solve cos(2x)=1-sin(x)

Answer:

The volume of the rectangular prism is 352 ft. The total surface area is 328 ft.

Step-by-step explanation:

Volume:

V = whl

V = 8 x 4 x 11

V = 352 ft

For finding surface area you have to find the lateral surface area: 152 ft, top surface area: 88 ft, and the bottom surface area: 88 ft. Add all that up and you get 328 ft.

Answer:

The Area of the shaded region would be 100 in^2 .

Step-by-step explanation:

Given:

Check the Attachment.

To Find:

The Area of Shaded Region

Solution:

The Triangle and the Rectangle have the same base(b) that is equal to the length(l) of the rectangle.

Note that Height of the triangle is same as breadth of the rectangle.

Now Let's come in the main solving part :-

We know that the formula of Area of the Triangle is ;

[tex]\boxed{ \rm \: Area \: of \: Triangle= \tt \: 1/2× \rm \: base×height , i.e. \: \tt \: 1/2× \rm\: b×h}[/tex]

Substitute the values where Base= 20 in and Length = 10 in:

[tex] \tt \: Area \: of \: Triangle=1/2×20 \: \times 10[/tex]

Now Solve it.

[tex] \tt \: Area \: of \: Triangle= \cfrac{1}{ \cancel2 {}^{1} } \times \cancel{20} {}^{10} \times 10[/tex]

[tex] \tt \: Area \: of \: T riangle = 10 \times 10[/tex]

[tex] \tt \: Area \: of \: Triangle=\boxed{\tt 100 \: in {}^{2}} [/tex]

Hence, the area of the shaded region is 100 sq.in or 100 in^2 .

[tex] \rule{225pt}{2pt}[/tex]

I hope this helps!

Let me know if you have any questions. :)

Answer:

20

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

First, we need to remember to use the order of operations:

Parentheses

Exponents

Multiplication/Division (whichever comes first)

Addition/Subtraction (whichever comes first)

Start by evaluating 2⁴ since exponents come first...

80/16*4

Now do the division first since it comes first in the equation...

5*4

Lastly do the multiplication...

20

1. Observe question

2. Employ Point-Slope formula

(y2 - y1)/(x2 - x1 )=

(-10-9)/(-6-9) =

-19/-15=

19/15

Slope: 19/15

Answer:[tex]\frac{19}{15}[/tex] or 1.26667

Step-by-step explanation:

m=rise over run=Δy over Δx

m=y2−y1x2−x1

m=−10−9−6−9

m=−19−15

m=19/15

Answer:

2.5

Step-by-step explanation:

y=ax+b

9= -2a+b <=> b= 9+2a

34=8a+b = 8a+9+2a = 10a + 9

a = (34-9)/10 = 2.5

Answer:

Step-by-step explanation:

Use the slope formula:

Answer:

12 years old

Step-by-step explanation:

let h = helmi's age and let s = son's age (right now)

10s = 3h

h + 5 + s + 5 = 62

h + s + 10 = 62

h + s = 52

3h + 3s = 156

10s + 3s = 156 (substitution)

13s = 156

s = 12

Answer:

Lynn's gross pay for the week is $29.12

Step-by-step explanation:

Lynn gets paid $2.08 for each usable machine part she makes. Out of the 440 parts she made this week, only 14 parts were usable.

Therefore, use the equation:

$2.08 x 14 = $29.12

Answer:

[tex]\red{ \boxed{ X= \frac{b - ac}{c - 1} }}[/tex]

Step-by-step explanation:

[tex]X+a = \frac{X+b}{c} \\ \\ \implies \: c(X+a) = X+b\\ \\ \implies \: cX+ac= X+b \\ \\ \implies \: cX - X = b - ac \\ \\ \implies \: X(c - 1) = b - ac \\ \\ \implies \: \huge \purple{ \boxed{ X= \frac{b - ac}{c - 1} }}[/tex]

Answer:

We want to use time so we will say

The time it takes to finish a jog, t, at the speed of s.

Step-by-step explanation:

The dependent variable we know depends on the independent variable.

Our independent variable is speed because it represents itself where time depends on speed. The reason it depends on speed is that the time to finish a jog depends on your speed.

