A 60kg student in a rowboat on a still lake decides to dive off the front of the boat. The student's horizontal acceleration is 2.0 m/s/s while in contact with the boat. What horizontal force does the student exert on the boat?
120 N toward the back of the boat
30 N toward the back of the boat
30 N toward the front of the boat
120 N toward the front of the boat

Answer:

a = 0.9

Step-by-step explanation:

For the quadratic equation \(\boxed{ax^2 + bx + c = 0}\) to have exactly one real root, the value of its discriminant, \(\boxed{b^2 - 4ac}\), must be zero.

For the given equation:

\(y = ax^2 - 6x + 10\),

• a = a

• b = -6

• c = 10.

Substituting these values into the formula for discriminant, we get:

\((-6)^2 - 4(a)(10) = 0\)

⇒ \(36 - 40a = 0\)

⇒ \(36 = 40a\)

⇒ \(a = \frac{36}{40}\)

⇒ \(a = \bf 0.9\)

Therefore the value of a is 0.9 when the given quadratic has exactly one root.

Answer:

The equation \(x=4\) represents in R^2 c) a line

The equation \(x=4\) represents in R^3 a) a plane

The equation \(y+3x=2\) represents in R^3 a) a plane

The equation \(z-4y=8\) represents d) a plane

The pair of equations \(y=2,z=8\) represents a) a line

Step-by-step explanation:

Let's start by studying each question :

1)

In R^2 , \(x=a\) with \(a\) ∈ IR is the equation of all vertical lines

In this case, the only free variable is the variable ''y''

R^2 has two dimensions (x and y) so if we set \(x=4\) we will have only one free variable in R^2 (which is a line in R^2). Therefore, \(x=4\) represents a line in R^2

Now, in R^3 we have three dimensions (x, y and z) so if we set \(x=4\) we will have only two free variables (y and z) and \(x=4\) will represent a plane (which have two dimensions) in R^3.

2) The equation \(y+3x=2\) in R^3 has the free variable ''z'' and given that we select a value (for example for ''x'') the another value from the variable ''y'' is determined. Finally, we have the free variables ''z'' and ''x'', and the variable ''y'' restricted for our choice of the variable ''x''.

The equation \(y+3x=2\) in R^3 (given that we have two free variables) represents a plane.

Using the same reasoning, the equation \(z-4y=8\) represents a plane (given that it has two free variables : ''y'' and ''x'')

Finally, the pair of equations \(y=2,z=8\) set values for ''y'' and ''z'' leading us ''x'' as the free variable. With only one free variable we will have a ''one dimensional'' geometric form. The one dimensional forms in R^3 are lines.

The final answer is a) a line.

The area of the rectangular figure with two semicircles on the opposite side is  36.56 sq cm.

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

Given, A rectangle with two semicircles on two opposite sides.

The length of the rectangle is 6cm and the width of the rectangle is 4cm.

The two given semicircles have a diameter of 4cm seems obvious.

∴ The area of the total figure is an area of the rectangle added to the area of 2 semicircles which makes up to a circle with a radius 2 cm.

∴ (4×6) + π(2)² sq cm.

= 24 + 4π sq cm.

= 24 + 12.56 sq cm.

= 36.56 sq cm.

The area which is not taken up in the rectangle and two circle questions are

(area of the rectangle - 2 times the area of a circle).

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Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

Answer:

True

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the amount of detectors sold in the current year = 350

percent increment = 105%

To get the amount sold the previous year, we will use the expression;

(105% of x) + x =  350

1.05x = 350 + x

1.05x + x = 350

2.05x = 350

x = 350/2.05

x = 170.7

Hence the amount sold the previous year was 170.7 detectors

Required two transformations are translated according to the rule (x, y) → (x + 8, y + 2) reflected across the x-axis.

How to find the two transformations applied to pentagon ABCDE to create A″B″C″D″E″?

To find the two transformations applied to pentagon ABCDE to create A″B″C″D″E″, we can compare the coordinates of corresponding vertices of both pentagons.

Starting with point A, we see that it has been translated 8 units to the right and 2 units up to become A″. Therefore, the first transformation is a translation according to the rule (x, y) → (x + 8, y + 2).

Next, we can compare the y-coordinates of point A and A″ to see if a reflection has been applied. We see that the y-coordinate of A has changed from 5 to -7 in A″, indicating that a reflection has been applied across the x-axis.

Therefore, the two transformations applied to pentagon ABCDE to create A″B″C″D″E″ are:

Translated according to the rule (x, y) → (x + 8, y + 2)

Reflected across the x-axis.

The other options can be ruled out as they do not correctly reflect the transformation that was applied.

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Answer:

3/4

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator. GCD of 75 and 100 is 25.

75 ÷ 25100 ÷ 25.

Reduced fraction: 34. Therefore, 75/100 simplified to lowest terms is 3/4.

Answer:

three equivalent fractions to 75/100 are 3/4 , 6/8 , & 12/16

Using Scale Factor, the value of x = 33.6.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Scale factor = Dimension of the new shape / Dimension of the original shape is the fundamental formula used to calculate it.

The formula is expressed as Scale factor = Larger figure dimensions Smaller figure dimensions in the event that the original figure is enlarged.

Dimension of the large triangle divided by the little triangle is the formula to utilize.

Based on the accompanying figure,

The little triangle's corresponding side length is 28, whereas the giant triangle's side length is x.

Scale factor = 6/5 Scale factor = 6/5 = 28

x = 33.6

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Complete Question -

If the figures below are similar with a scale factor of 6:5, find the value of x

Step-by-step explanation:

f(x)=15x+60 means that x is how many hours it took to make the statue. so if x is 75 then its f(75)=1125+60=1185. so the answer is D

Answer:

Terry's initial amount = £780

Step-by-step explanation:

Given that:

Ratio of Terry's money to Faye's money = 3 : 5

Let,

x be the amount of money.

