A parabolic heater has a cross section modeled by a parabola with vertex (0,0\right) and focus (2,0\right) . The heater has a depth of 5 inches. What is the width of the parabolic heater at its widest point? Round your answer to the nearest hundredth.

Answer:

c

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

on edge

Answer:

Its 49

Step-by-step explanation:

Can i get brainliest

Answer:

the equation would look like y = -3x + 10. The graph is...

Answer:

\( \mathsf{ {5x}^{2} + 28x + 21}\)

Option A is the right option.

Step-by-step explanation:

Let's find the area of large rectangle:

\( \mathsf{(3x + 6)(2x + 4)}\)

Multiply each term in the first parentheses by each term in the second parentheses

\( \mathsf{ = 3x(2x + 4) + 6(2x + 4)}\)

Calculate the product

\( \mathsf{ = 6 {x}^{2} + 12x + 12x + 6 \times 4}\)

Multiply the numbers

\( \mathsf{ = 6 {x}^{2} + 12x + 12x + 24}\)

Collect like terms

\( \mathsf{ = {6x}^{2} + 24x + 24}\)

Let's find the area of small rectangle

\( \mathsf{(x - 3)(x - 1)}\)

Multiply each term in the first parentheses by each term in the second parentheses

\( \mathsf{ = x( x - 1) - 3(x - 1)}\)

Calculate the product

\( \mathsf{ = {x}^{2} - x - 3x - 3 \times ( - 1)}\)

Multiply the numbers

\( \mathsf{ = {x}^{2} - x - 3x + 3}\)

Collect like terms

\( \mathsf{ = {x}^{2} - 4x + 3}\)

Now, let's find the area of shaded region:

Area of large rectangle - Area of smaller rectangle

\( \mathsf{6 {x}^{2} + 24x + 24 - ( {x}^{2} - 4x + 3)}\)

When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression

\( \mathsf{ = {6x}^{2} + 24x + 24 - {x}^{2} + 4x - 3}\)

Collect like terms

\( \mathsf{ = {5x}^{2} + 28x + 21}\)

Hope I helped!

Best regards!

Answer:

3y = 11x-16

Step-by-step explanation:

The general equation of a line that passes through two points can be written as;

y = mx + b

where m is slope and b is the y-intercept

Mathematically in this case;

m = (9-(-2)/(5-2) = 11/3

To write the equation, we use the one-point form

y-y1 = m(x-x1)

(x1,y1) = (2,-2)

y + 2 = 11/3(x-2)

y = 11x/3-22/3+ 2

y = 11x/3 -16/3

so;

3y = 11x - 16

Answer:

12/1

Step-by-step explanation:

Answer:

1:12 OR 1/12

Step-by-step explanation:

Jimmy charges a flat fee of $22 and $25 per hour in addition to the flat fee.

We have to find an expression that represents the following:

Jimmy works at Bob's place for h hours.

Remember that Jimmy charges a flat fee of $22, and he will charge $25 for every hour, since he worked h hours, the expression is:

This represents the flat fee of 22 plus an additional 25h, which represents that he charges 25 per hour.

Answer: 22+25h

According to the question 1.)  The equation of the tangent plane to \(\(z = -4x^2 - 5y^2 + 4y\)\) at the point \(\((0, 1, -1)\) is \(z = -6y + 5\).\)  2.) the equation of the tangent plane to \(\(z = 6e^{x^2-4y}\) at the point \((8, 16, 6)\) is \(z = 96x - 24y - 378\).\)  3.) After calculating this expression gives us the approximation for  \(\(f(4.3, 6.24)\).\)

1. )  To find the tangent plane to the equation \(\(z = -4x^2 - 5y^2 + 4y\)\) at the point \(\((0, 1, -1)\)\), we need to determine the coefficients \(\(a\), \(b\), and \(c\)\) in the equation \(\(z = ax + by + c\)\) that represents the tangent plane.

