-step explanation:
but 350 more accurately
Gven f(x) = -5x+9 If F(x)=-89. find x
Answer:
19.6 = X
Step-by-step explanation:
Plug in -89 for F(x)
Then just solve.
Get that 100.
5+2(10-4) ask question?
Answer: It is 17
Step-by-step explanation:
5+2(10-4)
5+2(6)
5+12
17
Answer: 17
Step-by-step explanation: you just have to simplify
The coordinates of both the pre-image and image of quadrilateral JKLM are listed in the table
below.
Which rule best represents this dilation?
A- (x, y) -> (4/11 x, 4/11 y)
B- (x,y) -> (3/22 x, 3/22 y)
C- (x, y) -> (11/4 x, 11/4 y)
D- (x, y) -> (22/3 x, 22/3 y )
Answer:
Option C.
Step-by-step explanation:
From the table attached,
Pre-image coordinates J(-8, 2) → Image coordinates J'(-22, 5.5)
J(-8, 2) → J'(-22, 5.5)
Since, rule for the dilation of a point is,
(x, y) → (kx, ky) [Here k = scale factor of dilation]
Therefore, kx = -22
k(-8) = -22
k = [tex]\frac{-22}{-8}[/tex]
k = 2.75
So the scale factor should be 2.75
From the given options,
Option A.
(x, y) → [tex]\frac{4}{11}(x, y)[/tex]
→ 0.36(x, y)
But value of k should be 0.36
Therefore, Incorrect option.
Option B.
(x, y) → [tex]\frac{3}{22}(x, y)[/tex]
→ 0.14(x, y)
k = 0.14
But the value of k should be 2.75
Incorrect option.
Option C.
(x, y) → [tex]\frac{11}{4}(x, y)[/tex]
→ 2.75(x, y)
k = 2.75
Therefore, this option is correct.
Option D.
(x, y) → [tex]\frac{22}{3}(x, y)[/tex]
→ 7.33(x, y)
k = 7.33
But the scale factor should be 7.33
Incorrect option.
When using inverse operations, what should you do to solve x + 7 = 10
Answer:
10-7=3
Step-by-step explanation:
Answer:
x=3
Step-by-step explanation:
Since we are doing inverse, the opposite of adding is subtracting, so 10-7 is 3.
Which linear inequality and its solution set is represented by the graph?
Answer:
im pretty sure its y is more than or equal to 3x - 4
Step-by-step explanation:
x/-4 = -1.1
I’m bad at one step equations so thank you if you help <3
x/-4 = -1.1
=> x = -1.1 × -4
=> x = 4.4
The table shows the relationship between y, the cost to rent a boat, and x, the mount of
time the boat is rented
Boat Rental Costs
Time,
Cost
(hours) (dollars)
1
32
5
104
Which grabest represents the relationship between x and y'shown in the table?
Boat Rental
Boat Rental
Answer: A
Step-by-step explanation:It shows the correct graph
A school bus uses 3/4 of a tank to drive back and fourth to school in a week with 5 school days. How much gas does the bus use to drive back and fourth to school in a week with 4 school days?
Answer:
3/5 of a tank
Step-by-step explanation:
You can use a proportion.
3/4 tank is to 5 days as x is to 4 days
(3/4)/5 = x/4
Cross multiply.
5x = 3/4 * 4
5x = 3
x = 3/5
Answer: 3/5 of a tank
Step-by-step explanation:
17 gallons of gas drive back and fourth
MARK BRAINLIEST!!!!!!! At a display booth at an amusement park, every visitor gets a gift bag. Some of the bags have items in them as shown in the table below. Items in the Gift Bags Items Bags Hat Every 2nd visitor T-shirt Every 7th visitor Backpack Every 10th visitor How often will a bag contain all three items? LCM or GCF?
Answer:
Step-by-step explanation:
you would find the least common multiple. If you have a set number of gift bags, and you want to find how many had all 3 at once, you would find the LCM that fit within the number of gift bags that you had in order to find it. in this case, it would be 1 in 70
please help me asap
Answer:
15/16-3/4 is 3/16. (1/8 simplified)
Step-by-step explanation: Let the 4 turn into a 16. Multiply 4 by 4 to get 16. Then, multiply the numerator by the number you multiplied for the denominator. 3x4 is 12. Now, can subtract. 15-12=3.
Answer:
#5 should be: 0.1875
and since its different to the ones you have it will be 1 bc the decimal shows as .1
Idk if u want #6 done bc it does not show all answers but i did it anyways :)
#6 should be:−18.16666667
and if there is no decimal points on this one eather it will be -18/16
Step-by-step explanation:
Hopefully this helped, if not HMU and I will try my best to get you a better answer!
Have a great day:)
And if u need help with anything Im here! :)