Terry's amount = 3x

Faye's amount = 5x

Now,

3x + 220 = 5x - 300

220+300 = 5x - 3x

520 = 2x

2x = 520

Dividing both sides by 2

\(\frac{2x}{2}=\frac{520}{2}\\x=260\)

Terry's initial amount = 3x = 3(260) = £780

Hence,

Terry's initial amount = £780

Answer:

A ................................

The probability that the third largest observation in the sample is less than 0.7 is  0.2401 =  24.01%.

The sample size n = 5,

Therefore the order statistics will be represented as X₁, X₂, X₃, X₄, and X₅.

Probability that X₃ is less than 0.7:

Since X₃ is the third largest observation =  (X₁ and X₂) < 0.7.

The probability that X₃ is less than 0.7 is (0.7)² = 0.49.

.

The probability that both X₁ and X₂ are less than or equal to 0.7 is (0.7)² = 0.49 because in a continuous uniform distribution, the probability of any single observation being less than 0.7 is 0.7 - 0 = 0.7.

We then get the product of both cases:

Probability = 0.49 * 0.49 = 0.2401

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Answer:

table b

Step-by-step explanation:

Edge

Answer:

10

Step-by-step explanation:

(15 x 40) / (15+40)

solve inside the parenthesis:

600/60

divide:

10

Answer:

x=3 or -3

Step-by-step explanation:

hope it helps

The graph of h(x) = (x-1)^2 - 9 is a U-shaped parabola that opens upwards, with the vertex at (1, -9), and it extends indefinitely in both directions.

The function h(x) = (x-1)^2 - 9 represents a quadratic equation. Let's analyze the different components of the equation to understand the behavior of the graph.

The term (x-1)^2 represents a quadratic term. It indicates that the graph will have a parabolic shape. The coefficient in front of the quadratic term (1) implies that the parabola opens upwards.

The constant term -9 shifts the graph downward by 9 units. This means the vertex of the parabola will be at the point (1, -9).

Based on this information, we can draw the following conclusions:

The graph will be a U-shaped curve with the vertex at (1, -9).

The vertex represents the minimum point of the parabola since it opens upward.

The parabola will be symmetric with respect to the vertical line x = 1 since the coefficient of the quadratic term is positive.

The graph will extend indefinitely in both directions.

To accurately plot the graph, you can choose several x-values, substitute them into the equation to find the corresponding y-values, and then plot the points on the graph. Alternatively, you can use graphing software or calculators that can plot the graph of the equation for you.

Remember to label the axes and indicate the vertex at (1, -9) to provide a complete representation of the graph of h(x) = (x-1)^2 - 9.

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Answer:

2·2·2·2 = 16

Step-by-step explanation:

everytime a number is raised by another, that means you are going to multiply the base number  times itself as many times as the exponents tells you. this is a little but tricky to explain, so let me give you some examples:

2² → in this case the base number is 2 and the exponent is 2 as well, so you will multiply 2 times itself, 2 times:

2² = 2 · 2 = 4

2³ → in this case the base number is 2 and the exponent is 3, so you will multiply 2 times itself, 3 times:

2³ = 2 · 2 · 2 = 8

In the question asked, 2 is being raised by 4, so you will multiply 2 times itself, 4 times:

2^4 = 2·2·2·2 = 16

the same format will be used regardless of the base number and the exponent

i hope this helps! :)

Answer:

the diameter is 24 so the ray is 12

circonference = 2*pi*R = 2*3.14*12= 75.36

x = 1 level

x + 4 (since it starts with 5 treasures and one level = 1) = 5

so if you want to see level 5 for instance it would be:

x+4 = y which would be 5+4 = y = 9

hope this helps

Answer: Changing the radius of an object by a given amount has a greater effect on the volume than changing the height by the same amount. The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height. If we change the radius by a given amount, say x, the new radius would be r+x. Hence, the new volume would be V' = π(r+x)²h = π(r²+2rx+x²)h = V + 2πrxh + πx²h. We can see that the volume change equals 2πrxh + πx²h. The first term is proportional to both the radius and the height, whereas the second term is proportional to the square of the radius and the height. Assuming that the height change is also x, the new volume would be V'' = πr²(h+x) = V + πr²x. We can see that the volume change is proportional to the radius squared and the change in height. Therefore, changing the radius by a given amount has a greater effect on the volume than changing the height by the same amount.

Answer:

183.3 in^3

Step-by-step explanation:

Find the volume of the rectangular bottom

V = l*w*h

V = 5*5*6 =150 in^3

Find the volume of the triangular pyramid

V = 1/3 Bh where B is the area of the base and h is the height

V = 1/3 ( 5*5) * 4 = 100/3

Add the two volumes together

150 + 100/3

150 +33.3

183.3 in^3

Answer:

4.10.99

Step-by-step explanation:

3.14 * 3.5

Answer:

x = 1 , x = 13

Step-by-step explanation:

(x - 7)² = 36 ( take square root of both sides )

x - 7 = ± \(\sqrt{36}\) = ± 6 ( add 7 to both sides )

x = 7 ± 6

then

x = 7 - 6 = 1

x = 7 + 6 = 13

Answer:

right now if you were to have a coke depending on the weather is from where you are standing effect how long it will take to melt

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given Equation :

\(y = \frac{1}{2} x - 3\)

Which is in slope intercept form :

\(y = mx + b\)

Where :

m = slope

b = y-intercept.

Thus , in the given Equation , the y-intercept is -3