First, we find the partial derivatives of \(\(z\) with respect to \(x\) and \(y\):\)

\(\(\frac{{\partial z}}{{\partial x}} = -8x\)\)

\(\(\frac{{\partial z}}{{\partial y}} = -10y + 4\)\)

Now, we substitute the point \(\((0, 1, -1)\)\) into these derivatives to obtain the slope of the tangent plane:

\(\(\frac{{\partial z}}{{\partial x}}(0, 1, -1) = -8(0) = 0\)\)

\(\(\frac{{\partial z}}{{\partial y}}(0, 1, -1) = -10(1) + 4 = -6\)\)

Hence, the tangent plane equation becomes:

\(\(z = -6y + c\)\)

Substituting the point \(\((0, 1, -1)\)\) into this equation, we can solve for the constant \(\(c\):\)

\(\(-1 = -6(1) + c\)\(-1 = -6 + c\)\(c = 5\)\)

Therefore, the equation of the tangent plane to \(\(z = -4x^2 - 5y^2 + 4y\)\) at the point \(\((0, 1, -1)\) is \(z = -6y + 5\).\)

2.)  To find the tangent plane to the equation \(\(z = 6e^{x^2-4y}\)\) at the point \(\((8, 16, 6)\),\) we follow a similar procedure.

The partial derivatives of \(\(z\)\) with respect to \(\(x\) and \(y\)\) are:

\(\(\frac{{\partial z}}{{\partial x}} = 12xe^{x^2-4y}\)\(\frac{{\partial z}}{{\partial y}} = -24e^{x^2-4y}\)\)

Substituting the point \(\((8, 16, 6)\)\) into these derivatives:

\(\(\frac{{\partial z}}{{\partial x}}(8, 16, 6) = 12(8)e^{8^2-4(16)} = 96e^{64-64} = 96\)\(\frac{{\partial z}}{{\partial y}}(8, 16, 6) = -24e^{8^2-4(16)} = -24e^{64-64} = -24\)\)

The equation of the tangent plane is:

\(\(z = 96(x-8) - 24(y-16) + 6\)\)

Therefore, the equation of the tangent plane to \(\(z = 6e^{x^2-4y}\) at the point \((8, 16, 6)\) is \(z = 96x - 24y - 378\).\)

3.)  To find the tangent plane to the equation \(\(z = 6y\cos(5x-2y)\)\) at the point \(\((2, 5, 30)\),\) we again calculate the partial derivatives.

The partial derivatives of \(\(z\)\) with respect to \(\(x\) and \(y\)\) are:

\(\(\frac{{\partial z}}{{\partial x}} = -30y\sin(5x-2y)\)\(\frac{{\partial z}}{{\partial y}} = 6\cos(5x-2y) - 30x\sin(5x-2y)\)\)

Substituting the point  \(\((2, 5, 30)\)\) into these derivatives:

\(\(\frac{{\partial z}}{{\partial x}}(2, 5, 30) = -30(5)\sin(5(2)-2(5)) = -150\sin(4) = -150\sin(4)\)\(\frac{{\partial z}}{{\partial y}}(2, 5, 30) = 6\cos(5(2)-2(5)) - 30(2)\sin(5(2)-2(5)) = 6\cos(0) - 60\sin(0) = 6\)\)

The equation of the tangent plane is:

\(\(z = -150\sin(4)(x-2) + 6(y-5) + 30\)\)

Therefore, the equation of the tangent plane to \(\(z = 6y\cos(5x-2y)\) at the point \((2, 5, 30)\) is \(z = -150\sin(4)x + 6y + 300\sin(4) + 30\).\)

To find the linear approximation to the equation \(\(f(x, y) = \frac{4\sqrt{xy}}{6}\)\) at the point \(\((4, 6, 8)\),\) we use the first-order Taylor expansion. The linear approximation can be represented as:

\(\(L(x, y) = f(a, b) + f_x(a, b)(x-a) + f_y(a, b)(y-b)\)\)

where \(\(a\) and \(b\)\) are the coordinates of the given point \(\((4, 6, 8)\), and \(f_x\) and \(f_y\)\) are the partial derivatives of \(\(f\)\) with respect to \(\(x\) and \(y\)\) respectively.

