12
Use upper rectangles with areas equal to
Marks: 1
Area = f(x) · A3
to estimate the area under the curve of f(x) = x, on the interval from (1,3). Partition the interval into four subintervals. Hint:
Area = (F(1.5) + f(2) + f(2.5) + f(3))Ar = (1.53 +23 +2.53 +33)Az, where Ax =
Choose one answer.
ST
3-1
4
a. 35
b. 42
c. 27
d d. 19

Solution given:

Cos[tex]\theta_{1}=\frac{10}{17}[/tex]

[tex]\frac{adjacent}{hypotenuse}=\frac{10}{17}[/tex]

equating corresponding value

we get

adjacent=10

hypotenuse=17

perpendicular=x

now

by using Pythagoras law

Hypotenuse ²=perpendicular²+adjacent ²

substituting value

17²=x²+10²

17²-10²=x²

x²=17²-10²

x²=189

doing square root

[tex]\sqrt{x²}=\sqrt{189}[/tex]

x=[tex]3\sqrt{21}[/tex]

now

In I Quadrant sin angle is positive

Sin[tex]\theta_{1}=\frac{perpendicular}{hypotenuse}[/tex]

Answer:

sin theta = 3 sqrt(21)/17

Step-by-step explanation:

cos theta = adj / hyp

We can find the opp by using the Pythagorean theorem

adj^2 + opp ^2 = hyp^2

10^2 +opp^2 = 17^2

100 + opp^2 = 289

opp^2 = 289-100

opp^2 = 189

Taking the square root

opp = sqrt(189)

opp = 3 sqrt(21)

Since we are in the first quad, opp is positive

sin theta = opp /hyp

sin theta = 3 sqrt(21)/17

Answer:

4x² - 8x - 60

Step-by-step explanation:

Given :-

Simplify ,

Trinomial expression :-

The polynomial function [tex](2x-10)(2x+6)[/tex] expressed as a trinomial is [tex]4x^2 - 8x - 60[/tex].

Given data:

The polynomial function is represented as A.

Now, the value of [tex]A=(2x-10)(2x+6)[/tex].

On simplifying the equation:

From distributive property to multiply the terms:

[tex]A=2x * 2x + 2x * 6 - 10 * 2x - 10 * 6[/tex]

[tex]A=4x^2 + 12x - 20x - 60[/tex]

On simplifying the equation:

[tex]A=4x^2 - 8x - 60[/tex]

Hence, the trinomial is [tex]4x^2 - 8x - 60[/tex].

To learn more about polynomial equations, refer:

https://brainly.com/question/13199883

#SPJ6

Answer:

[tex]m\angle WVT=40^{\circ}[/tex]

Step-by-step explanation:

When two secants or a secant and a tangent of a circle intersect outside the circle, the measure of the acute angle formed is equal to half of the positive difference of smaller and larger arc formed.

Therefore, we have the equation:

[tex]m\angle WVT=\frac{1}{2}(\widehat{TW}-\widehat{UW}),\\3x+4=\frac{1}{2}(14x+7-(7x+11))[/tex]

Distribute:

[tex]3x+4=\frac{1}{2}(14x+7-7x-11),\\\\3x+4=\frac{1}{2}(7x-4),\\\\3x+4=3.5x-2[/tex]

Add 2 to both sides and subtract [tex]3x[/tex] from both sides:

[tex]6=0.5x[/tex]

Divide both sides by 1/2:

[tex]x=\frac{6}{\frac{1}{2}}=6\cdot 2=12[/tex]

Now substitute [tex]x=12[/tex] into [tex]3x+4[/tex]:

[tex]m\angle WVT=3(12)+4,\\m\angle WVT=36+4,\\m\angle WVT=\boxed{40^{\circ}}[/tex]

Answer:

Step-by-step explanation:

This is most easily solved with calculus, believe it or not. It is way more direct and to the point, with a whole lot less math!

The position function is given. The velocity function is the first derivative of the position, so if we find the velocity function and set it equal to 0, we can solve for the amount of time it takes for the rocket to reach its max height. Remember from physics that at the top of a parabolic path, the velocity is 0.

If:

[tex]s(t)=-16t^2+112t+360[/tex], then the velocity function, the first derivative is:

v(t) = -32t + 112 and solve for t:

-112 = -32t so

t = 3.5 seconds. Now we know how long it takes to get to the max height, we just need to find out what the max height is.

