WHAT IF? The distance between consecutive bases on a baseball field is 90 feet. The player

decides to throw the ball to second base instead of third base. Which throw is longer?

2nd base

AQ

3rd base

O2nd base

O 3rd base

How much farther must the player throw the ball for the longer throw?

about

53°

ft

The divergence theorem of the equation S(2x+2y+z2)dS exists 4/3 π.

Let S be the boundary surface of E with the positive (outward) orientation, and let E be a straightforward solid region. Let F be a vector field with continuous partial derivatives on an open region containing E for each of its component functions. Then

\($\iint_S F \cdot d S=\iint_S F \cdot n d S=\iiint_E div Fdv$\),

where n be the outward normal of S.

Let the given equation be

The sphere S is x² + y² + z² = 1

By using concept,

\($$\iint_S F \cdot n d S=\iint_S\left(2 x+2 y+z^2\right) d S$$\)

Therefore,

\($$F \cdot n=2 x+2 y+z^2$$\)

Given that the sphere S is x² + y² + z² = 1

For S, n will be

\($n=\frac{x i+y j+z k}{\sqrt{x^2+y^2+z^2}}$$\)

After substituting the value of x² + y² + z² = 1

n = x i + y j + z k

Therefore,

F(xi + yj + zk) = 2x + 2y + z²

Consider F = Pi + Qj + Rk

\($& (P i+Q j+R k) \cdot(x i+y j+z k)=2 x+2 y+z^2 \\\)

Px + Qy + Rz = 2x + 2y + z²

By comparing the values, P = 2, Q = 2, R = z

So, F becomes

F = 2i + 2j + zk

By using the definition of Divergence,

\(${div} F=\left(\frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z}\right) \cdot(2 i+2 j+z k) \\\)

\($& =\frac{\partial}{\partial x}(2 i+2 j+z k)+\frac{\partial}{\partial y}(2 i+2 j+z k)+\frac{\partial}{\partial z}(2 i+2 j+z k) \\\)

= 0 + 0 + 1

div F = 1

By using Divergence Theorem,

\($ \iint_S F \cdot n d S=\iiint_E {div} F d V \\\)

\($& \iint_S\left(2 x+2 y+z^2\right) d S=\iiint_E 1 d V\)

Since \($\iiint_E 1 d V$\) is the volume of sphere with radius 1

\($& \iint_S\left(2 x+2 y+z^2\right) d S=\text { Volume of } E \\\)

\($& =\frac{4}{3} \pi(1)^3=\frac{4}{3} \pi\)

Thus,

\($\iint_S\left(2 x+2 y+z^2\right) d S=\frac{4}{3} \pi$$\)

Therefore, the divergence theorem of the equation S(2x+2y+z2)dS exists 4/3 π.

The complete question is:

Use the Divergence Theorem to evaluate S(2x+2y+z2)dS where S is the sphere x2+y2+z2=1.

To learn more about Divergence Theorem refer to:

https://brainly.com/question/17177764

#SPJ4

The divergence theorem of the equation S(2x+2y+z2)dS exists 4/3 π.

What is meant by divergence theorem?

Let S be the boundary surface of E with the positive (outward) orientation, and let E be a straightforward solid region. Let F be a vector field with continuous partial derivatives on an open region containing E for each of its component functions. Then

\(\iint_S F \cdot d S=\iint_S F \cdot n d S=\iiint_E d i v F d v\)

where n be the outward normal of S.

Let the given equation be

The sphere S is x² + y² + z² = 1

By using concept,

\(\iint_S F \cdot n d S=\iint_S\left(2 x+2 y+z^2\right) d S\)

Therefore,

\(\mathrm{F} \cdot n=2 x+2 y+z^2\)

Given that the sphere S is x² + y² + z² = 1

For S, n will be

\(n=\frac{x i+y j+z k}{\sqrt{x^2+y^2+z^2}}\)

After substituting the value of x² + y² + z² = 1

n = x i + y j + z k

Therefore,

F(xi + yj + zk) = 2x + 2y + z²

Consider F = Pi + Qj + Rk

\((P i+Q j+R k) \cdot(x i+y j+z k)=2 x+2 y+z^2\)

