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3 years ago

What is 14/ = 42/45

Mathematics

1 answer:

Dominik [7]3 years ago

5 0

Answer:

Step-by-step explanation:

14/ x= 42/45

Simplifying the right side by dividing the top and bottom by 6

14/ x= 7/9

Multiply the right by 2/2

14/x = 14/18

The denominator is 18

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An icicle with a diameter of 15.5 centimeters at the top, tapers down in the shape of a cone with a length of

Helga [31]

Answer:

Step-by-step explanation:

Note: I will leave the answers as fraction and in terms of pi unless the question states rounding conditions to ensure maximum precision.

From the question, we can tell it is a inversed-cone (upside down)

Volume of Cone = $\pi r^{2} \frac{h}{3}$

a) Given Diameter , d = 15.5cm and Length , h = 350cm,

we first find the radius.

$r = \frac{d}{2} \\=\frac{15.5}{2} \\=7.75cm$

We will now find the volume of the cone.

Volume of cone $\pi (7.75)^{2} \frac{350}{3} \\= \frac{168175\pi }{24}$

We know the density of ice is 0.93 grams per $1cm^{3}$

$1cm^{3} =0.93g\\\frac{168175\pi }{24} cm^{3} =0.93(\frac{168175\pi }{24} )\\= 20473 g$ (Nearest Gram)

b) After 1 hour, we know that the new radius = 7.75cm - 0.35cm = 7.4cm

and the new length, h = 350cm - 15cm = 335cm

Now we will find the volume of this newly-shaped cone.

Volume of cone = $\pi (7.4)^{2} \frac{335}{3} \\= \frac{91723\pi }{15} cm^{3}$

Volume of cone being melted = New Volume - Original volume

= $\frac{168175\pi }{24} -\frac{91723\pi }{15} \\= \frac{35697\pi }{40} cm^{3}$

c) Lets take the bucket as a round cylinder.

Given radius of bucket, r = 12.5cm (Half of Diameter) and h , height = 30cm.

Volume of cylinder = $\pi r^{2} h\\=\pi (12.5)^{2} (30)\\=\frac{9375\pi }{2} cm^{3}$

To overflow the bucket, the volume of ice melted must be more than the bucket volume.

Volume of ice melted after 5 hours = $5(\frac{35697\pi }{40} )\\=\frac{35697\pi }{8} cm^{3}$

See, from here of course you are unable to tell whether the bucket will overflow as all are in fractions, but fret not, we can just find the difference.

Volume of bucket - Volume of ice melted after 5 hours

= $\frac{9375\pi }{2} -\frac{35697\pi }{8 } \\=\frac{1803\pi }{8}cm^{3}$

from we can see the bucket can still hold more melted ice even after 5 hours therefore it will not overflow.

4 0

2 years ago

Math PLEASE HELP IM SO CONFUSED IM ATTACHING THE SLIDES!!!!

slavikrds [6]

Answer:

x = 19, TS = 22

Step-by-step explanation:

Use ratios to solve for x. Corresponding sides have same ratio.

(x + 5)/30 = (36 - 20)/20
(x + 5)/30 = 16/20 = 4/5
5(x + 5) = 4(30)
5x + 25 = 120
5x = 95
x = 19

(5x - 2)/(3x + 1) = 39/26
(5x - 2)/(3x + 1) = 3/2
2(5x - 2) = 3(3x + 1)
10x - 4 = 9x + 3
10x - 9x = 3 + 4
x = 7

TS = 3x + 1 = 3(7) + 1 = 22

4 0

3 years ago

Solve 4a = 20

olya-2409 [2.1K]

Here's the solutions :

1. solve for a :

$4a = 20$

$a = \dfrac{20}{4}$

$a = 5$

2. solve for y :

$3y + 9 = 24$

$3y = 24 - 9$

$3y = 15$

$y = \dfrac{15}{3}$

$y = 5$

3. solve for y :

$\dfrac{y}{3} - 5 = 4$

$\dfrac{y}{3} = 5 + 4$

$\dfrac{y}{3} = 9$

$y = 9 \times 3$

$y = 27$

4. solve for k :

$3 = 9 - 4k$

$3 - 9 = -4 k$

$- 6 = - 4 k$

$k = \dfrac{ - 6}{ - 4}$

$k = \dfrac{3}{2} \: \: \: or \: \: 1.5$

5. there's something wrong with this question.

6. solve for x :

$3x + 8 = 2$

$3x = 2 - 8$

$3x = - 6$

$x = \dfrac{ - 6}{3}$

$x = - 2$

i hope it helped...

6 0

3 years ago

Read 2 more answers

If the two adjacent angles are supplementary then their outer sides are???

Ainat [17]

Answer:

If the bisectors of two adjacent angles are perpendicular to each other, are the angles then supplementary angles?

Suppose two angles ABC and CBD are x and y.

x+y = 180 deg.

The bisector of angle ABC (BE) and the bisector of angle CBD (CF) will form angle EBF = (x/2)+(y/2) = 180/2 = 90 deg.

Conclusion: If the angle bisectors of two adjacent angles are perpendicular to eaxh other, the adjacent angles are supplementary angle

Adjacent angles are when the 2 angles have a common vertex and a common arm.

if the exterior sides of 2 adjacent angles are perpendicular, then the angles are complementary angles.

Then the sum of the 2 adjacent angles is a right angle - 90°.

When 2 angles add up to 90°, they are called a pair of complementary angles.

Step-by-step explanation:

6 0

3 years ago

The flight of a kicked football follows the quadratic function f(x)=−0.02x^2+2.2x+2, where f(x) is the vertical distance in feet

Sergio039 [100]

Answer:

110.9 feet

Step-by-step explanation:

The function that models the flight of the ball is

$f(x) = - 0.02 {x}^{2} + 2.2x + 2$ where f(x) is the vertical distance in feet and x is the horizontal distance the ball travels

If the ball hits the ground, then f(x)=0

$\implies - 0.02 {x}^{2} + 2.2x + 2 = 0$

The solution is given by the quadratic formula:

$x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a}$

We substitute a=-0.02, b=2.2, and c=2 to get:

$x = \frac{ - 2.2 \pm \sqrt{ {2.2}^{2} - 4 \times - 0.02 \times 2} }{2 \times - 0.02}$

This implies that:

$x = 110.90 \: or \: x = - 0.90$

Since we are dealing with time,

$x = 110.90$

To one decimal place, we have 110.9 feet

6 0

3 years ago