Answer:
Step-by-step explanation
Area of a triangle
A = ½bh
dA/dt = ½(b(dh/dt) + h(db/dt)
dA/dt = ½(4(9) + 12(-5))
dA/dt = ½(36 - 60)
dA/dt = ½(-24)
dA/dt = -12 cm²/s
The rate of change of the area of the triangle is [tex]-12 cm^2/s[/tex].
The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to an area of an open surface or even the boundary of a three-dimensional object, whereas the area of a plane region as well as plane area refers to a area of a shape or planar lamina. Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover a surface in a single coat. It is the two-dimensional equivalent of a curve's length.
A shape's area can be calculated by contrasting it with squares of a known size.
[tex]\frac{\mathrm{d} b(t)}{\mathrm{d} t}=-5cm/s[/tex]
[tex]\frac{\mathrm{d} h(t)}{\mathrm{d} t}=9 cm/s[/tex]
[tex]\frac{\mathrm{d}A }{\mathrm{d} t}=\frac{1}{2}\left (b\frac{\mathrm{d} h}{\mathrm{d} t} +h\frac{\mathrm{d} b}{\mathrm{d} t}\right )[/tex]
[tex]\frac{\mathrm{d} A}{\mathrm{d} t}=-12 cm^{2}/s[/tex]
Hence, The rate of change of the area of the triangle is [tex]-12 cm^2/s[/tex].
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contains ordered pairs
Answer:
which question ?
Step-by-step explanation:
A ball is thrown upward and outward from a height of 8 feet. The height of the ball, f(x), in feet, can be modeled by
f(x) = -0.1x² +0.6x+8
where x is the ball's horizontal distance, in feet, from where it was thrown. Use this model to solve parts (a) through (c).
WEB
a. What is the maximum height of the ball and how far from where it was thrown does this occur?
The maximum height is feet, which occurs feet from the point of release.
(Round to the nearest tenth as needed.)
Check the picture below.
let's change the decimal values to fractions, say 0.1 to 1/10 and 0.6 to 6/10 = 3/5, so then
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-\frac{1}{10}}x^2\stackrel{\stackrel{b}{\downarrow }}{+\frac{3}{5}}x\stackrel{\stackrel{c}{\downarrow }}{+8} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\left(-\cfrac{~~ \frac{3}{5}~~}{2\frac{-1}{10}}~~,~~8-\cfrac{\left( \frac{3}{5} \right)^2}{4\left(-\frac{1}{10} \right)} \right)\implies \left(\cfrac{~~ \frac{3}{5}~~}{\frac{1}{5}}~~,~~8+\cfrac{\frac{9}{25}}{\frac{2}{5}} \right)[/tex]
[tex]\left( \cfrac{3}{5}\cdot \cfrac{5}{1}~~,~~8+\left[ \cfrac{9}{25}\cdot \cfrac{5}{2} \right] \right)\implies \left(3~~,~~8+\cfrac{9}{10} \right)\implies \stackrel{\stackrel{\textit{maximum height}}{\qquad \downarrow }}{\underset{\underset{\textit{horizontal distance}}{\uparrow \qquad \quad }}{\left( 3~~,~~8\frac{9}{10} \right)}}[/tex]
19. Ram and Rahim are partners in a firm sharing profits in the ratio of 3: 2. Kabir is admitted as a partner for 1/5th share of profits. Machinery would be appreciated by 10% (Book Value of 80,000) and Building would be depreciated by 20% (Book Value of 2,00,000). Unrecorded Debtors of 1,250 would be brought to books. There is a liability of 2,750 included in Sundry Creditors that is not to be paid. What will be the Gain (Proñt Loss on revaluation? (a) Loss of 28,000. (c) Profit 28,000. (6) Loss 40,000. (d) Profit of 40,000.
Answer:
make me brainlist
Step-by-step explanation: firm sharing profits and losses in the ratio of 3
2. From Ist April, 2020 they decided to share the future profits equally. On this date, the General Reserve
showed a balance of 1,60,000; Revaluation of fixed assets resulted into a gain of "1,02,000 and stock resulted
to a loss of 22,000. On this date, the goodwill of the firm was valued at $3,60.000
Pas necessary journal entries for the above transactions on reconstitution of the form
Bolutions
(giving brainlelist if answered correctly!) which of the following inequalities is -4
?
Answer
A, B, E.
Hope you could get an idea from here.
Doubt clarification - use comment section.
Help me plz NO LINKS
Thanks
Answer:
please I am tired texting and answering questions.
