If the nominal rate of interest is 10% per annum and there is quarterly compounding, the effective rate of interest will be: a) 10% per annum b) 10.10 per annum c) 10.25%per annum d) 10.38% per annum​

Answer:

the number is 788......

y=x²-10x-7

a>0 so we will be looking for minimum

x=-b/2a=10/2=5

y=25-50-7=-32

Answer: (5;32)

y=-4x²-8x+1

а<0 so we will be looking for maximum

х=-b/2a=8/-8=-1

у=4+8+1=13

Maximum point (-1;13)

Answer:

cos C = 12/13

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

Cos theta = adj/ hyp

cos C = 36/39

Dividing the top and bottom by 3

cos C = 12/13

CosØ=Base/Hypotenuse

Answer:

Answer is D.

Step-by-step explanation:

Let the inverse be m:

[tex]{ \sf{m = \sqrt{x} - 8 }} \\ { \sf{m + 8 = \sqrt{x} }} \\ { \sf{x = {(m + 8)}^{2} }} \\ { \bf{f {}^{ - 1} (x) = {(x + 8)}^{2} }}[/tex]

Domain:

[tex]{ \sf{x \geqslant - 8}}[/tex]

First let's compute dx/dt

[tex]x = t - \frac{1}{t}\\\\x = t - t^{-1}\\\\\frac{dx}{dt} = \frac{d}{dt}\left(t - t^{-1}\right)\\\\\frac{dx}{dt} = 1-(-1)t^{-2}\\\\\frac{dx}{dt} = 1+\frac{1}{t^{2}}\\\\\frac{dx}{dt} = \frac{t^2}{t^{2}}+\frac{1}{t^{2}}\\\\\frac{dx}{dt} = \frac{t^2+1}{t^{2}}\\\\[/tex]

Now compute dy/dt

[tex]y = 2t + \frac{1}{t}\\\\y = 2t + t^{-1}\\\\\frac{dy}{dt} = \frac{d}{dt}\left(2t + t^{-1}\right)\\\\\frac{dy}{dt} = 2 - t^{-2}\\\\\frac{dy}{dt} = 2 - \frac{1}{t^2}\\\\\frac{dy}{dt} = \frac{2t^2}{t^2}-\frac{1}{t^2}\\\\\frac{dy}{dt} = \frac{2t^2-1}{t^2}\\\\[/tex]

From here, apply the chain rule to say

[tex]\frac{dy}{dx} = \frac{dy*dt}{dx*dt}\\\\\frac{dy}{dx} = \frac{dy}{dt} \times \frac{dt}{dx}\\\\\frac{dy}{dx} = \frac{dy}{dt} \div \frac{dx}{dt}\\\\\frac{dy}{dx} = \frac{2t^2-1}{t^2} \div \frac{t^2+1}{t^{2}}\\\\\frac{dy}{dx} = \frac{2t^2-1}{t^2} \times \frac{t^{2}}{t^2+1}\\\\\frac{dy}{dx} = \frac{2t^2-1}{t^2+1}\\\\[/tex]

We could use polynomial long division, or we could add 2 and subtract 2 from the numerator and do a bit of algebra like so

[tex]\frac{dy}{dx} = \frac{2t^2-1}{t^2+1}\\\\\frac{dy}{dx} = \frac{2t^2-1+2-2}{t^2+1}\\\\\frac{dy}{dx} = \frac{(2t^2+2)-1-2}{t^2+1}\\\\\frac{dy}{dx} = \frac{2(t^2+1)-3}{t^2+1}\\\\\frac{dy}{dx} = \frac{2(t^2+1)}{t^2+1}-\frac{3}{t^2+1}\\\\\frac{dy}{dx} = 2-\frac{3}{t^2+1}\\\\[/tex]

This concludes the first part of 4b

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

Now onto the second part.

Since t is nonzero, this means either t > 0 or t < 0.

If t > 0, then,

[tex]t > 0\\\\t^2 > 0\\\\t^2+1 > 1\\\\\frac{1}{t^2+1} < 1 \ \text{ ... inequality sign flip}\\\\\frac{3}{t^2+1} < 3\\\\-\frac{3}{t^2+1} > -3 \ \text{ ... inequality sign flip}\\\\-\frac{3}{t^2+1}+2 > -3 + 2\\\\2-\frac{3}{t^2+1} > -1\\\\-1 < 2-\frac{3}{t^2+1}\\\\-1 < \frac{dy}{dx}\\\\[/tex]

note the inequality signs flipping when we apply the reciprocal to both sides, and when we multiply both sides by a negative value.