Px + Qy + Rz = 2x + 2y + z²

By using the definition of Divergence,

= 0 + 0 + 1

div F = 1

By using Divergence Theorem,

\(\begin{aligned}& \iint_S F \cdot n d S=\iiint_E d i v F d V \\& \iint_S\left(2 x+2 y+z^2\right) d S=\iiint_E 1 d V\end{aligned}\)

Since\(\iiint_E 1 d V\)is the volume of sphere with radius 1\($$\begin{aligned}& \iint_S\left(2 x+2 y+z^2\right) d S=\text { Volume of } E \\& =\frac{4}{3} \pi(1)^3=\frac{4}{3} \pi\end{aligned}$$Thus,\iint_S\left(2 x+2 y+z^2\right) d S=\frac{4}{3} \pi\)

Therefore, the divergence theorem of the equation S(2x+2y+z2)dS exists 4/3 π.

Use the Divergence Theorem to evaluate S(2x+2y+z2)dS where S is the sphere x2+y2+z2=1.

To learn more about Divergence Theorem visit:

brainly.com/question/17177764

#SPJ4

Answer:

\(m\widehat {EB}\) = 96°

Step-by-step explanation:

From the figure attached,

m∠ECB = 25°

\(m\widehat {EB}={(4x+16)}\) degrees

\(m\widehat{DB}=(7x+6)\) degrees

From the theorem of secants intersecting outside the circle,

m∠ECB = \(\frac{1}{2}[m\widehat {DB}-m\widehat{EB}]\)

25° = \(\frac{1}{2}[(7x + 6) - (4x + 16)]\)

25° = \(\frac{1}{2}(3x-10)\)

50 = 3x - 10

3x = 60

x = \(\frac{60}{3}\)

x = 20

\(m\widehat {EB}\) = (4 × 20 + 16)°

        = (80 + 16)°

        = 96°

Therefore, measure of arc EB is 96°.

Answer:

96°

Step-by-step explanation:

Got it right on the test

The solution to all parts are given below:

The experimental probability of an event occurring is the number of times that it occurred when the experiment was conducted as a fraction of the total number of times the experiment was conducted.

1. The experiment is to spin the wheel and get the number and related to that number reward will be there.

2. The outcomes will be,

{1, 2, 3, 4, 5, 6, 7, 8}

3. Sample space

{1, 2, 3, 4, 5, 6, 7, 8}

4. Event of red with even number

= 2 , 6

5.  Event of red with odd number

= 3,7

Learn more about experiment here:

https://brainly.com/question/1748066

#SPJ1

Answer:

Step-by-step explanation:

h = 8 cm,  r = 3 cm

A = 2×πr² + 2πr×h = 2πr×(r + h)

A = 2π×3×(3 + 8) =  66π cm² ≈ 207.35 cm²

h = 2×8 = 16 cm ,      r = 3 cm ,   2×66π = 132π cm²

A = 2π×3×(3 + 16) =  114π cm² ≠ 132π cm²  

h = 8 cm ,        r = 2×3 = 6 cm  ,   2×66π = 132π cm²

A = 2π×6×(6 + 8) =  168π cm² ≠ 132π cm²    

Part(A),

The total surface area of the cylinder is 207.35 cm².

Part(B),

The new surface area is about 2.55 times the original surface area, not double.

Part(C),

The new surface area is about 3.64 times the original surface area, not double.

A. To find the surface area of the cylinder, we need to find the area of the two circular bases and the curved lateral surface.

The formula for the area of a circle is A = πr², where r is the radius. So the area of the two circular bases is:

2πr² = 2π(3cm)² = 56.55 cm²

The formula for the lateral surface area of a cylinder is A = 2πrh, where r is the radius and h is the height. So the lateral surface area of the cylinder is:

2πrh = 2π(3cm)(8cm) = 150.8 cm²

Therefore, the total surface area of the cylinder is:

Total Surface Area = 2πr² + 2πrh = 56.55 cm² + 150.8 cm² = 207.35 cm²

B. No, if we double the height of the cylinder while keeping the radius constant, the surface area will not double. The surface area will increase, but not double.

When we double the height, the new height becomes 2 times 8cm = 16cm. Using the formula for the surface area of the cylinder, we get:

New Total Surface Area = 2π(3cm)² + 2π(3cm)(16cm) = 2π(3cm)(28cm) = 528 cm²

The original surface area was 207.35 cm².

The new surface area is 528 cm².

So the new surface area is about 2.55 times the original surface area, not double.