Go back to the position function and sub in 3.5 for t to tell us that position of the rocket at 3.5 seconds, which translates to the max height:

[tex]s(3.5)=-16(3.5)^2+112(3.5)+360[/tex] and

s(3.5) = 206 feet. I imagine that your answer, if you had to choose one from the list, would be 200 feet, rounded a lot.

Answer:

y=4

Step-by-step explanation:

you multiply through by 3y^2

3y^4 - 18y^2 =30y^2

Collect like terms

3y^4=48y^2

divide through by y^2

3y^2=48

divide through by 3

y^2=16

take the square root of both sides

y=4

Answer:

4.5, - 27, 162, - 972, 5832

Step-by-step explanation:

Using the recursive rule and a₁ = 4.5 , then

a₂ = - 6a₁ = - 6 × 4.5 = - 27

a₃ = - 6a₂ = - 6 × - 27 = 162

a₄ = - 6a₃ = - 6 × 162 = - 972

a₅ = - 6a₄ = - 6 × - 972 = 5832

The first 5 terms are 4.5, - 27, 162, - 972, 5832

Answer:

74 feet per second

Step-by-step explanation:

Divide 1,110 by 15 to get 74, which is how many feet the antelope ran per second in its short burst.

Hope this helps!

Answer:

We may log in directly in our scientific calculator the given value ln 7 and get an answer of 1.9459. On the other hand, we can rewrite the expression as,

                            log to the base e or 7 = x

which can be written as,

                              e^x = 7

The value of x from this is still equal to 1.9459.

Step-by-step explanation:

Hello!

-9y > 9 <=>

<=> -9y ÷ (-9) > 9 ÷ (-9) <=>

<=> y < -1 <=>

<=> y ∈ { -∞; -1 }

Good luck! :)

Answer:

Have you gotten the answer. if yes Hmu... Aihs I sit beside you

Step-by-step explanation:

Answer:

Corina can make 3 friendship bracelets.

Step-by-step explanation:

Solve for how much string is needed for one friendship bracelet:

4 pieces × 1 foot

4 feet

Convert feet into inches (1 foot = 12 inches):

4 feet × 12 inches

48 inches

Divide the total string by each bracelet's string:

144 inches ÷ 48 inches

3 friendship bracelets

Answer:лаксдкннйд

Step-by-step explanation:

Answer:

Benito llega en segundo lugar.

Eladio llega en sexto lugar

Hermes llega en noveno lugar.

Step-by-step explanation:

Tenemos 3 amigos:

Benito

Hermes

Eladio

Hay 3 posiciones:

segundo

sexto

noveno.

Sabemos que:

Benito llegó antes que Hermes.

Cuando Eladio estaba llegando a la meta, solo Benito estaba descansando.

Es decir, cuando Eladio llego a la meta, Hermes aún no había llegado.

Eladio llegó a la meta antes que Hermes, pero después que Benito.

Entonces el primero en llegar es Benito, el segundo es Eladio y el tercero será Hermes.

Con la data inicial podemos decir que:

Benito llega en segundo lugar.

Eladio llega en sexto lugar

Hermes llega en noveno lugar.

Answers:

======================================

Explanation:

In this context, a zero is another term for x intercept or root. This is where the graph either touches or crosses the x axis. This occurs in three locations: x = -3, x = 2, and x = 0. So those are the three roots. That makes the first three statements true, while the remaining two others are false.

Side note: x = 0 doesn't always have to be involved. Its quite possible to have x = 0 not be an x intercept. The term "zero" is a bit misleading in that regard. I prefer either "root" or "x intercept" instead.

Answer:

[tex]{ \tt{ \frac{dy}{dx} ( {x}^{2}) = \frac{dy}{dx} ( \frac{x + y}{x - y}) }} \\ { \tt{2x = \frac{(x - y) \frac{dy}{dx} + (x + y) \frac{dy}{dx} }{ {(x - y)}^{2} } }} \\ { \tt{ \frac{dy}{dx}(2x) = 2x {(x - y)}^{2} }} \\ { \tt{ \frac{dy}{dx} = {(x - y)}^{2} }}[/tex]

Answer:

The area of D is 36 times bigger than C

Step-by-step explanation:

The scale factor is 1:6

We know the ratio of the areas is the ratio of the scale factor squared

1^2 : 6^2

1:36

The area of D is 36 times bigger than C

Answer:

.63

Step-by-step explanation:

bc the first three numbers are less then 0 so add the three probabilities and boom magic.