Given \(\(a = 4\) and \(b = 6\)\), we can calculate the partial derivatives:

\(\(f_x(x, y) = \frac{2\sqrt{y}}{3\sqrt{x}}\)\(f_y(x, y) = \frac{2\sqrt{x}}{3\sqrt{y}}\)\)

Substituting the values \(\((x, y) = (4, 6)\)\) into these derivatives:

\(\(f_x(4, 6) = \frac{2\sqrt{6}}{3\sqrt{4}} = \frac{\sqrt{6}}{3}\)\(f_y(4, 6) = \frac{2\sqrt{4}}{3\sqrt{6}} = \frac{2}{3\sqrt{6}}\)\)

Using these values, the linear approximation becomes:

\(\(L(x, y) = f(4, 6) + \frac{\sqrt{6}}{3}(x-4) + \frac{2}{3\sqrt{6}}(y-6)\)\)

Substituting \(\(f(4, 6) = \frac{4\sqrt{4\cdot6}}{6} = \frac{8\sqrt{6}}{3}\)\), the linear approximation is:

\(\(L(x, y) = \frac{8\sqrt{6}}{3} + \frac{\sqrt{6}}{3}(x-4) + \frac{2}{3\sqrt{6}}(y-6)\)\)

To approximate \(\(f(4.3, 6.24)\)\), we substitute \(\(x = 4.3\) and \(y = 6.24\)\) into the linear approximation:

\(\(f(4.3, 6.24) \approx \frac{8\sqrt{6}}{3} + \frac{\sqrt{6}}{3}(4.3-4) + \frac{2}{3\sqrt{6}}(6.24-6)\)\)

After calculating this expression gives us the approximation for\(\(f(4.3, 6.24)\).\)

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The value of the original integral is [² (4x − 2)³ da = [ f(u) du, where ՂԱ du = a to b,f(u) = (4u)³, a = (4a - 2)³, b = (4b - 2)³, andFI(u) = (4x - 2)³.

To evaluate the integral [² (4x − 2)³ da, we can use the method of u-substitution.

Let's make the substitution u = 4x - 2.

Then, we have du = 4 dx.

Now, we need to express the original integral in terms of the variable u. We replace da with du/4 and substitute the limits of integration:

[² (4x − 2)³ da = [ (4u)³ (du/4)

= [ u³ du.

The limits of integration also change when we perform the substitution:

When a = a (lower limit), we have

u = 4a - 2.

When a = b (upper limit), we have

u = 4b - 2.

Therefore, the new integral becomes:

[ u³ du, with the limits u = 4a - 2 to

u = 4b - 2.

Now, we can evaluate this integral using the fundamental theorem of calculus:

∫[ u³ du = [ (1/4) u⁴ ].

Applying the limits of integration:

[(1/4) (4b - 2)⁴ - (1/4) (4a - 2)⁴].

Simplifying and expanding:

[(1/4) (4⁴b⁴ - 2⁴) - (1/4) (4⁴a⁴ - 2⁴)].

Further simplification:

(1/4) (256b⁴ - 16 - 256a⁴ + 16).

Combining like terms:

(1/4) (256b⁴ - 256a⁴).

Finally, simplifying the coefficient:

64(b⁴ - a⁴).

Therefore, the value of the original integral [² (4x − 2)³ da = [ f(u) du, where ՂԱ du = a to b, f(u) = (4u)³, a = (4a - 2)³, b = (4b - 2)³, and FI(u) = (4x - 2)³, is 64(b⁴ - a⁴).

The value of the original integral [² (4x − 2)³ da = [ f(u) du, where ՂԱ du = a to b, f(u) = (4u)³, a = (4a - 2)³, b = (4b - 2)³, and FI(u) = (4x - 2)³, is 64(b⁴ - a⁴).

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Answer: -19.2

Step-by-step explanation:

Answer:

As we know that

\(\sf 1 \:Foot=12inches \)

\({:}\longrightarrow\)\(\sf {\dfrac {7}{12}}\:of \; 12 \)

\({:}\longrightarrow\)\(\sf {\dfrac {7}{{\cancel {12}}}}\times{\cancel { 12 }}\)

\({:}\longrightarrow\)\({\underline{\boxed{\bf 7inches}}}\)

It will take 22 years and 3 months to get the present value of $12,000 invested at 2.3% compounded monthly to get to $20,000 (future value).