C. No, if we double the radius of the cylinder while keeping the height constant, the surface area will not double. The surface area will increase, but not double.

When we double the radius, the new radius becomes 2 times 3cm = 6cm. Using the formula for the surface area of the cylinder, we get:

New Total Surface Area = 2π(6cm)² + 2π(6cm)(8cm) = 2π(6cm)(20cm) = 753.98 cm²

The original surface area was 207.35 cm².

The new surface area is 753.98 cm².

So the new surface area is about 3.64 times the original surface area, not double.

To know more about cylinders follow

https://brainly.com/question/29870289

#SPJ2

Answer:

10

13

15

17

22

Step-by-step explanation:

the first 5 terms will be 1,2,3,4 and 5.

I guess...

Answer:

a1 = 10

a2 = 13

a3 = 16

a4 = 19

a5 = 22

Step-by-step explanation:

Substitute in the value of  n  to find the  n

th term.

a1 = 3 (1) + 7

3 + 7 = 10

a2 = 3 (2) + 7

6 + 7 = 13

a3 = 3 (3) + 7

9 + 7 = 16

a4 = 3 (4) + 7

12 + 7 = 19

a5 = 3 (5) + 7

15 + 7 = 22

good luck, hope this helps :)

The result for the given data are-

Part A: A geometric sequence is being modelled by the data because they share a common ratio = 2.

Part B: The time in which she will complete station 5 calculated by recursive formula is 64 units.

Part C: The time in which she will complete the 9th station calculated by  explicit formula 512 units.

Any term of a series can be defined by its preceding term in a recursive formula (s).

We learn two things from recursive formulas: the first phrase in the series. The pattern rule states that any term can be derived from its preceding term.

Now, according to the question;

Part A: The data are modeling a geometric sequence since they have a common ratio of 2.

Part B: Use a recursive formula to determine the time she will complete station 5.

f(n)=f(n-1)×r

Where, r is the common difference

f(n)=f(5-1)×2

f(n)=f(4)×2

f(n)=(32)×2   {since, f(4) = 32)}

f(n)= 64

Part C: Use an explicit formula to find the time she will complete the 9th station.

f(n)=f(1)×r^(n-1)

f(n)=4×2^(8-1)

f(n)=4×(2^7)

f(n)=4×128

f(n)=512

To know more about the recursive formula, here

https://brainly.com/question/1275192

#SPJ4

The complete question is -

Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.

The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.

(1, 4), (2, 8), (3, 16), (4, 32)

Part A: Is this data modeling an arithmetic sequence or a geometric sequence?

Part B: Use a recursive formula to determine the time she will complete station 5.

Part C: Use an explicit formula to find the time she will complete the 9th station.

Answer:

The result for the given data are-

Part A: A geometric sequence is being modelled by the data because they share a common ratio = 2.

Part B: The time in which she will complete station 5 calculated by recursive formula is 64 units.

Part C: The time in which she will complete the 9th station calculated by  explicit formula 512 units.

What is recursive formula?

Any term of a series can be defined by its preceding term in a recursive formula (s).

We learn two things from recursive formulas: the first phrase in the series. The pattern rule states that any term can be derived from its preceding term.

Now, according to the question;

Part A: The data are modeling a geometric sequence since they have a common ratio of 2.

Part B: Use a recursive formula to determine the time she will complete station 5.

f(n)=f(n-1)×r

Where, r is the common difference

f(n)=f(5-1)×2

f(n)=f(4)×2

f(n)=(32)×2   {since, f(4) = 32)}

f(n)= 64

Part C: Use an explicit formula to find the time she will complete the 9th station.

f(n)=f(1)×r^(n-1)

f(n)=4×2^(8-1)

f(n)=4×(2^7)

f(n)=4×128

f(n)=512

To know more about the recursive formula, here

brainly.com/question/1275192

#SPJ4

The complete question is -

Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.

The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.

(1, 4), (2, 8), (3, 16), (4, 32)

Part A: Is this data modeling an arithmetic sequence or a geometric sequence?

Part B: Use a recursive formula to determine the time she will complete station 5.

Part C: Use an explicit formula to find the time she will complete the 9th station.

Explore all similar answers

Step-by-step explanation:

We cannot verify if each of the four functions g1(x), g2(x), g3(x), and g4(x) have a fixed point at p when f(p) = 0.