Answer:

[tex]\angle 72=BC-86/2[/tex]

[tex]144+86=BC[/tex]

[tex]BC=230[/tex]

[tex]BC=230/2[/tex]

[tex]\angle BAC= 115[/tex]°

~OAmalOHopeO

Answer: 33 tulips bloomed / 66 tulips did not bloom

Step-by-step explanation:

Total number of tulips = 99

Total number of tulips bloomed = 3/9 of total

Step One: Find the number of tulips that bloomed

99 × (3/9) = 99 × (1/3) = 33 tulips

Step Two: Find the number of tulips that did not bloom

99 - 33 = 66 tulips

Hope this helps!! :)

Please let me know if you have any questions

Answer:

1st option

Step-by-step explanation:

let y = f(x) and rearrange making x the subject

y = 2x + 1 ( subtract 1 from both sides )

y - 1 = 2x ( divide both sides by 2 )

[tex]\frac{y-1}{2}[/tex] = x

Change y back into terms of x with x being the inverse h(x)

h(x) = [tex]\frac{x-1}{2}[/tex] = [tex]\frac{1}{2}[/tex] x - [tex]\frac{1}{2}[/tex]

Answer:

Smaller factor/larger figure = 3/6 = ½

Step-by-step explanation:

Scale factor of similar figures is usually the ratio of one to the other.

In the diagram given, the scale factor is the length of any side of the smaller figure divided by the length of the corresponding side length of the bigger figure.

Length of smaller figure = 3

Corresponding length of larger figure = 6

Scale factor = smaller figure/larger figure = 3/6

Simplify

Scale factor = ½

9514 1404 393

Answer:

  a) 30.7 million

  b) 1.5% per year

  c) 42.0 million

  d) 2017

Step-by-step explanation:

a) The initial population is P(0) = 30.7 (million). The exponential term is 1 when t=0, so this number is the multiplier of the exponential term.

__

b) The growth factor is the base of the exponential term: 1.015. The growth rate is the difference between this and 1: 1.015 -1 = 0.015 = 1.5%.

The population is growing by 1.5% per year.

__

c) Fill in the value and do the arithmetic. t=2021 -2000 = 21.

  P(21) = 30.7·1.015^21 ≈ 41.968 ≈ 42.0

The population in Canada in 2021 is predicted to be 42.0 million.

__

d) For this we need to solve for t when P(t) = 40.

  40 = 30.7·1.015^t

  40/30.7 = 1.015^t

Taking logarithms gives ...

  log(40/30.7) = t·log(1.015)

  t = log(40/30.7)/log(1.015) ≈ 17.773

In 2017, the population is predicted to be less than 40 million; in 2018, it is predicted to be more than 40 million. Canada should anticipate hitting 40 million people in 2017.

_____

Additional comment

The second attachment shows the prediction described here is a little high relative to the actuals in the last few years.

Answer: x= 2/5 or x= 3

how?

Step 1: Subtract 17x from both sides

5x² + 6 -17x = 0

*PUT THEM IN ORDER* --> 5x² -17x + 6= 0

Step 2: Factor left side of equation:

(5x-2) (x-3) = 0

Step 3: Set factors equal to 0.

5x−2=0 or x−3=0

which gives us an answer of x= 2/5 or x=3

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{5x^2 + 6 =17x}\\\\\large\textsf{SUBTRACT 17x to BOTH SIDES}\\\\\mathsf{5x^2 + 6 - 17x = 17x - 17x}\\\\\mathsf{5x^2 - 17x + 6 = 0}\\\\\large\textsf{SET the LEFT SIDE to equal 0}\\\\\mathsf{(5x -2)(x -3)=0}\\\\\large\textsf{SET the FACTORS to EQUAL to 0}\\\\\mathsf{5x - 2 = 0\ or\ x - 3 = 0}\\\\\large\textsf{SIMPLIFY ABOVE AND YOU HAVE YOUR RESULT}\\\\\boxed{\boxed{\large\textsf{Answer: }\mathsf{\bf x = \dfrac{2}{3}\ or\ x = 3}}}\huge\checkmark[/tex]

