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2 years ago

What constant term should be added to both sides to complete the square on the left side?

Mathematics

1 answer:

grandymaker [24]2 years ago

6 0

Answer:

9/64

Step-by-step explanation:

Given

x² - 3/4x + _____ = 10

Need to complete square on the left side of equation

The square should be in the form of:

(a + b)² = a² + 2ab + b²

We see a = x therefore

2b = -3/4, so
b = -3/8 and
b² = (-3/8)² = 9/64

So the missing constant term is 9/64

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15. The height and yolume of a cylinder are 4cm and 616cm respectively. Calculate the diameter of the base. (take t = 27 쪽 A. 7c

irakobra [83]

Step-by-step explanation:

Given that,

Height of cylinder = 4 cm
Volume of cylinder = 616 cm³

To find,

Diameter of the base = ?

Firstly we'll find the base radius of the cylinder.

$\longmapsto\rm{V_{(Cylinder)} = \pi r^2h}\\$

According to the question,

$\longmapsto\rm{616= \dfrac{22}{7} \times r^2 \times 4}\\$

$\longmapsto\rm{616 \times 7 = 22 \times r^2 \times 4}\\$

$\longmapsto\rm{4312 = 88 \times r^2 }\\$

$\longmapsto\rm{\cancel{\dfrac{4312}{88}} = r^2 }\\$

$\longmapsto\rm{49 = r^2 }\\$

$\longmapsto\rm{\sqrt{49} = r }\\$

$\longmapsto\rm{7 \; cm = r }\\$

Now,

$\longmapsto\rm{Diameter = 2r }\\$

$\longmapsto\rm{Diameter = 2(7 \; cm) }\\$

$\longmapsto\bf{Diameter = 14 \; cm}\\$

The required answer is 14 cm.

4 0

2 years ago

Plz help, I don't need the show all work.

topjm [15]

Answer:

The answer is 108 cm²

Step-by-step explanation:

First, you have to find the height of the parallrelogram using trogonometric formula, sinθ = oppo./hypo. :

oppo. = height

hypo. = 9 cm

θ = 59°

sin 59° = height/9

height = 9 sin 59°

= 7.715 cm (4s.f)

Given that the formula of area of parallelogram is, A = base×height. Then, you can substitute the value into the formula :

base = 14 cm

height = 7.715 cm

A = 14 × 7.715

= 108 cm² (3s.f)

8 0

3 years ago

Read 2 more answers

1 and 2 are vertical angles. If the measure of 22 is 105°, find the measure of

sergey [27]

If i am not wrong the question of this woyld be the measure of 1 right . Because both of these are vertical angle so they are equal to each other “><“ like that so measure of 1 is 105 tô

6 0

2 years ago

If the mean proportional between x and 2 is 4, find x

Anastasy [175]

Answer:

explanation

b2=ac

16=2x

x=8

5 0

2 years ago

Read 2 more answers

Consider w=sqrrt2/2(cos(225°) + isin(225°)) and z = 1(cos(60°) + isin(60°)). What is w+ z expressed in rectangular form?

SVETLANKA909090 [29]

Answer:

Option (3)

Step-by-step explanation:

w = $\frac{\sqrt{2}}{2}[\text{cos}(225) + i\text{sin}(225)]$

Since, cos(225) = cos(180 + 45)

= -cos(45) [Since, cos(180 + θ) = -cosθ]

= - $\frac{\sqrt{2}}{2}$

sin(225) = sin(180 + 45)

= -sin(45)

= - $\frac{\sqrt{2}}{2}$

Therefore, w = $\frac{\sqrt{2}}{2}[-\frac{\sqrt{2}}{2}+i(-\frac{\sqrt{2}}{2})]$

= $-\frac{2}{4}(1+i)$

= $-\frac{1}{2}(1+i)$

z = 1[cos(60) + i(sin(60)]

= $[\frac{1}{2}+i(\frac{\sqrt{3}}{2})$

= $\frac{1}{2}(1+i\sqrt{3})$

Now (w + z) = $-\frac{1}{2}(1+i)+\frac{1}{2}(1+i\sqrt{3})$

= $-\frac{1}{2}-\frac{i}{2}+\frac{1}{2}+i\frac{\sqrt{3}}{2}$

= $\frac{(i\sqrt{3}-i)}{2}$

= $\frac{(\sqrt{3}-1)i}{2}$

Therefore, Option (3) will be the correct option.

3 0

2 years ago

Read 2 more answers