The area of the rectangle at L = 14 cm and B = 9 cm is increasing at 97 cm²/s.
What is the area of rectangle?
The area of a rectangle is given by -
A[R] = L x B
Given is the length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of 5 cm/s.
Now, we can write -
dL/dt = 3 cm/s
dB/dt = 5 cm/s
We know, that the area is -
A = LB
differentiating both sides with respect to [t], we get -
dA/dt = L dB/dt + B dL/dt
dA/dt = 5L + 3B
At L = 14 cm and B = 9 cm.
(dA/dt) [14, 9] = 5 x 14 + 3 x 9 = 70 + 27 = 97 cm²/s
Therefore, the area of the rectangle at L = 14 cm and B = 9 cm is increasing at 97 cm²/s.
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On Tuesday, Mrs. Myles assigned 7 more problems than she did on Monday. If she assigned x problems on Monday, write an expression to represent how many problems Mrs. Myles assigned on Tuesday
Answer:
Number of problems assigned on Tuesday = x+7
Step-by-step explanation:
Number of problems assigned on Monday = x.
Number of problems assigned on Tuesday is 7 more than that assigned on Monday.
Number of problems assigned on Tuesday = x+7. [In Matha we use + sign for more than]
The expression that will represent the number of problems Mrs. Myles assigned on Tuesday is x+7.
Answer: actually it 7 + x the other way around
Step-by-step explanation:
in the box below, enter the value that missing from the table.
There are 158 fourth grade studnets and 139 fifth grade students going on a field trip. There needs to be one caperone for every 8 kids. Explain how to find the number of caperones needed for the trip.
A jet plane is descending at a rate of 200 feet per second from an altitude of 36000 feet let x represent the number of seconds of descent and y represent the jet plane’s altitude in feet.
Which expression represents this situation?
A. y = 200x - 36000
B. y = 200x + 36000
C. y = -200x - 36000
D. y = -200x + 36000
FACTORIZE PLEASE, A LOT OF POINTS
64x^(3)-48x^(2)+12xy^(2)-y^(3)
or you can just put it in a smaller form by saying (4x - y)³
Jack Watkins earns a base salary of $1500 a month, plus a 4% commission on the sales he makes. What is his gross pay of his sales for the month are $8000.
A. 1520
B. 1532
C. 1700
D. 1820
Consider the equation x^2 + 12x + c = 0. If c = -28, list the steps to solve the equation by completing the square, and give the solution or solutions.
The solutions of the equation x² + 12x - 28 = 0 are x = 2 or x = -14.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
To solve the equation x² + 12x + c = 0, where c = -28, by completing the square.
Substitute c = -28 into the equation to get x² + 12x - 28 = 0.
x² + 12x = 28
Complete the square by adding the square of half the coefficient of x to both sides of the equation:
x² + 12x + (12/2)² = 28 + (12/2)²
x² + 12x + 36 = 64
(x + 6)² = 64
Take the square root of both sides of the equation.
x + 6 = ±8
x=8-6=2
x=-8-6=-14
Hence, the solutions of the equation x² + 12x - 28 = 0 are x = 2 or x = -14.
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Two triangles have side lengths 3, 4, 5 and 6, _____, 10, respectively. The triangles are similar to each other.
9
7
8
6.6
Answer:
The correct option is: 8
Step-by-step explanation:
Suppose, the missing side length in second triangle is [tex]x[/tex]
So, the side lengths of first triangle: [tex]3, 4, 5[/tex]
and the side lengths of second triangle: [tex]6, x, 10[/tex]
As two triangles are similar, that means their corresponding side lengths will be proportional.
So,
[tex]\frac{3}{6}=\frac{4}{x}\\ \\ 3x= 4*6\\ \\ 3x= 24\\ \\ x=\frac{24}{3}=8[/tex]
So, the missing side length in second triangle is 8.
The local weather person has been accurate in her predictions within 2 degrees temperature forecast 80% of the time. Find the probability that she is accurate...
a) exactly 3 out of the next 5 days
b) at least 4 of the next 5 days
Find 2 numbers that have... a product of 49 and a sum of 14
Find the sum or difference: 2.8 - -5.1
Solve the equation. Check for extraneous solutions
please help!!!
Express answer in exact form.
A regular hexagon with sides of 3" is inscribed in a circle. Find the area of a segment formed by a side of the hexagon and the circle.
(Hint: remember Corollary 1--the area of an equilateral triangle is 1/4 s2 √3.)
The table shows the calories burned during exercise.
(picture of the table attached)
Which statement is true?
A)The y-intercept of the function is (15, 75).
B)The rate of change is 15 calories burned per minute.
C)A linear function to model the calories burned, y, as a function of time in minutes, x, is y = 5x.
D)An exponential function to model the calories burned, y, as a function of time in minutes, x, is y = 5x.
Answer: C. A linear function to model the calories burned, y, as a function of time in minutes, x, is y = 5x.
Step-by-step explanation:
Find the equation for the line that passes through the point (−4,−2), and that is perpendicular to the line with the equation y−1=34(x+2).
Find the equation for the line that passes through the point (−4,−2), and that is perpendicular to the line with the equation y−1=34(x+2).
What are the coordinates of the image of vertex P after a reflection of rx-axis(x, y)? P'( , )
Answer: (-7, 4)
Step-by-step explanation:
help please
Sammy is planning a trip to Nashville. He knows the hotel costs $125 per night and the round trip flight is $159. He has a budget of $900 to spend on his trip. Which of the following inequalities represents his budget to determine how many nights he can stay in Nashville?
125n + 159 ≥ 900
125n + 159 ≤ 900
159n + 125 ≤ 900
159n + 125 ≥ 900
A tunnel is in the shape of a parabola. The maximum height is 16 m and it is 16 m wide at the base, as shown below.