Answer:

A:61°

B:72°

C:47°

Explanation:

I took the test and it was correct

Let's proof

PQ is the perpendicular bisector Hence

Now apply Pythagorean theorem

[tex]\\ \tt\hookrightarrow PQ^2+QD^2=PD^2[/tex]--(1)

[tex]\\ \tt\hookrightarrow PQ^2+CQ^2=PC^2[/tex]

As QD=CD

[tex]\\ \tt\hookrightarrow PQ^2+QD^2=PC^2[/tex]--(2)

From (1) and (2)

[tex]\\ \tt\hookrightarrow PC^2=PD^2[/tex]

[tex]\\ \tt\hookrightarrow PC=PD[/tex]

Answer:

Given [tex]\overline{\rm PQ}[/tex] is the [tex]\perp[/tex] bisector of [tex]\overline{\rm CD}[/tex]

⇒  [tex]\overline{\rm CQ}=\overline{\rm CD}[/tex]

⇒ ΔPQD ≅ ΔPQC

⇒ CP = PD

Step-by-step explanation:

Given [tex]\overline{\rm PQ}[/tex] is the [tex]\perp[/tex] bisector of [tex]\overline{\rm CD}[/tex]

⇒  [tex]\overline{\rm CQ}=\overline{\rm CD}[/tex]

⇒ ΔPQD ≅ ΔPQC

⇒ CP = PD

Answer:

3 days

Step-by-step explanation:

because a works twice as fast meaning they can do there work 3 times as fast

Answer:

63x + 18

Step-by-step explanation:

9 multiply 7x to give 63x

and 9 multiplies 2 to give 18

Answer:

Option C. 63x +18 is correct.

Step-by-step explanation:

7x ×9= 63x

2×9=18

=63x + 18

Hope it helps.......

Answer:

In its Plessy v. Ferguson decision (1896), the U.S. Supreme Court ruled that “separate but equal” facilities for African Americans did not violate the Fourteenth Amendment, ignoring evidence that the facilities for Black people were inferior to those intended for whites.

Step-by-step explanation:

hope that helps love

Answer:

15 cm

Step-by-step explanation:

540cm squared= 36 · b

540 ÷36= b

b= 15 cm

The average value of f(x) over [2, 6] is given by the definite integral,

[tex]\displaystyle f_{\rm ave[2,6]} = \frac1{6-2} \int_2^6 3\ln(2+x^3)\cos(x) \, dx[/tex]

and is approximately -1.67284.

The approximate average value of the function in the closed interval [2,6] is -1.628.

It is given that the f is the function given by:  [tex]\rm f(x) = 3ln(2+x^2)cosx[/tex]

It is required to find the average value of f in the closed interval [2,6]

It is defined as the mathematical approach to calculating the smaller parts or components.

We have function f:

[tex]\rm f(x) = 3ln(2+x^2)cosx[/tex]

For the average value in [2,6]

We integrate the function with lower limit 2 and higher limit 6.

[tex]\rm \int_{2}^{6}f(x) =\int_{2}^{6}( 3ln(2+x^2)cosx)\\[/tex]

The average value of the above function:

[tex]\rm =\frac{1}{6-2} \int_{2}^{6}( 3ln(2+x^2)cosx)\\[/tex]

Further solving:

[tex]\rm =\frac{3}{4} \int_{2}^{6}( ln(2+x^2)cosx)\\[/tex]

Further solving and applying limits we get:

[tex]=\frac{3}{4}\times-2.2304[/tex]

= -1.628

Thus, the approximate value of the function in the closed interval [2,6]

is -1.628.

Learn more about the integration here:

https://brainly.com/question/14502499

Answer:

1) [tex]\dfrac78[/tex]

2) [tex]\dfrac{17}{12} = 1 \frac{5}{12}[/tex]

3) [tex]\dfrac{53}{12}=4 \frac{5}{12}[/tex]

Step-by-step explanation:

1)

[tex]\dfrac38+\dfrac12=\dfrac38+\dfrac{1 \times4}{2 \times 4}=\dfrac38+\dfrac48=\dfrac78[/tex]

2)

[tex]\dfrac23+\dfrac34=\dfrac{2 \times 4}{3 \times 4}+\dfrac{3 \times3}{4 \times3}=\dfrac8{12}+\dfrac{9}{12}=\dfrac{17}{12}=1 \frac{5}{12}[/tex]

3)

First convert mixed number into improper fraction:

[tex]4 \frac23=\dfrac{3\times4+2}{3}=\dfrac{14}{3}[/tex]

[tex]\implies 4 \frac23-\dfrac{3}{12}=\dfrac{14}{3}-\dfrac{3}{12}=\dfrac{14\times4}{3\times4}-\dfrac{3}{12}=\dfrac{56}{12}-\dfrac{3}{12}=\dfrac{53}{12}=4 \frac{5}{12}[/tex]

The PDF for the wait time (denoted by the random variable X) is

[tex]f_X(x) = \begin{cases}\lambda e^{-\lambda x} & \text{if }x \ge 0 \\ 0 &\text{otherwise}\end{cases}[/tex]

where λ = 1/75. We want to find Pr[X > 70 | X ≥ 40]. Pierre has already been waiting for 40 min, so if he waits another 30 min he will have waited for a total of 70 min.

