Answer:
The base reduces at 3.75cm/min
Step-by-step explanation:
Given
Let
[tex]h \to altitude[/tex]
[tex]b \to base[/tex]
[tex]A \to Area[/tex]
So:
[tex]\frac{dh}{dt} = 1.5cm/min[/tex]
[tex]\frac{dA}{dt} = 1.5^2cm/min[/tex]
The area of a triangle is:
[tex]A = \frac{1}{2}bh[/tex]
Calculate b when [tex]A =88cm^2; h =8cm[/tex]
[tex]A = \frac{1}{2}bh[/tex]
[tex]88=\frac{1}{2} * b * 8[/tex]
[tex]88 =b * 4[/tex]
Solve for b
[tex]b = 88/4[/tex]
[tex]b = 22[/tex]
We have:
[tex]A = \frac{1}{2}bh[/tex]
Differentiate with respect to time
[tex]\frac{dA}{dt} =\frac{1}{2}(h\frac{db}{dt} + b\frac{dh}{dt})[/tex]
Substitute the following values in the above equation
[tex]\frac{dh}{dt} = 1.5cm/min[/tex] [tex]\frac{dA}{dt} = 1.5^2cm/min[/tex] [tex]b = 22[/tex] [tex]h = 8[/tex]
[tex]1.5 = \frac{1}{2}(8 * \frac{db}{dt} + 22 * 1.5)[/tex]
Multiply both sides by 2
[tex]3 = 8 * \frac{db}{dt} + 22 * 1.5[/tex]
[tex]3 = 8 * \frac{db}{dt} + 33[/tex]
Collect like terms
[tex]8 * \frac{db}{dt} = 3 -33[/tex]
[tex]8 * \frac{db}{dt} = -30[/tex]
Divide both sides by 8
[tex]\frac{db}{dt} = -\frac{30}{8}[/tex]
[tex]\frac{db}{dt} = -3.75[/tex]
what is the largest six-digit base five number? How do you know?
Answer:
999999.9>repeating
Step-by-step explanation:
.1 more and it will be 7 digits and not 6 Hope this helps :D
9514 1404 393
Answer:
444444₅ = 15624₁₀
Step-by-step explanation:
It will be 1 less than the smallest 7-digit base-5 number. That number is 5^6 = 15625, so the largest 6-digit base 5 number is 15624 in decimal. In base 5, it is 6 of the largest base-5 digits:
444444₅ = 15624₁₀
__
The digits of the number cannot be any larger than the largest base-5 digit. The base-5 digits are 0 to 4, so the largest is 4.
2x^2 + 3x - 12 when x = 5 help pls
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{2x^2 + 3x - 12}[/tex]
[tex]\mathsf{= 2(5)^2 + 3(5) - 12}[/tex]
[tex]\mathsf{5^2}[/tex]
[tex]\mathsf{= 5 \times 5}[/tex]
[tex]\mathsf{\bf = 25}[/tex]
[tex]\mathsf{2(25) + 3(5) - 12}[/tex]
[tex]\mathsf{2(25)}[/tex]
[tex]\mathsf{= \bf 50}[/tex]
[tex]\mathsf{3(5)}[/tex]
[tex]\mathsf{= \bf 15}[/tex]
[tex]\mathsf{= 50 + 15 - 12}[/tex]
[tex]\mathsf{50 + 15}[/tex]
[tex]\mathsf{= \bf 65}[/tex]
65 - 12
[tex]\mathsf{= \bf 53}[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: \bf 53}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Which statement regarding the diagram is true?
mMKL+mMLK=mJKM mKML+mMLK=mJKM mMKL+mMLK=180 mJKM+mMLK=180
Answer:
mKML+mMLK=mJKM
Step-by-step explanation:
A triangle is a polygon with three sides and three angles. Types of triangles are scalene, acute, obtuse, equilateral, isosceles, and right triangle.
As shown in the diagram, polygon MLK is a triangle. The sum of angles in a triangle is equal to 180°, hence:
m∠MLK + m∠KML + m∠MKL = 180° (sum of angles in a triangle).
m∠MKL = 180 - (m∠MLK + m∠KML) (1)
Also along line JL, the sum of angles on one side of a straight line is 180°, therefore:
m∠JKM + m∠MKL = 180° (sum of angles in a straight line)
m∠JKM + m∠MKL = 180° (2)
From equations 1 and 2, equating give:
m∠JKM + [180 - (m∠MLK + m∠KML)) = 180
m∠JKM + 180 - m∠MLK - m∠KML = 180
m∠JKM = m∠MLK + m∠KML
can someone please tell me the answer .