You should find that the same conclusion happens when we consider t < 0. Why? Because t < 0 becomes t^2 > 0 after we square both sides. The steps are the same as shown above.

So both t > 0 and t < 0 lead to [tex]-1 < \frac{dy}{dx}[/tex]

We can say that -1 is the lower bound of dy/dx. It never reaches -1 itself because t = 0 is not allowed.

We could say that

[tex]\displaystyle \lim_{t\to0}\left(2-\frac{3}{t^2+1}\right)=-1\\\\[/tex]

---------------------------------------

To establish the upper bound, we consider what happens when t approaches either infinity.

If t approaches positive infinity, then,

[tex]\displaystyle L = \lim_{t\to\infty}\left(2-\frac{3}{t^2+1}\right)\\\\\\\displaystyle L = \lim_{t\to\infty}\left(\frac{2t^2-1}{t^2+1}\right)\\\\\\\displaystyle L = \lim_{t\to\infty}\left(\frac{2-\frac{1}{t^2}}{1+\frac{1}{t^2}}\right)\\\\\\\displaystyle L = \frac{2-0}{1+0}\\\\\\\displaystyle L = 2\\\\[/tex]

As t approaches infinity, the dy/dx value approaches L = 2 from below.

The same applies when t approaches negative infinity.

So we see that [tex]\frac{dy}{dx} < 2[/tex]

---------------------------------------

Since [tex]-1 < \frac{dy}{dx} \text{ and } \frac{dy}{dx} < 2[/tex], those two inequalities combine into the compound inequality [tex]-1 < \frac{dy}{dx} < 2[/tex]

So dy/dx is bounded between -1 and 2, exclusive of either endpoint.

Answer:

y = 9√3

x = 18

Step-by-step explanation:

taking 30 as reference angle

b = y

p = 9

h = x

so

tan30 = p/b

1/√3 = 9/b

or, b = 9√3

so

[tex]h^2 = p^2 + b^2\\x^2 = 9^2 + y^2\\or, x^2 = 81 + (9\sqrt{3} )^2\\or, x^2 = 81 + 243\\or, x ^2 = 324\\or, x =\sqrt{324} \\\\so x = 18[/tex]

9514 1404 393

Answer:

  (c)  f(x) is an even degree polynomial with a positive leading coefficient.

Step-by-step explanation:

The leading terms of the two functions are ...

  f(x): x² (even degree, positive coefficient: 1)

  g(x): x³ (odd degree, positive coefficient: 1)

Then it is true that ...

  f(x) is an even degree polynomial with a positive leading coefficient

Answer: 9 miles I think but I dont know where her house is exactly.

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Learn more : https://brainly.com/question/17143411

Answer:

1a 300

b 180

c 330

d 1470

e 180

f 7344

Step-by-step explanation:

Step-by-step explanation:

if that is truly the full problem description, then we have

10x - x + 5 = 41

=>

9x = 36

our simply

x = 4

so, I am not sure, what your teacher wants to see as result.

there is an infinite number of equations I could find, all with the solution x = 4.

Answer:

undefined, invalid

and for a limit expression like a/x, x->0 we also say this is infinite.

Answer:

12x - 28° = 116°

7x + 32° = 116°

Step-by-step explanation:

12x - 28° and 7x + 32° are vertical angles. Vertical angles are congruent.

Therefore, to find the measure of each angle, we have to set each equation equal to each other as follows:

12x - 28° = 7x + 32°

Collect like terms

12x - 7x = 28 + 32

5x = 60

Divide both sides by 5

5x/5 = 60/5

x = 12

✔️12x - 28°

Plug in the value of x

12(12) - 28

= 144 - 28

= 116°

✔️7x + 32°

7(12) + 32

= 84 + 32

= 116°

Answer:

84.7

Step-by-step explanation:

of is another way to say multiply so what your doing is muliplying all the numbers

Answer:

84.7

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

Step-by-step explanation:

we don't see the parallelogram nor any description of it.

so, it is impossible to tell you the right answer.

as I only answer questions by don't ask any, I don't know how you can add a picture.

Step-by-step explanation:

the guys is wrong i checked

Answer:

Could you add a picture or answer choices so we know what to choose from?

Answer:

3

Step-by-step explanation:

[tex] \frac{3x - 3}{x} \div \frac{x - 1}{x} [/tex]

[tex] \frac{3(x - 1)}{x} \times \frac{x}{x - 1} = 3[/tex]

Answer:

C

Step-by-step explanation:

Since the triangles are similar, the scale factor is 100/5=20. So L/15=20, L=300

Answer:

The average speed of the 747 was of 600 miles per hour.