[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

cột số 2

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Using the identities

sec x = [tex]\frac{1}{cosx}[/tex] , csc x = [tex]\frac{1}{sinx}[/tex] , cot x = [tex]\frac{cosx}{sinx}[/tex] , then

sec²x cot²x

= [tex]\frac{1}{cos^2x}[/tex] × [tex]\frac{cos^2x}{sin^2x}[/tex] ( cancel out cos²x )

= [tex]\frac{1}{sin^2x}[/tex]

= csc²x → B

Answer:

Option c is correct

Step-by-step explanation:

From the screenshot I attached.

sinA/a=SinC/c

a/c=SinA/SinC

Thus a=cSinA/SinC

Answer:

∠4 = ∠8

Step-by-step explanation:

the lines are parallel if a pair of corresponding angles are congruent

Answer:

None.

Step-by-step explanation:

There is no expression for the square root of negative numbers. In other words it is undefined.

Answer:

4√5

Step-by-step explanation:

Let x be the first term in the geometric sequence. Then the next two terms in the sequence are xr and xr ², where r is some constant. (This is the defining characteristic of geometric sequences.)

The sum of the first three terms is 42, so

x + xr + xr ² = 42

x (1 + r + r ²) = 42

The third term is 3.2 times the sum of the other two, so that

xr ² = 3.2 (x + xr )

Solve the second equation for r :

xr ² = 3.2 x (1 + r )

We can divide both sides by x since x ≠ 0. (This is obvious, since if x was zero, then all three terms in the sequence would be 0.)

r ² = 3.2 (1 + r )

r ² = 3.2 + 3.2r

r ² - 3.2r - 3.2 = 0

r ² - 16/5 r - 16/5 = 0

5r ² - 16r - 16 = 0

(5r + 4) (r - 4) = 0

==>   r = -4/5 or r = 4

Since there are two possible values of r that might work, there are two possible sequences that meet the criteria.

Plug either of these solutions into the first equation:

r = -4/5   ==>   x (1 + (-4/5) + (-4/5)²) = 42

… … … … … …   21/25 x = 42

… … … … … …   x = 50

r = 4   ==>   x (1 + 4 + 4²) = 42

… … … … …  21x = 42

… … … … …  x = 2

Then the two possible answers would be

• if r = -4/5, then the three terms are {50, -40, 32}

• if r = 4, then they are {2, 8, 32}

Answer:

Step-by-step explanation:

A geometric series means that we multiply one number by a common ratio to get the second number. Let's say our first number is x, and our common ratio is y. We can write the first term is x, and to get the second number, we multiply x by our common ratio, y. For example, if 5 was the first number and 2 was the common ratio, the second number would be 5*2 = 10, and the third would be 10 * 2 = 20.

For our question, the first number is x, the second is x*y, and the third is x*y*y = x*y²

The sum of these three terms is 42, so we can say

x + x*y + x*y² = 42

Next, the third term is equal to 3.2 times the sum of the other two. First, we have 3.2 times something. That something is the sum of the other two, so we must prioritize calculating the sum of the first two numbers, and then multiply that by 3.2 to get the third. We can write this as

(x + x*y) * 3.2 = x*y²

factor out x

x * 3.2(1 +y) = x*y²

divide both sides by x

3.2(1+y) = y²

expand

3.2 + 3.2y = y²

subtract (3.2 + 3.2y) from both sides to make this a quadratic equation

y²-3.2y-3.2 = 0

use the quadratic formula to solve for y  (note that +- here stands for "plus or minus")

[tex]y = \frac{-(-3.2) +- \sqrt{3.2^{2}-4(-3.2)(1)} }{2} \\= \frac{3.2+-\sqrt{10.24+12.8} }{2} \\= \frac{3.2+- 4.8}{2}[/tex]

=  -0.8 or 4

With these two possibilities, we can try each in our other equation to see what works.

x + x*y + x*y² = 42

for y = -0.8

x + -0.8x + 0.64x = 42

x - 0.16x = 42

0.84x = 42

multiply both sides by 1/0.84 to isolate the x

x=50

This works, with x (the first number) =50, the second number being 50 * -0.8 = -40, and the third being -40 * -0.8 = 32. 50+(-40) = 10, 10*3.2=32, and 50-40+32 = 42

Next, for y=4, we have

x+4x + 16x= 42

21x = 42

divide both sides by 21 to isolate the x

This works as well, with x=2, the second value being 2*4 = 8, and the third value being 8*4 =32. 2+8=10, 10*3.2 = 32, and 2+8+32 = 42