Answer:
Step-by-step explanation:
Answer:
the last one
Step-by-step explanation:
congruent means they are the same and all sides of a square are the same size.
A bicycle wheel with radius 26" rotates through an arc that measures 80°. What is the length of the arc of the tire that touched the ground? 5.78 inches 11.56 inches 2.88 inches
Answer:
104/4 pi
Step-by-step explanation:
Answer: The circumference of a circle is:
Radius = r, Diameter = d, C = Circumference
C=2πr (as 2r=d)
C=πd
-------------
If the radius of the circle is 26" then its diameter must be 52".
This means that the bicycle wheel has a circumference of 52π".
I'm going to divide 52π" into 360 parts (because a circle is made up of 360 degrees). I'll then multiply this value by 80 to give you an answer.
Which function has the same y-intercept as the function
Y=2/3x-3?
Answer: 6x - 7y = 21
Step-by-step explanation:
sorry if its wrong
If the original quantity is 14 and new quantity is 35 what is the percent change
Answer:
150%
Step-by-step explanation:
given:
original quantity = 14
new quantity = 35
increased quantity = 35 - 14
=21
percent change = increased quantity /original quentity * 100%
=21/14 *100%
=21100/14 %
=150 %
What is the order of rotational symmetry of this shape .for brainlest
Answer:
4.
Step-by-step explanation:
The orientation of the shape is the same 4 times during 360 degree turn.
Answer:
4
Step-by-step explanation:
Rotational symmetry, also known as radial symmetry in biology, is the property a shape has when it looks the same after some rotation by a partial turn. An object's degree of rotational symmetry is the number of distinct orientations in which it looks exactly the same for each rotation.
Will Mark Brainlest Help pls
Answer:
13
HOPE THIS HELPS YOU......
40 oz < 3lb
Is it true or false ?
Answer:
True
Step-by-step explanation:
40oz = 2.5 lb
10 = 0.625
a triangular prism is 37 millimeters long and has a triangular face with a base of 42 millimeters and a height of 28 millimeters.The other two sides of the triangle are each 35 millimeters.What is the surface area of the triangular prism?
No links pls
Answer: 4145.43
Have a great day! ;)
What is the value of “a” in the function equation?
Answer: the value of A is 2
Step-by-step explanation:
Evaluate: (g + ƒ)(2)
From the graph,
g(2) = 4 ( from the coordinate (2,4))
[ The green line represent the function g(x)]
f(2)= 0
[ The red line represent the function f(x)]
(g + ƒ)(2) = g(2)+f(2) = 4+0 = 4
OPTION A is the correct answer
NO LINKS OR ELSE YOU'LL BE REPORTED! Only answer if you're very good at Math.
Ms. Nellies has 2 1/2 pints of vinegar for her students to use in a science experiment.Each group of students needs 3/8 pint of vinegar.Trey draws the number line model and writes the equation below to help Ms. Nellies figure out how many 3/8-pint serving of vinegar she has.Are Trey's number line model and equation correct?
Trey's number line is _______ because it represents the expression _________.The correct equation is _______.Ms. Nellies has enough vinegar for _________ groups of students.
1st blank box: correct or incorrect
2nd blank box: 2 1/2 x 3/4,2 1/2 ÷ 3/4,2 1/2 x 3/8,or 2 1/2 ÷ 3/8.
3rd blank box: 2 1/2 ÷ 3/8= 6 2/3,2 1/2 ÷ 3/8 = 3 1/3,2 1/2 x 3/8 = 2 3/16, or 2 1/2 ÷ 3/8 = 15/16
4th blank box: 2,6,3,or 0
Answers:
Trey's number line is incorrect because it represents the expression 2 1/2 ÷ 3/4.
The correct equation is 2 1/2 ÷ 3/8 = 6 2/3.
Ms. Nellies has enough vinegar for 6 groups of students.
===========================================================
Explanation:
Trey has the right idea, but made a mistake on how the tickmarks are set up. Focus on the interval from 0 to 1. This section is cut into 4 equal pieces. So each tickmark represents 1/4 of a unit.