Step-by-step explanation:

A small airplane flies 750 miles with an average speed of 250 miles per hour.

Velocity is distance divided by time, and here, we find the time of the small airplane. So

[tex]v = \frac{d}{t}[/tex]

[tex]250 = \frac{750}{t}[/tex]

[tex]250t = 750[/tex]

[tex]t = \frac{750}{250}[/tex]

[tex]t = 3[/tex]

1.75 hours after the plane leaves, a Boeing 747 leaves from the same point. Both planes arrive at the same time;

This means that it traveled 750 miles in 3 - 1.75 = 1.25 hours.

What was the average speed of the 747?

[tex]v = \frac{d}{t} = \frac{750}{1.25} = 600[/tex]

The average speed of the 747 was of 600 miles per hour.

Answer:

Answer:

Step-by-step explanation:

The decay rate of strontium-90 is -.0244 as given.

For b., we have to use the formula to find out how much is left after 30 years. This will be important for part d.

[tex]A(t)=400e^{-.0244(30)}[/tex] which simplifies a bit to

A(t) = 400(.4809461353) so

A(t) = 192.4 g

For c., we have to find out how long it takes for the initial amount of 400 g to decay to 100:

[tex]100=400e^{-.0244t}[/tex]. Begin by dividing both sides by 400:

[tex].25=e^{-.0244t[/tex] and then take the natural log of both sides:

[tex]ln(.25)=lne^{-.0244t[/tex] . The natural log and the e cancel each other out since they are inverses of one another, leaving us with:

ln(.25) = -.0244t and divide by -.0244:

61.8 years = t

For d., we figured in b that after 30 years, 192.4 g of the element was left, so we can use that to solve for the half-life in a different formula:

[tex]A(t)=A_0(.5)^{\frac{t}{H}[/tex] and we are solving for H. Filling in:

[tex]192.4=400(.5)^{\frac{30}{H}[/tex] and begin by dividing both sides by 400:

[tex].481=(.5)^{\frac{30}{H}[/tex] and take the natural log of both sides, which allows us to pull the exponent out front. I'm going to include that step in with this one:

ln(.481) = [tex]\frac{30}{H}[/tex] ln(.5) and then divide both sides by ln(.5):

[tex]\frac{ln(.481)}{ln(.5)}=\frac{30}{H}[/tex] and cross multiply and isolate the H to get:

[tex]H=\frac{30ln(.5)}{ln(.481)}[/tex] and

H = 28.4 years

Answer:

y = -1/2x -7

Step-by-step explanation:

3x + 6y = -42

Slope intercept form is

y = mx+b where m is the slope and b is the y intercept

Subtract 3x from each side

3x-3x+6y = -3x-42

6y = -3x-42

Divide each side by 6

6y/6 = -3x/6 - 42/6

y = -1/2x -7

Answer:

A. 1 + 3x = -89

B. x = -30

Step-by-step explanation:

Let the unknown variable be x.

A. Translating the word problem into an algebraic expression, we have;

1 + 3x = -89

B. To solve for the unknown variable;

1 + 3x = -89

3x = -89 -1

3x = -90

x = -90/3

x = -30

Check:

1 + 3x = -89

Substituting the value of x;

1 + 3(-30) = -89

1 + (-90) = -89

1 - 90 = -89

-89 = -89

Answer:

‼️D) To the right‼️

Explanation

There is an easy way to tell whether the graph of a quadratic function opens upward or downward: if the leading coefficient is greater than zero, the parabola opens upward, and if the leading coefficient is less than zero, the parabola opens downward.

Answer:

Y =-4X +21

Step-by-step explanation:

x1 y1  x2 y2

4 5  3 9

(Y2-Y1) (9)-(5)=   4  ΔY 4

(X2-X1) (3)-(4)=    -1  ΔX -1

slope= -4          

B= 21          

Y =-4X +21    

Answer:

[tex](y - 0) = \frac{1}{3} (x - 0)[/tex]

[tex]y = \frac{1}{3} x[/tex]

Answer:

Ask in English then I can help u

first invert fraction of the slope from 4/1 to 1/4 and switch sign. then figure out the y-intercept

the algebraic approach would work like this:

-4x + 10 = 1/4x + b

plug in what you got, here: the intersection information

-4*(4) + 10 = 1/4*(4) + b

-16 + 10 = 1 + b

-6 = 1 + b

-7 = b

Step-by-step explanation:

here's the answer to your question