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3 years ago

Find the area of a cross section parallel to the base of a cylinder with a radius of 2.5 cm and a height of 12 cm

Mathematics

1 answer:

Luda [366]3 years ago

6 0

Answer: 227.77 cm 2 here is your answer,

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Step-by-step explanation:

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Solve the equation by factoring. 8x^2+10x-7=0 What is the solution set?

nydimaria [60]

Answer:

$\large \text{$x_1$}=-\dfrac{7}{4}, \large \text{$x_2$}=\dfrac{1}{2}$

Step-by-step explanation:

Given: 8x² + 10x - 7 = 0

When factoring trinomials of the form ax² + bx + c:

multiply the leading coefficient and the last term.
find the product factors that add to give you the coefficient of the middle term.
rewrite the polynomial with those factors replacing the middle term.

1. Split the middle term:

⇒ 8 × -7 = -56 [multiply the leading coefficient and the last term]

⇒ 14, -4 [find the product factors that add to the middle term's coefficient]

⇒ 8x² + 14x - 4x - 7 = 0 [rewrite with those factors replacing the middle term.]

2. Factor by grouping:

⇒ 8x² + 14x - 4x - 7 = 0 [factor out 2x]

⇒ 2x(4x + 7) - 4x - 7 = 0 [factor out -1 or the negative sign]

⇒ 2x(4x + 7) -1(4x + 7) = 0 [factor out 4x + 7]

⟹ (4x + 7)(2x - 1) = 0

3. Separate into 2 cases:

4x + 7 = 0
2x - 1 = 0

Case 1:

⇒ 4x + 7 = 0 [subtract 7 from both sides]

⇒ 4x + 7 - 7 = 0 - 7

⇒ 4x = -7 [divide both sides by 4]

⇒ 4x ÷ 4 = -7 ÷ 4

⟹ x = $\bold{-\dfrac{7}{4}}$

Case 2:

⇒ 2x - 1 = 0 [subtract 1 from both sides]

⇒ 2x - 1 + 1 = 0 + 1

⇒ 2x = 1 [divide both sides by 2]

⇒ 2x ÷ 2 = 1 ÷ 2

⟹ x = $\bold{\dfrac{1}{2}}$

Solutions:

$\large \text{$x_1$}=-\dfrac{7}{4}, \large \text{$x_2$}=\dfrac{1}{2}$

Learn more about quadratic equations here:

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7 0

2 years ago

Read 2 more answers

A had $360 more than B. When A spent $144 and B spent half of his money, A had 6 times as much money as B, Find the ratio of the

Karolina [17]

Answer:

13:3

Step-by-step explanation:

A=x B=y

first; x= 360+y

later;x= 216+y

A:B

216+y: 1/2y = 6: 1

216+y/y÷2 =6/1

216+y = 3y

y = 108

first; x =360+y

360 +108

468

A:B = 468:108

13:3

3 0

3 years ago

100 POINTS + BRAINLIST

mojhsa [17]

Problem 1

Since point P is the tangent point, this means angle OPT is a right angle

angle OPT = 90 degrees

Let's use the Pythagorean theorem to find the missing side 'a'

a^2 + b^2 = c^2

a^2 + 7^2 = 12^2

a^2 + 49 = 144

a^2 = 144 - 49

a^2 = 95

a = sqrt(95)

a = 9.7467943

a = 9.7

----------------

Let's use the sine and arcsine rule to find angle y

sin(angle) = opposite/hypotenuse

sin(y) = 7/12

y = arcsin( 7/12 )

y = 35.6853347

y = 35.7

The value of y is approximate. Make sure your calculator is in degree mode. Arcsine is the same as inverse sine or $\sin^{-1}$

====================================================

Problem 2

Focus on triangle OHP. This may or may not be a right triangle. The goal is to test if it is or not.

We use the converse of the Pythagorean theorem to check.

Recall that the converse of the Pythagorean theorem says: If a^2+b^2 = c^2 is a true equation, then the triangle is a right triangle. The value of c is always the longest side. The order of a and b doesn't matter.

In this case we have

a = 7
b = 13
c = 16

Which leads to

a^2 + b^2 = c^2

7^2 + 13^2 = 16^2

49 + 169 = 256

218 = 256

We get a false equation at the end, since both sides aren't the same number, which means the original equation is false.

We don't get a^2 + b^2 = c^2 to be true, therefore this triangle is not a right triangle.

Consequently, this means angle OPH cannot possible be 90 degrees (if it was then we'd have a right triangle). Therefore, point P is not a tangent point.

You follow the same basic idea for triangle OQH and show that point Q is not a tangent point either. Or you could use a symmetry argument to note that triangle OPH is a mirror reflection of triangle OQH over the line segment OH. This implies that whatever properties triangle OPH has, then triangle OQH has them as well for the corresponding pieces.

7 0

3 years ago

Read 2 more answers

The product of (-2)(-5)(-7)

Effectus [21]

(-2)(-5)(-7)
(10)(-7)
-70
The product is -70

3 0

3 years ago

Read 2 more answers

What’s the answer ??? ( someone please help )

Fofino [41]

It would probably be B because it said between -30 and 130

3 0

3 years ago