Going 3 tickmarks across means 3/4 of a unit is represented. Since each larger arc represents 3/4 of a unit, this means we're dividing the 2 & 1/2 over 3/4 instead of 3/8
That's why Trey's model represents 2 1/2 ÷ 3/4
The value 3 & 1/3 at the end is correct. Visually we see 3 whole jumps plus an extra 1/3 of a jump to arrive at 2 & 1/2. But again, Trey didn't cut the number line up in the right way, so it doesn't matter that he arrived at the correct result of 3 & 1/3 since his initial setup is faulty.
------------------------------
See the diagram below to see what Trey should have drawn. Notice each tickmark represents 1/8 instead of 1/4. Each large blue arc jump represents 3/8 of a unit. We have exactly 6 of these blue arcs plus 2 additional smaller arcs that are 1/3 of the blue arc. So that accounts for the 1/3+1/3 = 2/3 portion.
Overall, we would say that the equation is 2 1/2 ÷ 3/8 = 6 2/3
If you're curious why that equation works, check out the steps below
[tex]2 \frac{1}{2} \div \frac{3}{8} = \frac{5}{2} \div \frac{3}{8}\\\\2 \frac{1}{2} \div \frac{3}{8} = \frac{5}{2} \times \frac{8}{3}\\\\2 \frac{1}{2} \div \frac{3}{8} = \frac{5*8}{2*3}\\\\2 \frac{1}{2} \div \frac{3}{8} = \frac{40}{6}\\\\2 \frac{1}{2} \div \frac{3}{8} = \frac{20}{3}\\\\2 \frac{1}{2} \div \frac{3}{8} = \frac{18+2}{3}\\\\2 \frac{1}{2} \div \frac{3}{8} = \frac{18}{3}+\frac{2}{3}\\\\2 \frac{1}{2} \div \frac{3}{8} = 6+\frac{2}{3}\\\\2 \frac{1}{2} \div \frac{3}{8} = 6\frac{2}{3}\\\\[/tex]
So again, the equation is 2 1/2 ÷ 3/8 = 6 2/3
------------------------------
What does this all mean? Well it means the teacher can break up the vinegar into 6 whole parts plus an additional 2/3 of a part.
In other words, 6 groups will get 3/8 of a pint each. The leftover part 2/3 isn't enough to form that 7th group. Notice in the diagram below, we have 2/8 = 1/4 of a pint which is smaller than 3/8 of a pint.
1/4 = 0.25
3/8 = 0.375
So this is another way to see that the leftovers isn't enough to form a 7th group.
Therefore, she has enough vinegar for 6 groups
this................................................................................................
Answer:
5
Step-by-step explanation:
3-(-2)
the two negative signs cancel out and it turns into
3 + 2
3 + 2 = 5
Answer:
5
Step-by-step explanation:
minus * minus = plus
3-(-2) = 3 + 2 = 5
NEED HELP ASAP PLEASE
Assume that a three-month CD purchased for $3000 pays simple interest at an annual rate of 10%. How much total interest does it earn?
$ ____
What is the balance at maturity? ______
Answers:
interest = $75balance at maturity = $3075=============================================================
Explanation:
The simple interest formula is
i = p*r*t
where in this case,
p = 3000 = principal (amount deposited)r = 0.10 = annual interest rate in decimal formt = 3/12 = 0.25 = number of yearsSo,
i = p*r*t
i = 3000*0.10*0.25
i = 75 is the amount of interest earned
This adds onto the initial deposit to get the final balance when the CD matures (ie when you're able to withdraw the money without penalties)
The balance at maturity is p+i = 3000+75 = 3075 dollars
---------------
In short, you deposit $3000 into the CD and have to wait 3 months for the amount to update to $3075.
i need help finding the answer with step by step
Answer:
x= -1
Step-by-step explanation:
if
f(x) = -x-3
and
f(x) = -2
than
-x-3 = -2; add 3 to both sides
-x-3+3 = -2+3
-x = 1 ; multiply both sides by -1
x= -1
At a sale this week, a suit is being sold for $235.60. This is a 62% discount from the original price.
What is the original price?
Answer:
$620
Step-by-step explanation:
（1-62%）X=235.6
X=235.6/38%
X=620
The original price is $620
4( x + 2) + 6x in the simplest form
Answer:
10x+8
Step-by-step explanation:
4( x + 2) + 6x
Distribute
4x+8 +6x
Combine like terms
10x+8
Answer:
10x+8
Step-by-step explanation:
4x+8+6x
(4x+6x)+8
10x+8
I need to solve for X Y and Z please and thank you
9514 1404 393
Answer:
x = 5y = 30z = 8Step-by-step explanation:
The rhombus has several relevant properties.