To verify that if f(p) = 0, then each of the four functions g1(x), g2(x), g3(x), and g4(x) have a fixed point at p, we need to substitute p into each function and check if the result is equal to p.

g1(x) = (3+x-2x^2)^(1/4)

Let's substitute p into g1(x):

g1(p) = (3+p-2p^2)^(1/4)

To verify if g1(p) = p, we need to show that (3+p-2p^2)^(1/4) = p.

Since this is not an algebraic manipulation that can be solved easily, we cannot confirm if g1(x) has a fixed point at p without further calculations or approximations.

g2(x) = (x+3-x^4/2)^(1/2)

Let's substitute p into g2(x):

g2(p) = (p+3-p^4/2)^(1/2)

To verify if g2(p) = p, we need to show that (p+3-p^4/2)^(1/2) = p.

Since this is not an algebraic manipulation that can be solved easily, we cannot confirm if g2(x) has a fixed point at p without further calculations or approximations.

g3(x) = (x+3/x^2+2)^(1/2)

Let's substitute p into g3(x):

g3(p) = (p+3/p^2+2)^(1/2)

To verify if g3(p) = p, we need to show that (p+3/p^2+2)^(1/2) = p.

Since this is not an algebraic manipulation that can be solved easily, we cannot confirm if g3(x) has a fixed point at p without further calculations or approximations.

g4(x) = (3x^4+2x^2+3)/(4x^3+4x-1)

Let's substitute p into g4(x):

g4(p) = (3p^4+2p^2+3)/(4p^3+4p-1)

To verify if g4(p) = p, we need to show that (3p^4+2p^2+3)/(4p^3+4p-1) = p.

Since this is not an algebraic manipulation that can be solved easily, we cannot confirm if g4(x) has a fixed point at p without further calculations or approximations.

Therefore, based on algebraic manipulations alone, we cannot verify if each of the four functions g1(x), g2(x), g3(x), and g4(x) have a fixed point at p when f(p) = 0. Further calculations or approximations would be required to determine the fixed points of these functions.

To learn more about algebraic manipulations visit;

https://brainly.com/question/32858114

#SPJ11

Answer:

see explanation

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, image to original.

A

scale factor = \(\frac{3}{9}\) = \(\frac{1}{3}\)

B

scale factor = \(\frac{9}{3}\) = 3

Answer:

{-3, 2, -5, 1, 6}

Step-by-step explanation:

The domain is the set of input values.

The given property “If AB=CD then CD=AB” is known as the symmetric property. Symmetric property is a type of equivalence relation in mathematics that states that if the relation between two elements is in the form of "if A is related to B, then B is related to A," then this type of relation is symmetric.

For such more question on symmetric

https://brainly.com/question/20168388

#SPJ8

Avea received 28 stickers when brianna, and carson in the ratio 1:3:4 and  brianna received 21 stickers.

The ratio is defined as the comparison of two or more quantities of the same units, which shows how much bigger one quantity is than another.

Given,The ratio of the distribution of stickers among Avea, Brianna and Carson is 1:3:4

The number of stickers Briana received is 21

Let us consider x as the common factor of the given ratio then, The number of stickers received by the girls are

Avea = xBriana = 3x

Carson = 4x

As we know 3x = 21 x

 = 21/3

= 7

then,4x

= 4×7

= 28

The number of stickers that Avea received is 28. Hence, the answer is 28

Read more about ratios :

brainly.com/question/12024093

#SPJ4

Answer:

they are 4 i think

Step-by-step explanation:

5 x 4 = 20

Answer:

100

Step-by-step explanation:

20 divided by 1/5 = 20 x 5/1 = 100

A correlation coefficient, r can never be less than -1 or greater than 1. Thus, d. 1.032 is not possible as a correlation coefficient.

The correlation coefficient, r is a measure of the direction and strength of the linear relationship between two variables. The correlation coefficient (r) varies between -1 and 1, with -1 indicating a perfect negative correlation, 0 indicating no correlation, and 1 indicating a perfect positive correlation. A value greater than 1 or less than -1 is not possible. Therefore, the value that could not represent a correlation coefficient is d. 1.032.

