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2 years ago

Please help me on this

Mathematics

1 answer:

AlekseyPX2 years ago

8 0

9514 1404 393

Answer:

10 ft

Step-by-step explanation:

The midsegment length is the average of the other two lengths.

(QR +PS)/2 = TU

QR +PS = 2×TU . . . . . . . . . . . . . . . multiply by 2

QR = 2×TU -PS = 2(14 ft) -18 ft . . . subtract PS; substitute given values

QR = 10 ft

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10.)A child-sized swimming pool can be modeled by a cylinder. The pool has a diameter of 6 1/2 feet and a height of 12 inches. T

Luba_88 [7]

Answer:

165.47≈165 Gallons of Water

Step-by-step explanation:

According To the Question,

Given, A child-sized swimming pool can be modeled by a cylinder. The pool has a diameter of 6 1/2 feet (or) 6.5 feet (radius is 3.25 feet) and a height of 12 inches(1 feet).

The pool is filled with water to 2/3 of its height (H= 2/3 feet) .

Volume of Cylinder = π×R²×H , now put values, we get

Volume = 3.14×3.25²×2/3

Volume = 22.122 foot³ .

And, One cubic foot equals 7.48 gallons of water

Thus, 22.122 cubic foot equals to 165.47≈165 gallons of water .

8 0

2 years ago

A sheet of paper 90 cm-by-66 cm is made into an open box (i.e. there's no top), by cutting x-cm squares out of each corner and f

NNADVOKAT [17]

Answer:

$26 - \sqrt{181}$ cm

Step-by-step explanation:

The volume of the box is:

V = height * length * width

V = x*(66 - 2*x)*(90 - 2*x)

V = (66*x - 2*x^2)*(90 - 2*x)

V = 5940*x - 132*x^2 - 180*x^2 + 4*x^3

V = 4*x^3 - 312*x^2 + 5940*x

where x is the length of the sides of the squares, in cm.

The mathematical problem is :

Maximize: V = 4*x^3 - 312*x^2 + 5940*x

subject to:

x > 0

2*x < 66 <=> x < 33

In the maximum, the first derivative of V, dV/dx, is equal to zero

dV/dx = 12*x^2 - 624*x + 5940

From quadratic formula

$x = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)}$

$x = \frac{624 \pm \sqrt{(-624)^2 - 4(12)(5940)}}{2(12)}$

$x = \frac{624 \pm \sqrt{104256}}{24}$

$x = \frac{624 \pm \sqrt{2^6*3^2*181}}{24}$

$x = \frac{624 \pm 8*3*\sqrt{181}}{24}$

$x_1 = \frac{624 + 24*\sqrt{181}}{24}$

$x_1 = 26 + \sqrt{181}$

$x_2 = \frac{624 - 24*\sqrt{181}}{24}$

$x_2 = 26 - \sqrt{181}$

But $x_1 > 33$ , then is not the correct answer.

5 0

2 years ago

Find the equation of the line.<br> Use exact numbers.<br> y =<br> X +

puteri [66]

Answer:

$y = \frac{3}{4} x - 2$

Step-by-step explanation:

Remmeber this:

$slope = \frac{rise}{run}$

The y-intercept is where the lone goes through the y-axis.

5 0

2 years ago

What expression is the simplified form of “-12+5a-a-6a+8a+8+3a”? Please explain your reasoning.

kramer

Combine like terms:

-12 + 5a - a - 6a + 8a + 8 + 3a

$-12 + 5a - a - 6a + 8a + 8 + 3a$

5a - a = 4a

4a - 6a = -2a

-2a + 8a = 6a

6a + 3a = 9a

-12 + 8 = -4

Answer

$9a - 4$

4 0

3 years ago

Read 2 more answers

Suppose a fair 6-sided die is tossed five times. What is the probability that we see at least one three in the five tosses?

Marta_Voda [28]

Answer:

C. 0.1667

Step-by-step explanation:

1/6 +0/6 + -1/6

The closest answer is C. 0.1667

Based on 2nd throw of dice shows zero then 0.1667 of the answer is shown on the 3rd throw in decimal form of -1/6

3 0

2 years ago