Find the area of the shaded sector of the circle

Kendra charges $11 to shovel a driveway. She shoveled 4 driveways on Saturday and then some more on Sunday. She made $143 for th

Svet_ta [12734]

Let the quantity of driveways shoveled on Sunday be x

For 4 driveways, Kendra charges = 4*11=44

Thus,

143 = 44 + 11x

And this equation models the situation described.

By subtracting 44 from both sides,[

143-44 = 11x

99 = 11x

Dividing both sides by 11 results in

x = 9

Thus, she shoveled 9 driveways on Sunday.

7 0

1 month ago

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Madame Dubois bought 20 pearl necklaces for $500. Becoming bored quickly, she sold 3/4 of them at $40 each. She sold the rest at

Leona [12618]

$725, 3/4 of 20 equals 15 necklaces. 15 times 40 equals 600. Then, 5 times 25 results in 125. Finally, 125 plus 600 equals 725.

4 0

2 months ago

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Let c1(t) = eti + (sin(t))j + t3k and c2(t) = e−ti + (cos(t))j − 6t3k. Find the stated derivatives in two different ways to veri

Zina [12379]

Answer:

$i ( e^{t} - e^{-t})+ j (cost-sin t)+ k (-15t^{2})$

$\frac{d}{dx}(e^x) = e^x$

Step-by-step explanation:

Step 1:-

We have c1(t) = e^ t i + (sin(t))j + t³k

and c2(t) = e^−t i + (cos(t))j − 6t³k.

By adding c1(t) and c2(t):

c1(t)+c2(t) = e^ t i + (sin(t))j + t³k + e^−t i + (cos(t))j − 6t³k

Now, employing the derivative formula:

$\frac{d}{dx}(e^x) = e^x$

$\frac{d}{dx}(sinx) = cosx\\\frac{d}{dx}(cosx) = -sinx$

Next, differentiate with respect to 't'

$\frac{d}{dt}c_{1}+ c_{2} } = e^ t i +cost j +3t^2 k - e^-t i - sintj -18t^2 k$

By factoring out i, j, and k terms, we arrive at:

$\frac{d}{dt}(C_{1} +C_{2} ) = i ( e^{t} - e^{-t})+ j (cost-sin t)+ k (-15t^{2})$

7 0

2 months ago

12-5x-4kx=y solve for x

PIT_PIT [12445]

$12-5x-4kx=y:x$

$-5x-4kx=y-12$

$-x(5+4k)=y-12$

$-x= \dfrac{y-12}{5+4k}$

$x=- \dfrac{y-12}{5+4k}$

7 0

2 months ago

A child designs a flag in the shape of a rhombus, as shown in the diagram below. Which expression can be used to determine the s

Zina [12379]

Which formula can be applied to find the side length of the rhombus?

The correct answer is the first choice: 10/Cos(30°)

Explanation:

1. The figure shows a right triangle, where the hypotenuse is denoted by "x," and this is the length you are solving for. Therefore, you have:

Cos(α)=Adjacent side/Hypotenuse

α=30°
 Adjacent side=(20 in)/2=10 in
Hypotenuse=x

2. Inputting these numbers into the equation yields:

Cos(α)=Adjacent side/Hypotenuse
 Cos(30°)=10/x

3. Hence, by isolating the hypotenuse "x," you arrive at the expression to find the side length of the rhombus, as shown below:

x=10/Cos(30°)

7 0

2 months ago