MATHEMATICS HIGH SCHOOL

2(8n2 + 9n) +
+ 9n) + 3(4n- 7n)

Answers

Answer 1

Answer:

Answer:

n = 0 or n = -9/16

Step-by-step explanation:

Solve for n:

2 (8 n^2 + 9 n) - 9 n = 0

Hint: | Write the quadratic polynomial on the left hand side in standard form.

Expand out terms of the left hand side:

16 n^2 + 9 n = 0

Hint: | Factor the left hand side.

Factor n from the left hand side:

n (16 n + 9) = 0

Hint: | Find the roots of each term in the product separately.

Split into two equations:

n = 0 or 16 n + 9 = 0

Hint: | Look at the second equation: Isolate terms with n to the left hand side.

Subtract 9 from both sides:

n = 0 or 16 n = -9

Hint: | Solve for n.

Divide both sides by 16:

Answer: n = 0 or n = -9/16

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Workings Please.

1. A 210° sector of a circle of radius 10cm is used to make a cone. Find the radius of the base of the cone and it's height.

Answers

Answer: radius = 5.83 cm height = 8.12 cm

Step-by-step explanation:

First, let's find the circumference of the 210° section of the circle.

$C=2\pi r\bigg((\theta)/(360^o)\bigg)\n\n\nC=2\pi(10)\bigg((210^o)/(360^o)\bigg)\n\n\nC=(35)/(3)\pi$

The circumference of the the cone is $(35)/(3)\pi$ . We can use this to find the radius .

$C=2\pi r\n\n(35)/(3)\pi=2\pi r\n\n\n(35\pi)/(3\cdot 2\pi)=r\n\n\n(35)/(6)=r\n\n\n5.83=r$

When you fold the 210° section into a cone, the slant height is the original radius of 10. We can use the radius and slant height of the cone to form a right triangle with the height. Use the Pythagorean Theorem to find the height.

radius² + height² = slant height²

$(35)/(6)^2\ +\ h^2=10^2\n\n\n.\qquad \quad h^2=10^2-\bigg((35)/(6)\bigg)^2\n\n.\qquad \quad h=\sqrt{(6^2(10)^2-35^2)/(6^2)}\n\n\n.\qquad \quad h=\sqrt{(2375)/(36)}\n\n\n.\qquad \quad h=8.12$

a box with no top is constructed from a 10 inch x 12 inch piece of cardboard by cutting out congruent squares from each corner of the cardboard and then folding the resulting tabs. We determined the volume of that box (in cubic inches) is given by V(x) = 4x³ - 44x² + 120x where x denotes the length of the side of the square which is removed from each corner (in inches), 0 < x < 5. Solve the inequality V(x)≥80 analytically and interpret your answer in the context of that example.

Answers

Answer:

$To solve the inequality $V(x) \geq 80$, we'll first set up the inequality and then find the values of $x$ that satisfy it.The inequality is $4x^3 - 44x^2 + 120x \geq 80$.Let's simplify it further:$4x^3 - 44x^2 + 120x - 80 \geq 0$.Now, we need to find the values of $x$ that make this inequality true.We can start by factoring the expression:$4(x^3 - 11x^2 + 30x - 20) \geq 0$.$

$Now, let's factor the cubic polynomial inside the parentheses:$x^3 - 11x^2 + 30x - 20 = (x - 2)(x - 5)(x - 2)$.Now, the inequality becomes:$4(x - 2)(x - 5)(x - 2) \geq 0$.To determine the intervals where this inequality is satisfied, we can use a sign chart. We'll consider the values of $x$ that make each factor and the whole expression positive or negative.$

$1. $x - 2$ is positive for $x > 2$ and negative for $x < 2$.\n2. $x - 5$ is positive for $x > 5$ and negative for $x < 5$.\n3. $x - 2$ is positive for $x > 2$ and negative for $x < 2$.Now, consider the overall sign of the expression $4(x - 2)(x - 5)(x - 2)$:- Positive when all three factors are positive (i.e., $x > 5$).- Negative when exactly one factor is negative (i.e., $2 < x < 5$).- Positive when all three factors are negative (i.e., $x < 2$).$

$So, the solution to the inequality $V(x) \geq 80$ is:\[x < 2 \text{ or } 2 < x < 5.\]$

Step-by-step explanation:

In the context of the example, this means that the side length of the square removed from each corner must be less than 2 inches or between 2 and 5 inches for the volume of the box to be greater than or equal to 80 cubic inches. This helps determine the range of valid values for

x to achieve the desired volume for the box.

Final Answer:

The solution to the inequality V(x) ≥ 80 is x ≥ 3.5 inches.

Explanation:

To solve the inequality V(x) ≥ 80, we set the equation 4x³ - 44x² + 120x ≥ 80 and simplify. This simplifies to x³ - 11x² + 30x - 20 ≥ 0, which can be factored as (x - 3.5)(x - 2)(x - 2.857) ≥ 0. Since x represents the side length of the squares removed from the corners, it cannot be negative, so we focus on the values of x that make the expression on the left side of the inequality greater than or equal to zero. This leads us to the solution x ≥ 3.5 inches.

In the context of the example, when the side length of the squares removed from each corner is 3.5 inches or larger, the resulting box has a volume greater than or equal to 80 cubic inches. This means that to achieve a box with a volume of at least 80 cubic inches, you need to remove squares with sides of at least 3.5 inches.

Learn more about inequality

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HELP IMMA DIE find the inverse for each relation {(-5,1),(-5,-1)(-5,8)}
a. (8,-5) (1,-5) (-5.8)
b. (-5,1) (-5,-1) (-5,8)
c. (-1,5), (1.-5) (8,5)
d. (1,-5) (-1,-5), (8,-5)

Answers

Answer:

(5,-1) (5,1) (5,-8)

Step-by-step explanation:

A cereal company used to fill the boxes with 16 ounces of cereal. They have reduced that amount to 14 ounces. The percent decrease is 87.5%. True or false

Answers

Answer:

False

Step-by-step explanation:

Given: A cereal company used to fill the boxes with 16 ounces of cereal. They have reduced that amount to 14 ounces.

Decreased amount = 16 -14 = 2 ounces.

Now let's find the decreased percentage using the following formula.

Decrease percent = $(decreased amount)/(original amount) *100$

= $(2)/(16) *100$

= $(200)/(16)$

= 12.5%

The percentage of decrease is 12.5%.

Therefore, the answer is false

This is a true statement

%87.5 = .875 in decimal form
multiply 16 by 8.75 and it will give you 14

hope this helped

The first four terms of a sequence are shown below:9, 5, 1, −3

Which of the following functions best defines this sequence? (5 points)

A f(1) = 9, f(n + 1) = f(n) − 4; for n ≥ 1
B f(1) = 9, f(n + 1) = f(n) + 4; for n ≥ 1
C f(1) = 9, f(n + 1) = f(n) − 5; for n ≥ 1
D f(1) = 9, f(n + 1) = f(n) + 5; for n ≥ 1