The period that it will take the present value to reach a certain future value can be determined using an online finance calculator with the following parameters for periodic compounding.

I/Y (Interest per year) = 2.3%

PV (Present Value) = $12,000

PMT (Periodic Payment) = $0

FV (Future Value) = $20,000

Results:

N = 266.773

266.73 months = 22 years and 3 months (266.73 ÷ 12)

Total Interest = $8,000.00

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Answer:

Its A ( 1.05, -0.5)

Step-by-step explanation:

Answer:

≠ (not equal)

Step-by-step explanation:

Out of the three choices provided, it has to be the not equal sign. We know this because the absolute value of 1 is how far away 1 is from 0, which is 1. Which then makes our equation: 1 ____ -1.

From here, it's easy to tell that -1 is smaller than 1, they're not equal, and it is possible. Since we have eliminated all other possible answers, we know it has to be ≠.

Log(1), log(-1), log(i) and ii are all numbers written in the form a + bi. Log(1) = 0; log(-1) = undefined; log(i) = 0.5i; ii = -1; a = -1 and b = 0 because the number is in the form a + bi.

Given numbers are;• log(1)• log(-1)• log(i)• iiFor all numbers written in the form a + bi, we must find a and b. Here's how to do it: log(1)In this case, the log is taken in base 10. The result of this is 0. So, we have: log(1) = 0Therefore, a=0 and b=0 because the number is not in the form a + bi. log(-1)In this case, the log is taken in base 10. The result of this is undefined. This is because there is no power to which we can raise 10 to get -1. So, we have: log(-1) = undefinedTherefore, a=undefined and b=undefined because the number is not in the form a + bi. log(i)In this case, the log is taken in base 10. The result of this is 0.5iπ. So, we have: log(i) = 0.5iπTherefore, a=0 and b=0.5π because the number is in the form a + bi. iiIn this case, we are finding the square of i. i is a complex number given as i = 0 + 1i. Therefore, we have: i2 = (0 + 1i)2= (0)2 + 2(0)(1i) + (1i)2= -1This is because i2 = -1. Now, we can write ii as: ii = i × i= (0 + 1i) × (0 + 1i)= 0 + 0i + 0i + 1i2= -1So, we have: ii = -1Therefore, a=-1 and b=0 because the number is in the form a + bi.

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Answer:

\(2x - 25 = 87 \\ 2x = 87 + 25 \\ 2x = 112 \\ \frac{2x}{2} = \frac{112}{2} \\ x = 56\)

I USED THE REASON ALTERNATE ANGLES ARE EQUAL

Answer: x = 3

Step-by-step explanation:

I guess that the equation is:

(45 - 3x)^1/2 = x - 9

so let's solve it for x.

first, we can square both sides:

(45 - 3x) = (x - 9)^2 = x^2 - 18x + 81

now we can write this as a quadratic equation:

x^2 - 18x + 81 - 45 + 3x = 0

x^2 -15x + 36 = 0

now we can use the Bhaskara's equation to find the solutions for that equation:

where for a equation a*x^2 + b*x + c = 0

the solutions are:

\(x = \frac{-b +- \sqrt[2]{b^2 -4ac} }{2a}\)

here a = 1, b = -15 and c = 36

\(x = \frac{15 +- \sqrt[2]{15^2 -4*36} }{2} = \frac{15+- 9}{2}\)

then the solutions are:

x = (15 + 9)/2 = 24/2 = 12

x = (15 - 9)/2 = 6/2 = 3

where 12 is the solution for the positive (45 - 3x)^1/2 and x = 3 is the extraneous solution (because it works for the negative  (45 - 3x)^1/2)

Answer:

3

Step-by-step explanation:

Answer:

\(= \frac{2m^2n^8}{3}\)

Step-by-step explanation:

Given expression is

\((\frac{4m^{-2}n^8}{9m^{-6}n^{-8}} )^{\frac{1}{2}\)

The correct simplified form is shown below:-

From the above equation, we will simplify

we will shift \(m^{-6}\) to the numerator and we will use the negative exponent rule, that is

