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3 years ago

Which option shows cos Ø?

Mathematics

1 answer:

MrMuchimi3 years ago

7 0

B
sohcahtoa

cah
adjacent over hypotenuse
5/29

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find three consecutive even integers so that the twice the sum of the second and third is twelve less than six times the first

zysi [14]

n, n + 2, n + 4 - three consecutive even integers

the twice the sum of the second and third: 2[(n + 2) + (n + 4)]

twelve less than six times the first: 6n - 12

The equation:

2[(n + 2) + (n + 4)] = 6n - 12

2(n + 2 + n + 4) = 6n - 12

2(2n + 6) = 6n - 12 use distributive property

(2)(2n) + (2)(6) = 6n - 12

4n + 12 = 6n - 12 subtract 12 from both sides

4n = 6n - 24 subtract 6n from both sides

-2n = -24 divide both sides by (-2)

n = 12

n + 2 = 12 + 2 = 14

n + 4 = 12 + 4 = 16

<h3>Answer: 12, 14, 16</h3>

4 0

3 years ago

A 65-story office tower has a height of 910 feet. Write an expression to find the height of each story. Then, use the expression

gizmo_the_mogwai [7]

Assuming each story is the same height
910=65 stories put together
910=65 times (height of each story)
910=65h
divide both sides by 65
14=h
each story is 14 feet

the equation is 910=65h

4 0

4 years ago

Read 2 more answers

What is the function doing in the interval -3 7 poin Decreasing Increasing

disa [49]

Answer:

increasing

Step-by-step explanation:

6 0

3 years ago

Which equation is equivalent

yawa3891 [41]

The equation that is equivalent is -2+(-7).

7 0

3 years ago

EXPLAIN why we placed the value of x= 4/3( the minimum value) into the equ of gradient(dy/dx) [in the answer, marking scheme att

aliina [53]

$y=x(x-2)^2$
$\implies y'=(x-2)^2+2x(x-2)=3x^2-8x+4=(3x-2)(x-2)=0$
$\implies x=\dfrac23,x=2$

are the critical points, and judging by the picture alone, you must have $b=\dfrac23$ and $a=2$ . (You might want to verify with the derivative test in case that's expected.)

Then the shaded region has area

$\displaystyle\int_0^2x(x-2)^2\,\mathrm dx=\dfrac43$

I'll leave the details to you.

Now, for part (iv), you're asked to find the minimum of $\dfrac{\mathrm dy}{\mathrm dx}=y'$ , which entails first finding the second derivative:

$y'=3x^2-8x+4$
$\implies y''=6x-8$

setting equal to 0 and finding the critical point:

$6x-8=0\implies x=\dfrac86=\dfrac43$

This is to say the minimum value of $\dfrac{\mathrm dy}{\mathrm dx}$ *occurs when $x=\dfrac43$ *, but this is not necessarily the same as saying that $\dfrac43$ is the actual minimum value.

The minimum value of $\dfrac{\mathrm dy}{\mathrm dx}$ is obtained by evaluating the derivative at this critical point:

$m=\dfrac{\mathrm dy}{\mathrm dx}\bigg|_{x=4/3}=3\left(\dfrac43\right)^2-8\left(\dfrac43\right)+4=-\dfrac43$

4 0

4 years ago