A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 16 meters and its width from left to right is 16 meters.
What is the vertical clearance 7 m from the edge of the tunnel?
15.4 m
0.3 m
15.7 m
0.6 m
plz help
(4+3.2)×[(9−2)+2.5]
What is -1 3/5 x -2/3 as a mixed number?
Find the value of the lesser root of x 2-8x+7=0
Express 0.0037 as a power of 10.
To express 0.0037 as a power of 10, we move the decimal point 3 places to the right, resulting in 3.7 × 10⁻³.
Explanation:To express 0.0037 as a power of 10, we need to count the number of places we have to move the decimal point to get a number between 1 and 10. In this case, we have to move the decimal point 3 places to the right, so the power of 10 is -3.
0.0037 = 3.7 × 10-3
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f(x) = cos(x)
f'(x) = -sin(x)
f'(π/2) = -sin(π/2)
f'(π/2) = -1
My answer to this question is A. -1, but I am posting it here because several students got B. +1 as their answer. Can anyone confirm the answer as A?
Given: ABCD is a trapezoid, AC ⊥ CD AB = CD, AC=the square root of 75 , AB = 5 Find: AABCD
In this attached picture according to the conditions of the problem we have an isosceles trapezoid and since we know that legs are equal (AD=BC=5 cm), we have to calculate bases and height in order to find the area. Working with the triangle BCD, we apply Pythagoras theorem and find that CD = [tex] \sqrt{75+25} [/tex] = 10 cm. Since BDC is a right triangle, applying theorem for the area of triangles, we find that [tex] \frac{1}{2} * BF = \frac{1}{2} * 5 * \sqrt{75} [/tex] and BF= [tex] 0.5\sqrt{75} [/tex]. Since ABCD is an isosceles trapezoid, triangles ADE and BFC are congruent with Angle Side Angle theorem. Then, DE=FC and with the help of Pythagoras theorem, DE=FC=2.5 cm. Then, AB=EF=5 cm and the area of the trapezoid is [tex]A= BF * \frac{AB+CD}{2} = 0.5 \sqrt{75} * \frac{5+10}{2} = 18.75 \sqrt{3} cm^{2} [/tex]
The area of the given trapezoid will be [tex]\frac{75}{4} \sqrt{3}[/tex].
It is given that
In trapezoid ABCD
AE ⊥ CD
AC = √75
AD=BC =5
AB =5
In the triangle ADC
From Pythagoras theorem
AC²+AD²=DC²
(√75)² +5² = DC²
DC=10
Let DE=CF=x (Isosceles trapezoid)
What is isosceles Trapezoid?
Trapezoid in which the base angles are equal and therefore the left and right side lengths are also equal.
AB=EF= DC-2x
5 = DC-2x
x=5/2
AE = [tex]\sqrt({5^{2} } -(5/2)^2)\\\\[/tex]
AE = [tex]\sqrt{75} /2[/tex]
So, the area of the trapezoid ABCD = [tex]\frac{1}{2} *(AB+CD)*AE[/tex]
Area of the trapezoid ABCD = [tex]\frac{1}{2} *(5+10)*\frac{\sqrt{75} }{2}[/tex]
Area of the trapezoid ABCD = [tex]\frac{75}{4} \sqrt{3}[/tex]
Therefore, The area of the given trapezoid ABCD will be [tex]\frac{75}{4} \sqrt{3}[/tex].
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A laptop company has discovered their cost and revenue functions for each day: c(x) = 3x2 − 10x + 200 and r(x) = −2x2 + 100x + 50. if they want to make a profit, what is the range of laptops per day that they should produce? round to the nearest number which would generate profit.
Which of the following shows that polynomials are closed under subtraction when polynomial 5x − 6 is subtracted from 3x2 − 6x + 2?
3x2 − 11x + 8 may or may not be a polynomial
3x2 − 11x + 8 will be a polynomial
3x2 − x + 4 may or may not be a polynomial
3x2 − x + 4 will be a polynomial
Tip: Every 2 after 3x is an exponent.. so it would be 3x^2
The hypotenuse of a right triangle is 5 m long. The longer leg is 1 m longer than the shorter leg. Find the side lengths of the triangle.
The Pythagorean theorem is used to determine the lengths of a right triangle's sides. When we know the hypotenuse length and the fact that one leg is 1m longer than the other, we can solve for the lengths to be approximately 3m and 4m.
Explanation:The subject of your question is related to the geometric concept of right triangles and the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².
In this problem, we know the hypotenuse = 5m and the longer leg is 1m longer than the shorter leg. Let's denote the shorter leg as 'x' m. Consequently, the longer leg is 'x+1' m. Applying the Pythagorean theorem, we get: (x)² + (x+1)² = 5².
Solving this equation, we find x~3m (shorter leg) and x+1~4m (longer leg). These are the lengths of the sides of your right triangle.
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The tank shown is a cylinder with diameter equal to 4 feet and height equal to 12 feet. the tank holds 1130 gallons of rainwater when full. how many gallons of water are in the tank when the depth of the water is 9 feet?
What is the length of AC?
Circle P is tangent to the x-axis and the y-axis. If the coordinates of the center are (r, r), find the slope of the line through the origin and the center.
The value of slope of the line through the origin and the center is,
⇒ Slope = 1
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Circle P is tangent to the x-axis and the y-axis.
And, the coordinates of the center are (r, r),
Now, The value of slope of the line through the (0, 0) and the center (r, r) is,
⇒ Slope = (r - 0) / (r - 0)
⇒ Slope = r/r
⇒ Slope = 1
Thus, The value of slope of the line through the origin and the center is,
⇒ Slope = 1
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