Given, the correlation coefficient varies between -1 and 1. The value that could not represent a correlation coefficient is 1.032 since it is greater than 1. A correlation coefficient, r of -1 indicates a perfect negative correlation where one variable decreases as the other increases. A correlation coefficient, r of 1 indicates a perfect positive correlation where both variables move in the same direction. A correlation coefficient of 0 indicates no linear relationship between the two variables.  A correlation coefficient, r can never be less than -1 or greater than 1.

Thus, d. 1.032 is not possible as a correlation coefficient.

Learn more about correlation coefficient visit:

brainly.com/question/29978658

#SPJ11

Answer: C. -1

Step-by-step explanation: -1 is your "a" value and is your leading coefficient.

Answer:

\(y+2=-3(x-2)\)

Step-by-step explanation:

The point-slope form of the straight line is given as

\(y-y_1=m(x-x_1)\)

Here \(m=-3\) and \((x_1, y_1)=(2, -2)\)

\(y+2=-3(x-2)\)

Answer:

78 degrees because they are congruent angles

Answer:

7/2

Step-by-step explanation:

√(x2 - x1)² + (y2 - y1)²

√(7 1/2 - 7 1/2)² + [-2 1/2 - (-6)]²

√(0)² + (7/2)²

√49/4

= 7/2

Answer:

10/11

Step-by-step explanation:

Answer:

\( ★\:\:\sqrt{ \frac{100}{121} } = \sqrt{ \frac{10 \times 10}{11 \times 11} } = \sqrt{ \frac{ {(10)}^{2} }{ {(11)}^{2} } }= \boxed{\frac{10}{11} }✓ \\ \)

Answer:

80 degrees

Step-by-step explanation:

What we see in this drawing is a triangle formed by three lines. In order to solve this problem, we need to know that when two lines intersect, the two angles formed are supplementary (meaning they add up to 180 degrees). For example, the 150-degree angle, and the angle right next to it (the angle on the left side of the triangle) add up to 180 degrees. This means that the left-most angle of the triangle is 180-150, which is 30 degrees

We can figure out the topmost angle of the triangle using the same method. We know that the angle outside the triangle is 130 degrees, so the angle right next to it (in this case, right below it), is 180-130, or 50 degrees.

Next, we use the fact that triangles are 180 degrees on the inside to figure out the third angle (the one on the right, right next to angle 1). We know that the other two angles are 30 and 50 degrees, and if you add that up, you get 80 degrees. The last angle, then, is 180-80, or 100 degrees.

Lastly, we know that the rightmost angle of the triangle and angle 1 add up to 180 degrees. In other words, 100+Angle1=180. Therefore, Angle 1 is 180-100 or 80 degrees.

Answer:

C

Step-by-step explanation:

Factor: Something which is multiplied by something else. A factor can be a number, variable, term, or a longer expression. For example, the expression 7x(y+3) has three factors: 7 , x , and (y+3) .

The 98% confidence interval for the number of chocolate chips per cookie in Big Chip cookies is approximately 13.5529 to 15.0471 chips.

To find the 98% confidence interval for the number of chocolate chips per cookie in Big Chip cookies, we'll use the t-distribution since the sample size is relatively small (n = 61) and we don't know the population standard deviation.

The formula for the confidence interval is:

\(CI = \bar X \pm t_{critical} \times \dfrac{s } {\sqrt{n}}\)

where:

X is the sample mean,

\(t_{critical\) is the critical value for the t-distribution corresponding to the desired confidence level (98% in this case),

s is the sample standard deviation,

n is the sample size.

First, let's find the critical value for the t-distribution at a 98% confidence level with (n-1) degrees of freedom (df = 61 - 1 = 60). You can use a t-table or a calculator to find this value. For a two-tailed 98% confidence level, the critical value is approximately 2.660.

Given data:

X (sample mean) = 14.3

s (sample standard deviation) = 2.2

n (sample size) = 61

\(t_{critical\) = 2.660 (from the t-distribution table)

Now, calculate the confidence interval:

\(CI = 14.3 \pm 2.660 \times \dfrac{2.2} { \sqrt{61}}\\CI = 14.3 \pm 2.660 \times \dfrac{2.2} { 7.8102}\\CI = 14.3 \pm 0.7471\)

Lower bound = 14.3 - 0.7471 ≈ 13.5529

Upper bound = 14.3 + 0.7471 ≈ 15.0471

To know more about confidence intervals follow

https://brainly.com/question/32452107

#SPJ4

Answer:

Desk is 2 1/2 ft. by 4 1/2 ft.

