MATHEMATICS HIGH SCHOOL

The decimal d is formed by writing in succession all the positive integers in increasing order after the decimal point; that is, d = 0.123456789101112 . . . . What is the 100th digit of d to the right of the decimal point?

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

We are given that a decimal number d

d=0.12345678...

Where d is formed by writing in succession all the positive integers in increasing order after decimal point.

We have to find the 100th digit of d to the right of the decimal point.

Place of first digit 1 after decimal=Tenth

Place of second digit 2 after decimal=Hundredth

Place of third digit 3 after decimal=Thousandth

Therefore, 100th digit of d to the right of the decimal point=2

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This figure shows the nose cone of a rocket used for launching satellites. The nose cone houses the satellite until the satellite is placed in orbit. What is the volume of the nose cone?45 cubic feet
60 cubic feet
90 cubic feet
180 cubic feet

Answers

see the attached figure to better understand the problem

we know that

The volume of the cone is equal to

$V=(1)/(3) \pi r^(2) h$

in this problem

$r=(6)/(2) =3\ ft\n \n h=15\ ft$

Substitute the values in the formula above

$V=(1)/(3)* \pi* 3^(2)* 15\n \n V=45\pi \ ft^(3)$

therefore

the answer is

The volume of the nose cone is $45\pi \ ft^(3)$

The formula to get the volume of a cone is
V = (1/3)πr²h
where V is the volume
r is the radius at the base
h is the height

No values are given but simple substitution should give the correct answer.

Find solution to logarithm.

Answers

$\log5x+\log(x-1)=2\n D:5x>0 \wedge x-1>0\n D:x>0 \wedge x>1\n D:x>1\n \log5x(x-1)=2\n 10^2=5x^2-5x\n 5x^2-5x-100=0\n x^2-x-20=0\n x^2-5x+4x-20=0\n x(x-5)+4(x-5)=0\n (x+4)(x-5)=0\n x=-4 \vee x=5\n -4\not \in D\Rightarrow x=5$

$log_pa=b\ \ \ \Leftrightarrow\ \ \ p^b=a\n\nloga+logb=log(a\cdot b)\ \ \ \Rightarrow\ \ \ D:\ a>0\ \ \ and\ \ \ b>0\n ----------------------------- \nlog(5x)+log(x-1)=2\ \ \ \Rightarrow\ \ \ D:\ 5x>0\ \ \ and\ \ \ x-1>0\n.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x>0\ \ \ and\ \ \ \ \ \ \ \ x>1\n.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ D=(1;+\infty)\n\nlog[5x\cdot(x-1)]=2\ \ \ \Leftrightarrow\ \ \ 5x(x-1)=10^2$

$5x^2-5x=100\ /:5\n\nx^2-x-20=0\n\nx^2-5x+4x-20=0\n\nx(x-5)+4(x-5)=0\n\n(x-5)(x+4)=0\ \ \ \Leftrightarrow\ \ \ x-5=0\ \ \ or\ \ \ x+4=0\n.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=5\ \ \ or\ \ \ \ \ \ \ \ x=-4\n\n5\in D;\ \ \ -4\notin D\n\nAns.\ x=5$

How many triangles exist with the given angle measures 55,45,90 degrees A.Exactly one unique triangle exists with the given angle measures.

B .No triangle exists with the given angle measures.

C. More than one unique triangle exists with the given angle measures.

Answers

No triangle exists with the given angle measures ( 55° , 45° and 90° )

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

And , the measure of ∠ABC = 90°

Now , the measure of ∠BAC = 55°

And , the measure of ∠ACB = 45°

For the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

And , 90° + 55° + 45° = 190°

Therefore , the triangle is not possible

Hence , there is no triangle with measures ( 55° , 45° and 90° )

To learn more about triangles click :

brainly.com/question/16739377

#SPJ2

Answer: The correct answer is B.

The first thing to check is the sum of the angles. 32 + 51 + 97 = 180. Therefore, the sides equal 180 and we can have a triangle because all triangles have exactly 180 degrees.

Second, the number of triangles with these measures is endless. Imagine taking the initial triangle and doubling the size. The angles don't change but the triangle does. We could keep doubling the size forever.

Add. -26.41 53.74
a. 80.15
b. 27.33
c. 27.33
d. 80.15

Answers

Hello,

High school ??? (must i do it by integral calculus? )

..... 53.74
-....26.41
________
.....27.33
Answer C

HELP ASAP!!! PLEASE IT'S DUE AT 4:00PM TODAY PLEASE!Describe the difference between a Non-Linear Form and a Neither Linear, Nor Non-Linear Form.

Answers

Answer:

Linear means something related to a line. All the linear equations are used to construct a line. A non-linear equation is such which does not form a straight line. It looks like a curve in a graph and has a variable slope value.

Step-by-step explanation:

Which linear inequality is represented by the graph?