\(= (\frac{4m^{-2}n^8m^6}{9n^{-8}} )^{\frac{1}{2}\)

now we will shift the \(n^{-8}\) to the numerator and we will use the negative exponent rule, that is

\(= (\frac{4m^{-2}n^8m^6n^8}{9} )^{\frac{1}{2}\)

here we will solve the above equation which is shown below

\(= (\frac{4m^4n^{16}}{9}) ^\frac{1}{2}\)

So,

\(= (\frac{(2)^2(m^2)^2(n^8)^2}{(3)^2} ^\frac{1}{2}\)

Which gives result

\(= \frac{2m^2n^8}{3}\)

Answer:

16

Step-by-step explanation:

you would get c alone so you subtract 5 to the other side

Answer:

-6

Step-by-step explanation:

5+-11= -6

5--6= -11

Calculator

Answer:

see explanation

Step-by-step explanation:

a² + 8a

using the method of completing the square

add ( half the coefficient of the a- term)²

a² + 2(4)a + 16

= (a + 4)²

Answer:

Step-by-step explanation:

d +   d

        _

        2

Using the formula for volume of cube and with the provided volume and side, the answer is 6cm.

A cube is a three-dimensional solid object in geometry that is surrounded by six square faces, facets, or sides, three of which meet at each vertex.

We get the volume of a cube by thrice multiplying the side length.

Suppose we have a side length of cube = l cm

The required formula is for volume is:

\(V = l ^ {3}\)

As per question, the side length of cube = z

l=z

V = z³

V=216 ³

\(l=\sqrt[3]{216}\)

\(l=6cm\)

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Answer:

\((x-1)^2+(y+1)^2=\frac{1}{4}\)

Step-by-step explanation:

The equation of a circle with center \((h,k)\) and radius \(r\) is given by \((x-h)^2+(y-k)^2=r^2\).

What we're given:

Substituting given values, we get:

\((x-1)^2+(y-(-1))^2=\frac{1}{2}^2,\\\boxed{(x-1)^2+(y+1)^2=1/4}\)

Therefore, Drug C has a stronger impact on cell survival compared to Drug A, making it the drug with the greatest effect.

To draw a representation of the survival curve and identify the drug that has the greatest effect on cell survival, we can use a graph where the x-axis represents the drug concentration in μg/ml, and the y-axis represents the percentage of cell survival.

Since Drug B has no IC90 value, it means that it does not reach a concentration that causes a 90% reduction in cell survival. Therefore, we can assume that Drug B has no significant effect on cell survival and can omit it from the survival curve.

For Drug A and Drug C, we have IC90 values of 5 and 3 μg/ml, respectively. This means that when the drug concentration reaches these values, there is a 90% reduction in cell survival.

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Answer:

A

Step-by-step explanation:

Answer:

Reflection over y = 1

Step-by-step explanation:

Answer:

D. The money that Kai started with before he mowed any lawns.

Step-by-step explanation:

We Know

The equation is y = mx + b

The x represents the number of lawns that Kai mows.

What does the y-intercept represent in this equation?

The y-intercept is when the x = 0, meaning the y-intercept is the amount of money he has when mowing 0 lawn. So, the answer is D.

Answer:

The Answer is D

Step-by-step explanation:

The average velocity from t = 2s to t = 4s would be - 48 ft/s.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that an object is thrown upward with initial velocity of 48 feet per second from a high of 120 feet. The height of the object t seconds after it is thrown is given by h(t) = - 16t² + 48t + 120.

Average rate of change of velocity with time is called average velocity. Mathematically -

v{avg.} = Δx/Δt                                                         .... Eq { 1 }

Δx = x(4) - x(2)

Δx = - 16(4)² + 48(4) + 120 - {- 16(2)² + 48(2) + 120}

Δx = - 96

Δt = 4 - 2 = 2

So -

v{avg.} = Δx/Δt = -96/2 = - 48 ft/s

Therefore, the average velocity from t = 2s to t = 4s would be - 48 ft/s.

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Step-by-step explanation:

x² + (2x)² = (√180)²

x² + 4x² = 180

5x² = 180

x² = 180/5

x² = 36

x = √36 (and no - √36 because x ≥ 0)

x = 6