What is the area of a triangle with the Base of √10 and a height of √13
Answer:
5.70
Step-by-step explanation:
[tex] a = \frac{1}{2} bh \\ \frac{ \sqrt{10} \sqrt{13} }{2} \\ \frac{ \sqrt{130} }{2} [/tex]
[tex]a = \frac{11.401}{2} \\ = 5.70[/tex]
Answer:
5.70
Step-by-step explanation:
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I need help on this question pls
Answer:
t = 17.5 f = 12
Step-by-step explanation:
If MNOP is a square, you know that each angle is going to be 90°. To solve, let's first set each equation equal to 90°:
[tex]90 = 4t + 20[/tex]
and
[tex]90 = 7f + 6[/tex]
Then solve both equations:
[tex]90 = 4t + 20 \\ 70 = 4t \\ 17.5 = t[/tex]
and
[tex]90 = 7f + 6 \\ 84 = 7f \\ 12 = f[/tex]
I hope that helps!
A bag contains 4 red balls and 6 blue balls. If 3 balls are selected at random, find the probability of selecting 3 red balls?
What is the value of 40 1/2÷3 1/2
Answer:
81/7 (11.57, 11 4/7)
Step-by-step explanation:
Lets rewrite these mixed fractions
[tex]40\frac{1}{2}=\frac{81}{2}[/tex]
[tex]3\frac{1}{2} =\frac{7}{2}[/tex]
Here we can do divide these two numbers:
[tex]\frac{\frac{81}{2} }{\frac{7}{2} }=\frac{81}{7}[/tex]
The answer therefore is 81/7, or 11.571 (11 4/7)
Please help me will give brainliest
Answer:
f(x) = 8.917x³ + 2x² + 0.083x - 7
Step-by-step explanation:
f(x)= y
Let the coefficients of x³, x², x be a, b, c and the constant be d
y= ax³ + bx² + cx + d
When y = -65, x = -2
-65= a(-2)³ + b(-2)² + c(-2) + d
-65= -8a + 4b - 2c + d ...eq. 1
When y = -14, x = -1
-14= a(-1)³ + b(-1)² + c(-1) + d
-14= -a + b - c + d ...eq. 2
When y = -7, x = 0
-7= a(0)³ + b(0)² + c(0) + d
-7 = d ...eq.3
When y = 4, x = 1
4= a(1)³ + b(1)² + c(1) + d
4= a + b + c + d ...eq. 4
when y = 78, x = 2
78 = a(2)³ + b(2)² + c(2) + d
78= 8a + 4b + 2c + d ...eq. 5
From eq. 3, d is - 7
putting d as - 7 in equations 1, 2, 4 and 5
In eq. 1,
-65= -8a + 4b - 2c - 7
-58= -8a + 4b - 2c ...eq. 6
In eq. 2
-14= -a + b - c - 7
-7= -a + b - c ...eq. 7
In eq. 4,
4= a + b + c - 7
11= a + b + c ...eq. 8
In eq. 5
78= 8a + 4b + 2c - 7
85= 8a + 4b + 2c ...eq.9
Subtracting eq. 9 from eq. 6
-143 = -16a - 4c... eq 10
subtracting eq. 8 from eq 7
-18= -2a - 2c
9= a + c
a = 9 - c ...eq 11
putting a as 9 - c in eq. 10
-143 = -16(9 - c) - 4c
-143 = -144 + 16c - 4c
1= 12c
c = 1/12 or 0.083
putting c as 1/12 in eq. 11
a = 9 - 1/12
a = 107/12 or 8.917
Putting a as 107/12 and c as 1/12 in eq. 8
11= 107/12 + b + 1/12
multiplying through by 13
132 = 107 + 12b + 1
132 - 108 = 12b
24= 12b
b = 24/12
= 2
Therefore, a= 8.917, b= 2, c= 0.083 and d = -7
f(x) = 8.917x³ + 2x² + 0.083x - 7
math problem need help give 5 stars and good rating if do
Answer:
The answer is A, 20%.
Step-by-step explanation:
If you find 30 out of 150, it is 20%. A simple way to do it is add 30 up until you get 150. So in this case it is 5 times. Then you do 100% divided by 5 which is 20%. Hope this helps!
4/k =8/3 what is k?
Answer:
1.5
Step-by-step explanation:
4 x 2 = 8, so k x 2 = 3
3 / 2 = 1.5
Please help. Will give brainliest.
Answer:
i am going to but 11 bagels but i am going to buy them for a price under 5$
i am also going to buy 4 extra if we are still hungry
Step-by-step explanation:
i dunno you prob need a anwser with little thought like this becuase of auto grading systems hope this helps
The price of an item has risen to $152 today. Yesterday it was $95. Find the percentage increase.