Step-by-step explanation:

The scale is 1/2 inch = 1 foot.

To change from drawing size to real size, multiply the drawing size in inches by 2 and change to ft.

Desk is 1 1/4 inches by 2 1/4 inches.

1 1/4 × 2 = 2 1/2

2 1/4 × 2 = 4 1/2

Desk is 2 1/2 ft. by 4 1/2 ft.

The approximate size of the cover that Maria will need to buy is 45. 84 square feet

The formula for calculating the circumference of a circle is expressed as;

Circumference = πr²

Where 'r' is the radius of the circle

Now, let's substitute the value of the circumference

24 = 2 × 3. 14 × r

r = 24/6. 28

r = 3. 82 feet

Formula for area = πr²

Substitute value of r

Area = 3. 14 × (3. 82)²

Area = 3. 14 × 14. 59

Area = 45. 84 square feet

Hence, the value is  45. 84 square feet

Learn more about area here:

https://brainly.com/question/25292087

#SPJ1

Answer:

Step-by-step explanation:

3/9 = 1/3

xy^2/x^8y^6 = 1/x^(8-1)y^(6-2) = 1/x^7y^4

therefore, 1/3x^7y^4

The given integral is ∫(1 to 0) (4/³√x)dx = ∫(0 to 1) (4x^(-1/3))dx

To find the integral of this form, we use the power rule of integration of the function x^n.

∫x^n dx = (x^(n+1))/(n+1) + C,

where C is the constant of integration

Now, we have ∫(0 to 1) (4x^(-1/3))dx = 4 ∫(0 to 1) (x^(-1/3))dx

Applying the power rule of integration,

∫(0 to 1) (x^(-1/3))dx = 3[x^(2/3)] (0 to 1)

= 3[1^(2/3) - 0^(2/3)]

= 3 × 1

= 3

Therefore, the integral is equal to 4 × 3 = 12.

Hence, the answer is 12.

To know more about integration  visit:

https://brainly.com/question/31744185

#SPJ11

In this particular data set, 10 is the only value that occurs more than once, so it is the only mode

The mode is the value that occurs most frequently in a data set. In the given data set {10, 30, 10, 36, 26, 22}, we can see that the value 10 occurs twice, and all other values occur only once. Therefore, the mode of the data set is 10, since it occurs more frequently than any other value in the set.

Note that a data set can have multiple modes if two or more values occur with the same highest frequency. However, in this particular data set, 10 is the only value that occurs more than once, so it is the only mode.

To learn more about frequently visit:

https://brainly.com/question/13959759

#SPJ11

The abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

Given the equation x^2 = 2y.

The coordinates of the point are (4,1).We have to find the abscissa on the curve that is nearest to this point.So, let's solve this question:

To find the abscissa on the curve x2 = 2y which is nearest to the point (4,1), we need to apply the distance formula.In terms of x, the formula for the distance between a point on the curve and (4,1) can be written as:√[(x - 4)^2 + (y - 1)^2]But since x^2 = 2y, we can substitute 2x^2 for y:√[(x - 4)^2 + (2x^2 - 1)^2].

Now we need to find the value of x that will minimize this expression.

We can do this by finding the critical point of the function: f(x) = √[(x - 4)^2 + (2x^2 - 1)^2]To do this, we take the derivative of f(x) and set it equal to zero: f '(x) = (x - 4) / √[(x - 4)^2 + (2x^2 - 1)^2] + 4x(2x^2 - 1) / √[(x - 4)^2 + (2x^2 - 1)^2] = 0.

Now we can solve for x by simplifying this equation: (x - 4) + 4x(2x^2 - 1) = 0x - 4 + 8x^3 - 4x = 0x (8x^2 - 3) = 4x = √(3/8)The abscissa on the curve x^2 = 2y that is nearest to the point (4,1) is x = √(3/8).T

he main answer is that the abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

The abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

To know more about abscissa visit:

brainly.com/question/32034993

#SPJ11

The scale factors are given as follows:

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

Considering two equivalent side lengths, the scale factors are given as follows:

More can be learned about dilation at brainly.com/question/3457976

#SPJ1

Answer:

1

Step-by-step explanation:

the square root of 64

√64 = 8

8 - 7 = 1