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2 years ago

Ara has a cube with side lengths of 4.2 cm. Which is the best estimate of the volume of the cube?

1 answer:

6 0

4.2³ = 74.088. If the 4.2 is accurate, this is actually not an estimate but an exact answer. You can of course round it to 74, then it becomes an estimate.

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Find all the missing elements. NEED HELP PLZZZZ

IgorC [24]

Answer:

B=42°

C=98°

c=10.7 units

Step-by-step explanation:

Given

Angle A = Ф = 40°
a=8
b=7

We know that trigonometric ratio as

sin Ф = opposite/hypotenuse

cos Ф = adjacent/hypotenuse

tan Ф = opposite/adjacent

sin A = sin 40 = opposite/hypotenuse

From the diagram, it is clear that the opposite of angle A is a=8 and the hypotenuse is 'c'.

also the angle

sin A = sin 40 = opposite/hypotenuse = a/c = 8/c

sin 40 = 8/c

c = 8/sin 40

c = 8/0.745

c = 10.7

so the value of c will be: 10.7 units

tan B = opposite/adjacent

= b/a

= 0.9

$B=\tan ^{-1}\left(0.9\right)$

$=42^{\circ \:}$

Therefore, the value of B = $42^{\circ \:}$

As the sum of the angles of triangle ABC is 180.

i.e.

A+B+C = 180

(40)° + (42)° + C = 180°

C = 180° - 40° - 42°

= 98°

Therefore, the value of C = 98°

Hence,

B=42°

C=98°

c=10.7 units

7 0

3 years ago

A train travels at a constant speed of 24

Masja [62]

Answer:

Step-by-step explanation:

d = 24 x h

since d is the distance in order to get that we need to multiply the speed times time and get the answer

3 0

2 years ago

Read 2 more answers

Which is a better deal: a 12-ounce soft drink for $1.59 or a 16-ounce soft drink for a 1.99

REY [17]

The 16-ounce soft drink for $1.99 is better because it may be 40 cents more but it's also bigger :)

7 0

2 years ago

Read 2 more answers

Evaluate S5 for 300 + 150 + 75 + … and select the correct answer below. 18.75 93.75 581.25 145.3125

Savatey [412]

we have that

$300 + 150 + 75 +...$

Let

$a1=300\\ a2=150\\ a3=75$

we know that

$\frac{a2}{a1} =\frac{150}{300} \\\\ \frac{a2}{a1}=0.5 \\ \\ a2=a1*0.50$

$\frac{a3}{a2} =\frac{75}{150} \\\\ \frac{a3}{a2}=0.5 \\ \\ a3=a2*0.50$

$a(n+1)=an*0.50$

Is a geometric sequence

Find the value of $a4$

$a(4)=a3*0.50$

$a(4)=75*0.50$

$a(4)=37.5$

Find the value of $a5$

$a(5)=a4*0.50$

$a(5)=37.5*0.50$

$a(5)=18.75$

Find $S5$

$S5=a1+a2+a3+a4+a5\\ S5=300+150+75+37.5+18.75\\ S5=581.25$

therefore

the answer is

$581.25$

Alternative Method

Applying the formula

$S_n=\frac{a_1 (1-r^n)}{1-r} \\\\a_1=300 \\ r=\frac{1}{2}\\\\ S_5=\frac{300(1-(\frac{1}{2})^5)}{1-\frac{1}{2}}\\\\=\frac{300(1-\frac{1}{32})}{\frac{1}{2}}\\\\=\frac{300 \times \frac{31}{32}}{\frac{1}{2}}\\\\=\frac{75 \times \frac{31}{8}}{\frac{1}{2}}\\\\=\frac{\frac{2325}{8}}{\frac{1}{2}}\\\\=\frac{2325}{8} \times 2\\\\=\frac{2325}{4}\\\\=581 \frac{1}{4}\\\\=581.25$