Answer:
60% increase
Step-by-step explanation:
152 - 95 = -57
57 / 95 = 0.6
0.6 x 100 = 60
A train travels 150 miles in three hours at the same rate how many miles will it travel in eight hours
Answer:400
Step-by-step explanation:
150 / 3 = 50 so 50 x 8= 400
ABCD is a parallelogram. Determine the value of a.
Answer:
a = 6
Step-by-step explanation:
The opposite sides of a parallelogram are congruent , so
BA = CD , that is
7a - 3 = 3 + 6a ( subtract 6a from both sides )
a - 3 = 3 ( add 3 to both sides )
a = 6
Answer:D
Step-by-step explanation:
I took the test
Find the domain of the graphed function.
Answer:
A
Step-by-step explanation:
the domain is all the possible numbers that the x can be, so to find this from the graph you find the x-value of the leftmost point, which is -1 in this case, and the x-value of the rightmost point, which is 3. this means the range of values would be -1 <= x <= 3
[tex]3^{2x+1} -4.9^{x} =-9[/tex]
Is 111111 divisible by 37?
Answer:
Yes
Step-by-step explanation:
3003 woooow
Answer:
yes
Step-by-step explanation:
A is divisible by B, if after dividing them, A ÷ B, the remainder is zero.
If a batch of cookies uses
2
2
3
cups of sugar, then how much sugar is needed to make 5 batches of cookies
Answer:
13 1/3 cups of sugar
Step-by-step explanation:
Which is the equation of a parabola with Vertex (0,0) and directrix x=-2?
Answer:
y^2 = 8x
or
x = 1/8 y^2.
Step-by-step explanation:
The general form for this type of parabola is
y^2 = 4ax where the focus is at (a, 0) and the directrix is x = -a
So the equation is y^2 = 4*2x
that is y^2 = 8x.
Identify the function as a power function, a polynomial function, or neither.
[tex]fx=\frac{x^2}{x^2-1}[/tex]
Answer:
I think this is neither. As you can see the value of x reaches infinity and negative infinity, the value gets infinetly closer to 1.
HELP!!!! PLZZZZZZZZZZ
Answer:
2x³ + 4x² cub. inches
3x³ + 36x² + 105x cub. inches
x³ + 32x² + 105x cub. inches
Step-by-step explanation:
Volume of the small box = x × 2x × (x + 2)
= 2x²(x + 2)
= 2x³ + 4x² cubic inches
Volume of the large box = (x + 5)(x + 7) × 3x
= (x² + 12x + 35) × 3x
= 3x³ + 36x² + 105x cubic inches
Difference between Volume of large box and small box = 3x³ + 36x² + 105x - (2x³ + 4x²)
3x³ + 36x² + 105x - 2x³ - 4x²
x³ + 32x² + 105x cubic inches
write clearly please
Answer: this is 4
Step-by-step explanation: A+b=2+2=4
harold bought 3 pounds of red apples
Answer:
what's your question?
Which expression shows a way to find 20% of 950
1/20 / 950
1/20 • 950
1/5 • 950
1/5 / 950
Answer:
C
Step-by-step explanation:
20% x 950
Calculate 20% x 950 = 190
Match the options one by one and there
Answer:
C: 1/5 · 950Step-by-step explanation:
I got it correct on I-ready.
Hope this helps!!
Hep help help help help math math
Answer:
5(37)+10
10(17.5)+5
Step-by-step explanation:
5x+10=180
-10 -10
5x=170
divide by 5
x=37
---------------------
10x+5=180
-5 -5
10x=175
divide by 10
x=17.5
John made 357$ for 17 hours of work.
At the same rate, how many hours would he have to work to make $237???
Answer: 14 hours
Step-by-step explanation: First I found the unit rate of how much money per hour. So, 357 divided by 17 = 21. So know I know that she earns 21$ per hour. Then, I did 237 divided by 17 which would be 13 remainder 16. Since he only get paid if he works for a full hour, I think the answer would be 14.
[tex]\begin{array}{ccll} \$&hrs\\ \cline{1-2} 357&17\\ 237&x \end{array}\implies \cfrac{357}{237}=\cfrac{17}{x}\implies \implies \cfrac{119}{79}=\cfrac{17}{x}\implies 119x=1343 \\\\\\ x = \cfrac{1343}{119}\implies x = \cfrac{79}{7}\implies x = 11\frac{2}{7}\leftarrow \textit{11 hours, 17 minutes and 8 seconds}[/tex]
suppose we want to choose 2 colors, without replacement from 3 colors red,bule and green
What is 3894 x 6? Use the distributive property to solve.
Answer: 23,364
Step-by-step explanation:6 x 3000 + 6 x 800 + 6 x 90 + 6 x 4