The sides are all the same lengthDiagonals are perpendicular bisectors of each otherDiagonals divide the rhombus into congruent trianglesThe last of these relations can be used to find x:
7x° = 35°
x = 35°/7° = 5
The second of the relations can be used to find y:
3y° = 90°
y = 90°/3° = 30
The first of the relations can be used to find z:
10z -8 = 5z +32
5z = 40 . . . . . . . . . add 8-5z
z = 40/5 = 8
Consider the following equation. -2x + 6 =[-2/3] + 5
Answer:
that's my answer
hope it helps
Determine the list of numbers 14, 18 and 33 can be measured of the sides of a triangle if so clarify the triangle as a cute right or obtuse
9514 1404 393
Answer:
no
Step-by-step explanation:
The measures 14, 18, 33 cannot correspond to the sides of a triangle. The two short sides total 32 in length, so cannot meet up with the ends of the side whose length is 33. A triangle cannot be formed.
What is the MEDIAN or Q2 of the data set: 24, 25, 29, 30, 31, 31, 32, 34, 34?
Answer:
31
Step-by-step explanation:
Median = middle number in terms of value
Usually the first step is to list the numbers in order from least to greatest however the numbers are already listed in order from least to greatest
24, 25, 29, 30, 31, 31, 32, 34, 34
We the just go to the middle number
The middle number would be 31
So we can conclude that the median is 31
Answer and I will give you brainiliest
Answer:
x = 60 degree
Step-by-step explanation:
90 + 90 + 2x - 10 + 2x + 2x + 10 = 540 degree (sum of 5 interior angles)
180 + 6x = 540
6x = 540 - 180
x = 360/6
x = 60 degree
A set of eight cards contains one joker. Player A chooses 5 cards at random,
Player B takes the remaining three cards. What is the probability that Player A has the joker?
Player A discards 4 cards and Player B discards two cards. It is known that the joker has not been discarded, what is the probability that Player A has the joker?
Answer:
56%
Step-by-step explanation:
because of the 56% it had to be true to be in the question at all.
If the measure of angle 2 Is (4x+10)degrees and the measure of angle 3 is (3x-5)degrees, what is the measure of angle 2 in degrees?
Answer:
110°
Step-by-step explanation:
4x+10 + (3x-5) = 180
7x + 5 = 180
7x = 175
x = 25
∠2 = 4(25) + 10 = 110
The measure of angle 2 in degrees, when both lines are perpendicular, is approximately 58.56 degrees.
To find the measure of angle 2 when the lines are perpendicular, we can set up an equation. Since the angles are formed by perpendicular lines, we know that the sum of angle 2 and angle 3 will be equal to 90 degrees. Mathematically, we can write this as:
(4x + 10) + (3x - 5) = 90
Now, let's solve the equation to find the value of x. First, combine like terms:
4x + 3x + 10 - 5 = 90
7x + 5 = 90
Next, isolate x by subtracting 5 from both sides:
7x = 85
Finally, divide by 7 to solve for x:
x = 85 / 7 ≈ 12.14
Now that we have the value of x, we can find the measure of angle 2 by substituting x back into its expression:
Angle 2 = 4x + 10
Angle 2 = 4(12.14) + 10
Angle 2 ≈ 48.56 + 10
Angle 2 ≈ 58.56 degrees
To know more about angle here
https://brainly.com/question/4316040
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Can somone help me solve this
Answer:
solid shade above
Step-by-step explanation:
graph line same way you would if it was an equal sign
all the y's that are greater are above the line
its solid because is greater than OR equal to. Equal to includes the line itself as a set of solutions
0.0543 nearest whole number
Answer:
0
Step-by-step explanation:
Ignore the next 2 numbers after 0.05. To the nearest whole number, round 0.05 to the nearest tenth, 0.1. Then round that to the nearest whole number, 0, which is your answer.
Find the surface area of a square pyramid with side length 4 and slant height 5.
Answer:
56
Step-by-step explanation:
the surface area = (4×4) + (4×½×4×5)
= 16 + 40
= 56
Find the area of the triangle, WILL GIVE BRAINLIEST
Answer:
10 cm^2
Step-by-step explanation:
area= 1/2 b*h
1/2 (5) (4)
= 1/2 (20)
=10
area= 10cm^2
Answer:
a = 10cm²
Step-by-step explanation:
a = (1/2)bh
a = (1/2)(5)(4)
a = 10cm²
