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3 years ago

if PQ || RS and the slope of PQ= x-1/4 and the slope of RS is 3/8 then find the value of x justify algebraically and numerically

Mathematics

1 answer:

Artemon [7]3 years ago

5 0

The value of x is 5/8.

Step-by-step explanation:

Given,

The lines PQ and RS are parallel to each other.
slope of PQ= x-1/4
slope of RS = 3/8

The slopes of parallel lines are equal.

slope of PQ = slope of RS

⇒ x-1/4 = 3/8

⇒ (4x-1)/4 = 3/8

⇒ 8(4x-1) = 4(3)

⇒ 32x-8 = 12

⇒ 32x = 20

x = 20/32

x = 5/8

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In a doctor's waiting room, there are 14 seats in a row. Eight people are waiting to be seated. There is someone with a very bad

diamong [38]

Answer: 12,972,960

Step-by-step explanation: There are 14 chairs and 8 people to be seated. But among the 8. three will be seated together:

So 5 people and (3) could be considered as 6 entities:

Since the order matters, we have to use permutation:

¹⁴P₆ = (14!)/(14-6)! = 2,162,160, But the family composed of 3 people can permute among them in 3! ways or 6 ways. So the total number of permutation will be ¹⁴P₆ x 3!

2,162,160 x 6 = 12,972,960 ways.

Another way to solve this problem is as follow:

5 + (3) people are considered (for the time being) as 6 entities:

The 1st has a choice among 14 ways

The 2nd has a choice among 13 ways

The 3rd has a choice among 12 ways

The 4th has a choice among 11 ways

The 5th has a choice among 10 ways

The 6th has a choice among 9ways

So far there are 14x13x12x11x10x9 = 2,162,160 ways

But the 3 (that formed one group) could seat among themselves in 3!

or 6 ways:

Total number of permutation = 2,162,160 x 6 = 12,972,960

5 0

3 years ago

Use cylindrical coordinates to evaluate the triple integral ∭ where E is the solid bounded by the circular paraboloid z = 9 - 16

4vir4ik [10]

Answer:

$\mathbf{\iiint_E E \sqrt{x^2+y^2} \ dV =\dfrac{81 \ \pi}{80}}$

Step-by-step explanation:

The Cylindrical coordinates are:

x = rcosθ, y = rsinθ and z = z

From the question, on the xy-plane;

$9 -16 (x^2 + y^2) = 0 \\ \\ 16 (x^2 + y^2) = 9 \\ \\ x^2+y^2 = \dfrac{9}{16}$

$x^2+y^2 = (\dfrac{3}{4})^2$

where:

0 ≤ r ≤ $\dfrac{3}{4}$ and 0 ≤ θ ≤ 2π

∴

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} \int ^{\dfrac{3}{4}}_{0} \int ^{9-16r^2}_{0} \ r \times rdzdrd \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} \int ^{\dfrac{3}{4}}_{0} r^2 z|^{z= 9-16r^2}_{z=0} \ \ \ drd \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} \int ^{\dfrac{3}{4}}_{0} r^2 ( 9-16r^2}) \ drd \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} \int ^{\dfrac{3}{4}}_{0} ( 9r^2-16r^4}) \ drd \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} ( \dfrac{9r^3}{3}-\dfrac{16r^5}{5}})|^{\dfrac{3}{4}}_{0} \ drd \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} ( 3r^3}-\dfrac{16r^5}{5}})|^{\dfrac{3}{4}}_{0} \ drd \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} ( 3(\dfrac{3}{4})^3}-\dfrac{16(\dfrac{3}{4})^5}{5}}) d \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV =( 3(\dfrac{3}{4})^3}-\dfrac{16(\dfrac{3}{4})^5}{5}}) \theta |^{2 \pi}_{0}$

$\iiint_E E \sqrt{x^2+y^2} \ dV =( 3(\dfrac{3}{4})^3}-\dfrac{16(\dfrac{3}{4})^5}{5}})2 \pi$

$\iiint_E E \sqrt{x^2+y^2} \ dV =(\dfrac{81}{64}}-\dfrac{243}{320}})2 \pi$

$\iiint_E E \sqrt{x^2+y^2} \ dV =(\dfrac{81}{160}})2 \pi$

$\mathbf{\iiint_E E \sqrt{x^2+y^2} \ dV =\dfrac{81 \ \pi}{80}}$

4 0

3 years ago

What else would need to be congruent to show that ABC = DEF by SAS?

Alona [7]

The answer us A.

Line AC needs to be congruent to DF because for SAS (side angle side) we have a side (BA and DE) and an angle (A and D) so we need another side.

3 0

3 years ago

Read 2 more answers

Here are the first four terms of a sequence.

Nataly_w [17]

Answer:

aₙ = 2n² + n + 1

Step-by-step explanation:

We observe that the difference of terms is 4, 7 and 15 and next level difference is 4. It means the sequence is quadratic.

We can compare this with simple quadratic sequence

1, 4, 9, 16

and find out that doubling each term gives us

2, 8, 18, 32

This is close to our sequence, write the terms as follows to find exact rule

The first term:

a₁ = 4 = 2*1² + 2 = 2*1² + 1 + 1

The second term

a₂ = 11 = 2*2² + 3 = 2*2² + 2 + 1

The third term:

a₃ = 22 = 2*3² + 4 = 2*3² + 3 + 1

The fourth term:

a₄ = 37 = 2*4² + 5 = 2*4² + 4 + 1

The nth term as per observation above is:

aₙ = 2n² + n + 1

8 0

2 years ago

2x +5y=10 writing equations in slope intercept form

rosijanka [135]

Answer: y=-2/5x+2

Solving Steps:
2x+5y=10 - Move the variable to the right
5y=10-2x - Divide both sides by five
y=2-2/5x - Reorder the terms
y=-2/5x+2

7 0

3 years ago