By definition of conditional probability,

Pr[X > 70 | X ≥ 40] = Pr[X > 70 and X ≥ 40] / Pr[X ≥ 40]

If X > 70, then automatically X ≥ 40 is satisified, so the right side reduces to

Pr[X > 70 | X ≥ 40] = Pr[X > 70] / Pr[X ≥ 40]

Use the PDF or CDF to find the remaining probabilities. For instance, using the PDF,

[tex]\mathrm{Pr}[X > 70] = \displaystyle \int_{-\infty}^{70} f_X(x) \, dx = \int_0^{70} f_X(x) \, dx \approx 0.3932[/tex]

Or, using the CDF,

[tex]F_X(x) = \displaystyle \int_{-\infty}^x f_X(t) \, dt = \begin{cases}0&\text{if }x<0 \\ 1-e^{-\lambda x} & \text{if }x \ge 0\end{cases}[/tex]

[tex]\implies \mathrm{Pr}[X > 70] = 1 - \mathrm{Pr}[X \le 70] = 1 - F_X(70) \approx 0.3932[/tex]

Similarly, you'll find that Pr[X ≥ 40] ≈ 0.5866.

It follows that

Pr[X > 70 | X ≥ 40] ≈ 0.3932 / 0.5866 ≈ 0.6703

Answer/Step-by-step explanation:

The graph of the equation y = 1/2x on the coordinate plane is plotted below

The given equation is:

y = 1/2x

The equation is of the form:

y  =  mx  +  c

where m represents the slope

and c represents the y-intercept

Comparing the equation y = 1/2x  with y = mx + c

The slope, m = 1/2

The y-intercept, c = 0

The line graph with slope, m = 1/2, and y-intercept, c = 0 is plotted below

[RevyBreeze]

Answer:

y > 4x + 1.

Step-by-step explanation:

The other person that listed their answer was also correct.

In order to make an equation as such, we need to find the slope of this line and the y-intercept. The y-intercept is the "+b" in y=mx+b. The slope is mx. So, to identify the slope we need to calculate rise over run on the graph, which is 4. So:

y __ 4x + __.

On the y-intercept, the y crosses and meets at the point (0,1) on the x-intercept exactly, so we don't need to worry about there being any fractions right now. So:

y __ 4x + 1.

Now, because this line has a positive slope, the inequality symbol is "chomping" at the y, like this:

y > 4x + 1.

I hope that this helps.

The answer in the form y = mx + b, using the appropriate inequality symbol in place of the equal sign is y = -2x + 3

The inequality symbol is less than (<). This means that all points below the line y = -2x + 3 satisfy the inequality.

To understand why this is the case, let's consider a few points on the line y = -2x + 3. For example, the point (0, 3) is on the line. If we plug these coordinates into the inequality, we get:

y = -2x + 3

3 = -2(0) + 3

3 = 3

This is a true statement, so we know that the point (0, 3) satisfies the inequality.

Now, let's consider a point that is below the line y = -2x + 3. For example, the point (1, 1) is below the line. If we plug these coordinates into the inequality, we get:

y = -2x + 3

1 = -2(1) + 3

1 = 1

This is also a true statement, so we know that the point (1, 1) satisfies the inequality.

Therefore, we can conclude that all points below the line y = -2x + 3 satisfy the inequality y < -2x + 3.

Here is a graph of the inequality y < -2x + 3.

As you can see from the graph, all points below the line y = -2x + 3 satisfy the inequality y < -2x + 3.

To learn more about inequality here:

https://brainly.com/question/20383699

#SPJ2

Answer:

16 dollars

Step-by-step explanation:

The price includes the price of an empty bag B and the price of popcorn that is proportional to x (the number of ounces). Let each popcorn cost A$. Then the price of bag y = Ax + B

Given x = 10, y = 6, so 6 = 10A + B    (1)

Given x = 20, y = 8, so 8 = 20x + B   (2)

(2) - (1): 2 = 10A, so A = 2/10 = 0.2

Sub it into (1), 6 = 10*0.2 + B = 2 + B, so B = 6 - 2 = 4

We got y = 0.2x + 4

Check: x = 35, y = 0.2*35 + 4 = 11 (right)

x = 48, y = 0.2*48 + 4 = 13.6 (right)

Now find y when x = 60

y = 0.2*60 + 4 = 16 dollars

Answer: x = 11; y = -1.

Step-by-step explanation:

-9y + 2 = x        (1)

-x - 3y = -8        (2)

Substitute x from Equation 1 into Equation 2:

-(-9y + 2) - 3y = -8

9y - 2 - 3y = -8

9y - 3y = -8 + 2

6y = -6

y = -1

Substitute y into Equation 1 and find x:

-9 * (-1) + 2 = x

x = 11

Answer:

i think his work is popular today because it was aheaahead of his time and yes  i do think his songsongs created today will be popular in 400 years. Step-by-step explanation:

Answer:

you didnt attach the picture or assignment

Answer:

m<20

Step-by-step explanation:

m must be less than 20

m < 20

or

20 > m

All customers in Mogale City, irrespective of income, receive the first 6 kls of water free.